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THIN film contacts, in which a thin conducting film constitutes at least one of the contacting members, are basic circuit structures in modern electronic devices. They are widely used in micro-electronic and micro-electromechanical systems, and in semiconductor material and device characterization [1], [2]. In miniaturization of electronics, current crowding and Joule heating are important issues [3], [4], [5].
We consider two basic types of thin film contact: the vertical type [Fig. 1(a)] and the horizontal type [Fig. 1(b)]. In the vertical contact [Fig. 1(a)], the thin film base AB is an equipotential; the current flow is orthogonal to AB, but is tangential to the thin film edges BC and AH. In the horizontal contact [Fig. 1(b)], the thin film edges BC and AH are equipotentials. The current flow is orthogonal to BC and AH, but is tangential to the thin film base AB. As a result, the constriction resistance (also known as the spreading resistance), as well as current crowding at the edges G and D for these two types of thin film contacts are very different. We assume that there are only two contact members, denoted as Region I and Region II, between the electrodes [Fig. 1(a) and (b)]. The interface GD is perfectly smooth and does not contain a resistive sheet.
In this paper, we focus mainly on the vertical contact shown in Fig. 1(a), and provide a comprehensive study of the constriction resistance and the current flows in regions I and II. We point out the marked difference in current crowding at the corners (edges) D and G between vertical contact [Fig. 1(a)] and horizontal contact [Fig. 1(b)]. Without loss of generality, we assume that the top terminal EF is grounded..
The vertical thin film contact has been studied by several authors [6], [7], [8], [9], [10], [11], [12]. In particular, Hall [6] studied the Cartesian geometry using conformal mapping. Denhoff [12] studied the constriction resistance of a round thin film contact by solving Laplace equation using analytic, numerical, and finite element methods. These studies are restricted to the highly special cases of Fig. 1(a): assuming either equal resistivity, $\rho_{1}=\rho_{2}$ [6], or $h_{1}\to 0$ [7], [8], [9], [12]. We relax these two assumptions in this paper.
The horizontal thin film contact has also been studied extensively, in both Cartesian [1], [2], [13], [14], [15], [16], [17] and cylindrical geometry [15], [16], [17], [18], [19]. Most recently, we treated the 3-terminal horizontal thin film contact in great detail [20], with arbitrary resistivities and geometric dimensions in the individual contact members, as well as arbitrary (unequal) voltages at the terminals BC and AH [Fig. 1(b)]. We found severe current crowding at the edges D and G, for $\rho_{1}=0$, when the thin film thickness $h_{2}$ is small [17]. There is a great variety of current crowding in 3-terminal horizontal thin film contact [20].
In both Cartesian and cylindrical geometries [Fig. 1(a)], the resistivities $\rho_{1}$ and $\rho_{2}$, and the geometric dimensions $a$, $b$, $h_{1}$, and $h_{2}$ may assume arbitrary values. Thus, this paper is applicable to both thin and thick films, and Region I may represent a resistive thin film by letting $h_{1}$ small and $\rho_{1}$ large. Following the same procedure in studying the bulk contact resistance [21], [22] and the horizontal thin film contacts [15], [20], we analytically solve Laplace equation in Regions I and II of Fig. 1(a), then match the boundary conditions at the contact interface. The potential profile and the constriction resistance are calculated from this exact formulation.
In Section II, we consider the Cartesian vertical thin film contact. We present a formula for the constriction resistance and illustrate the current pattern. We compare our results to those obtained from the MAXWELL 2-D finite element code [23]. In Section III, we consider the cylindrical vertical thin film which is qualitatively similar to the Cartesian solution of Section II. Concluding remarks are given in Section IV. Only the major results will be presented in the main text. Their derivations are given in the appendices.
Since the geometry [Fig. 1(a)] is symmetrical about the vertical $z$-axis, so also are the current flow patterns and the field lines. The field lines are normal to the two terminals AB and EF. The total current is $I=V_{0}/R$, where $R$ is the resistance between these two terminals, which we find to be TeX Source $$R=\rho_{1}{{h_{1}}\over{2a\times W}}+{{\rho_{2}}\over{4\pi W}}\overline{R}_{c}({{a}\over{b}},{{h_{1}}\over{a}},{{a}\over{h_{2}}},{{\rho_{1}}\over{\rho_{2}}})+\rho_{2}{{h_{2}}\over{2b\times W}},\eqno{\hbox{(1)}}$$ where $W$ denotes the channel width in the third ignorable dimension that is perpendicular to the paper. In (1), the first term represents the bulk resistance of Region I. The third term represents the bulk resistance of Region II. The second term represents the remaining constriction (spreading) resistance, $R_{c}$, and is expressed as $R_{c}={{\rho_{2}}\over{4\pi W}}\overline{R}_{c}$ for the Cartesian case. The normalized $\overline{R}_{c}$ depends on the aspect ratios $a/b$, $h_{1}/a$, and $a/h_{2}$, and on the resistivity ratio $\rho_{1}/\rho_{2}$, as explicitly shown in (1). The exact expression for $\overline{R}_{c}$ is derived in Appendix A (A7).
If we use the exact expression (A7) in the numerical evaluation of $\overline{R}_{c}$, we call the result the "exact theory". [In the infinite sum in (A7), we use $10^{4}$ terms; we also use $10^{4}$ terms in the infinite sum in (A3b) to solve for $B_{n}$, $n=1, 2,..,10^{4}$.] From the vast amount of data that we collected from the exact theory at various combinations of $h_{1}$, $h_{2}$, $\rho_{1}$, $\rho_{2}$, $a$, and $b$, we attempted to construct simple fitting formulas for $\overline{R}_{c}$ so that the values of $\overline{R}_{c}$, or the bounds of $\overline{R}_{c}$, may be easily obtained without solving the infinite matrix (A3b). The bounds on $\overline{R}_{c}$ are identical to the corresponding asymptotic limits of $\overline{R}_{c}$, which in some cases (but not all) were solved in the literature by other means. Thus, the numerical fitting formulas, given for instance in (2), (3), (5), and (6), are synthesized from a judicious combination of these asymptotic limits, and from the numerical data generated from the exact theory. We validated the exact theory and the synthesized fitting formulas with MAXWELL 2-D simulation codes in Figs. 2, 3, 4, 6, 7, and 8. Similar approaches were used in our recent treatment of the horizontal thin film contact [20].
The exact theory of $\overline{R}_{c}$ (A7) is plotted in Fig. 2 as a function of $b/a$, for $\rho_{1}/\rho_{2}=1$ with various $a/h_{2}$ and $h_{1}/a$. For a given $a/h_{2}$, $\overline{R}_{c}$ increases as $b/a$ increases. For $a/h_{2}$ on the order of 1 or larger, $\overline{R}_{c}$ approaches almost a constant as $b/a$ becomes large. For a given $b/a$, $\overline{R}_{c}$ decreases as $a/h_{2}$ increases. The effect of $h_{1}/a$ on $\overline{R}_{c}$ is minor. $\overline{R}_{c}$ increases slightly as $h_{1}/a$ increases. The effect of $h_{1}/a$ becomes even less significant as $a/h_{2}$ increases.
Since $\overline{R}_{c}$ is relatively insensitive to $h_{1}/a$, in Fig. 3 we plot $\overline{R}_{c}$ as a function of $a/h_{2}$ at various values of $b/a$ and $\rho_{1}/\rho_{2}$, in the limit of $h_{1}/a\to\infty$. When $a/h_{2}\ll 1$, $\overline{R}_{c}$ approaches a constant value (independent of $h_{2}$) for a given $b/a$. This is due to the fact that if both $h_{2}$ and $h_{1}$ become much larger than $a$, the structure in Fig. 1(a) will become a semi-infinite constriction channel, whose constriction resistance is independent of $h_{1}$ and $h_{2}$, which was studied in detail in [22]. When $a/h_{2}>1$, $\overline{R}_{c}$ decreases as $a/h_{2}$ increases. As $a/h_{2}\rightarrow\infty$, $\overline{R}_{c}=2\pi\left({{{h_{2}}\over{a}}-{{h_{2}}\over{b}}}\right)\rightarrow 0$, which is in sharp contrast to the behavior of the horizontal Cartesian thin film contact studied in [15], [16], [17], [20], where the current flows parallel to the thin film bottom boundary, and $\overline{R}_{c}$ (which has a different definition for the horizontal contact [17], [20]) approaches a finite constant of 2.77 as $a/h_{2}\rightarrow\infty$.
By comparing the data calculated analytically from the exact theory (A7), with the published scalings for some limiting cases [6], [21], [22], [24], we synthesized an accurate, analytical scaling law for the constriction resistance of a general vertical thin film contact, in the $h_{1}/a\rightarrow\infty$ limit, TeX Source $$\eqalignno{&\left.{\overline{R}_{c}\left({{{a}\over{b}},{{a}\over{h_{2}}}, {{\rho_{1}}\over{\rho_{2}}}}\right)}\right\vert_{h_{1}/a\to\infty} \cr&=\cases{\overline{R}_{c0}\left({{b}\over{a}}\right)+0.2274\times\left({{2\rho_{1}} \over{\rho_{1}+\rho_{2}}}\right)\times g\left({{b}\over{a}}\right),\matrix{&{{{a}\over{h_{2}}}<\tan \left({{{\pi}\over{2}}{{b}\over{a}}}\right)}}\hfill\cr p\left({{a}\over{h_{2}}}\right)\times\left({1+{{0.2274}\over{q(b/a)}} \times{{\rho_{1}-\rho_{2}}\over{\rho_{1}+\rho_{2}}}}\right),\matrix{&{{{a}\over{h_{2}}}>\tan\left({{{\pi}\over{2}}{{b}\over{a}}}\right)},}}&{\hbox{(2)}} \cr& \overline{R}_{c0}\left({b/a}\right)=4\ln(2b/\pi a)+4\ln (\pi/2)\times f(b/a),\cr & f(b/a)=0.03250(a/b)+1.06568(a/b)^{2}-0.24829(a/b)^{3}\cr &\quad+0.21511(a/b)^{4},\cr & g(b/a)=1-1.2281(a/b)^{2}+0.1223(a/b)^{4}-0.2711(a/b)^{6}\cr &\quad+0.3769(a/b)^{8},\cr & p(a/h_{2})=2\pi (h_{2}/a)-4(h_{2}/a)\tan^{-1}(h_{2}/a)\cr &\quad+2\ln\left[{(h_{2}/a)^{2}+1}\right]-2\pi(h_{2}/b),\cr & q(b/a)=2\left(\scriptstyle{{{b}\over{a}}+{{a}\over{b}}}\right)\ln\left(\scriptstyle{{1+a/b}\over{1-a/b}}\right)+4\ln\left(\scriptstyle{{b/a-a/b}\over{4}}\right).&{\hbox{(3a-3e)}}}$$
Equation (2) is also plotted in Fig. 3, showing excellent agreement with the exact theory (A7) for arbitrary value of $a$, $b(>a)$, $h_{2}$, $\rho_{1}$, and $\rho_{2}$, in the limit of $h_{1}/a\rightarrow\infty$.
In (3), $\overline{R}_{c0}\left({b/a}\right)$, $f(b/a)$, and $g(b/a)$ are derived by Lau and Tang [21], and by Zhang and Lau [(5) and (6) of [22]],1 $p(a/h_{2})$ is derived by Hall [(45) of [6], assuming $\rho_{1}/\rho_{2}=1$ and $h_{1}/a\rightarrow\infty$], $q(b/a)$ is derived by both Hall [(42) of [6], assuming $\rho_{1}/\rho_{2}=1$, $h_{1}/a\rightarrow\infty$, and $h_{2}/a\rightarrow\infty$] and Smythe [24]. The breakpoint in (2), ${{a}\over{h_{2}}}=\tan\left({{\pi a}\over{2b}}\right)$, was also stated by Hall [(46) of [6]]. At ${{a}\over{h_{2}}}=\tan\left({{\pi a}\over{2b}}\right)$, there is a discontinuity between the two expressions in (2). This discontinuity at the breakpoint is also seen in the dotted curves in Fig. 3 which plot (2). The size of this step discontinuity is always less than 2% of the exact value of $\overline{R}_{c}$ [6].
Fig. 4(a) shows the exact theory for $\overline{R}_{c}$ (A7) as a function of $\rho_{1}/\rho_{2}$, for various $a/h_{2}$ and $h_{1}/a$. Fig. 4(b) shows the exact theory for $\overline{R}_{c}$ (A7) as a function of $h_{1}/a$, for various $a/h_{2}$ and $\rho_{1}/\rho_{2}$. In both Fig. 4(a) and (b), we fixed $b/a=30$. In general, as either $\rho_{1}/\rho_{2}$ or $h_{1}/a$ increases, $\overline{R}_{c}$ increases. It is important to recognize from Figs. 2 –4 that dependence of $\overline{R}_{c}$ on $h_{1}/a$ and on $\rho_{1}/\rho_{2}$ is not significant, and that the major dependence of $\overline{R}_{c}$ is on $a/h_{2}$ and on $b/a$. Thus, for a given $a/h_{2}$ and $b/a$ in Figs. 3 and 4, the bounds of the curves are fairly accurately predicted by (2), which are plotted as dashed lines, for all values of $h_{1}/a$ and $\rho_{1}/\rho_{2}$.
The field line equation, $y=y(z)$, may be numerically integrated from the first order ordinary differential equation $dy/dz=E_{y}/E_{z}=(\partial\Phi/\partial y)/(\partial\Phi/\partial z)$ where $\Phi$ is given by (A1). The field lines in the right half of the thin film structure [Fig. 1(a)] are shown in Fig. 5 for the special case of $\rho_{1}/\rho_{2}=1$, and $h_{1}/a=0.01$ with various $a/h_{2}$. We set $b/a=30$ in all calculations in Fig. 5. Note that the variation of $a/h_{2}$ in Fig. 5 may be interpreted this way: $a$, $b$, and $h_{1}$ are held fixed, $h_{2}$ decreases, i.e., $h_{2}=5a$, $a$, and 0.2 $a$, from Fig. 5(a)–(c). (Similar interpretation applies to other figures.) It is clear that as $a/h_{2}$ increases, the spreading of the field lines (also the current flow lines) in Region II becomes less significant. This explains the decrease in $\overline{R}_{c}$ as $a/h_{2}$ increases, as shown in Fig. 3. In the limit of $h_{2}\rightarrow 0$, there will be little spreading of field lines (little current crowding) at the edge of the constriction, leading to zero constriction resistance (Fig. 3), in sharp contrast to the horizontal contact [15], [17], [20]. Note from Fig. 5 that the field lines in Region I are almost straight, and are fairly uniformly spaced across the interface in all the cases, implying minimal enhanced heating at the edges G and D in a vertical contact [Fig. 1(a)]. We also found that as either $h_{1}/a$ or $\rho_{1}/\rho_{2}$ increases, the spreading of the field lines in Region II slightly increases (not shown). The field line distribution is relatively insensitive to $h_{1}/a$ or $\rho_{1}/\rho_{2}$, as compared to the effect of $a/h_{2}$.
For the circular thin film vertical contact [Fig. 1(a)], the z-axis is the axis of rotation. The total current is $I=V_{0}/R$, where $R$ is the resistance between the two terminals AB and EF, given by TeX Source $$R={{\rho_{1}h_{1}}\over{\pi a^{2}}}+{{\rho_{2}}\over{4a}}\overline{R}_{c}\left({{{a}\over{b}},{{h_{1}}\over{a}},{{a}\over{h_{2}}},{{\rho_{1}}\over{\rho_{2}}}}\right)+{{\rho_{2}h_{2}}\over{\pi b^{2}}}.\eqno{\hbox{(4)}}$$
In (4), the first and third terms represent the bulk resistance of Region I and II, respectively. The second term represents the remaining constriction resistance, $R_{c}$, and is expressed as $R_{c}={{\rho_{2}}\over{4a}}\overline{R}_{c}$ for the circular case. The normalized $\overline{R}_{c}$ depends on the aspect ratios $a/b$, $h_{1}/a$ and $a/h_{2}$, and on the resistivity ratio $\rho_{1}/\rho_{2}$, as explicitly shown in (4). The exact expression for $\overline{R}_{c}$ is derived in Appendix B (B6).
The exact theory of $\overline{R}_{c}$ (B6) is plotted in Fig. 6 as a function of $b/a$, for $\rho_{1}/\rho_{2}=1$ with various $h_{1}/a$ and $a/h_{2}$. For a given $a/h_{2}$, $\overline{R}_{c}$ increases as $b/a$ increases. However, $\overline{R}_{c}$ becomes almost constant for large $b/a$, independent of the value of $a/h_{2}$, which is different from the Cartesian case in Fig. 2, where $\overline{R}_{c}$ increases logarithmically with $b/a$ if $a/h_{2}$ is small [(2a) and (3a)]. For a given $b/a$, $\overline{R}_{c}$ decreases as $a/h_{2}$ increases. $\overline{R}_{c}$ increases only slightly as $h_{1}/a$ increases. The effect of $h_{1}/a$ becomes even less significant as $a/h_{2}$ increases (Fig. 6).
