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| Extensions of Positive Definite Functions on Amenable Groups
Bakonyi, M.; Timotin, D.
Let $S$ be a subset of an amenable group $G$ such that $e\in S$ and $S^{-1}=S$. The main result of this paper states that if the Cayley graph of $G$ with respect to $S$ has a certain combinatorial property, then every positive definite operator-valued function on $S$ can be extended to a positive definite function on $G$. Several known extension results are obtained as corollaries. New applications are also presented.
| Homotopy and the Kestelman-Borwein-Ditor Theorem
Bingham, N. H.; Ostaszewski, A. J.
The Kestelman--Borwein--Ditor Theorem, on embedding a null sequence by translation in (measure/category) ``large'' sets has two generalizations. Miller replaces the translated sequence by a ``sequence homotopic to the identity''. The authors, in a previous paper, replace points by functions: a uniform functional null sequence replaces the null sequence, and translation receives a functional form. We give a unified approach to results of this kind. In particular, we show that (i) Miller's homotopy version follows from the functional version, and (ii) the pointwise instance of the functional version follows from Miller's homotopy version.
| Generalized D-symmetric Operators II
Bouali, S.; Ech-chad, M.
Let $H$ be a separable, infinite-dimensional, complex Hilbert space and let $A, B\in{\mathcal L }(H)$, where ${\mathcal L}(H)$ is the algebra of all bounded linear operators on $H$. Let $\delta_{AB}\colon {\mathcal L}(H)\rightarrow {\mathcal L}(H)$ denote the generalized derivation $\delta_{AB}(X)=AX-XB$. This note will initiate a study on the class of pairs $(A,B)$ such that $\overline{{\mathcal R}(\delta_{AB})}= \overline{{\mathcal R}(\delta_{A^{\ast}B^{\ast}})}$.
| Generalized Solution of the Photon Transport Problem
Chang, Yu-Hsien; Hong, Cheng-Hong
The purpose of this paper is to show the existence of a generalized solution of the photon transport problem. By means of the theory of equicontinuous $C_{0}$-semigroup on a sequentially complete locally convex topological vector space we show that the perturbed abstract Cauchy problem has a unique solution when the perturbation operator and the forcing term function satisfy certain conditions. A consequence of the abstract result is that it can be directly applied to obtain a generalized solution of the photon transport problem.
| Elements in a Numerical Semigroup with Factorizations of the Same Length
Chapman, S. T.; García-Sánchez, P. A.; Llena, D.; Marshall, J.
Questions concerning the lengths of factorizations into irreducible elements in numerical monoids have gained much attention in the recent literature. In this note, we show that a numerical monoid has an element with two different irreducible factorizations of the same length if and only if its embedding dimension is greater than two. We find formulas in embedding dimension three for the smallest element with two different irreducible factorizations of the same length and the largest element whose different irreducible factorizations all have distinct lengths. We show that these formulas do not naturally extend to higher embedding dimensions.
| Star-Shapedness and $K$-Orbits in Complex Semisimple Lie Algebras
Cheung, Wai-Shun; Tam, Tin-Yau
Given a complex semisimple Lie algebra $\mathfrak{g}=\mathfrak{k}+i\mathfrak{k}$ ($\mathfrak{k}$ is a compact real form of $\mathfrak{g}$), let $\pi\colon\mathfrak{g}\to \mathfrak{h}$ be the orthogonal projection (with respect to the Killing form) onto the Cartan subalgebra $\mathfrak{h}:=\mathfrak{t}+i\mathfrak{t}$, where $\mathfrak{t}$ is a maximal abelian subalgebra of $\mathfrak{k}$. Given $x\in \mathfrak{g}$, we consider $\pi(\mathop{\textrm{Ad}}(K) x)$, where $K$ is the analytic subgroup $G$ corresponding to $\mathfrak{k}$, and show that it is star-shaped. The result extends a result of Tsing. We also consider the generalized numerical range $f(\mathop{\textrm{Ad}}(K)x)$, where $f$ is a linear functional on $\mathfrak{g}$. We establish the star-shapedness of $f(\mathop{\textrm{Ad}}(K)x)$ for simple Lie algebras of type $B$.
