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Journal of the Brazilian Society of Mechanical Sciences and Engineering
versão impressa ISSN 1678-5878
J. Braz. Soc. Mech. Sci. & Eng. vol.32 no.4 Rio de Janeiro out./dez. 2010
A vibroacoustic application of modeling and control of linear parameter-varying systems
Jan De CaignyI; Juan F. CaminoII; Ricardo C. L. F. OliveiraIII; Pedro L. D. PeresIV; Jan SweversV
IKatholieke Universiteit Leuven, Department of Mechanical Engineering Celestijnenlaan 300B, B-3001, Heverlee, Belgium. email@example.com
IIUniversity of Campinas - UNICAMP School of Mechanical Engineering 13083-970 Campinas, SP, Brazil. email@example.com
IVUniversity of Campinas - UNICAMP School of Electrical and Computer Engineering 13083-970 Campinas, SP, Brazil. email@example.com
VKatholieke Universiteit Leuven Department of Mechanical Engineering Celestijnenlaan 300B, B-3001, Heverlee, Belgium. firstname.lastname@example.com
This paper applies recent advances in both modeling and control of Linear Parameter-Varying (LPV) systems to a vibroacoustic setup whose dynamics is highly sensitive to variations in the temperature. Based on experimental data, an LPV model is derived for this system using the State-space Model Interpolation of Local Estimates (SMILE) technique. This modeling technique interpolates linear time-invariant models estimated at distinct operating conditions of the system (in this case, different temperatures). Using the obtained LPV model, gain-scheduled and robust multiobjective H2/H∞ state feedback controllers are designed such that can consider a priori known bounds on the rate of parameter variation. Numerical simulations using the closed-loop systems are performed to validate the controllers and to show the advantages and versatility of the proposed techniques.
Keywords: Gain-scheduled and robust control, LPV modeling, H2 and H∞ performance, linear parameter-varying systems
A main source of noise within aircraft cabins is the vibration of the surrounding structure, usually denoted as structural noise (Berglund et al., 1996; Persson and Björkman, 1988). Research in the area of acoustics has shown that active control strategies are efficient in reducing this noise in the low frequency range (see, for example, Alujevic et al., 2008; Camino and Arruda, 2009; Donadon et al., 2006; Fuller and von Flotow, 1995; Kaiser et al., 2003; Meurers et al., 2002; Sas et al., 1995). Several of these techniques assume that the plant under consideration is linear time-invariant (LTI), although this is not a realistic assumption for some applications. For instance, aircraft structures are frequently subjected to temperature variations that cause significant changes in its dynamics. To use robust control synthesis techniques for such parameter-varying systems, the nominal model and the uncertainty bounds should be appropriately determined, to ensure a realistic trade-off between performance and robustness. For most practical applications, however, this is a difficult task, and the estimated uncertainty set is in general too conservative. Therefore, a more elaborate control strategy should be investigated which can be used for linear parameter-varying (LPV) systems. This topic has received attention from the control community for over a decade, during which there has been a continuing effort to design LPV controllers, scheduled as a function of the varying parameters, that achieve higher performance while still guaranteeing stability for all possible parameter variations (see, for instance, Apkarian and Adams, 1998; Apkarian et al., 1995; Leith and Leithead, 2000; Packard, 1994; Rugh and Shamma, 2000; Scherer, 2001; Shamma and Athans, 1992). In the LPV control framework, the scheduling parameters that govern the variation of the dynamics of the system are usually a priori unknown, but measured or estimated in real-time (Shamma and Athans, 1991).
Two distinct approaches are commonly used to control LPV systems: interpolating gain-scheduling (IGS) control and linear parameter-varying (LPV) control. In IGS control, the design is split into two parts. First, LTI controllers are designed for linearized models of the system, estimated at several fixed operating conditions. Second, a parameter-dependent controller is obtained by interpolating these LTI controllers. Although the stability of the closed-loop system is not guaranteed, this approach has been successfully used in many practical applications (Aouf et al., 2002; De Caigny et al., 2007; Nichols et al., 1993). In LPV control, on the other hand, stability of the closed-loop system is guaranteed during the design phase. Several analysis and synthesis techniques for LPV systems have been proposed based on different types of Lyapunov functions. For instance, the well-known quadratic stability approach uses a constant Lyapunov matrix that allows arbitrarily fast variation of the scheduling parameters (Kaminer et al., 1993; Peres et al., 1994). Obviously, this yields conservative controllers for practical applications where the rate of parameter variation is bounded. To mitigate some of the conservatism associated with the approaches based on quadratic stability, many synthesis procedures based on parameter-dependent Lyapunov functions have been proposed. For instance, synthesis procedures for H2 and H∞ gain-scheduled and robust static output feedback controllers have been presented (De Caigny et al., 2008a,b, 2010a) for polytopic discrete-time LPV systems with an a priori known bound on the rate of parameter variation. The case where the system can have a homogeneous polynomial dependency on the scheduling parameter has been considered in De Caigny et al. (2009a, 2010a, 2010b). Most LPV control design techniques require an LPV model of the system that accurately describes the variation of the system dynamics over the workspace. However, while identification of linear time invariant (LTI) systems based on measured input-output (IO) data has been intensely studied and LTI model estimation algorithms are widely spread, estimation of LPV models remains a difficult problem which is still in a state of development. In the literature, there exist two main approaches to obtain LPV models: a global identification approach (see, for example, Bamieh and Giarré, 2002; Felici et al., 2007; Lee and Poolla, 1999; Nemani et al., 1995; Verdult and Verhaegen, 2005) and a local modeling approach (see, for example, De Caigny et al., 2008c, 2009b, 2011; Lovera and Mercere, 2007; Paijmans et al., 2008; Steinbuch et al., 2003; Wassink et al., 2005). The global approach is based on the assumption that it is possible to perform a global experiment by exciting the system while the scheduling parameters are persistently changing the system dynamics. In case it is impossible to perform a global experiment, it is appropriate to use a local approach, based on the interpolation of a set of local LTI models that are estimated using a collection of local experiments, performed by exciting the system at different fixed operating conditions. To properly interpolate these local models, all local LPV modeling techniques require that the local LTI models are transformed in a consistent state-space form to assure that they are defined with respect to a consistent state-space basis. Afterwards, an appropriate methodology is applied to construct an LPV model that interpolates these consistent local models. The main drawback of the local approach is the fact that the time propagation of the scheduling parameter is not used. Therefore, these local methods are more suitable for systems with scheduling parameters that vary slowly in time; a common guideline in interpolating gain-scheduling control practice (Shamma and Athans, 1992).
The aim of this paper is to show the recent advances in both modeling and control of LPV systems using a vibroacoustic setup as a practical application. First, experimental data is used to obtain an LPV model of the vibroacoustic setup using the State-Space Model Interpolation of Local Estimates (SMILE) technique; a local LPV modeling technique developed in De Caigny et al. (2008c, 2009b). Second, using the obtained LPV model, multiobjective H2/H∞ gain-scheduled and robust static state feedback controllers are computed. The LPV control design is then validated through numerical simulations. Finally, the advantages and disadvantages of the proposed LPV modeling and control design techniques are discussed. The paper is organized as follows. In the next section, the vibroacoustic application is introduced. The following section starts by presenting an overview of the SMILE technique which is then used to obtain an LPV model of the vibroacoustic setup. The synthesis conditions for gain-scheduled and robust H2 and H∞ state feedback control which are applied to the obtained LPV model is then presented as well as the concluding remarks.
Vibroacoustic Application
This section describes the vibroacoustic setup (displayed in Fig. 1), that consists of a lexan plate clamped on a rigid baffle in a semi-anechoic room (see Donadon et al., 2006, for details). The exogenous disturbance that causes the vibration of the plate is provided by a point force driven by a shaker. The control input , used to attenuate the sound pressure inside the semi-anechoic room, is provided by a flexural moment driven by a piezoelectric patch attached to the plate. The output z is the sound pressure measured by a single microphone, located in the semi-anechoic room near the plate.
The experiments performed by the authors in Donadon et al. (2006) revealed that the system dynamics was highly sensitive to the temperature in the semi-anechoic room. Therefore, the setup is an LPV system with the temperature as the scheduling parameter. For the modeling of this vibroacoustic setup, it is necessary to consider a local LPV modeling approach because of the slow rate of variation of the temperature. Indeed, since the temperature can only be changed slowly, a long measurement should have to be performed to ensure the conditions of persistent excitation of the scheduling parameter (Bamieh and Giarré, 2002), resulting in an intractable amount of data. Therefore, performing local identification experiments, for different fixed values of the temperature, is the most convenient option.
To apply the local approach, frequency response functions (FRFs) were measured from the disturbance w and the control input to the output z at four different temperatures θ ∈{22.9º, 23.4º, 24.4º, 25.4º}. Based on the measured FRFs, a 10th-order discrete-time state-space LTI model has been estimated at each operating condition, using the subspace identification method (Ljung, 1999; van Overschee and Moor, 1996; Verhaegen, 1994) implemented in the Matlab Identification toolbox. Figure 2 presents the magnitude and phase of the experimentally obtained FRFs (black, dashed) and of the corresponding estimated LTI models (red, solid) in the frequency range 120 - 260 Hz. All the estimated models have five complex poles, for instance, the poles of the estimated model from w to z corresponding to the temperature 22.9º are located at 135 Hz, 160 Hz, 206 Hz, 247 Hz, and 253 Hz. The LTI models clearly show a good correspondence to the FRFs. The next section shows how to use the SMILE technique to obtain an LPV model by interpolating these four LTI models. Notice that the output sound pressure z is given by z = (jω)u + (jω)w, where (jω) and (jω) denote respectively the transfer functions from the disturbance and the control input to the output z. In the active noise control community, (jω) is referred as the primary source and (jω) as the secondary source.
LPV Modeling Using the Smile Technique
This section presents how to use the SMILE technique to model the vibroacoustic setup. For a detailed presentation, see De Caigny et al. (2008c). The notation in this section is as follows: matrices associated with the interpolating LPV model are denoted using standard math font, e.g., A0, ...; matrices associated with the local LTI models are denoted using San Serif font, e.g., Aℓ, ...; the subscript ℓ indicates the index of the local model. Throughout the paper, the discrete-time state-space model
is indicated by
The interpolating LPV model is chosen to have the following state-space representation affine in the single scheduling parameter θ ∈:
A0, A1 ∈n×n, B0, B1 ∈ n×r, C0, C1 ∈ s×n, and D0, D1 ∈ s×r.
This choice has the advantage that the LPV model H(θ) given by model (1) can be used in LPV control synthesis techniques for affine LPV models (for example, Amato et al., 2005; Apkarian et al., 1995; de Souza and Trofino, 2006; Lu et al., 2008) as well as in the linear fractional transformation framework (for example, Packard, 1994; Scherer, 2001). Moreover, when θ is bounded, model (1) can be converted exactly in a polytopic LPV model1 with two vertices, which is useful since control synthesis for polytopic models has been widely studied (De Caigny et al., 2008a, 2008b; Leite and Peres, 2004; Montagner et al., 2007; Oliveira and Peres, 2008). The recent work De Caigny et al. (2011) has extended the LPV modeling technique to consider a more general class of LPV models that can be parameterized using a homogeneous polynomial dependency on the scheduling parameter, which include as a particular case, affine models.
The aim of the SMILE technique is to estimate the system matrices of model (1) such that the resulting LPV model H(θ) interpolates the local LTI models
identified at distinct operating conditions, that is, for different fixed values of the scheduling parameter θ , indicated by for l = 1, ..., . All local LTI models are assumed to have the same number of states n, the same number of inputs r and the same number of outputs s. As the state-space representation is not unique, the local models (2) cannot be readily interpolated since it is not guaranteed that they are represented with respect to the same state-space basis. Therefore, a similarity transformation matrix Tl needs to be calculated for each local model such that the transformed models