In Fig. 7, we plot $\overline{R}_{c}$ as a function of $a/h_{2}$ for various values of $\rho_{1}/\rho_{2}$, in the limit of $h_{1}/a\to\infty$. As noted above, $\overline{R}_{c}$ is independent of $b$ for large $b/a$; we set $b/a=30$ for the calculation in Fig. 7. When $a/h_{2}\ll 1$, $\overline{R}_{c}$ approaches a constant value (independent of $h_{2}$) for a given $b/a$. This is due to the fact that if both $h_{2}$ and $h_{1}$ become much larger than $a$, the structure in Fig. 1(a) will become a semi-infinite constriction channel, whose constriction resistance is independent of $h_{1}$ and $h_{2}$, which was studied in detail in [22]. When $a/h_{2}>1$, $\overline{R}_{c}$ decreases as $a/h_{2}$ increases. As $a/h_{2}\rightarrow\infty$, $\overline{R}_{c}\sim h_{2}/a\rightarrow 0.$ This is in sharp contrast to the behavior of the horizontal cylindrical thin film contact studied in [15], [16], [17], [20], in which the current flows parallel to the thin film bottom boundary, and $\overline{R}_{c}$ (which has a different definition for the horizontal contact [17], [20]) approaches a finite constant of 0.28 as $a/h_{2}\rightarrow\infty$.
By comparing the data calculated from the exact theory (B6) with the published scalings for some limiting cases [12], [22], [25], we synthesized an accurate, analytical scaling law for the normalized constriction resistance of a general cylindrical vertical thin film contact, in the $h_{1}/a\rightarrow\infty$ limit, given by (5) and (6) at the bottom of this page, TeX Source $$\eqalignno{&\left.{\overline{R}_{c}\left({{{b}\over{a}},{{a}\over{h_{2}}},{{\rho_{1}}\over{\rho_{2}}}}\right)}\right\vert_{h_{1}/a\to\infty}=\cases{\overline{R}_{c0}\left({{b}\over{a}}\right)+{{\Delta}\over{2}}\times\left({{2\rho_{1}}\over{\rho_{1}+\rho_{2}}}\right)\times g\left({{b}\over{a}}\right),\hfill\cr\matrix{&{{\rm when}\left[\matrix{a/h_{2}\leq 1.8a/b\quad{\rm if}\quad b/a\geq 4.37,{\rm or}\hfill\cr a/h_{2}\leq\left[{1-(a/b)^{2}}\right]^{-1}{\rm if}\quad b/a<4.37\hfill}\right];}}\hfill\cr\left[{p\left({{a}\over{h_{2}}}\right)-{{4}\over{\pi}}\left({{a}\over{b}}\right)^{2}{{h_{2}}\over{a}}}\right]\times\left({1+{{\Delta}\over{\bar R_{c0}\left({b/a}\right)}}\times{{\rho_{1}}\over{\rho_{1}+\rho_{2}}}}\right),\matrix{&{\rm otherwise,}}}&{\hbox{(5)}} \cr&\qquad\quad\bar R_{c0}\left({b/a}\right)=1-1.41581(a/b)+0.06322(a/b)^{2}+0.15261(a/b)^{3}+0.19998(a/b)^{4},\cr&\qquad\quad g(b/a)=1-0.3243(a/b)^{2}-0.6124(a/b)^{4}-1.3594(a/b)^{6}+1.2961(a/b)^{8},\cr&\qquad\quad p(a/h_{2})=\cases{[1+0.441271\left({a/h_{2}}\right)+0.194720\left({a/h_{2}}\right)^{2}-0.009732\left({a/h_{2}}\right)^{3}\hfill\cr-0.046505\left({a/h_{2}}\right)^{4}+0.002110\left({a/h_{2}}\right)^{5}+0.052204\left({a/h_{2}}\right)^{6}\hfill\cr-0.011044\left({a/h_{2}}\right)^{7}]^{-1}, 0<a/h_{2}\leq0.4;\hfill\cr 4\times [0+0.31338(h_{2}/a)-0.25134(h_{2}/a)^{2}+0.12512(h_{2}/a)^{3}\hfill\cr-0.03436(h_{2}/a)^{4}+0.003908(h_{2}/a)^{5}], 0.4<a/h_{2}<\infty,}&{\hbox{(6a-6c)}}}$$ where $\Delta=32/3\pi^{2}-1=0.08076$. Equation (5) is also plotted in Fig. 7, showing excellent agreement with the exact theory (B6) for arbitrary value of $a$, $b(>a)$, $h_{2}$, $\rho_{1}$, and $\rho_{2}$, in the limit of $h_{1}/a\rightarrow\infty$.
In (6), $\overline{R}_{c0}\left({b/a}\right)$ is synthesized by Timsit [25], $g(b/a)$ is derived by us [(2) of [22]], and $p(a/h_{2})$ is from Denhoff [(26) and (28) of [12]]. At the breakpoint, ${{a}\over{h_{2}}}=1.8{{a}\over{b}}$ or ${{a}\over{h_{2}}}={{1}\over{1-(a/b)^{2}}}$, there is a discontinuity between the two expressions in (5). The size of this step discontinuity is within 2% of the exact value of $\overline{R}_{c}$ (B6) in the worst case.
Fig. 8(a) shows the exact theory for $\overline{R}_{c}$ (B6) as a function of $\rho_{1}/\rho_{2}$, for various $a/h_{2}$ and $h_{1}/a$. Fig. 8(b) shows the exact theory for $\overline{R}_{c}$ (B6) as a function of $h_{1}/a$, for various $a/h_{2}$ and $\rho_{1}/\rho_{2}$. Spot checks by MAXWELL 2-D code [23] are also shown in Fig. 8. In general, as either $h_{1}/a$ or $\rho_{1}/\rho_{2}$ increases, $\overline{R}_{c}$ increases. It is important to recognize from Figs. 6 –8 that the dependence of $\overline{R}_{c}$ on $h_{1}/a$ and $\rho_{1}/\rho_{2}$ is not significant, and that the major dependence of $\overline{R}_{c}$ is on $b/a$ and on $a/h_{2}$, similar to the Cartesian case in Section II. Thus, for a given $a/h_{2}$ in Fig. 8, the bounds of the curves are fairly accurately predicted by (5), which are plotted as dashed lines.
The field lines for the cylindrical case (not shown) are very similar to those in Fig. 5 for the Cartesian case. In the limit of $h_{2}\rightarrow 0$, there will be little spreading of field lines (little current crowding) at the edge of the constriction, leading to zero constriction resistance (Fig. 7), in sharp contrast to the horizontal contact [17], [20].
This paper presented an exact solution for the constriction resistance in a vertical thin film contact with dissimilar materials, for both Cartesian and cylindrical geometries. The model assumed arbitrary geometric aspect ratios and arbitrary resistivities in the individual contact members. The constriction resistance was calculated analytically, and spot-checked against the MAXWELL 2-D code. The current flow patterns from the exact theory were displayed. Scaling laws for, and bounds on, the constriction resistance were presented for arbitrary values of $h_{1}$, $h_{2}$, $\rho_{1}$, $\rho_{2}$, $a$, and $b(>a)$ [Fig. 1(a)].
We found that the normalized constriction resistance $\overline{R}_{c}$ depended predominantly on $b/a$ and on $h_{2}/a$, i.e., on the geometry of Region II; but was relatively insensitive to $h_{1}/a$, and to $\rho_{1}/\rho_{2}$, i.e., insensitive to the geometry or resistivity of Region I [Fig. 1(a)]. We also found that in the limit of small film thickness $(h_{2}\rightarrow 0)$, there was hardly any current crowding in the vertical contact represented in Fig. 1(a). The current was distributed quite uniformly across the interface GD, implying minimal enhanced heating at the edges G and D in Fig. 1(a). This was in sharp contrast to a horizontal thin film contact [Fig. 1(b)], where the current that crosses the interface GD was highly concentrated near the edges G and D. In fact, at least half of the current flew within a distance of 0.44 $h_{2}$($h_{2}\rightarrow 0$ [17]) of the two edges G and D in Fig. 1(b), suggesting severe local heating there for the horizontal thin film contact.
The formulation follows that of [15], [20], and [22]. Referring to Fig. 1(a), EF is grounded, and AB is biased with a voltage of $+V_{0}$. The solutions to Laplace's equation are, TeX Source $$\eqalignno{&\Phi_{+}(y,z)=A_{0}(z-h_{1})+\sum_{n=1}^{\infty}{A_{n}\cos\left({{n\pi y}\over{a}}\right)\sinh\left({n\pi{{z-h_{1}}\over{a}}}\right)},\cr &\qquad 0<z<h_{1},\left\vert y\right\vert\in (0,a),\cr &\Phi_{-}(y,z)=V_{0}+B_{0}(z+h_{2})+\sum_{n=1}^{\infty}{B_{n}\cos\left({{n\pi y}\over{b}}\right)\sinh\left({n\pi{{z+h_{2}}\over{b}}}\right)},\cr &\qquad-h_{2}<z<0,\left\vert y\right\vert\in (0,b),&{\hbox{(A1)}}}$$ where $\Phi_{\rm{+}}$ and $\Phi_{\rm{-}}$ are the electrical potential in the regions I and II respectively, and $A_{\rm{n}}$ and $B_{\rm{n}}$ are the coefficients that need to be determined.
At the interface $z=0$, from the continuity of electrical potential and current density, we have the following boundary conditions TeX Source $$\eqalignno{&\qquad\quad\Phi_{+}=\Phi_{-},\qquad z=0,\left\vert y\right\vert\in(0,a)&{\hbox{(A2a)}} \cr&{{1}\over{\rho_{1}}}{{\partial\Phi_{+}}\over{\partial z}}={{1}\over{\rho_{2}}} {{\partial\Phi_{-}}\over{\partial z}},\qquad z=0,\left\vert y\right\vert\in (0,a),&{\hbox{(A2b)}}\cr&\qquad\quad{{\partial\Phi_{-}}\over{\partial z}}=0,\matrix{&}z=0,\left\vert{y}\right\vert\in(a,b)&{\hbox{(A2c)}}}$$
From (A1) and (A2a), eliminating coefficient $A_{\rm{n}}$ in favor of $B_{\rm{n}}$, we have TeX Source $$\eqalignno{&{-}A_{n}\sinh\left({n\pi{{h_{1}}\over{a}}}\right)=\sum_{m=1}^{\infty} {g_{mn}B_{m}}\sinh\left({m\pi{{h_{2}}\over{b}}}\right),&{\hbox{(A3a)}} \cr&{{\rho_{1}}\over{\rho_{2}}}nB_{n} \cosh\left(n\pi{{h_{2}}\over{b}}\right)+\sum_{m=1}^{\infty}{\gamma_{nm}B_{m}}\sinh\left({{m\pi h_{2}}\over{b}}\right)\cr&\qquad={{2}\over{\pi}}{{\sin\left({n\pi a/b}\right)}\over{n\pi a/b}},\matrix{&}n=1,2,3\ldots&{\hbox{(A3b)}}}$$ where TeX Source $$\eqalignno{\gamma_{nm}=&\,\gamma_{mn}=\displaystyle\sum_{l=1}^{\infty}lg_{nl}g_{ml}\coth\left({{l\pi h_{1}}\over{a}}\right),\cr g_{mn}=&\,\displaystyle{{2}\over{a}}\int\limits_{0}^{a}{dy\cos\left({{m\pi y}\over{b}}\right)\cos\left({{n\pi y}\over{a}}\right).}&{\hbox{(A4)}}}$$
In deriving (A3b), we have assumed that $aA_{0}=+1$. The infinite matrix in (A3b) can be solved directly for $B_{n}$ with convergence guaranteed [22], from which $A_{n}$ follows in (A3a).
The total current from AB to EF is, [Fig. 1(a)] TeX Source $$I=2W\int_{0}^{a}{{{1}\over{\rho_{1}}}\left.{{\partial\Phi_{+}}\over{\partial z}}\right\vert}_{z=0}dy={{2W}\over{\rho_{1}}},\eqno{\hbox{(A5)}}$$ where we have used (A1) and $aA_{0}=+1$, and $W$ is the width in the third, ignorable dimension that is perpendicular to the paper. The terminal voltage $V_{0}$ may be expressed in terms of $B_{\rm{n}}$ as TeX Source $$V_{0}=-{{h_{1}}\over{a}}-B_{0}h_{2}-{{1}\over{a}}\sum_{n=1}^{\infty}{B_{n}\sin h\left({{n\pi h_{2}}\over{b}}\right)}{{\sin\left({n\pi a/b}\right)}\over{n\pi a/b}}\eqno{\hbox{(A6)}}$$
We found $B_{0}=(\rho_{2}/\rho_{1})/b$, after taking $\partial\Phi_{-}/\partial z$ in (A1) and using (A2b) and 2c) in the resultant Fourier series.
The constriction resistance, $R_{c}$, is defined as the difference between the resistance from AB to EF, $R=V_{0}/I,$ and the bulk resistance, $R_{u}=\rho_{1}h_{1}/2aW+\rho_{2}h_{2}/2bW$, TeX Source $$\eqalignno{R_{c}\equiv&\,{{\rho_{2}}\over{4\pi W}}\overline{R}_{c}={{V_{0}}\over{I}}-R_{u},\cr{\bar R_{c}}=&\,\bar R_{c}\left({{{a}\over{b}},{{h_{1}}\over{a}},{{a}\over{h_{2}}},{{\rho_{1}}\over{\rho_{2}}}}\right)=2\pi{{\rho_{1}}\over{\rho_{2}}}\sum_{n=1}^{\infty}{B_{n}\sinh\left({{n\pi h_{2}}\over{b}}\right)}{{\sin\left({n\pi a/b}\right)}\over{n\pi a/b}}.\cr& &{\hbox{(A7)}}}$$
Equation (A7) is the exact expression for the constriction resistance of Cartesian vertical thin film contact [Fig. 1(a)] for arbitrary values of $a$, $b(b>a)$, $h_{1}$, $h_{2}$ and $\rho_{1}/\rho_{2}$. In (A7), $B_{\rm n}$ is solved from (A3b). Equation (A7) appears in (1) of the main text.
The solutions to Laplace's equation in cylindrical geometry are [15], [20], [22], TeX Source $$\eqalignno{&\Phi_{+}(r,z)=A_{0}(z-h_{1})+\sum_{n=1}^{\infty}{A_{n}J_{0}\left({\alpha_{n}r}\right)\sinh\left[{\alpha_{n}(z-h_{1})}\right]},\cr&\qquad\sim\sim0<z<h_{1},r\in (0,a);\cr &\Phi_{-}(r,z)=V_{0}+B_{0}(z+h_{2})+\sum_{n=1}^{\infty}{B_{n}J_{0}\left({\beta_{n}r}\right)}\sinh\left[{\beta_{n}(z+h_{2})}\right],\cr &\qquad\sim\sim-h_{2}<z<0,r\in (0,b),&{\hbox{(B1)}}}$$ where $\Phi_{+}$ and $\Phi_{-}$ are the electrical potential in the regions I and II, respectively, $\alpha_{\rm{n}}$ and $\beta_{\rm{n}}$ satisfy $J_{1}(\alpha_{\rm{n}}a)=J_{1}(\beta_{\rm{n}}b)=0$, $J_{0}(x)$ and $J_{1}(x)$ are the Bessel functions of order zero and one respectively, and $A_{\rm{n}}$ and $B_{\rm n}$ are the coefficients that need to be determined.
At the interface $z=0$, from the continuity of electrical potential and current density, we have the following boundary conditions: TeX Source $$\eqalignno{&\qquad\quad\Phi_{+}=\Phi_{-},\quad z=0,r\in(0,a),&{\hbox{(B2a)}}\cr& {{1}\over{\rho_{1}}}{{\partial\Phi_{+}}\over{\partial z}}={{1}\over{\rho_{2}}} {{\partial\Phi_{-}}\over{\partial z}},\matrix{&}z=0, r\in(0,a),& {\hbox{(B2b)}}\cr&\qquad\quad{{\partial\Phi_{-}}\over{\partial z}}=0,\matrix{&}z=0, r\in (a,b).&{\hbox{(B2c)}}}$$
From (B1) and (B2a), the coefficient $A_{\rm{n}}$ is expressed in terms of $B_{\rm{n}}$, TeX Source $$\eqalignno{&-A_{0}h_{1}=\sum_{n=1}^{\infty}{B_{n}\sinh\left({\beta_{n}h_{2}}\right){{2J_{1}\left({\beta_{n}a}\right)}\over{\beta_{n}a}}+V_{0}} +B_{0}h_{2},&{\hbox{(B3a)}}\cr&\qquad-\sinh (\alpha_{n}h_{1})A_{n}=\sum_{m=1}^{\infty}{B_{m}\sinh\left({\beta_{m}h_{2}}\right)g_{mn}},\cr&\qquad\sim\sim g_{mn}={{2}\over{a^{2}J_{0}^{2}(\alpha_{n}a)}}\int\limits_{0}^{a} {rdrJ_{0}\left({\alpha_{n}r}\right)J_{0}\left({\beta_{m}r}\right), n\geq 1.}&\hbox{(B3b)}}$$ Combining (B2b) and (B2c) and (B3b), we obtain TeX Source $$\eqalignno{&{{\rho_{1}}\over{\rho_{2}}}{{b}\over{a}}\beta_{n}bJ_{0}^{2}(\beta_{n}b)\cosh (\beta_{n}h_{2})B_{n}+\sum_{m=1}^{\infty}{\gamma_{nm}B_{m}}\sinh\left({\beta_{m}h_{2}}\right)\cr&={{2J_{1}\left({\beta_{n}a}\right)}\over{\beta_{n}a}},\matrix{&}n=1,2,3\ldots,&\hbox{(B4)}}$$ where TeX Source $$\gamma_{nm}=\gamma_{mn}=\sum_{l=1}^{\infty}{g_{nl}g_{ml}\alpha_{l}aJ_{0}^{2}\left({\alpha_{l}a}\right)\coth\left({\alpha_{l}h_{1}}\right)},\eqno{\hbox{(B5)}}$$ and $g_{nl}$ and $g_{ml}$ is in the form of the last part in (B3b). In deriving (B4), we have set $aA_{0}=1$ for simplicity.
The total resistance from $AB$ to $EF$ is $R=V_{0}/I$, where $I=\int\limits_{0}^{a}{\left({{{1}\over{\rho_{1}}}\left.{{\partial\Phi_{+}}\over{\partial z}}\right\vert_{z=0}}\right)2\pi rdr}=\pi a/\rho _{1}$ is the total current from AB to EF [Fig. 1(a)], and $V_{0}$ can be found from (B3a) with $B_{0}=\left({\rho_{2}/\rho_{1}}\right)a/b^{2}$. This expression for $B_{0}$ is obtained after taking $\partial\Phi_{-}/\partial z$ in (B1) and using (A2b) and (A2c) in the resultant Fourier series.
The constriction resistance, $R_{c}$, is the difference between the total resistance $R$ and the bulk resistance $R_{u}=\rho_{1}h_{1}/\pi a^{2}+\rho_{2}h_{2}/\pi b^{2}$. We find TeX Source $$\eqalignno{&\hskip-20ptR_{c}\equiv{{\rho_{2}}\over{4a}}\overline{R}_{c}={{V_{0}}\over{I}}-R_{u},\cr&\bar R_{c}\left({{{a}\over{b}},{{h_{1}}\over{a}},{{a}\over{h_{2}}},{{\rho_{1}}\over{\rho_{2}}}}\right)={{8}\over{\pi}}{{\rho_{1}}\over{\rho_{2}}}\sum_{n=1}^{\infty}{B_{n}\sinh\left({\beta_{n}h_{2}}\right){{J_{1}\left({\beta_{n}a}\right)}\over{\beta_{n}a}}},&{\hbox{(B6)}}}$$ which is the exact expression for the circular vertical thin film constriction resistance with dissimilar materials for arbitrary values of $a$, $b(b>a)$, $h_{1}$, $h_{2}$ and $\rho_{1}/\rho_{2}$. In (B6), $B_{n}$ is solved from (B4). Equation (B6) appears in (4) of the main text.
We thank Derek Hung for help in data collection.
This work was supported in part by an AFOSR Grant on the Basic Physics of Distributed Plasma Discharge, AFOSR Grant FA9550-09-1-0662, L-3 Communications Electron Devices Division. The review of this paper was arranged by editor C. C. McAndrew.