| Characteristic Varieties for a Class of Line Arrangements
Dinh, Thi Anh Thu
Let $\mathcal{A}$ be a line arrangement in the complex projective plane $\mathbb{P}^2$, having the points of multiplicity $\geq 3$ situated on two lines in $\mathcal{A}$, say $H_0$ and $H_{\infty}$. Then we show that the non-local irreducible components of the first resonance variety $\mathcal{R}_1(\mathcal{A})$ are 2-dimensional and correspond to parallelograms $\mathcal{P}$ in $\mathbb{C}^2=\mathbb{P}^2 \setminus H_{\infty}$ whose sides are in $\mathcal{A}$ and for which $H_0$ is a diagonal.
| Non-splitting in Kirchberg's Ideal-related $KK$-Theory
Eilers, Søren; Restorff, Gunnar; Ruiz, Efren
A. Bonkat obtained a universal coefficient theorem in the setting of Kirchberg's ideal-related $KK$-theory in the fundamental case of a $C^*$-algebra with one specified ideal. The universal coefficient sequence was shown to split, unnaturally, under certain conditions. Employing certain $K$-theoretical information derivable from the given operator algebras using a method introduced here, we shall demonstrate that Bonkat's UCT does not split in general. Related methods lead to information on the complexity of the $K$-theory which must be used to classify $*$-isomorphisms for purely infinite $C^*$-algebras with one non-trivial ideal.
| Lefschetz Numbers for $C^*$-Algebras
Emerson, Heath
Using Poincar\'e duality, we obtain a formula of Lefschetz type that computes the Lefschetz number of an endomorphism of a separable nuclear $C^*$-algebra satisfying Poincar\'e duality and the Kunneth theorem. (The Lefschetz number of an endomorphism is the graded trace of the induced map on $\textrm{K}$-theory tensored with $\mathbb{C}$, as in the classical case.) We then examine endomorphisms of Cuntz--Krieger algebras $O_A$. An endomorphism has an invariant, which is a permutation of an infinite set, and the contracting and expanding behavior of this permutation describes the Lefschetz number of the endomorphism. Using this description, we derive a closed polynomial formula for the Lefschetz number depending on the matrix $A$ and the presentation of the endomorphism.
| On the Generalized Marcinkiewicz Integral Operators with Rough Kernels
Fan, Dashan; Wu, Huoxiong
A class of generalized Marcinkiewicz integral operators is introduced, and, under rather weak conditions on the integral kernels, the boundedness of such operators on $L^p$ and Triebel--Lizorkin spaces is established.
| On the Norm of the Beurling-Ahlfors Operator in Several Dimensions
Hytönen, Tuomas P.
The generalized Beurling-Ahlfors operator $S$ on $L^p(\mathbb{R}^n;\Lambda)$, where $\Lambda:=\Lambda(\mathbb{R}^n)$ is the exterior algebra with its natural Hilbert space norm, satisfies the estimate $$\|S\|_{\mathcal{L}(L^p(\mathbb{R}^n;\Lambda))}\leq(n/2+1)(p^*-1),\quad p^*:=\max\{p,p'\}$$ This improves on earlier results in all dimensions $n\geq 3$. The proof is based on the heat extension and relies at the bottom on Burkholder's sharp inequality for martingale transforms.
| Fundamental Solutions of Kohn Sub-Laplacians on Anisotropic Heisenberg Groups and H-type Groups
Jin, Yongyang; Zhang, Genkai
We prove that the fundamental solutions of Kohn sub-Laplacians $\Delta + i\alpha \partial_t$ on the anisotropic Heisenberg groups are tempered distributions and have meromorphic continuation in $\alpha$ with simple poles. We compute the residues and find the partial fundamental solutions at the poles. We also find formulas for the fundamental solutions for some matrix-valued Kohn type sub-Laplacians on H-type groups.
| Linear Maps on $C^*$-Algebras Preserving the Set of Operators that are Invertible in $\mathcal{A}/\mathcal{I}$
Kim, Sang Og; Park, Choonkil
For $C^*$-algebras $\mathcal{A}$ of real rank zero, we describe linear maps $\phi$ on $\mathcal{A}$ that are surjective up to ideals $\mathcal{I}$, and $\pi(A)$ is invertible in $\mathcal{A}/\mathcal{I}$ if and only if $\pi(\phi(A))$ is invertible in $\mathcal{A}/\mathcal{I}$, where $A\in\mathcal{A}$ and $\pi:\mathcal{A}\to\mathcal{A}/\mathcal{I}$ is the quotient map. We also consider similar linear maps preserving zero products on the Calkin algebra.