are defined with respect to the same basis. Once the models (3) have been calculated, an optimization problem can be formulated and solved to find the optimal system matrices of the interpolating LPV model (1). Assuming that the m MIMO LTI models (2) are available, the SMILE technique consists of five steps to compute an interpolating LPV model (see the flowchart in Fig. 3).
These five steps are now briefly presented and applied to the four (= 4) local 10th-order 2-input 1-output LTI models identified for the vibroacoustic setup.
STEP 1: Choose one input-output (IO) combination (i, j) for all original local MIMO models obtain local SISO models
For the vibroacoustic setup, the IO combination (i, j) = (1,2) from the control input to the microphone z is chosen, thus yielding four LTI SISO models, (1,2), l =1, ..., 4.
STEP 2: Calculate the poles pl (independent of the choice of IO-combination (i, j)) and zeros zl,(1,2) of the original local SISO models . Sort these poles and zeros such that they are in the same order for all local SISO models . Fig. 4 shows the real and imaginary part of the poles and zeros of the 4 local SISO models as a function of the varying temperature θ. All local models have 5 complex conjugated pole pairs, 1 non-minimum phase real zero and 4 complex conjugated zero pairs. The sorting of the poles and zeros is indicated in Fig. 4 with solid lines that connect corresponding poles (resp. zeros) for the 4 different local temperatures.
STEP 3: Divide the local SISO models into a gain multiplied by the series connection of τ1 1st-order and τ2 2nd-order state-space submodels expressed in the observable form. Then, explicitly calculate this series connection to obtain a new and consistent state-space representation of the local SISO models (denoted as ). Since all LTI SISO models are 10th-order, they can be represented by a gain multiplied by the series connection of τ2 = 5 2nd-order submodels. In Fig. 4 this division is emphasized by assigning the poles and zeros 5 different markers and colors: poles and zeros with the same marker and color are assigned to the same LTI SISO submodel.
STEP 4: Calculate, for each local model , the similarity transformation matrix Tl that transforms the system matrices of into those of . Apply this transformation matrix Tl to the corresponding original MIMO LTI model to obtain the model Hl.
STEP 5: To obtain the system matrices of the interpolating MIMO LPV model (1), the following linear least-squares cost function is minimized
where || ||F represents the Frobenius norm of a matrix.
Figure 5 compares the 4 local LTI MIMO models (red, solid) to the obtained interpolating LPV model (black, solid with dots), evaluated at 11 equidistantly spaced temperatures in the interval [22.9º; 25.4º]. The LPV model clearly shows a smooth interpolation of the local MIMO models.
The quality of the fit can also be numerically verified by comparing the vector of Hankel singular values (Moore, 1981) of the local LTI models with the interpolating LPV model evaluated at the four local operating conditions. These vectors, for the LTI and the LPV case, are respectively denoted by Glti[i] and Glpv[i], for i = 1, ..., 4. Table 1 presents the relative difference between these two vectors, calculated as ║ Glti[i] - Glpv[i] ║2 / ║ Glti[i] ║2.
Gain-Scheduled and Robust H2 and H∞ State Feedback
This section presents synthesis procedures for gain-scheduled and robust H2 and H∞ state feedback controllers for discrete-time polytopic LPV systems with known bounds on the rate of parameter variation. First, the modeling of the uncertainty domain is introduced, then the synthesis conditions are given and afterwards state feedback controllers are computed for the LPV model obtained in the previous section. A schematic view of the closed-loop system is shown in Fig. 6, in which the model H(α) already contains the transfer functions of the primary and the secondary sources.
Modeling of the Uncertainty Domain
Consider the polytopic discrete-time linear parameter-varying system
where the system matrices
A(α(k)) ∈n×n, Bw(α(k)) ∈n×r, Bu(α(k)) ∈n×m, Cz(α(k)) ∈s×n, Dw(α(k)) ∈ s×r, and Du(α(k)) ∈s×m belong to the polytope
with the vector of time-varying parameters α(k) ∈N belonging to the unit simplex given by
The rate of variation of the parameters Δαi(k) = αi(k+1) - αi(k), i = 1, ... , N, is assumed to be limited by an a priori known bound b ∈ such that
with 0 < b < 1. Compared to synthesis procedures based on quadratic stability, that allows Δαi(k) to be arbitrarily large, synthesis procedures that yield less conservative controllers can be derived by explicitly taking into account that Δαi(k) satisfies Eq. (7), as discussed in (Oliveira and Peres, 2008).
Gain-Scheduled Control Synthesis
The goal is to provide a parameter-dependent state feedback control law u(k) = K(α(k))x(k), with K(α(k)) ∈m×n, such that the closed-loop system
is exponentially stable with a guaranteed H2 and H∞ performance for all possible parameter variation. A solution to the gain-scheduled H∞ state feedback design problem, in terms of a finite set of LMIs defined in the vertices of the polytope (5), is provided by the next theorem.
Theorem 1: Let the saclar η be given. If there exist, for i = 1, ..., N, matrices Gi ∈n×n, Zi ∈m×n and symmetric positive-definite matrices Pi ∈ RRn×n such that
for i = 1, ..., N and ℓ = 1, ..., N and
for ℓ = 1, ..., N, i = 1, ..., N-1 and j = i+1, ..., N, then the parameter-dependent static state feedback gain
stabilizes system (4) with a guaranteed H∞ performance bounded by .
The proof for Theorem 1 can be found in De Caigny et al. (2008b). The next theorem provides a finite set of LMIs for the design of a gain-scheduled H2 state feedback controller for system (4).
Theorem 2: If there exist, for i = 1, ..., N, matrices Gi ∈n×n, Zi ∈m×n, and symmetric positive definite matrices Pi ∈n×n and Wi ∈p×p such that
for i = 1, ..., N and ℓ = 1, ..., N,
for ℓ = 1, ..., N, i = 1, ..., N-1 and j = i+1, ..., N,
for i = 1, ..., N,
for i = 1, ..., N-1 and j = i+1, ..., N, then the parameter-dependent state feedback gain (9) stabilizes system (4) with a guaranteed H2 performance bounded by v given by v2 = max Tr {Wi}. The proof for Theorem 2 can be found in De Caigny et al. (2008a).
By combining the LMI conditions presented in Theorems 1 and 2, it is possible to design mixed H2/H∞ controllers. Multiobjective H2 and H∞ specifications can be imposed on different closed-loop input-output combinations by appropriately selecting the right input-output channels of the open-loop system (4) and applying the control synthesis procedures of Theorem 1 or 2, using the same variables Gi and Zi for all performance specifications. For each performance specification, however, a different set of Lyapunov matrices can be used. This mixed H2/H∞ synthesis technique extends the G shaping paradigm, presented in de Oliveira et al. (2002) for uncertain LTI systems, to the class of polytopic LPV systems with bounds on the rate of parameter variation.
Robust Control Synthesis
Robust state feedback controllers (k) = Kx(k) can be easily derived from Theorems 1 and 2, as shown in the following corollaries.
Corollary 1: If there exist matrices Gi ∈n×n, Zi ∈m×n, and symmetric positive-definite matrices Pi ∈n×n, for i = 1, ..., N, such that (8) holds for i = 1, ..., N and ℓ = 1, ..., N, with Gi = G and Zi = Z, for i = 1, ..., N, then the robust state feedback gain K = ZG-1 stabilizes system (4), with a guaranteed H∞ performance bounded by .
Corollary 2: If there exist matrices Gi ∈n×n, Zi ∈m×n, and symmetric positive-definite matrices Pi ∈n×n and Ri ∈p×p, for i = 1, ..., N, such that (10) holds for i = 1, ..., N and ℓ = 1, ..., N and (11) holds for i = 1, ..., N, with Gi = G and Zi = Z, for i = 1, ..., N, then the robust static output feedback gain K = ZG-1 stabilizes system (4), with a guaranteed H2 performance ν given by v2 = max Tr {Wi}.
Obviously, robust multiobjective H2/H∞ state feedback controllers can be obtained as well, by combining the results of these two corollaries for different performance specifications.
The following subsection presents the numerical results obtained using the proposed gain-scheduled and robust multiobjective H2/H∞ state feedback synthesis conditions.
Numerical Results
The aim of this subsection is to design gain-scheduled and robust state feedback controllers for the vibroacoustic system by applying the synthesis conditions to the LPV model computed in previous section. The goal of the control design is to minimize an upper bound γ2 on the closed-loop H2 performance from the disturbance to the output z (indicated here as ║Twz║2), while an upper bound γ1 is enforced on the closed-loop H∞ performance from the disturbance w to the control signal u (indicated here as ║Twu║∞) to obtain controllers that do not have excessively large control signals.
To use the synthesis conditions of Theorems 1 and 2 and Corollaries 1 and 2, the affine LPV model obtained with the SMILE technique is converted to a polytopic model with two vertices. For this model, the corresponding two scheduling parameters are given by
with θmin = 22.9º and θmáx = 25.4º. Note that αi > 0, for i = 1, 2, and that α1 + α2 = 1. Consequently, α = [α1 α2]T belongs to the unit simplex Λ2 as defined in (6).
The obtained controllers are validated through numerical simulations. First, Pareto optimal curves that describe the trade-off between the obtained upper bound γ2 on ║Twz║2 and the imposed upper bound γ1 on ║Twu║∞ are presented. Afterwards, the performance of the gain-scheduled controllers is analyzed using Bode plots and time domain simulations.
1) Pareto optimal curves: Figure 7 shows the trade-off curve between the imposed upper bound γ1 on ║Twu║∞ and the obtained upper bound γ2 on ║Twz║2for two bounds b = 0.2 and b = 0.8 on the rate of parameter variation. The bound γ1 takes values in a fine grid of the interval [0;50]. In this figure, the label GS denotes gain-scheduled control designs (dashed lines) and the label R denotes robust control designs (solid lines). For each bound (b = 0.2 and b = 0.8), one gain-scheduled and one robust H2 controller is calculated without the bound γ1 on ║Twu║∞ using Theorem 2 and Corollary 2. These four designs (indicated in Fig. 7 with dotted lines for the gain-scheduled case and with dash-dotted lines for the robust case) provide the best achievable upper bound on ║Twz║2, that is, the smallest achievable value for γ2, denoted by . The value of for each control design case is given in Table 2. As can be seen from Fig. 7, the mixed H2/H∞ control designs always provide a bigger upper bound γ2 > , thus having worse guaranteed performance compared to the H2 control design. It is also clear that the performance decreases as the bound b on the rate of parameter variation increases. For small values of γ1 the synthesis conditions become infeasible (indicated with squares). As expected, the gain-scheduled controllers GS outperform the robust controllers R.
2) Performance of the gain-scheduled controllers obtained for b = 0.2: The performance of the gain-scheduled control design for the case b = 0.2 is now analyzed using Bode plots (see Fig. 8) for five equidistantly spaced temperatures in the interval [22.9º; 25.4º]. The following three controllers are compared:
Controller K1: no upper bound on ║Twu║∞, yielding the smallest achievable upper bound on ║Twz║2 (Fig. 8a, red);
Controller K2: upper bound γ1 = 35 on ║Twu║∞ (Fig. 8b, green);
Controller K3: upper bound γ1 = 10 on ║Twu║∞(Fig. 8c, magenta).
The Bode magnitude plot from the disturbance to the microphone z of the open-loop system is indicated using black lines.
From Fig. 8, it is clear that compared to the open-loop system, all controllers improve the H2 performance from the disturbance w to the microphone z, for all temperatures. Controller K1 yields the best H2 performance (see Fig. 8a). However, since no upper bound is imposed on║Twu║∞, the red curves in the right side of Fig. 8a have the highest peaks, thus requiring large control authority. Compared to controller K1, controller K2 yields slightly worse H2 performance (as can be seen in the left side of Fig. 8b), but since an upper bound γ1 = 35 is imposed on║Twu║∞, the green curves in the right side of Fig. 8b have slightly smaller peaks compared to Fig. 8a. The third controller K3 is designed with a significantly tighter bound γ1 = 10 on ║Twu║∞ and consequently the curves in the right side of Fig. 8c are significantly lower compared to the curves associated with K1 and K2.
Thus, controller K3 requires less control authority. However, the obtained H2 performance is also considerably worse, as can be seen in the left side of Fig. 8c.
The difference between these three controllers can also be seen in Fig. 7. Controller K1 is indicated with the red dotted line and provides the lowest possible upper bound . Controller K2 is indicated with the green diamond and provides a slightly bigger upper bound γ2, but guarantees an upper bound γ1 = 35 on║Twu║∞. Controller K3 is indicated with the magenta diamond and provides a significantly bigger upper bound γ2, but guarantees a smaller upper bound γ1 = 10 on║Twu║∞. The upper bound γ1 = 35 corresponds to 20 log10 35 ≈ 31[dBref=1Pa/N] and is indicated in Fig. 8b with the green dashed line, while the upper bound γ1 = 10 corresponds to 20 log10 10 = 20[dBref=1Pa/N] and is indicated in Fig. 8c with the magenta dashed line.
Figure 9 shows a time domain simulation, where a unit impulse is applied (at t = 0) to the open-loop system and to the closed-loop systems computed using the three controllers K1, K2 and K3 described above. The time interval used for the simulation is t ∈ [0; 0.1]. During the simulation, the scheduling parameter (the temperature) changes randomly in the interval [22.9º; 25.4º] with a bounded rate of variation b = 0.2. The open-loop response from the disturbance to the microphone z (black) is compared with the closed-loop response computed using the controllers K1 (red), K2 (green) and K3 (magenta). The time simulation emphasizes again the difference between the 3 controllers. Controller K1 shows the best attenuation of the disturbance (as can be seen in the left side of Fig. 9a), but results in the highest peaks in the control signals (as can be seen in the right side of Fig. 9b). Controller K2 yields slightly worse disturbance attenuation, but has smaller peaks in the control signal (see Fig. 9b).