The authors are with the Department of Nuclear Engineering and Radiological Sciences, University of Michigan, Ann Arbor, MI 48109-2104 USA (e-mail: email@example.com; firstname.lastname@example.com).
Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org.
1An anonymous referee suggested alternate, elegant fitting formulas, $f(x)=3/[(2x-1)(2+x)]$, $g(x)=(4/x^{2})(x^{2}-1)^{2}/(4x^{2}-3)$ where $x=b/a(>1)$. While these fitting formulas for $f(x)$ and $g(x)$ are not as accurate as (3b) and (3c), they may be used for most practical purposes. We wish to thank this referee for his/her careful reading of the manuscript.
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Rubrics are kurtz essay often disappointed. Pasinetti L. L. (1979), Structural Change and Economic Growth', Review of Political Economy that Pigou held).
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Hungry Caterpillar "Happy Birthday" Printable Party Banner - Petite Party Studio
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Turing completeness
|This article includes a list of references, but its sources remain unclear because it has insufficient inline citations. (July 2014) (Learn how and when to remove this template message)
In computability theory, a system of data-manipulation rules (such as a computer's instruction set, a programming language, or a cellular automaton) is said to be Turing complete or computationally universal if it can be used to simulate any single-taped Turing machine. The concept is named after English mathematician Alan Turing. A classic example is lambda calculus.
A closely related concept is that of Turing equivalence – two computers P and Q are called equivalent if P can simulate Q and Q can simulate P. The Church–Turing thesis conjectures that any function whose values can be computed by an algorithm can be computed by a Turing machine, and therefore that if any real-world computer can be simulated by a Turing machine, it is Turing equivalent to a Turing machine. A Universal Turing machine can be used to simulate any Turing machine and by extension the computational aspects of any possible real-world computer.[NB 1]
To show that something is Turing complete, it is enough to show that it can be used to simulate some Turing complete system. For example, an imperative language is Turing complete if it has conditional branching (e.g., "if" and "goto" statements, or a "branch if zero" instruction. See OISC) and the ability to change an arbitrary amount of memory (e.g., the ability to maintain an arbitrary number of variables). Since this is almost always the case, most (if not all) imperative languages are Turing complete if the limitations of finite memory are ignored.
Non-mathematical usage[edit]
In colloquial usage, the terms "Turing complete" or "Turing equivalent" are used to mean that any real-world general-purpose computer or computer language can approximately simulate the computational aspects of any other real-world general-purpose computer or computer language.
Real computers constructed so far are essentially similar to a single-tape Turing machine; thus the associated mathematics can apply by abstracting their operation far enough. However, real computers have limited physical resources, so they are only linear bounded automaton complete. In contrast, a universal computer is defined as a device with a Turing complete instruction set, infinite memory, and infinite available time.
Formal definitions[edit]
In computability theory, several closely related terms are used to describe the computational power of a computational system (such as an abstract machine or programming language):
- Turing completeness
- A computational system that can compute every Turing-computable function is called Turing-complete (or Turing-powerful). Alternatively, such a system is one that can simulate a universal Turing machine.
- Turing equivalence
- A Turing-complete system is called Turing equivalent if every function it can compute is also Turing computable; i.e., it computes precisely the same class of functions as do Turing machines. Alternatively, a Turing-equivalent system is one that can simulate, and be simulated by, a universal Turing machine. (All known Turing-complete systems are Turing equivalent, which adds support to the Church–Turing thesis.)
- (Computational) universality
- A system is called universal with respect to a class of systems if it can compute every function computable by systems in that class (or can simulate each of those systems). Typically, the term universality is tacitly used with respect to a Turing-complete class of systems. The term "weakly universal" is sometimes used to distinguish a system (e.g. a cellular automaton) whose universality is achieved only by modifying the standard definition of Turing machine so as to include input streams with infinitely many 1s.
Turing completeness is significant in that every real-world design for a computing device can be simulated by a universal Turing machine. The Church–Turing thesis states that this is a law of mathematics – that a universal Turing machine can, in principle, perform any calculation that any other programmable computer can. This says nothing about the effort needed to write the program, or the time it may take for the machine to perform the calculation, or any abilities the machine may possess that have nothing to do with computation.
Charles Babbage's analytical engine (1830s) would have been the first Turing-complete machine if it had been built at the time it was designed. Babbage appreciated that the machine was capable of great feats of calculation, including primitive logical reasoning, but he did not appreciate that no other machine could do better. From the 1830s until the 1940s, mechanical calculating machines such as adders and multipliers were built and improved, but they could not perform a conditional branch and therefore were not Turing complete.
In the late 19th century, Leopold Kronecker formulated notions of computability, defining primitive recursive functions. These functions can be calculated by rote computation, but they are not enough to make a universal computer, because the instructions which compute them do not allow for an infinite loop. In the early 20th century, David Hilbert led a program to axiomatize all of mathematics with precise axioms and precise logical rules of deduction which could be performed by a machine. Soon, it became clear that a small set of deduction rules are enough to produce the consequences of any set of axioms. These rules were proved by Kurt Gödel in 1930 to be enough to produce every theorem. However, they will always prove some theorems as both true and false, for an axiomatization not simpler than Peano arithmetic.
The actual notion of computation was isolated soon after, starting with Gödel's incompleteness theorem. This theorem showed that axiom systems were limited when reasoning about the computation which deduces their theorems. Church and Turing independently demonstrated that Hilbert's Entscheidungsproblem (decision problem) was unsolvable,[1] thus identifying the computational core of the incompleteness theorem. This work, along with Gödel's work on general recursive functions, established that there are sets of simple instructions, which, when put together, are able to produce any computation. The work of Gödel showed that the notion of computation is essentially unique.
Computability theory[edit]
The first result of computability theory is that it is impossible in general to predict what a Turing-complete program will do over an arbitrarily long time. For example, it is impossible to determine for every program-input pair whether the program, operating on the input, will eventually stop or will continue forever (see halting problem). It is impossible to determine whether the program will return "true" or whether it will return "false". For any characteristic of the program's eventual output, it is impossible to determine whether this characteristic will hold. This can cause problems in practice when analyzing real-world computer programs. One way to avoid this is to cause programs to stop executing after a fixed period of time (timeout), or to limit the power of flow control instructions. Such systems are not Turing complete by design.
Another theorem shows that there are problems solvable by Turing-complete languages that cannot be solved by any language with only finite looping abilities (i.e., any language that guarantees every program will eventually finish to a halt). Given a guaranteed halting language, the computable function which is produced by Cantor's diagonal argument on all computable functions in that language is not computable in that language.
Turing oracles[edit]
A computer with access to an infinite tape of data may be more powerful than a Turing machine: for instance, the tape might contain the solution to the halting problem, or some other Turing-undecidable problem. Such an infinite tape of data is called a Turing oracle. Even a Turing oracle with random data is not computable (with probability 1), since there are only countably many computations but uncountably many oracles. So a computer with a random Turing oracle can compute things that a Turing machine cannot.
Digital physics[edit]
All known laws of physics have consequences that are computable by a series of approximations on a digital computer. A hypothesis called digital physics states that this is no accident, that it is because the universe itself is computable on a universal Turing machine. This would imply that no computer more powerful than a universal Turing machine can be built physically (see Church–Turing thesis – Philosophical implications).
The computational systems (algebras, calculi) that are discussed as Turing complete systems are those intended for studying theoretical computer science. They are intended to be as simple as possible, so that it would be easier to understand the limits of computation. Here are a few:
- Automata theory
- Formal grammar (language generators)
- Formal language (language recognizers)
- Lambda calculus
- Post–Turing machines
Most programming languages, conventional and unconventional, are Turing-complete. This includes:
- All general-purpose languages in wide use.
- Procedural programming languages such as C, Pascal.
- Object-oriented languages such as CIL, Java, Smalltalk.
- Multi-paradigm languages such as Ada, C++, Common Lisp, Object Pascal.
- Most languages using less common paradigms
- Functional languages such as Lisp and Haskell.
- Logic programming languages such as Prolog.
- Declarative languages such as XSLT.[2]
- Esoteric programming languages, a form of mathematical recreation in which programmers work out how to achieve basic programming constructs in an extremely difficult but mathematically Turing-equivalent language.
Rewrite systems are also Turing-complete.
Turing completeness is an abstract statement of ability, rather than a prescription of specific language features used to implement that ability. The features used to achieve Turing completeness can be quite different; Fortran systems would use loop constructs or possibly even goto statements to achieve repetition; Haskell and Prolog, lacking looping almost entirely, would use recursion. Most programming languages are describing computations on von Neumann architectures, which have memory (RAM and register) and a control unit. These two elements make this architecture Turing-complete. Even pure functional languages are Turing-complete.[3]
Turing completeness in declarative SQL is implemented through recursive common table expressions.[4] Unsurprisingly, procedural extensions to SQL (PLSQL, etc.) are also Turing complete. This illustrates one reason why relatively powerful non-Turing-complete languages are rare: the more powerful the language is initially, the more complex are the tasks to which it is applied and the sooner its lack of completeness becomes perceived as a drawback, encouraging its extension until it is Turing complete.
The untyped lambda calculus is Turing complete, but many typed lambda calculi, including System F, are not. The value of typed systems is based in their ability to represent most typical computer programs while detecting more errors.
Rule 110 and Conway's Game of Life, both cellular automata, are Turing complete.
Many games are Turing-complete by accident.
Video games:
Card games:
Zero-person games (simulations):
- Conway's Game of LifeCite error: A
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(in fact not everybody agrees with that, for example Francis McCabe argues that CSS is not Turing-complete because there is no option to define functions in CSS[12]).
See also[edit]
- ^ Hodges, Andrew (1992) [1983], Alan Turing: the enigma, London: Burnett Books, p. 111, ISBN 0-04-510060-8
- ^ "Universal Turing Machine in XSLT". unidex.com. Retrieved 2010-07-05.
- ^ http://www.cs.utexas.edu/users/boyer/ftp/ics-reports/cmp37.ps. (The book of Thomas Rauber and Gudula Rünger "Parallel programming: for multicore and cluster systems", 2010 provides an introduction for computation models.)
- ^ "Cyclic Tag System". PostgreSQL.org. Retrieved 2014-09-10.
- ^ Hamilton, Linus. (2 December 2014). Braid is Undecidable. Cornell University Press.
- ^ Adam P. Goucher. "Spartan universal computer-constructor". LifeWiki. Retrieved 22 June 2009.
- ^ Cedotal, Andrew (16 April 2010). "Man Uses World's Most Difficult Computer Game to Create … A Working Turing Machine". Retrieved 2 June 2015.
- ^ a b c d Zwinkau, Andreas (20 October 2013). "Accidentally Turing-Complete". Retrieved 2 June 2015.
- ^ Kaye, Richard. (31 October 2007). Infinite Versions of Minesweeper are Turing Complete. The University of Birmingham Press.
- ^ swni. "I made a programmable Turing-complete computer in Factorio". Reddit. Retrieved 28 June 2016.
- ^ McIntyre, Robert (9 June 2013). "Pokemon Yellow Total Control Hack". Retrieved 22 June 2015.
- ^ https://frankmccabe.wordpress.com/2008/09/30/sub-turing-complete-programming-languages/
Further reading[edit]
- Brainerd, W.S., Landweber, L.H. (1974), Theory of Computation, Wiley. ISBN 0-471-09585-0
- Simplest 'universal computer' wins student $25,000 by Jim Giles, New Scientist, October 24, 2007.
- The Universal Turing Machine: A Half-Century Survey (1995), ed. Rolf Herken, Springer Verlag. ISBN 3-211-82637-8
- Turing, A. M. (1936). "On Computable Numbers, with an Application to the Entscheidungsproblem" (PDF). Proceedings of the London Mathematical Society. 2 (published 1936–37). 42: 230–65. doi:10.1112/plms/s2-42.1.230. (and Turing, A.M. (1938). "On Computable Numbers, with an Application to the Entscheidungsproblem: A correction". Proceedings of the London Mathematical Society. 2. 43 (published 1937). pp. 544–6. doi:10.1112/plms/s2-43.6.544.)