Finally, controller K3 performs significantly worse in attenuating the disturbance, but does not require large control signals (see Fig. 9c).
The numerical results presented in Figs. 7, 8 and 9 show the potential of the proposed multiobjective H2/H∞ gain-scheduled and robust control design techniques. Based on the trade-off curves shown in Fig. 7, a specific controller can be chosen that yields a guaranteed closed-loop H2 performance, while still guaranteeing an upper bound on the H∞ performance from the disturbance w to the control signal u. Certainly, the main drawback of the proposed control design is its current limitation to the state feedback case. In many engineering applications, such as the vibroacoustic setup in this paper, it is impossible to measure all states of the system and consequently full state feedback laws cannot be directly implemented in practice. However, no results yet exist in the literature that provide gain-scheduled dynamic output feedback controllers that consider bounds on the rate of parameter variation. It is important to stress the incorporation of a priori known bounds on the rate of parameter variation into the synthesis procedure, since for the vibroacoustic application, quadratic stability based approaches fail to yield a feasible set of synthesis conditions.
There are two possible strategies that can be used to achieve gain-scheduled dynamic output feedback controllers. The first possibility is to consider the joint design of a gain-scheduled state observer and a gain-scheduled state feedback controller. The second possibility is to derive synthesis conditions for gain-scheduled dynamic output feedback controllers. These are interesting open questions the authors plan to investigate in future works.
Although no experimental validation is provided in this paper, the proposed state feedback synthesis conditions are valuable for several reasons. First, the state feedback controllers provide the best possible closed-loop performance that can be achieved for the vibroacoustic system. Second, the state feedback synthesis results might be the first step towards the design of a dynamic output feedback controller in the form of a full order observer combined with a state feedback law. Third, the influence of the bound b on the rate of variation can be easily verified by calculating different trade-off curves as presented in Fig. 7. Fourth, this paper also shows that recent theoretical results for LPV control have the potential to be applied to models obtained from experimental data.
This paper shows that recently developed techniques to model and control linear parameter-varying systems can be applied to realistic engineering problems, in this case a vibroacoustic setup whose dynamics are highly sensitive to temperature variation. Based on experimentally obtained FRFs, a set of LTI models is estimated for different fixed temperatures. Then, an LPV model is derived for the vibroacoustic setup by interpolating these local LTI models using the State-space Model Interpolation of Local Estimates (SMILE) technique. Gain-scheduled and robust multiobjective H2/H∞ state feedback controllers are designed using LMI synthesis conditions based on a parameter-dependent Lyapunov matrix. These synthesis procedures consider a priori known bounds on the rate of parameter variation, which reduces the conservatism generally associated with methods that allow arbitrarily fast parameter variation, like the quadratic stability based approaches. Numerical simulations clearly show the advantages and versatility of the proposed modeling and control design procedures.
The authors would like to thank the Vibroacoustic Lab at the University of Campinas (UNICAMP) for providing the experimental data used in the paper. The authors R. C. L. F. Oliveira and P. L. D. Peres are supported by grants from CAPES, CNPq and FAPESP. The author J. F. Camino is supported through grants from CAPES and FAPESP project 09/03304-5. The authors J. De Caigny and J. Swevers are supported through the following funding: project G.0446.06 of the Research Foundation - Flanders (FWO - Vlaanderen), K.U.Leuven - BOF EF/05/006 Center-of-Excellence Optimization in Engineering and the Belgian Programme on Interuniversity Attraction Poles, initiated by the Belgian Federal Science Policy Office. The scientific responsibility rests with its author(s).
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Apkarian, P. and Adams, R.J., 1998, "Advanced gain-scheduling techniques for uncertain systems", IEEE Transactions on Control Systems Technology, Vol. 6, No. 1, pp. 21-32. [ Links ]
Apkarian, P., Gahinet, P. and Becker, G., 1995, "Self-scheduled H∞control of linear parameter-varying systems - A design example", Automatica, Vol. 31, No. 9, pp. 1251-1261. [ Links ]
Bamieh, B. and Giarré, L., 2002, "Identification of linear parameter varying models", International Journal of Robust and Nonlinear Control, Vol. 12, No. 9, pp. 841-853. [ Links ]
Berglund, B., Hassmén, P. and Job, R.F.S., 1996, "Sources and effects of low-frequency noise", J. Acoust. Soc. Am., Vol. 99, No. 5, pp. 2985-3002. [ Links ]
Boyd, S., El Ghaoui, L., Feron, E. and Balakrishnan, V., 1994, "Linear Matrix Inequalities in Systems and Control Theory", Vol. 15 of Stud. Appl. Math. SIAM, Philadelphia. [ Links ]
Camino, J.F. and Arruda, J.R.F., 2009, "H2 and H∞feedforward and feedback compensators for acoustic isolation", Mechanical Systems and Signal Processing, Vol. 23, No. 8, pp. 2538-2556. [ Links ]
De Caigny, J., Camino, J.F., Paijmans, B. and Swevers, J., 2007, "An application of interpolating gain-scheduling control", Proc. of the 3rd IFAC Symp. Syst., Struct. and Control (SSSC07), Foz do Iguassu, Brazil (cdrom). [ Links ]
De Caigny, J., Camino, J.F., Oliveira, R.C.L.F., Peres, P.L.D. and Swevers, J., 2008a, "Gain scheduled H2-control of discrete-time polytopic time varying systems", Congresso Brasileiro de Automática, pp. 1-6, Juiz de Fora, Brazil (cdrom). [ Links ]
De Caigny, J., Camino, J.F., Oliveira, R.C.L.F., Peres, P.L.D. and Swevers, J., 2008b, "Gain-scheduled H∞-control of discrete-time polytopic time-varying systems", Proceedings of the 47th IEEE Conference on Decision and Control, pp. 3872-3877, Cancun, Mexico. [ Links ]
De Caigny, J., Camino, J.F. and Swevers, J., 2008c, "Identification of MIMO LPV models based on interpolation", Proceedings of the International Conference on Noise and Vibration Engineering, pp. 2631-2644, Leuven, Belgium. [ Links ]
De Caigny, J., Camino, J.F., Oliveira, R.C.L.F., Peres, P.L.D. and Swevers, J., 2009a, "Gain-scheduled H∞-control for discrete-time polytopic LPV systems using homogeneous polynomially parameter-dependent Lyapunov functions", Proceedings of the 6th IFAC Symposium on Robust Control Design, pp. 19-24, Haifa, Israel. [ Links ]
De Caigny, J., Camino, J.F. and Swevers, J., 2009b, "Interpolating model identification for SISO linear parameter-varying systems", Mechanical Systems and Signal Processing, Vol. 23, No. 8, pp. 2395-2417. [ Links ]
De Caigny, J., Camino, J.F., Oliveira, R.C.L.F., Peres, P.L.D. and Swevers, J., 2010a, "Gain-scheduled H2 and H∞control of discrete-time polytopic time-varying systems", IET Control Theory & Applications, Vol. 4, No. 3, pp. 362-380. [ Links ]
De Caigny, J., Camino, J.F. and Swevers, J., 2011, "Interpolation-based modelling of MIMO LPV systems", IEEE Transactions on Control Systems Technology, Vol. 19, No. 1, pp 46-63. [ Links ]
De Oliveira, M.C., Geromel, J.C. and Bernussou, J., 2002, "Extended H2 and H∞norm characterizations and controller parameterizations for discrete-time systems"¸ Intern. Journal of Control, Vol. 75, No. 9, pp. 666-679. [ Links ]
De Souza, C.E. and Trofino, A. 2006, "Gain-scheduled H2 controller synthesis for linear parameter varying systems via parameter-dependent Lyapunov functions", International Journal of Robust and Nonlinear Control, Vol. 16, No. 5, pp. 243-257. [ Links ]
Donadon, L.V., Siviero, D.A., Camino, J.F. and Arruda, J.R.F., 2006, "Comparing a filtered-XLMS and an H2 controller for the attenuation of the sound radiated by a panel", Proceedings of the International Conference on Noise and Vibration Engineering, pp. 199-210, Leuven, Belgium. [ Links ]
Felici, F., van Wingerden, J.W. and Verhaegen, M., 2007, "Subspace identification of MIMO LPV systems using a periodic scheduling sequence", Automatica, Vol. 43, No. 10, pp. 1684-1697. [ Links ]
Fuller, C.R. and von Flotow, A.H., 1995, "Active control of sound and vibration", IEEE Control Systems Magazine, Vol. 15, No. 6, pp. 9-19. [ Links ]
Kaiser, O.E., Pietrzko, S.J. and Morari, M. 2003, "Feedback control of sound transmission through a double glazed window", Journal of Sound and Vibration, Vol. 263, No. 4, pp. 775-795. [ Links ]
Kaminer, I., Khargonekar, P.P. and Rotea, M.A., 1993, "Mixed H2/H∞control for discrete-time systems via convex optimization", Automatica, Vol. 29, No. 1, pp. 57-70. [ Links ]
Lee, L.H. and Poolla, K., 1999, "Identification of linear parameter-varying systems using nonlinear programming", Journal of Dynamic Systems, Measurement, and Control, Vol. 121, No. 1, pp. 71-78. [ Links ]
Leite, V.J.S. and Peres, P.L.D., 2004, "Robust control through piecewise Lyapunov functions for discrete time-varying uncertain systems", International Journal of Control, Vol. 77, No. 3, pp. 230-238. [ Links ]
Leith, D.J. and Leithead, W.E., 2000, "Survey of gain-scheduling analysis and design", Intern. Journal of Control, Vol. 73, No. 11, pp. 1001-1025. [ Links ]
Ljung, L., 1999, "System Identification: Theory for the User", Prentice-Hall, Upper Saddle River, NJ, USA. [ Links ]
Lovera, M. and Mercere, G., 2007, "Identification for gain-scheduling: a balanced subspace approach", Proceedings of the American Control Conference, pp. 858-863, New York, NY, USA. [ Links ]
Lu, B., Choi, H., Buckner, G.D. and Tammi, K., 2008, "Linear parameter-varying techniques for control of a magnetic bearing system", Control Engineering Practice, Vol. 16, No. 10, pp. 1161-1172. [ Links ]
Meurers, T., Veres, S.M. and Elliot, S.J., 2002, "Frequency selective feedback for active noise control", IEEE Control Systems Magazine, Vol. 22, No. 4. [ Links ]
Montagner, V.F., Oliveira, R.C.L.F., Peres, P.L.D. and Bliman, P.-A., 2007, "Linear matrix inequality characterization for H∞and H2 guaranteed cost gain-scheduling quadratic stabilisation of linear time-varying polytopic systems", IET Control Theory & Applications, Vol. 1, No. 6, pp. 1726-1735. [ Links ]
Moore, B.C., 1981, "Principal component analysis in linear systems: Controllability, observability, and model reduction", IEEE Transactions on Automatic Control, Vol. 26, No. 1, pp. 17-32. [ Links ]
Nemani, M., Ravikanth, R. and Bamieh, B.A., 1995, "Identification of linear parametrically varying systems", Proceedings of the 34th IEEE Conference on Decision and Control, pp. 2990-2995, New Orleans, LA, USA. [ Links ]
Nichols, R.A., Reichert, R.T. and Rugh, W.J., 1993, "Gain scheduling for H-infinity controllers: A flight control example", IEEE Transactions on Control Systems Technology, Vol. 1, No. 2, pp. 69-79. [ Links ]
Oliveira, R.C.L.F. and Peres, P.L.D., 2008, "Robust stability analysis and control design for time-varying discrete-time polytopic systems with bounded parameter variation", Proceedings of the American Control Conference, pp. 3094-3099, Seattle, WA, USA. [ Links ]
Packard., A., 1994, "Gain scheduling via linear fractional transformations", Systems & Control Letters, Vol. 22, No. 2, pp. 79-92. [ Links ]
Paijmans, B., Symens, W., van Brussel, H. and Swevers, J., 2008, "Experimental identification of affine LPV models for mechatronic systems with one varying parameter", European Journal of Control, Vol. 14, No. 1, pp. 16-29. [ Links ]
Peres, P.L.D., Geromel, J.C. and Souza, S.R., 1994, "H2 output feedback control for discrete-time systems", Proceedings of the American Control Conference, pp. 2429-2433, Baltimore, MD, USA. [ Links ]
Persson, K. and Björkman, M., 1988, "Annoyance due to low frequency noise and the use of the dBA scale", Journal of Sound and Vibration, Vol. 127, No. 3, pp. 491-497. [ Links ]
Rugh, W.J. and Shamma, J.S., 2000, "Research on gain scheduling", Automatica, Vol. 36, No. 10, pp. 1401-1425. [ Links ]
Sas, P., Bao, C., Augusztinovicz, F. and Desmet, W., 1995, "Active control of sound transmission through a double panel partition", Journal of Sound and Vibration, Vol. 180, No. 4, pp. 609-625. [ Links ]
Scherer, C.W., 2001, "LPV control and full block multipliers", Automatica, Vol. 37, No. 3, pp. 361-375. [ Links ]
Shamma, J.S. and Athans, M., 1991, "Guaranteed properties of gain scheduled control for linear parameter-varying plants", Automatica, Vol. 27, No. 3, pp. 559-564. [ Links ]
Shamma, J.S. and Athans, M., 1992, "Gain scheduling: potential hazards and possible remedies", IEEE Control Systems Magazine, Vol. 12, No. 3, pp. 101-107. [ Links ]
Steinbuch, M., van de Molengraft, R. and van der Voort, A., 2003, "Experimental modelling and LPV control of a motion system", Proceedings of the American Control Conference, pp. 1374-1379, Denver, CO, USA. [ Links ]
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Verhaegen, M., 1994, "Identification of the deterministic part of MIMO state-space models given in innovations form from input-output data", Automatica, Vol. 30, No. 1, pp. 61-74. [ Links ]
Wassink, M.G., van de Wal, M., Scherer, C.W. and Bosgra, O., 2005, "LPV control for a wafer stage: beyond the theoretical solution", Control Engineering Practice, Vol. 13, No. 2, pp. 231-245. [ Links ]
Paper accepted April, 2010.
Technical Editor: Domingos Alves Rade.
1 See Boyd et al. (1994) for an introduction on polytopic models and LMI representation.
The symbol * within a matrix represents the symmetric term of the matrix.