text:
Davenport School District nurse Janice Telsrow reminded Superintendent Art Tate and about 40 people Wednesday at Walcott School how important school nurses are to the education of the district's children.
Telsrow spoke at the last of six forums offered for people to comment on the district's budget, which could include in the future outsourcing nurses, janitors and security guards.
Proposed school boundaries were another hot topic at the forums.
"We know the students and their parents," Telsrow, who is the nurse at Buffalo and Wilton elementary schools, said. "We often know their extended families. We know their health history. We are an integral part of a child's education."
Those are all advantages over any nurse who comes in as an outsourced employee, she said.
Kevin Hodson, a 30-year employee as a janitor, said no janitorial company could provide all of the services that regular school janitors provide without the district spending a lot more money. The district, he said, "will pay through the nose" for services beyond emptying trash cans, mopping floors and dusting.
"For the 30 years I've been here, and in each contract negotiation, guess what, they're threatened to lay us off," he said. "Well, I'm not begging for my job anymore."
Hodson said that as student enrollment has fallen, the number of principals and administrators has risen. "Why look at the bottom of the totem pole every time you cut the budget?" he said.
Redrawing the district's boundaries to level attendance at all schools to about 85 percent capacity has been a passionate issue since Tate introduced it — especially true of the issue of open enrollment at the high school level.
Several people commented both for and against keeping open enrollment at the district's three high schools during Wednesday's session.
Tate said he and members of the school board will read all of the comments made at the forums and submitted online. "We're going to find all those nuggets of information that will help us make the best decisions for the good of the students and the district."


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from Midland, TX
I used these products in my art classes. Loved that they get delivered fast.
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Best Film Ever!
By Suz
from Utah
I love this Graphix Dura-Lar film. The thickness is perfect for my projects. I cut stencils with this film, and have never had one rip or bleed when painting. This is a solid product and is the best I've seen.
special use, not what it is meant for
By mingy
from Boaton, MA
I have a large printer that refuses to print on anything but materials supplied by its own company. After learning to bypass the computerized detector I experimented with other materials and managed to ruin the printheads. I found that Dura-Lar was perfect for my purposes (after spraying shellac on it)
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Copic Refills
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Copics are expensive, no question. Blicks had the largest in store selection and one of the only store that carry the refills in the store. If I can't find it in the store I can always hop on line and find anything I'm looking for. There's a hobby store by my house that sells copics, but I'd rather drive an extra 15 minutes to blicks since they have better prices, bigger selection and the staff is amazing
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text:
'There will be bumps in your life, but the fun is in fixing them': Simon Cowell posts rambling tweets about his health, promotes his projects and offers life advice
Getting it off his chest: Simon Cowell posted 17 message to Twitter in less than an hour. The Syco boss wrote about his work, health and the secret to happiness
Simon Cowell doesn't update his Twitter feed regularly but on Tuesday morning he posted 17 messages in less than an hour.
The Syco boss wrote about his latest TV shows, his health, the secret to happiness and how overcoming obstacles in life is 'fun' in the series of tweets to the social networking site.
Simon began by apologising for not posting over the past four days and addressed The X Factor.
He wrote: 'There will be a lot of changes on X factor uk and USA. But good changes. I feel excited for both shows this year.'
The 53-year-old then went on to promote stars signed to his label and wrote: 'One direction continue to amaze me. Hard workers but still the nicest guys you could hope to work with.'
He also wrote about his Emblem 3, Fifth Harmony and Tate from the US version of his show, before mentioning Ella Henderson and James Arthur from the UK talent show.
Simon revealed he had seen some early footage of the One Direction movie calling it 'very, very exciting' and he also promoted the Paul Potts film, which he labelled 'brilliant'.
After listing everything he has been working on he told his 6.5million followers that friends and family matter more than work.
Scroll down for video
Offering advice: Simon addressed many issues and told his 6.5million followers that family and friends are the most important things in life
Long rant: The 53-year-old had plenty to say and used most of his tweets to promote his acts
He wrote: 'And with everything I have been working on it made me realise that your friends and family are still the most important things in your life.'
'Sorry to cram all this in. Have read some strange things about me recently. I am happy. Healthy. And enjoying life. Hope you are too.'
'What I have realised is there will be bumps in your life but the fun is fixing them. If it was always easy life would be boring.'
Times are changing: Simon told fans that there will be big changes to the X Factor in the UK and the US and he is very excited
Simon's posts comes after
'midas-touch' for TV shows has been called into question with his latest
offering Food Glorious Food flopping earlier this month, with just
2.6million viewers tuning in for the first episode.
Last year his X Factor for dogs show That Dog Can Dance also received disappointing ratings.
Simon told fans that he was working on something 'very close' to him but didn't reveal what the new project was.
He did tell fans to check out his latest projection You Generation and One Direction are set to launch Simon's latest worldwide talent hunt with a live online interview.
Cowell is creating the year-long contest in which hopefuls with a range of skills from make-up artists to chefs will audition on video sharing website YouTube.
So proud: The Syco boss also gushed about One Direction who he said 'amaze him'
The boy band - one of the biggest acts on the media mogul's books - will mark the launch of the competition on Wednesday evening with a live streamed interview just before they take the stage for their latest sell-out concert.
Each fortnight organisers will hold a new contest to find the best in a different skill, and will be judged by experts in that field as well as executives from Cowell's company Syco.
Each winner will receive a cash prize every second Friday and eventually 26 finalists will go forward with the hope of winning a grand prize at the end of the year.
The X Factor and Britain's Got Talent supremo announced the new online talent search earlier this month.
Cowell said of his decision to turn to YouTube: 'We wanted to devise a way that it's easier for you to get noticed.'
He said he became aware of the power of YouTube when Susan Boyle's audition from Britain's Got Talent was seen by people around the world. Her performance of I Dreamed A Dream is said to have been seen more than 500 million times.
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The randomness dominating crew skills
View Single Post
Quote: Originally Posted by
To try and keep this short and sweet I'll make a "list" of my issues with it.
- The system used to give you missions is extremely frustrating. I am constantly having to choose between four companion gift missions and a fabric mission as a cybertech. This does not help me when I have all of my companions maxed out on affection.
I'll agree with this one and pass it off as a bug. I don't think they intended for that to happen.
- When I am able to send my companions out on a mission I am looking for I am unable to specify which item I want them to get because each grade of materials has multiple items available so I'm unable to even specify for my companions to get one material instead of another. If I receive the "wrong" material then I'm left to hope that I get a mission for it and that I get material X this time around instead of material Y. To add to this problem, the quantities you receive from the missions is extremely small. I have had companions crit a mission and come back with two of one material, the one I really need, and ten of another.
That is intended. If you could just select what you want and get a ton of it on demand, then everyone would be able to craft EVERYTHING and the market would get inflated. This system is designed to weed out everyone who is not committed to hard core crafting by demanding a huge time and credit investment. This system is for those who are willing to miss the crit on the materials they need 10 times in a row, not people who want a "give me Polyfibe" button.
- When I reverse engineer things I am only permitted a relatively small chance to get the next tier of that item. Sometimes I make two items and get the next tier and other times I make 20 or more and still don't get the next tier.
Again, if you only had to reverse engineer 3 items to get the good stuff, then EVERYONE would be a master crafter. We can't have that. You either dedicate yourself wholly to your craft or you don't. It's not our problem if you don't want to spend the time doing it.
- If I do get the next tier of that item it is randomly assigned a stat. I started with green earpieces and found out that they have quite a few different blue variations for one green earpiece. Each of those blue earpieces then have multiple variations on them as well making it difficult to get the useful patterns to make and sell or patterns you would like to use for yourself.
Rarity = uniqueness of a master crafter. The rarer a specific item is, the better it is for business because people like you won't put in the time to make it, and would rather just buy it.
- There is no reliable way to gather stuff yourself since it is really not much different than the results you see from sending companions out on missions. This is not a terrible way to get materials, it is a much more effective way of getting materials since you can get results much quicker than you could otherwise even if those results are completely random, but it is still dominated by randomness. Sometimes you will get three of material X and sometimes you will get two of material Y from the same creatures of the same level.
So? crafting is not meant to be condensed into a formula of "run around in this circuit getting exactly 4 aluminum over and over again until you craft a specific number of items to get a purple". That is slow and boring. The slot machine system works to simulate RNG without feeling too dull.
I really hope Bioware somehow finds a nice middle ground to remove some of the randomness and give the player more control over their crew skills because currently it feels like they really dropped the ball on what could have been a really good part of the game. I'm curious to see what some other people think about this and see if people generally agree with me or if the general consensus is that it is fine the way it is now.
I disagree with you...in almost every way possible.