text: The following reply was made to PR port-sparc/3287; it has been noted by GNATS. From: "Guillaume Lasmayous" <gls%netbsd.org@localhost> To: gnats-bugs%gnats.NetBSD.org@localhost Cc: Subject: PR/3287 CVS commit: pkgsrc/x11/x3270 Date: Sun, 24 Mar 2013 18:05:19 +0000 Module Name: pkgsrc Committed By: gls Date: Sun Mar 24 18:05:19 UTC 2013 Modified Files: pkgsrc/x11/x3270: Makefile distinfo Log Message: Update x11/x3270 to 3.3.12ga12. Contains the fix for CVE-2012-5662. Upstream changes: ----------------- [All] Added logic to verify the name in the host certificate. [All] Pass all SSL-related parameters to the pr3287 session. [x3270] On the Connect menu, made the recent host list a pull-right sub-menu, if there is an ibm_hosts file in use. [x3270] The -trace option now implies event tracing as well. [x3270] Spaces are now allowed in the file transfer dialog local file name. [all] Corrected issues when invalid Unicode characters are encountered during a file transfer. [x3270, wc3270] Corrected a crash when tracing without a file, when the monitor window was closed. [all] Changed the CGCSGID for cp930 (Japanese) 0x080b012c (2059, 300) to 0x0172012c (370, 300). To generate a diff of this commit: cvs rdiff -u -r1.33 -r1.34 pkgsrc/x11/x3270/Makefile cvs rdiff -u -r1.9 -r1.10 pkgsrc/x11/x3270/distinfo Please note that diffs are not public domain; they are subject to the copyright notices on the relevant files.