text:
Reviewed By Hunter R (HAMPTON, GA) Reviewed for a 2007 Toyota Tacoma —5/27/2016 5:44 AM
Easy install and looks great!
Reviewed By Steve V (Bartlett, TN) Reviewed for a 2015 Toyota Tacoma —12/11/2015 6:34 AM
The grills are great. Fit perfectly and installs as per the instructions. If you would like more photos I can send them or retake the photos if you would like a better shot.
Reviewed By Kenedy N (Port Lavaca, TX) Reviewed for a 2015 Toyota Tundra —9/18/2015 3:26 PM
Grille arrived a few days after I placed the order. Instructions were straight forward and easy to follow. Easy to install but would be very helpful if you had at least two more people. Cutting of existing grille is required which is the only downside.


text:
accounts payable jobs near Houston, TX
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Ability to process high volume number of invoices while maintaining accuracy. Full cycle Accounts Payable. Accounts Payable Specialist job in North Houston, TX....
Accounts Payable Specialist job in Greenspoint area of Houston, TX
Accounting Principals - Houston, TX
Coordinate approval processes of all AP invoices. Code invoices to correct account classification. High volume processing experience, including up to 1,200...
Temp to Hire Accounts Payable Clerk job
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Processing freight invoices including matching sales invoice and coding. Handle all invoice discrepancies and communicating with vendors....
Accounting Manager
Odfjell - Houston, TX
Accounts Receivable - together with Sales and Customer Service, assists with the preparation of customer invoices, oversees maintenance of unpaid customer...
Managing Partner, Technical Accounting
Aventine Hill Partners, Inc. - Houston, TX
5000 Fastest Growth Companies list for the past three years. Health, dental, vision and flexible spending account. CPA....
Accounting Assistant
KK Group - Houston, TX
>Input accounts payable invoices & print checks in accounting system. >Minimum of 6 months work experience in an accounting, financial, and or management...
Accounts Payable Supervisor Job North East of Downtown, Houston, TX
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Reconcile Vendor statements and call for missing invoices or problem invoices. Answer vendor phone calls regarding payment or various issues....
Team Data Entry Clerk
Transport Service Co. - La Porte, TX
Their employment on the basis of any status or. No person will be discriminated against in any aspect of. Answer all phone calls to the terminal and address....
Accounting Administrator
Stage Stores - Houston, TX
Partner with Accounts Payable and capital project owners to clear capital invoices not posted into projects. As part of executing our strategy, we are investing...
Accounts Payable Job in the South East side of Houston, TX
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Process vendor invoices for approval and payment, including three-way match. Assist with vendor setup and payment processes....