subset: commoncrawl


text:
Please review the online photographs and specifications of our new yachts and centrally listed brokerage yachts and let us know how we may best serve your interests.
The Argos Gulfstream 92 has been reviewed by many yachting professionals, editors, & competitors alike with overwhelming praise. Extremely veratile yacht with speed and long range. Now offering same quality, styling, and features in a 70' model.
This model can be built on the same hull from 62' to 75'.
Meet the Argos. She's an entirely new and uncompromised motor yacht experience, designed and built to overcome accepted trade-offs. The result: style, performance and trans-oceanic range, reliability and safety.
The Argos motor yacht is the result of a breakthrough concept and design by Argos Marine. The approach eliminates many of the trade-offs that characterize motor yacht purchase and ownership.
To ensure owner distinction and high investment value, Worldwide production of the Argos Offshore Performance Series is limited to three vessels per year. The Argos G92 launched July, 2009, and will be followed by the introduction of the Argos G100, the Argos All Oceans Series 125', and the Argos 74' Commuter in the Fall of 2009. Most recently, hull #1 of the Argos 70' model was launched and delivered to her Florida based owner, February 2012.


text:
Autumn is definitely on its way and when AW comes, I do love a bit of monochrome. This weekend, it was about family and friends so a pretty chilled out Saturday outfit was needed.
Topshop Studded Jumper .:. River Island Shiny Leggings .:. Mulberry Bag .:. Topshop Studded Shoes
I bought this jumper last winter but I love the detail of the studs (even when the studs fall off and you have to painstakingly superglue them back on… but what wouldn't you do for fashion, eh?!). I like to wear shiny/leather look leggings with a simple knit as it gives it a little more edge and makes it look that little bit more dressy. Usually I add a necklace or something to give an outfit a little more 'oomph' (?!), but as the jumper is already studded, I didn't think it needed it, so instead I wore my little studded shoes, which complete the look in my opinion.
What do you think to monochrome?


text:
Porting DOS Applications to Linux
With a little care, the average DOS application can be easily ported to the Linux system. This article looks at some of the techniques involved, and tries to provide a small "builder's kit" of handy little DOS routines people always want under Linux.
DOS programs written in the C and C++ languages generally run in a variety of different memory models with their own segmentation semantics. The simplest is the "tiny" model, where all of the program and data are referenced off one segment. All three segment registers (CS, DS, and SS) point to the same place to suit the way the processor wishes to work. The Linux kernel executes programs in the 32-bit equivalent of tiny mode. Because offsets are 32-bit, not 16-bit, a program can utilise 4GB of address space before segmentation becomes an issue. Thus you get the simplicity of tiny model without the limitations.
As a result of this the DOS keywords near, far, and huge, have no meaning to Linux. These can be removed, or if you are trying to maintain a common source tree, you can add these lines instead:
#if defined(__linux__) #define far #define near #define huge #define register #endif
gcc, the normal Linux C compiler, understands the register keyword, but the code optimiser is sufficiently good that using register is normally a bad idea.
Many DOS C compilers support an inline keyword. gcc also supports this.
gcc supports all the ANSI C types you would expect and some extensions. The size of the normal types is, however, different from that of DOS compilers, and frequently causes problems when porting. Here is a summary for sizes on Linux/i386 (Linux on other architectures, such as the 64-bit Alpha, will differ in some respects):
Type Name Linux DOS time/small DOS large DOS huge char 8 bits 8 bits 8 bits 8 bits short 16 bits 16 bits 16 bits 16 bits int 32 bits 16 bits 16 bits 16 bits long 32 bits 32 bits 32 bits 32 bits pointer 32 bits 16 bits 32 bits 32 bits largest array 4GB* 64KB 64KB 640KB
* Actually, because some of the address space is reserved and used for other things, you can't get above about 2GB at the moment.
DOS programmers generally make good use of prototypes to avoid mysterious crashes caused by passing the wrong type. Mixing short and long under Linux normally just results in mysterious value changes in passed parameters, so the habit of prototyping is a good one to get into. Furthermore, you can tell gcc to warn you about any routine which has no prototype by adding the compiler flag -Wstrict-prototypes. All of the C library and system calls have prototypes, provided the correct header files are included.
The GNU C compiler is an extremely flexible tool. Although it compiles much slower than most of the DOS compilers, and is (intentionally) without an Integrated Development Environment, it has a wide range of abilities and flexibility that few DOS compilers can touch. People who have used DJGPP to write 32-bit DOS extender programs will be familiar with gcc, although in its Linux and Unix form it is somewhat easier to work with.
It is worth knowing how to tell gcc how to cope with different "flavours" of code. It can become a traditional K&R C compiler, by using the -traditional option, a strict ANSI compiler, by using the -ansi option, or a GNU C compiler—ANSI + GNU extensions. In addition, you can ask it to perform a wide range of sanity checks with the -pedantic and -Wall options. For a typical program, the compiler will generate a lot of warnings, many of which will give insights into potential problems. For example, the compiler will check to see that the conversion options in the format strings of printf()/scanf() and their family of functions match the types of the variables they will interpret.
The optimiser is controllable both by a general level of optimisations, using the -O1 or -O2 options, and on a per-optimisation basis for those speed-critical special cases. The optimiser performs a wide range of peephole and global optimisations, including intelligent allocation of registers, loop unrolling, and even instruction scheduling on RISC CPUs.
The GNU C compiler, linker, and debugger are all described in complete documents available from the Free Software Foundation, which you can either buy as books (the money goes to fund more free software work) or print yourself.
To cover the compiler, debugging tools, make, and other programs in full would require several more articles. If the documentation and documentation viewer are all installed, typing info gdb, info gcc, and info ld should give you a good start. (If the info program is not installed, the Emacs editor can also be used to read documentation in the info format.) Fans of graphical user interfaces may also like to pick up tgdb as a graphical front end for the gdb debugger, and xwpe, a look-alike of a well-known DOS C development environment, built on top of gcc, make, and gdb.
Error in listing 2
The second call to signal in term_ctrlz should be a call to kill, i.e. kill( getpid(), SIGSTOP );


text:
All Possible Solutions: Diophantine Equations
Date: 12/06/2002 at 14:29:26 From: Chris Subject: Algebra problem I've tried everything that I can think of and I can't figure out how to do this. Could you please try it and let me know how to do it? I have the answer (16 Combos, 17 Hot dogs, 22 Hamburgers, 25 Sodas), but I do not know what method to use to solve it. Thanks! Lance and Mario were working in the snack bar at the Turbulent Tunas Concert. They sold hot dogs for $1.65, hamburgers for $2.35, sodas for $.85, and the combo plate with fries, salad, a hamburger; and soda for $3.89. They sold 80 items in an hour for $163.24. How many of each kind of food did they sell, and how much did they make on each kind of food?
Date: 12/09/2002 at 00:23:51 From: Doctor Greenie Subject: Re: Algebra problem Hello, Chris - You apparently have one of many possible solutions to this problem. I have found several others and have not completed the task of finding all solutions. Following is a description of how you can go about finding all the solutions to this problem. You are selling the following items: $1.65 -- hot dog $2.35 -- hamburger $0.85 -- soda $3.89 -- combo 80 items were sold for a total of $163.24. Suppose we let D = # (hot) Dogs sold H = # Hamburgers sold S = # Sodas sold C = # Combos sold Then we have two equations; one says the total number of items sold is 80, and the other says the total cost of those items is $163.24. To avoid working with decimals, we write the second equation in terms of cents instead of dollars. The two equations are then (1) D + H + S + C = 80 (2) 165D + 235H + 85S + 389D = 16324 To limit the types of combinations we need to search for, notice that the prices of a hot dog, a hamburger, and a soda are all multiples of 5. That means the total cost of the hot dogs, hamburgers, and sodas is a multiple of 5, so that total cost of those items has final digit 0 or 5. Since the total cost of all items sold is $163.24, that means that the total cost of the combos has final digit either 4 or 9. This in turn means that the number of combos sold must be a number with final digit either 1 or 6. So we have the following possibilities at this point: # combos cost of combos # other items cost of other items ---------------------------------------------------------------- 1 3.89 79 159.35 6 23.34 74 139.90 11 42.79 69 120.45 16 62.24 64 101.00 21 81.69 59 81.55 26 101.14 54 62.10 31 120.59 49 42.65 36 140.04 44 23.20 41 159.49 39 3.75 The largest number of combos that could have been sold is 41, because with the next possible number, 46, the cost of the combos is by itself more than the total amount of the sales. Also, examination of the last two columns in the above table shows that there will be no solutions with either 36 or 41 combos, because the cheapest item is 85 cents, and you can't get the total in the last column by selling the number of items in the next-to-last column. And for the possible combination with 31 combos and 49 other items, the cost of 49 sodas is $41.65, so there won't be a solution with 31 combos either. However, it is possible and even likely that there are solution(s) for any of the other numbers of combos in the table. Following is how to find all the solutions with 6 combos sold; you can try to use the same process to find the solutions with other numbers of combos. We have 6 combos sold, for a total of $23.34; leaving 74 other items with a total cost of $139.90. So now, with C=6, we have the following equations: D+H+S = 74 165D+235H+85S = 13990 We can solve this pair of equations by eliminating the "S" variable - by factoring a constant of 5 out of the second equation and then multiplying the first equation by 17: 33D+47H+17S = 2798 17D+17H+17S = 1258 ------------------ 16D+30H = 1540 The approach at this point is to solve this equation for one of the variables in terms of the other and then to use the fact that the variables have integer values to determine the possible combinations of values for D and H. 16D = 1540-30H 16D = (1600-32H) + (2H-60) D = (100-2H) + (2H-60)/16 100 is an integer; and H is an integer, so 2H is an integer. For D to be an integer, then, (2H-60)/16 must be an integer, so (2H-60) must be a multiple of 16. We then get the following solutions with C=6: H D=(100-2H)+(2H-60)/16 S = 80-(C+H+D) ------------------------------------------------ 30 (100-60)+0 = 40 80-(6+30+40) = 4 38 (100-76)+1 = 25 80-(6+38+25) = 11 46 (100-92)+2 = 10 80-(6+46+10) = 18 The values chosen for H are those which make (2H-60) a multiple of 16. The next larger value of H would give a negative value for D, so this table shows all the solutions with C=6. We can check these three solutions to the problem: combos (C): 6 @ $3.89 = $23.34 hamburgers (H): 30 @ $2.35 = $70.50 hot dogs (D): 40 @ $1.65 = $66.00 sodas (S): 4 @ $0.85 = $ 3.40 ------- $163.24 combos (C): 6 @ $3.89 = $23.34 hamburgers (H): 38 @ $2.35 = $89.30 hot dogs (D): 25 @ $1.65 = $41.25 sodas (S): 11 @ $0.85 = $ 9.35 ------- $163.24 combos (C): 6 @ $3.89 = $23.34 hamburgers (H): 46 @ $2.35 =$108.10 hot dogs (D): 10 @ $1.65 = $16.50 sodas (S): 18 @ $0.85 = $15.30 ------- $163.24 You can follow the same procedure to find the other solutions to the problem. I did some quick calculations to verify that there is at least one solution with 1 combo sold and at least one solution with 26 combos sold; so I suspect there will also be at least one solution each with 11, 16, or 21 combos sold. Equations like those in this problem - where the number of unknowns is more than the number of equations, and where the values of the unknowns are integers - are called Diophantine equations. If you would like a better understanding of problems like this, try searching the Dr. Math archives using the keyword "Diophantine" and take a look at some of the pages that the search provides to you. I hope all this helps. Please write back if you have any further questions about any of this. - Doctor Greenie, The Math Forum http://mathforum.org/dr.math/
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text:
Escaping From History: The Life of Houdini
By: Evan & Makano Q.
Egypt, Age 11
Harry Houdini was born on on March 24, 1847. He was famous for his increible skills in escape artistry. He was also known for being a great Magician. His real name was Erich Weisz. He started afilm buisness after acting in some films. He died on Halloween,1926 at age 52.


text:
need interview advice - (Feb/17/2014 )
I just finished an interview with a company, the team I would be working on and with the hiring manager. I have reached the 2nd interview round which involves the chief scientific officer and chief operation officer who will interview me. What types of questions would people at this level ask me? I never interviewed with anyone past the hiring manager. Please give me some examples. Thanks in advance.
Depends on position u r applying. If its managerial post, some time they are more interested in personality. In case scientific interview be prepared of area for which u r expected to being posted. Good Luck.


text:
Wednesday, August 10, 2016
Ali Lee promises to make zero error when hosting Olympics Game event 2016
Actress Ali Lee (李佳芯) attended the worshipping ceremony of Olympics Games 2016 hosted by TVB at Tseung Kwan O TVB City. When mentioned about she pronounced Olympics Cup as World Cup during live broadcast previously, Ali expressed the audiences loved to take note of her mistake and promised she will make zero error this time: "But I will be in-charge of relaxing segment such as discussing about the gossips related to sport people." She also hoped the sport people from Hong Kong will achieve good results.
Source: ON.CC (HK)
Translated by: tvfan @ Asian E-News Portal
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text:
Hello, chaps.
I currently have a Fuji F11, which I know is an excellent camera with very good image quality. I couldn't be happier with it, very good battery life too.
But the thing is, it is a little chunky for going out with.
So I was wondering what cameras you would recommend, when I say small, I mean something that could fit into a jean pocket without any problems and you wouldn't be able to feel it too much.
I have seen the Fuji, Z1,Z2,Z3 and V10. All had ok reviews, would the V10 be small enough?
I have only looked at Fuji so far as I have always had Fuji cameras, but if anyone knows better that would be absolutely great.
So, if you have any views or recommendations please post here.
Any help would be much appreciated.


text:
I have been a member of Konig.org for a month now and would like to thank all of you that have made it such a wonderful experiance. I have learned more in a month about the place my grandfather Kurt H. Claussner went missing in action in April ,1945 then in my entire life. Most people in America know little about what you call "The Great Patriotic War" and even less about the battles of East Prussia. The photos that the members post make me see what he must have seen and your explanations and documentation of how the battle unfolded make me understand what it must have been like for him.
If not for the loss of my grandfather, my father would never have moved from Chemnitz, Germany to America where I was born. Imagine how the battle of Konigsberg changed history, because he did not come back I was able to grow up on McDonalds and Kentucky Fried Chicken. My father married an American women who had several family members fight in the war, my father had two uncles (two brothers) one fought for the Germans and one fought the Japanese for the U.S. Army.
I would like to share some photos of not only my grandfather, but all of my family.


text:
New subscription
Active within 3162 Days
I am from Columbia, MO and I've been a Club Horse member for 8 years, 8 months and 3 days
Nicknames: Alex
Age: 21 years old
Gender: Mare
Breed: Abaco Barb
Height: 15
Color: mix
Type of Riding: jumping
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text:
What does EOL mean in Astronomy?
This page is about the meanings of the acronym/abbreviation/shorthand EOL in the Academic & Science field in general and in the Astronomy terminology in particular.
Earth Observing Laboratory
Find a translation for EOL in other languages:
Select another language:
What does EOL mean?
- Eöl
- Eöl, called the Dark Elf, is a fictional character in J. R. R. Tolkien's Middle-earth legendarium. He is introduced in The Silmarillion as an Elf of Beleriand and is a character existing in some form from the earliest to the latest writings.
Discuss this EOL abbreviation with the community:
Use the citation below to add this abbreviation to your bibliography:
"EOL." Abbreviations.com. STANDS4 LLC, 2018. Web. 18 Mar. 2018. <https://www.abbreviations.com/term/1423086>.


text:
John Galliano has hit back at claims that his Jewish lawyer Stephane Zerbib walked out on him. A statement released from the Galliano camp earlier today said "Mr Zerbib was dismissed as Mr Galliano's lawyer some weeks ago following the discovery of apparent irregularities in respect of his firm's administration of Mr Galliano's financial affairs over a number of years."
The is designer preparing to go to court next week for hearings ahead of his public slander trial in France after allegedly making anti-Semitic remarks to a couple in a Parisian cafe.
Zerbib previously defended Galliano in the press by saying, "Anyone can go to a bar, drink a little and get into a fight with someone ... It's alcohol mixed with medications. You're very vulnerable when you're in this state."
Barring Ashley Olsen's vintage Dior dress, there was a notable absence of Christian Dior gowns on the red carpet at the Met Ball last night - and no designs created by John Galliano's eponymous label.


text:
Small but perfectly formed, some of the titchiest wonders of the natural world have been revealed in their full glory by groups of chemists, biologists, materials researchers and botanists working in laboratories round the world. These are the winners, and short-listed finalists, of one of science's longest-running imaging competitions: the Nikon Small World awards. This year, scientists from 63 countries sent in entries for the competition which this year is celebrating its 35th anniversary. These microscopic submissions are not merely judged for their informational content and their technical proficiency but for their visual impact. A selection of some of the most striking are displayed here.
These works, selected by competition judges, include close-up photographs of iridescent crystals of the mineral cacoxenite; a starfish embryo; an extinct marine diatom; a butterfly egg nestling among the buds of a flower; trout alevin; and a caddis fly larva head. This year's first prize went to the image, shown at the centre of this article, of a close-up view of the heart of a mosquito. Taken by Jonas King, of the biological sciences department of Vanderbilt University, in Nashville, Tennessee, the image involved the use of a technique known as fluorescence microscopy which exploits the fact that certain substances can be made to emit one kind of light while being bathed in a different form of radiation. Typically the emitted radiation is of longer wavelength than that of the light shone on the specimen. For example, many minerals, crystals, resins and organic compounds emit light when bathed in ultraviolet radiation. By carefully tailoring the radiation shone on their sample, the Vanderbilt team were able to create a photograph that shows the delicate traceries of tissue inside a mosquito's heart.


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Sign up for Equitymaster's free daily newsletter, The 5 Minute WrapUp and get access to our latest Multibagger guide (2018 Edition) on picking money-making stocks.This is an entirely free service. No payments are to be made.
Here is the latest stock price and chart of SHRI JAGDAMB.
|Live BSE Quotes
|Mar 21, 2018 (Close)
|Price (Rs)206.60
|Open (Rs) 207.00
|High (Rs) 207.40
|Low (Rs) 197.10
|% Change0.90
|Volume 215
|Value (Rs) 42,527
|52-Week H/L 209.75 / 67.60
|Live NSE Quotes
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|BSE Sensex | CNX Nifty
A slew of initial public offers (IPOs) are hitting the market in this month. One of the latest in the offering is Lemon Tree Hotels Ltd.
Should you apply for the IPO of state-run military aircraft maker Hindustan Aeronautics?
Should you apply for the IPO of Bharat Dynamics, India's first state-owned missile manufacturer?
Should you subscribe to the IPO of Apollo Micro Systems Ltd?
Should you subscribe to the IPO of Khadim India Ltd?
Should you subscribe to the IPO of Mahindra Logistics Ltd?More Views on News
The markets seem confused. They're neither going up nor down. What should investors do? Consider Safe Stocks. Here's the top 5 Safe Stocks in the market today.
The Indian Railways recently received 1.5 crore applications for 90,000 vacancies.
India's biggest private bank just barred bitcoin and cryptocurrency purchases through its cards. Why did it take such a drastic measure? And what does it mean for bitcoin? Read on to find our more...
PersonalFN explains the three things robo advisory platforms don't tell you.
The market capitalisation of private sector lender HDFC Bank now exceeds the market capitalisation of all public-sector banks combined.More


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CafeMom Veteran
she is very girly and...
she is athletic, hyper,...
Click on a link to search for moms with the same information
Click on a link to search for other moms with the same favorites
by karigirl posted at 3:22 PM on Jan. 18
, 2008
Would you like to get a FREE Avon ANEW Transforming Lift Cream? Visit this page, http://www.AvonCream.VizVaz.com
Hi! Welcome to CafeMom!
Feel free to join the CafeMom Newcomers Club.
To find us, click the 'groups' tab above then click 'active groups'.
It is a great place to get started and make friends.
I hope to see you there!
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text: Hello, I just download the mptest kernel, netbsd-GENERIC.MP and tried to boot from my i386 system on a dual P90 board. It is a very old board. The number of the board is VEGA P54C-IDP ystem board. It boots ok with single cpu kernel. The system halt at. .. cpu0 .. .. cpu1 .. .. ioapic0 at mainbus0 apid 0 (I/O APIC) ioapic0:pa 0xfec00000, virtual wire mode, version11, 16 pins mainbus0: WARNING: interrupts not configured panic: lazy bum Stopped in swapper at cpu_Debugger+0x4 leave (cpu0)db> Sorry, I don't how to dump the exact messages. Clarence