text:
Episode 2
Ronnie's Animal Crackers Episode 2 of 6
We meet a cat breeder who is making a stand against the cat breeding establishment, and a breeder of 'blue' French bulldogs who will stop at nothing to indulge her favourite diva dog. We also meet owners of camels, one of whom proves to be a bit of a handful.
And Ronnie Corbett's new rescue dog Baz continues to give him heartache. A dog-training expert takes them both to a local park for a few important lessons in trying to develop their relationship.
Last on
Sat 21 Nov 2015 11:30
BBC Two except Wales
More episodes
|Ronnie Corbett
|Series Producer
|Mark Jones
|Executive Producer
|Will Daws
|Executive Producer
|Stuart Cabb


text:
This January there's an epidemic of personalized productivity posts floating around the internet. No shame in joining the fun I say. Being a freelancer is challenging. I didn't make these 5 up just to have a post, they really work for me and I when I don't stick to them I drift badly. They're really simple but some may not have occurred to you.
Read on about the 5 things I avoid to stay productive.
Continue reading 5 THINGS I DON'T DO TO GET STUFF DONE1 Comment


text:
|Re: Rolling clinic - I have been looking at one of EMS' one day kayak clinics. They offer them at a variety of locations over the summer. Might be easier to execute than lining up a custom class. Of course if you had a whole group of people there might be a deal to b
|Apr 6, 2010
|Rolling clinic - Hey guys, I'm Jessica, I'm new to the group. A lot of people seemed to like my meet-up idea to do a rolling clinic, but it doesn't seem like you can post comments on the meet-up idea page, so I thought this was a better plan
|Mar 16, 2010
|Anyone on the South Shore? - Hello Paddlers, I'm down in Norwell, 20 miles S of Boston. I would welcome any meetups in this area. If I were more experienced, I'd start a meetup..........but the tides can be tricky to predict. So if any of you know other paddlers down
|Denise R.
|Jul 27, 2009
|(no subject) - .hmmessage P { margin:0px; padding:0px } body.hmmessage { font-size: 10pt; font-family:Verdana } Hi there, Are any of you interested in meeting up in Winthrop, MA to ka
|Jul 27, 2009
|Hey - Preview not available
|Jul 13, 2009
|Surf film night -
|Frank R.
|Mar 26, 2009
|Re: [paddling-38] Outrigger and Dragon Boat Gear - great, Frank. I will keep you in touch. --- On Sun, 3/8/09, Frank Rickman wrote: > From: Frank Rickman > Subject: [paddling-38] Outrigger and Dragon Boat Gear > To: paddling-38
|Mar 9, 2009
|Outrigger and Dragon Boat Gear - Aloha; ?? I just wanted to let everyone know that I will be opening up a Outrigger and Dragon Boat shop. If anyone is in need of a paddle or any clothing items, please shoot me an email at a
|Frank R.
|Mar 8, 2009
|Hawaiian Outrigger Canoe Racing in Boston - Got an appetite for fun? We invite anyone interested to join us on the water to give outrigger paddling a try. We?re committed to expanding the outrigger community on the East Coast and welcome both novice and experienced paddlers. N
|May 27, 2008
|Boston Paddling Group Survey - What Type Of Boat Do You Own? - All, I'm conducting a survey for the Boston Paddling Meetup group for use in forming a future event in a few months. Do you own a boat and if so, how many and what type of boat do you own? Are interested in meeting on a we
|user 2.
|Jan 29, 2008
|Change in River trip this Saturday - Hello everyone, I have received feedback that 1:00 is too late to start the day trip. Please note that I have changed the time to 11:00 a.m. I hope this will increase your desire to join. Janine Remondi Organizer
|Janine R.
|Aug 9, 2007
|Welcome - Hello, Over the past 48 hours I have been notified of several new members to the Boston Paddle Group I look forward to planning future trips with you and remind you to check the Meetup event calendar. Please feel fr
|Janine R.
|Aug 9, 2007
|Information on kayak rental - Ahoy one and all. I apologize that it took me so long to get this information for you regarding rental fees. Please go to the website below. http://www.paddleboston.
|Janine R.
|Aug 9, 2007
|meeting place for August meet - Hello everyone, I enjoy ocean kayaking and was thinking about Walllaston (Quincy) MA on August 11, What are your thoughts? [address removed]
|Janine R.
|Jul 29, 2007
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text:
Email us @ email@example.com
Summer Camps and Clinics
9-13 Year Old All Levels Summer Camp at Hermosa Valley
Monday Thru Thursday 9am-12pm
Week of 25th
Click here for more info and to sign up!
13s and 14s Advanced Summer Clinics at Dana Middle School
Monday thru Wednesday
Week of July 25th
Click here for more info and to sign up!
12-14s Int/Advanced August Clinic
Mondays at Del Aire Park Gym in August
Click here for more info and to sign up!
Palos Verdes
Palos Verdes Beginner Clinics
Thursdays and Sundays in July and August for ages 9-13
Click here for more info and to sign up!
Palos Verdes Intermediate and Advanced Clinics for 13s-16s
Monday thru Wednesday in July and August
Click Here for more info and to sign up!
News and Updates
Surfside Volleyball 2017 Season Info
Girls tryouts for 15s and 16s are on Sunday, August 14th - Time/Location TBD
Girls tryouts for 14 & under are on Friday, October 7th - time/location TBD
Coaches and expected teams for the 2017 season:
15-Legends PV: Jace Olsen and Loriann Perkins
15-Legends MB: Walter Hernandez and Amanda Ilgunas
16-Legends: Lindsey Breeden and TBA
16-1 PV: Emily Cook and Johnny Tibbils
16-Gold MB: Katie Rotondo and Spencer Fournell
16-Gold PV: Madi Smith and TBA
Pre-Tryout Clinics at Adventurplex click here!
Pre-Tryout Clinics at South click here!
Girls 12-14s Pre-Tryout Fall Clinics in MB Area Click here!
South/PV High Pre-tryout clinics TBA.
Congratulations to Surfside 13-Legends for earning their bid to JUNIOR NATIONALS!
Great job to all our teams who competed in Junior National Qualifiers in LA and RENO!
Surfside 12-Legends: 1st place and a bid to JUNIOR NATIONALS
Surfside 13 Legends: 9th place overall
Surfside 14 PV Legends: 2nd place in 14 USA and a bid to JUNIOR NATIONALS
Surfside 14 MB Legends: 5th place in 14 USA at the Far Western JNQ
Surfside 15-Legends: 5th place and an OPEN BID TO JUNIOR NATIONALS
Surfside 16-Legends: 4th place overall
CONGRATULATIONS SURFSIDE 15 LEGENDS on your OPEN BID to JUNIOR NATIONALS!
Congratulations to Surfside 14-PV LEGENDS and Surfside 12-LEGENDS on their bids to Junior National Championships in Indianapolis!
Surfside 12-Legends finished 1st place and went an undefeated 20-0 for the weekend!
Surfside 14-PV Legends finished 2nd place in 14 USA and earned their bid!
Congratulations to Surfside 18-Legends Libero, Lauren Gurbach, on her commitment to COLUMBIA University! We are so proud of you, Lauren!
Great Job to all of our Surfside Teams in Mandatory #1 and Colorado Crossroads Junior National Qualifier the past two weekends!
Surfside has 8 teams competing in the GOLD division of the SCVA, with three teams playing in Division 1!
Surfside 18-Gold Finished top 25 in the Colorado Crossroads Junior National Qualifier.
Surfside 15-Legends finished 10th in the 15-OPEN Junior National Qualifier.
Surfside Volleyball Club is now partnering with LEGENDS Socks! We can't wait to #BeALegend this season!
CONGRATULATIONS to Alex Newton, Surfside 18-1 Setter/Opp, on her commitment to WILLIAMS COLLEGE!!
We are so proud of you, Alex! Your Surfside Coaches and teammates can't wait to watch your future success.
Surfside wants to welcome our new coaches for the 2016 season! Click on their names below to learn more.
Chad Grossman
Assistant Coach Surfside 18-1
Jeff Liu
Head Coach Surfside 17-1
Congratulations to Surfside 13-PV for an amazing season finishing top 10 in the SCVA and earning a National bid to Junior Nationals in New Orleans! Great job girls!
Congratulations to Surfside 14-1 on an undefeated weekend in Reno and taking home the Gold and a bid to Junior Nationals in New Orleans!
Fantastic Job by all of our Surfside Teams this past weekend at the Southern California Junior National Qualifier!
Surfside 12's Finished 4th out of 72 teams!
Surfside 13's finished 4th and 17th out of 92 teams!
Surfside 14's finished 9th in Open!
Surfside 15's finished 15th out of 124 teams!
Surfside 15's also finished 2nd and Surfside 16's finished 4th at the Spokane Junior National Qualifier!
Good luck to all our teams competing this weekend in both Los Angeles and Reno!
Great article by John Kessel from USAV: http://m.teamusa.org/USA-Volleyball/Features/2015/March/30/You-are-Paying-for-Practice-Not-Playing
2015 Summer Camps and Clinics
Click on your age group below for more info and how to sign up:
Summer Camp for girls ages 9-13
Advanced Clinics for 13/14 Girls
Advanced Clinics for 15/16 Girls
Special MOCK HIGH SCHOOL TRYOUTS clinic for incoming Freshman
Info about PALOS VERDES CLINICS will be posted by May 1
Check out this great sports blog article on teams!
The "Best Team" May Not Be What Is Best For Our Kids
Great job to our 15's, 13's and 12's this past weekend! Surfside 12-1 and 13-PV are both starting off the year in Division 1 of their age groups!
Congratulations to all of our Surfside Teams who played this past weekend!
All Surfside 14's teams placed 1st in their pools, and Surfside 14-1's are the NUMBER ONE TEAM of all 14's teams going into the next tournament!
Surfside 13's and 15's also played great and finished 2nd in their pools to be in the top of their age groups in the GOLD Division.
Surfside is excited to announce our new
Head Coach,
Gary Demian!
Coach Gary comes to Surfside after 10 years of coaching in Denver, Colorado. Read more about Gary here, and sign up for high school age clinics to get to know him!
Click here to view the 2015 SCVA Girls Volleyball Tournament Schedule. The 2015 season includes a NEW 13 & Under Division separate from the 14's division. Mark your calendars now for all tournament dates, and make sure you are aware of when the SoCal Qualifiers are for Spring Break planning!
Surfside Coach and Director Hayley Blanchard hired as new Head Coach of Mira Costa Girls Volleyball! Check out the article in Tuesday's Daily Breeze.
Archived News and Updates


text:
26 days ago
nelson : Bitcoin politics - Excellent detail on all the Chinese activity in Bitcoin#
3 month ago
nelson : Chinese-American websites - Parallel Internet for Chinese speakers in the US#
4 month ago
nelson : Chinese Crowd Formations - Nice set of photos#
7 month ago
nelson : Chinese map distortions - Google Maps in China shows odd artifacts to comply with Chinese security law#
7 month ago
nelson : BBC tests China - Terrifying flight in a tiny aircraft over highly militarized disputed territory#
8 month ago
nelson : Hoverboard origin - Interesting tale of Chinese manufacturing culture#
10 month ago
nelson : Cyberattack negotiation - US/China in talks for first ever cyberwarfare agreement. Very limited, more of a symbol.#
11 month ago
nelson : Vincent Lau 刘梓晨 - A plastic surgery enthusiast popular on Weibo#
14 month ago
nelson : China: Through the Looking Glass - Great exhibit at the Met looking at Orientalist exoticism and China#
14 month ago
nelson : Yi action camera - Inexpensive, hackable video camera, Chinese competitor to GoPro#
15 month ago
nelson : GitHub DDOS statistics - Excellent detailed info from Google#
16 month ago
nelson : China vs GitHub - 3 days in now to a massive DDoS attack, apparently by the Chinese government#
16 month ago
nelson : Chinese Mobile App UI Trends - Invaluably detailed info for how Chinese mobile apps differ from US#
18 month ago
nelson : Fear Chinese Firewall - What happens when your server becomes the victim of a Chinese Great Firewall misconfiguration?
Andy Baio : Craig Hockenberry on Chinese DNS poisoning - well, that explains the DDoS I've been dealing with for the last 12 days#
19 month ago
nelson : China astroturfing - Minor hack reveals government propaganda faking Internet buzz#
21 month ago
nelson : Notes From Behind the Firewall - Quick overview of some differences in the parallel Chinese Internet#
23 month ago
nelson : China v. Google MITM - Fake SSL certs in the wild#
23 month ago
nelson : Shenzhen trip report - Joi Ito and bunnie visit the greatest electronics manufacturing place in the world#
27 month ago
nelson : Eve Online China - Parallel development of Eve Online in the Chinese instance#
28 month ago
nelson : IE6 usage map - Microsoft's stats on usage; 20% or more in China#
28 month ago
nelson : The 49-U6U Slaughterhouse - Biggest space battle in Eve Online to date happened on the Chinese server#
29 month ago
nelson : Weibo - SINA English - China's enormous Twitter-like service has an English interface#
30 month ago
nelson : Weibo hamstrung - Chinese government's crackdown has severely curtailed usage of China's Twitter-like service#
36 month ago
nelson : China hacking US water plants - Notorious Chinese hacking group, probably Army, caught in a honeypot and counter-hacked#