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First Place Red Bulls Run Unbeaten Streak to Five with 1-1 Tie
May 11, 2013 - Major League Soccer (MLS) - New York Red Bulls News Release
HARRISON, NJ "" Midfielder Lloyd Sam scored his first MLS goal as the first place New York Red Bulls ran their unbeaten streak to five with a 1-1 tie against the New England Revolution at Gillette Stadium Saturday night. With the draw, New York moved to 21 points with a 6-4-3 record and is leading the Eastern Conference by one point.
New York begins a three-game homestand on May 19, hosting defending MLS Cup Champion, the LA Galaxy, at 1:00 PM at Red Bull Arena. For tickets, call 1.877.RBSOCCER or log onto www.newyorkredbulls.com.
Fabian Espindola tried to put the Red Bulls ahead in the 14th minute, firing a left-footed blast past the right post. Later, Heath Pearce got his head on a New York corner kick and nodded it wide. In the 38th minute, Revolution forward Dimitry Imbongo ran at the Red Bulls' defense and his shot was saved by goalkeeper Luis Robles.
New England went ahead in the 54th minute. Chris Tierney's corner kick towards the near post was volleyed by Diego Fagundez and blocked off the line by New York's Kosuke Kimura. However, Fagundez got to his own rebound first and put it in from close range.
However, the Red Bulls responded immediately. Forward Andre Akpan, making his first start as a Red Bull, slid it into the box to Sam, who controlled the pass and put it inside the left post for his first career MLS goal.
• Discuss this story on the Major League Soccer message board...
Major League Soccer Stories from May 11, 2013
- Columbus Crew blanked by Colorado Rapids - Columbus Crew SC
- REACTION: Crew End Homestand with Loss to Rapids - Columbus Crew SC
- Teibert scores first two pro goals, Mattocks secures result - Vancouver Whitecaps FC
- Buddle, Powers and Defense Send Rapids Past Crew, 2-0 - Colorado Rapids
- First Place Red Bulls Run Unbeaten Streak to Five with 1-1 Tie - New York Red Bulls
- San Jose Earthquakes Fall 4-0 on Road vs. Seattle Sounders FC - San Jose Earthquakes
- Neagle, Sounders FC Pound San Jose 4-0 - Seattle Sounders FC
- Impact Comes Back Twice from a One Goal Deficit to Win 3-2 against Real Salt Lake - Montreal Impact
- Chicago Fire Fall 1-0 to Philadelphia Union - Chicago Fire
- Houston Dynamo Host Sporting Kansas City on Sunday Seeking Third Consecutive Win - Houston Dynamo
- Real Salt Lake Concedes Two Late Goals to Fall 3-2 at Montreal Impact - Real Salt Lake
- Philadelphia Union Earn 1-0 Victory against Chicago Fire - Philadelphia Union
The opinions expressed in this release are those of the organization issuing it, and do not necessarily reflect the thoughts or opinions of OurSports Central or its staff.
Other Recent New York Red Bulls Stories
- Four New York Red Bulls Earn National Team Call Ups
- Early Penalty Kick Dooms New York, Loses to RSL, 1-0
- Match Preview: Red Bulls Head West to Face Real Salt Lake
- Dates Set for Red Bulls - Chivas Guadalajara SCCL Semifinal Matchup
- New York Red Bulls U-23's Qualify for 2018 U.S. Open Cup


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Elyce Hues of Mt. Angel, Ore., and Jarhid Brown of Juneau will be married on June 21 in a private ceremony in Juneau. A reception will be held on July 5 at Silver Fall Lodge in Oregon.
The bride-elect is the daughter of Ron and Donna Hues of Mt. Angel. She is a graduate of the University of Oregon and works in Portland, Ore.
The groom-elect is the son of James and Tina Brown of Juneau. He is a graduate of Juneau-Douglas High School and is a musician in Portland.
© 2018. All Rights Reserved. | Contact Us


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Yamaha Flute Lyre
The Yamaha Flute or Piccolo Lyre is a marching book holder which is suitable for flute or piccolo. It consists of an adjustable wrist strap with metal lyre attachment. Heavy-duty nickel-plated brass for durability; extra-firm spring for maximum holding power.
Regular $39.95
Our price $27.95
Available in Montreal
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Yamaha Flute Lyre
Yamaha Flute Lyre


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The World Health Organization (WHO) has announced plans to research the potential health risks of microplastics in...
A second career for its three founders, one New Hampshire dealer has stayed savvy for nearly 25 years
In 1989, Secondwind Environmental opened its doors in Manchester, N.H., bringing new life to water treatment in the state and a new career for its three founders. Christine Fletcher and her husband, Crispin Fletcher, both left the computer industry while their third business partner, Jan Beauvais, left a job in the manufacturing industry.
"We just had a desire to do something that felt a little more connected locally," Christine said. "Between the three of us, my husband was sort of the environmental guy, I have an MBA in finance, so I was sort of the business person, and our third person was more the pure science guy with the bio-chem background."
Secondwind Environmental soon changed names to Secondwind Water Systems upon realizing that water treatment was complicated and versatile enough to keep busy, according to Christine.
The company now serves more than 9,000 residential and commercial customers, manages 130 small public water supplies and installs and monitors the performance of more than 100 systems for gasoline contamination.
Learning to Do Things Differently
When the business first opened, Christine found selling to be one of the most challenging things for all three founders.
"My joke inside the company was the only thing I had ever sold in my life was Girl Scout cookies," Christine said. "It just didn't come naturally, but we found that when you really like your product and have confidence in your company, it's easier to sell."
Just as Christine embraced learning how to sell, she has remained open to change during nearly 25 years of business. She remembers trying to decide if the business could afford one of the first car phones, but now it has purchased iPhones for its staff, because expectations to constantly be connected to e-mail are so great.
A recent technological challenge and opportunity for Secondwind Water Systems came in 2013: moving the company's information system to the cloud. The switch allowed the company to get rid of its hefty server room and keep everything more up to date, according to Christine.
"It was scary! You never can just sit back and run the business," she said. "You're always having to learn new things and implement change in your company."
Another one of those changes has come with utilizing more mobile technologies. Currently, the company's technicians have mobile devices they use in the home to access data and write work orders.
"I assume over the years mobile will become a natural, easy thing to do, where technicians can take the credit card in the home," Christine said. "Sometimes I feel like the latest and greatest just cause a headache, so I hope some of these things will eliminate the headaches and make business better."
Generating Leads
Secondwind Water Systems has found the Internet playing a large role in getting new business.
"When the Yellow Pages stopped being a major source of leads, we were going to go out of business if we didn't find some new leads," Christine said. "Things like having a blog and an e-mail newsletter take a little bit to get going, but once you have [them] started, it's not too expensive."
New Hampshire is rural geographically, so the company has found it costs a lot of money to cover the whole state to find the people who will spend money on water treatment. The Internet is a way to get a lot of marketing for not a lot of money, according to Christine.
Relying on just the Internet, however, is not an option.
"Our No. 1 source of leads is referrals from the install base. There is no question, and it's been that way for about 20 years," Christine said. "[People] used to maybe hear about us through a customer, but then go to the Yellow Pages. Now they hear about us from a customer and then come to us through the Internet."
Continuing Education
Secondwind Water Systems has made it a priority to educate both its veteran employees, some of whom have been with the company for more than 15 years, and its new hires.
Over the years, the company has developed what it calls "the configurator." This includes all the company's rules of how to know what to configure under which water quality circumstances.
"Ten years ago it felt like this arduous process. The poor sales guys couldn't figure out what to sell when, and they always had to call the office for help," Christine said. "It was just a matter of getting all the knowledge that was in the heads of the old-timers and getting it organized in such a way that a new-timer could access it."
Technicians still receive hands-on experience for them to get totally comfortable, but this at least exposes them to the concepts, she added.
Elevating Water Treatment
Secondwind Water Systems has seen a shift in the customers it serves since it first opened. The company's first customers were people who had problem water, according to Christine.
"Now we have definitely seen water quality be elevated in the minds of people," she said. "The percentage of people who believe that the water quality matters from a health perspective has increased. The percentage of people who want to know what's in their water has increased."
Christine described the water of many of the customers as "New Hampshire soup," which includes a mixture of water problems, often low- to moderate- hardness paired with iron or manganese. The state also has lots of corrosive water with low pH and low mineral content that can destroy plumbing, as well as water with hydrogen sulfide-type odors.
"The nice thing from a dealer perspective is the customer can see or smell these problems, and it's bothering them in the home," she said.
Naturally occurring health issues in some New Hampshire water, such as arsenic, uranium and radon, also are sources of revenue for the business.
Secondwind Water Systems developed a reputation early on for a money-back guarantee that Christine said just makes sense with all these different water conditions.
"We'd stick with it until we solved the problem," she said. "It's nice to have the feeling that your customers value what you do."