text:
PARIS May 30 World No.2 Novak Djokovic overcame a minor scare to beat Croatian 25th seed Marin Cilic 6-3 6-2 6-7(2) 6-4 and advance into the fourth round of the French Open on Friday.
Djokovic, chasing the only grand slam title to elude him, was in complete control until the end of the third set, when the big-serving Cilic forced him to a tiebreak, which the six-times grand slam champion lost 7-2.
Normal service resumed afterwards and Djokovic, although not playing his best tennis, finished it off on Cilic's serve when the Croatian double faulted.
He will next face either Frenchman Jo-Wilfried Tsonga, the 13th seed, or Polish 22nd seed Jerzy Janowicz. (Reporting by Julien Pretot; Editing by Toby Davis)
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IBM will work with the University of Pittsburgh Medical Center to bring to the market "smart" hospital room technology that automatically organizes and prioritizes nurses' and other providers' tasks. "Our SmartRoom solution tackles the everyday problems of simplifying work flow, making documentation easier and giving nurses more quality time at the bedside," a UPMC unit executive said.
Full Story:Healthcare IT News, InformationWeek


text: kardboredbocks Play via YouTube OPEN IN APP NSFW Safe Is this playlist safe for work? Epic Videogame Music May 12, 2011 | 8 tracks | 368 19 | Stats 大谷幸Danny BaranowskyHarry Gregson-Williams electronicgameemotionalsoundtracknostalgia Liked Collect Share Edit Liked! Share this mix with friends: Epic Videogame Music Wrong video Collect Share Liked! Share this mix with friends:


text:
Asian-Pacific markets were mixed Monday as investors debated whether the Federal Reserve was close to scaling back its stimulus initiatives. Japan's Nikkei 225 gained 1.3%. Hong Kong's Hang Seng Index rose 1.4%. Australia's S&P/ASX 200 slid 0.3%. China's Shanghai Composite edged up 0.2%. South Korea's Kospi fell 0.4%. India's Sensex was down 0.9%.
Full Story:CNBC, The Economic Times (India)


text:
Walmart Customers Set Fireworks Display on Fire
A prank turned extremely scary in a Phoenix area Walmart store last week as a fireworks display was ignited.
A prank turned extremely scary in a Phoenix area Walmart store last week as a fireworks display was ignited.
A Texas man is accused of throwing stolen Walmart steaks at cops during a high-speed chase.
Two men from the Bronx were arrested for allegedly stealing almost $1,500 dollars' worth of merchandise from a local Walmart.
State Police arrested 3 women from Newburgh for allegedly stealing merchandise from a local Walmart. Police say one suspect had an outstanding warrant out for her arrest.
Have you seen the Michael Jackson impersonator that has been spotted dancing in public in the Hudson Valley?
A woman is accused of biting off a Walmart employees finger while trying to steal $40 worth of condom and lube.
A couple who got engaged at Walmart were arrested after allegedly stealing a sex toy from Spencer's.
What product you should check your freezer for?
It might be the most wonderful headline I'll ever get a chance to write, and it's also as real as it is insane.
With critics increasingly pressuring Walmart to improve conditions for their employees, the company has implemented some new, significant changes in policy.


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As a result of a cooperation between Brookhaven National Laboratory and eV Products a generation of high performance readout ASICs was developed. The ASICs, realized in CMOS 0.5 μm technology, are available in several different versions, single or multi-channel and with unipolar or bipolar shaper, in view of their use in research, spectroscopy, medical, safeguard and industrial applications. Four innovative circuit solutions are implemented in the ASICs: (i) a high linearity compensated continuous reset system which self-adapts to a wide range of detector leakage currents with minimum noise contribution; (ii) a high order shaper realized by using the follow-the-leader feedback (FLF) approach; (iii) a class AB rail-to-rail output stage with high driving capability; (iv) a baseline holder (BLH) for the baseline stabilization. The basic structure of the ASICs, a description of the circuit solutions and the preliminary experimental results are reported
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Garvin County District Attorney Office
Contact Information
Garvin County District Attorney Office
Garvin County Courthouse
201 West Grant Street
Pauls Valley, OK 73075-3248
Telephone: (405) 238-1141
Facsimile: (405) 238-5018
Email: email@example.com
Website: www.da.co.cleveland.ok.us/garvin_county.htm
Google Map
Office Hours
About Garvin County District Attorney Office
The Garvin County legal staff consists of approximately 13 staff members including A.D.A.'s, support staff, child support enforcement, and investigators. From time to time additional attorneys and/or support staff are reassigned from Cleveland County to Garvin County as necessary.
District Attorney Biography
District Attorney Greg Mashburn graduated from Idabel High School in 1990. Mashburn attended Harding University in Arkansas on a football scholarship, graduating in 1995. He then obtained his Juris Doctorate from the University Of Oklahoma School Of Law in 1998. Greg Mashburn spent a decade learning to incarcerate criminals as an Assistant District Attorney in Oklahoma County. There he built an impressive record, becoming a Division Chief just six years after he began his career. Since taking over the District Attorney's office in January of 2007, Greg has re-organized the office to better manage the caseload and ensure that victims are properly cared for in the criminal justice system. This, together with an improved relationship with other law enforcement departments within the district, has led to a dramatic increase in both the quality and success rate of cases which, in turn, will lead to a safer District 21.
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This page (Garvin County District Attorney Office) was first created by sfazeli on Aug 21, 2010 8:05 am and to date has been edited 1 times, with the last edit made by sfazeli on Aug 21, 2010 8:05 am.
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For massive damage!
"I'm kindling at maximum speed as is, sir!"
Heheh… 'Kindle' is such a funny verb for some reason.
dude you've obviously got a lighter or something why don't you help a motherfucker out a little
LARPer invokes Our Weapons Are Useless!
LARPer fails morale check!
Will performs Sweeping Advance!
NAME — Get an avatar
EMAIL — Required / not published
- Beep boop -


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Filter by:
Content type:
Stage 1&2
Stage 2&3
Stage 3&4
Stage 4&5
Challenge level:
A game for 2 players. Given a board of dots in a grid pattern, players take turns drawing a line by connecting 2 adjacent dots. Your goal is to complete more squares than your opponent.
How many different triangles can you make on a circular pegboard that has nine pegs?
Hover your mouse over the counters to see which ones will be
removed. Click to remover them. The winner is the last one to
remove a counter. How you can make sure you win?
A tetromino is made up of four squares joined edge to edge. Can
this tetromino, together with 15 copies of itself, be used to cover
an eight by eight chessboard?
Exchange the positions of the two sets of counters in the least possible number of moves
A game for two players on a large squared space.
How can you arrange the 5 cubes so that you need the smallest number of Brush Loads of paint to cover them? Try with other numbers of cubes as well.
You have 4 red and 5 blue counters. How many ways can they be
placed on a 3 by 3 grid so that all the rows columns and diagonals
have an even number of red counters?
This challenge involves eight three-cube models made from
interlocking cubes. Investigate different ways of putting the
models together then compare your constructions.
Investigate how the four L-shapes fit together to make an enlarged
L-shape. You could explore this idea with other shapes too.
Here are more buildings to picture in your mind's eye. Watch out -
they become quite complicated!
How can you paint the faces of these eight cubes so they can be put
together to make a 2 x 2 cube that is green all over AND a 2 x 2
cube that is yellow all over?
A game has a special dice with a colour spot on each face. These three pictures show different views of the same dice. What colour is opposite blue?
An extension of noughts and crosses in which the grid is enlarged
and the length of the winning line can to altered to 3, 4 or 5.
A game for 1 or 2 people. Use the interactive version, or play with friends. Try to round up as many counters as possible.
Imagine a 4 by 4 by 4 cube. If you and a friend drill holes in some of the small cubes in the ways described, how many will not have holes drilled through them?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
will be?
How can the same pieces of the tangram make this bowl before and after it was chipped? Use the interactivity to try and work out what is going on!
Can you fit the tangram pieces into the outline of Little Ming?
Cut four triangles from a square as shown in the picture. How many
different shapes can you make by fitting the four triangles back
Here are some arrangements of circles. How many circles would I need to make the next size up for each? Can you create your own arrangement and investigate the number of circles it needs?
Imagine a 3 by 3 by 3 cube made of 9 small cubes. Each face of the large cube is painted a different colour. How many small cubes will have two painted faces? Where are they?
Given the nets of 4 cubes with the faces coloured in 4 colours, build a tower so that on each vertical wall no colour is repeated, that is all 4 colours appear.
In each of the pictures the invitation is for you to: Count what you see. Identify how you think the pattern would continue.
Triangle numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
Can you fit the tangram pieces into the outline of Granma T?
You have 27 small cubes, 3 each of nine colours. Use the small cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of every colour.
I've made some cubes and some cubes with holes in. This challenge
invites you to explore the difference in the number of small cubes
I've used. Can you see any patterns?
How many different ways can you find of fitting five hexagons
together? How will you know you have found all the ways?
Try this interactive strategy game for 2
A dog is looking for a good place to bury his bone. Can you work
out where he started and ended in each case? What possible routes
could he have taken?
A magician took a suit of thirteen cards and held them in his hand
face down. Every card he revealed had the same value as the one he
had just finished spelling. How did this work?
Can you fit the tangram pieces into the outline of these rabbits?
What is the greatest number of squares you can make by overlapping
three squares?
An irregular tetrahedron is composed of four different triangles.
Can such a tetrahedron be constructed where the side lengths are 4,
5, 6, 7, 8 and 9 units of length?
Investigate the number of paths you can take from one vertex to
another in these 3D shapes. Is it possible to take an odd number
and an even number of paths to the same vertex?
Can you cut up a square in the way shown and make the pieces into a
Can you fit the tangram pieces into the outline of the telescope and microscope?
In how many ways can you fit two of these yellow triangles
together? Can you predict the number of ways two blue triangles can
be fitted together?
Can you find ways of joining cubes together so that 28 faces are
Can you make a 3x3 cube with these shapes made from small cubes?
Here you see the front and back views of a dodecahedron. Each
vertex has been numbered so that the numbers around each pentagonal
face add up to 65. Can you find all the missing numbers?
Can you fit the tangram pieces into the outline of Little Ming playing the board game?
Can you fit the tangram pieces into the outline of this telephone?
How many DIFFERENT quadrilaterals can be made by joining the dots
on the 8-point circle?
Imagine a wheel with different markings painted on it at regular
intervals. Can you predict the colour of the 18th mark? The 100th
Can you fit the tangram pieces into the outline of Little Fung at the table?
Can you fit the tangram pieces into the outline of this brazier for roasting chestnuts?
Can you fit the tangram pieces into the outlines of these clocks?
We start with one yellow cube and build around it to make a 3x3x3 cube with red cubes. Then we build around that red cube with blue cubes and so on. How many cubes of each colour have we used?


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04 April 2014 at 6:35 PM
Jena Malone Goes Nearly Naked for New The Shoe Music Video!
About this photo set: Jena Malone goes naked with only some tiny flowers covering her private parts in this new music video for her band The Shoe's song "Dead Rabbit Hopes"! The… Read More Here
Photo #: 3084687
Posted to Jena Malone, Music Video, NSFW, The Show
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