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Release Notes: The table creation code in vmysql.c and vpgsql.c was consolidated. SQL_BUF_SIZE was increased from 600 to 2048 for Oracle, Postgres, and Sybase. qnprintf() was added to vpopmail.c for escaping strings in SQL queries. Use qnprintf() when building queries in vmysql.c, vpgsql.c, voracle.pc, and vsybase.c. Multiple fixes were made to vpgsql.c related to freeing PGresults and attempting to access NULL PGresults when reporting errors.
Release Notes:
Release Notes: The 5.3 development series is now stable. Be sure to read the UPGRADE file and various README files if upgrading from a previous version.
Release Notes: This release includes many bugfixes.
Release Notes: This version started with fixes to the build/install process and expanded to include some more minor bugfixes and feature requests. A 5.4 release should be close.
Release Notes:
Release Notes: Some minor changes were made to vlimits.c to make it compile, but more work is needed. Various LDAP fixes were made, the vlimits structure was updated, and valias_line was changed from the "blob" type to "text". There was a minor fix for users-big-dir and a fix for vipmap for displaying the usage. host_in_locals now converts addresses to IPv4 so that ip-alias works with courier-imap.
Release Notes: More error checking was added to vpopbull. The limits API was added to manage restrictions on the maximum number of accounts, forwards, aliases, and mailing lists. The administration guide was updated to reflect the limits features. Automatic directory creation is now done in vpopbull if a user account has not had a directory assigned to it. Wildcard support was added to the vdelivermail valias functions. Various typographical errors were fixed. vdelivermail now has support for exit codes in .qmail files.
Release Notes: This release adds one last patch for the vgetent problem, comments out the lseek definition for BSD users, replaces the old qmail-pop3d-maildirquota patch with the qmail-maildir++ patch (which adds Maildir++ support not only to qmail-pop3d, but also to qmail-local), and updates the documentation.
Release Notes: Backported changes from 5.3.6 development release, a vgetent() fix for support of clear text passwords on old sites without clear text, vpopbull fixes for distribution of newsletter to all local users, a fix for calculation of quotas, and exit code checking in vdelivermail for scripts.


text: On Thursday, August 24, 2006 10:41 am, Arjan van de Ven wrote:> The reason for adding this infrastructure is that power management in> the idle loop needs to make a tradeoff between latency and power> savings (deeper power save modes have a longer latency to running code> again).What if a processor was already in a sleep state when a call to set_acceptable_latency() latency occurs? Should there be a callback so they can be woken up? A callback would also allow ACPI to tell the user "disabling C3 because of device <foo>" or somesuch, which might be nice.Also, should subsystems have the ability to set a lower bound on latency? That would mean set_acceptable_latency() could fail, indicating that the user should buy a better device or a system with better realtime guarantees, which is also valuable info.Comments aside, this is a nice interface, should help clarify things for devices with response time limits.Thanks,Jesse-To unsubscribe from this list: send the line "unsubscribe linux-kernel" inthe body of a message to firstname.lastname@example.com majordomo info at http://vger.kernel.org/majordomo-info.htmlPlease read the FAQ at http://www.tux.org/lkml/


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Re: Daniel Pickett b. 1771 d. 1854 buried in Erie Cty, PA
In reply to:
Re: Daniel Pickett b. 1771 d. 1854 buried in Erie Cty, PA
John Aitkin 12/11/10
I believe that I have the same 'old' file which you reference, showing that Parnell Pickett (1758) was the child of Ebenezer and Parnell and the father of Rev. Daniel. It included the names of four sons of Daniel and Anna and reported that Anna died in 1812, before her children were born. Another problem is that Parnell Pickett (1858) was female and married James Hawley in 1779.
Also, the 'Notes Ependatory' to the Case biop does not say that Rev Daniel's parents MOVED to Canada though that is the implication. These notes have gross errors about Rev Dan marrying E F Ingersoll in the 1790's when he was in his 'early twenties' when, in fact, Ingersoll was his second wife who he married in his mid thirties.
The notes from Dan's g-grandson, Betherl S. Pickett, clearly state that Dan grew up in New England, as opposed to the 'home grown' Canadian statements.
As stated before, the facts surrounding Rev Dan are confusing and contradictory. No one source is complete and beyond challenge.
Similarly, whileno histories of the Bostwicks and Wheelers include Rev Dan with the nine other children of Ebenezer and Parnell, neither do they report that Parnell died within two years after the last child (and before the publications of the family histories).
Ms Taylor, as a direct descendant of Rev Dan; and who purports to possess personal memorabilia of the Reverend, has given a more credible explanation than any other available. Certainly, she is subject to challenge but not with unsupported and grossly erroneous reports.


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Eflorist Discount Code: 15% Off
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Click here to use the Eflorist voucher code online
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I tested the Eflorist discount code on a lovely bunch of roses and lilies, and it worked very well. The discount code can be applied as you go through the checkout process.
If you're on a bit of a budget though, they have value bouquets starting from £24.95.
Thanks to carleast on HUKD!
TOPICS: Home


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In a bid to increase its market share in the Indian market, Toyota Kirloskar Motor, the Indian subsidiary of the Japanese carmaker, is working on a bunch of all new cars. The company is planning to enter some new segments as well including the mid-sized sedan and compact SUV. While the Vios could be the company's mid-sized sedan for India, there is no clarity on the compact SUV yet.
Here' a list of the car that Toyota India is contemplating to launch in the next 12-18 months.
1. Toyota Vios
Toyota is testing this mid-sized sedan in India for several months and was expected to bring it to 2016 Delhi Auto Expo, but seems like, Toyota wants to keep things under wraps for a while. Upon its launch the Vios will take on the likes of Honda City, Maruti Suzuki Ciaz and Hyundai Verna.
(The Upcoming Toyota Vios)
Toyota India hasn't officially said anything about this, but the company made it clear that its focus is on bigger cars instead of mass-segment products. Two small cars that the company has already tried its luck with are Etios Sedan and Etios Liva hatchback, and both of them are struggling to lure buyers today. The new-generation of the Vios shares its styling with the Corolla and Camry, and features a similar front-fascia.
Expected Launch – Mid 2016
Estimated Price: 7.5 – 12 Lakh
2. Toyota Etios Facelift
Toyota's entry level sedan Etios is all set to undergo yet another facelift. Introduced in 2010, the sedan was built exquisitely for the Indian market and has undergone various mild facelifts over the years. This time around, Toyota India is expected to bestow cosmetic upgrades on the sedan. Caught undergoing test runs, the sedan is likely to receive a new grille, revised bumper in front and redesigned fog lamp housings. Cabin will reportedly get subtle updates such as a new digital instrument cluster, new upholstery and steering wheel.
(Upcoming Toyota Etios Facelift / Image Credit: Motoroids)
Engine set-up of the Toyota Etios Facelift will remain unchanged featuring similar 1.5 litre petrol and 1.4 litre diesel units paired to a five-speed manual transmission. In the highly contested compact sedan segment, Etios has a number of rivals to compete with including Maruti Swift Dzire, Honda Amaze, Hyundai Xcent and Ford Figo Aspire.
Expected Launch – Around Festive Season
Estimated Price – 6.5 lakh – 9 Lakh
3. Toyota Fortuner Facelift
Toyota's muscular Fortuner is all set to get even better featuring aplenty tweaks both on and under the skin. Already available for sale in Australian market, the new generation model surpasses the preceding version in every aspect. Built on the modular Toyota New Generation Architect platform, the premium SUV looks sleeker, sportier and weighs much lighter.
(Toyota Fortuner Facelift)
On the outside, the SUV gets new twin-slat grille, reworked bumper, LED DRLs, 12 spoke alloy wheels and LED tail lamps. Interiors offer increased space and features like large touchscreen infotainment system display and four spoke steering wheel with mounted controls for audio and telephony etc are available Mechanically, the car is all new as it gets newly developed GD diesel engines including a 2.4 litre 2GD-FTV unit good for 148bhp and 400Nm and a 2.8 litre 1GD-FTV powertrain putting out 177bhp and 450Nm. Transmission choices may include either a six-speed manual or a six-speed auto box, while there will be an option for an AWD. In a bid to curb the price of the Upcoming Fortuner, Toyota India is looking at heavy localization of up to or beyond 80 percent.
Expected Launch – 2017
Estimated Price – 20 Lakh – 25 Lakh


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Heather - posted on 01/27/2009 ( 20 moms have responded )
I've been CDing for about 6 months and have only done it at home. I've used disposables when we're away from home. Recently, I've begun thinking about using cloth when out for the day (would still use disposables when leaving DD with a nursery or when we're gone overnight). I know I would need a wet bag of some sort. Would the pail liner I use at home be sufficient or would I need something made specifically as a wet bag? (The pail liner I use is just a simple pail liner made from some kind of nylon. The outside does feel damp after diapers have sat in it for a day.) What else should I consider?


text:
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Please white-list or disable AboveTopSecret.com in your ad-blocking tool.
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reply to post by GypsK
"I feel like my best friend died and I'm morning"
Originally posted by TFCJay
reply to post by GypsK
"I feel like my best friend died and I'm morning"
Speaking from experience of losing my best friend at a young age and quitting smoking.... I would rather have the constant craving for a cigarette every minute of every day for the rest of my life then go through the pain for so much as 1 hour of losing my best friend again.
When I say young age I mean he was 32 years old and I was 33.
And to you OP, I hope for 2 things for you...
1. You are successful at butting out for good.
2. You and your best friend live to be best friends until you are old and wrinkly together.
edit on 1-1-2013 by TFCJay because: (no reason given)
The nicotine content of popular American-brand cigarettes has slowly increased over the years, and one study found that there was an average increase of 1.6% per year between the years of 1998 and 2005. This was found for all major market categories of cigarettes.
Originally posted by ganjoa
By way of assistance, several close friends have had tremendous success with electronic cigarettes using vegetable glycerine based nicotine (polyethylene glycol seems unhealthy) - one friend just substituted e-cigs for combustible smokes and states that he sees health benefits in 2-3 weeks. My 2cents for your consideration.


text:
Pearl Vision Artisan II Drum Set EmeraldPearl Vision Birch Artisan II New Fusion Shell Pack Emerald Fade Eucalyptus Based on the original Vision formula of inner birch plies with a basswood exterior, these shells pump out perfectly balanced tone. Exclusive Artisan II photo-finishes provide the eye-popping look of exotic woods without the use of rare resources. Cymbals and hardware sold separately.
|Product Name
|Pearl Vision Artisan II Drum Set Emerald


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You are here: Home » Families » HMGFM Home » Progenitors: Q
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[This information is from Vol. IV, p. xxix of Hudson-Mohawk Genealogical and Family Memoirs, edited by Cuyler Reynolds (New York: Lewis Historical Publishing Company, 1911). It is in the Reference collection of the Schenectady County Public Library at R 929.1 R45. Some of the formatting of the original, especially in lists of descendants, may have been altered slightly for ease of reading.]
Pieter, bought Adriaen van Ilpendam's brickyard at Albany, in 1668; had a son, Wouter Pieterse, who married (first) Neeltje Gysbertse; (second) Cornelia Bogart, at Albany, Oct. 4, 1696; his third son, Johannes, removed to Niskayuna, marrying (first) Magtelt Janse Post; (second) Anna Clute, Oct. 20, 1700. Renier (or Reynier) Quackenbos came from Oestgeest, Holland, and married (first) Lysbet Janse, of Flushing, at New Amsterdam, March 2, 1674; (second) Claesje Jacobsen, Sept. 13, 1692, and their children were baptised in Albany. Adriaen Quackenbos resided for a time at Schodack, marrying Catharina Van Schaick, Jan. 18, 1699. The name was also spelled Quackenbush, Quackenbusch, and Quackenbosch.
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