| Generalized Quandle Polynomials
Nelson, Sam
We define a family of generalizations of the two-variable quandle polynomial. These polynomial invariants generalize in a natural way to eight-variable polynomial invariants of finite biquandles. We use these polynomials to define a family of link invariants that further generalize the quandle counting invariant.
| Hardy Inequalities on the Real Line
Sababheh, Mohammad
We prove that some inequalities, which are considered to be generalizations of Hardy's inequality on the circle, can be modified and proved to be true for functions integrable on the real line. In fact we would like to show that some constructions that were used to prove the Littlewood conjecture can be used similarly to produce real Hardy-type inequalities. This discussion will lead to many questions concerning the relationship between Hardy-type inequalities on the circle and those on the real line.
| Measures with Fourier Transforms in $L^2$ of a Half-space
Shayya, Bassam
We prove that if the Fourier transform of a compactly supported measure is in $L^2$ of a half-space, then the measure is absolutely continuous to Lebesgue measure. We then show how this result can be used to translate information about the dimensionality of a measure and the decay of its Fourier transform into geometric information about its support.
| Additive Families of Low Borel Classes and Borel Measurable Selectors
Spurný, J.; Zelený, M.
An important conjecture in the theory of Borel sets in non-separable metric spaces is whether any point-countable Borel-additive family in a complete metric space has a $\sigma$-discrete refinement. We confirm the conjecture for point-countable $\mathbf\Pi_3^0$-additive families, thus generalizing results of R. W. Hansell and the first author. We apply this result to the existence of Borel measurable selectors for multivalued mappings of low Borel complexity, thus answering in the affirmative a particular version of a question of J. Kaniewski and R. Pol.
| Measurements and $G_\delta$-Subsets of Domains
Bennett, Harold; Lutzer, David
In this paper we study domains, Scott domains, and the existence of measurements. We use a space created by D.~K. Burke to show that there is a Scott domain $P$ for which $\max(P)$ is a $G_\delta$-subset of $P$ and yet no measurement $\mu$ on $P$ has $\ker(\mu) = \max(P)$. We also correct a mistake in the literature asserting that $[0, \omega_1)$ is a space of this type. We show that if $P$ is a Scott domain and $X \subseteq \max(P)$ is a $G_\delta$-subset of $P$, then $X$ has a $G_\delta$-diagonal and is weakly developable. We show that if $X \subseteq \max(P)$ is a $G_\delta$-subset of $P$, where $P$ is a domain but perhaps not a Scott domain, then $X$ is domain-representable, first-countable, and is the union of dense, completely metrizable subspaces. We also show that there is a domain $P$ such that $\max(P)$ is the usual space of countable ordinals and is a $G_\delta$-subset of $P$ in the Scott topology. Finally we show that the kernel of a measurement on a Scott domain can consistently be a normal, separable, non-metrizable Moore space.
| A Bilinear Fractional Integral on Compact Lie Groups
Chen, Jiecheng; Fan, Dashan
As an analog of a well-known theorem on the bilinear fractional integral on $\mathbb{R}^{n}$ by Kenig and Stein, we establish the similar boundedness property for a bilinear fractional integral on a compact Lie group. Our result is also a generalization of our recent theorem about the bilinear fractional integral on torus.
| Recurrence Relations for Strongly $q$-Log-Convex Polynomials
Chen, William Y. C.; Wang, Larry X. W.; Yang, Arthur L. B.
We consider a class of strongly $q$-log-convex polynomials based on a triangular recurrence relation with linear coefficients, and we show that the Bell polynomials, the Bessel polynomials, the Ramanujan polynomials and the Dowling polynomials are strongly $q$-log-convex. We also prove that the Bessel transformation preserves log-convexity.
| Universal Power Series in $\mathbb{C}^N$
Clouâtre, Raphaël
We establish the existence of power series in $\mathbb{C}^N$ with the property that the subsequences of the sequence of partial sums uniformly approach any holomorphic function on any well chosen compact subset outside the set of convergence of the series. We also show that, in a certain sense, most series enjoy this property.
| The Structure of the Unit Group of the Group Algebra ${\mathbb{F}}_{2^k}D_{8}$
Creedon, Leo; Gildea, Joe
Let $RG$ denote the group ring of the group $G$ over the ring $R$. Using an isomorphism between $RG$ and a certain ring of $n \times n$ matrices in conjunction with other techniques, the structure of the unit group of the group algebra of the dihedral group of order $8$ over any finite field of chracteristic $2$ is determined in terms of split extensions of cyclic groups.
| Homogeneous Suslinian Continua
Daniel, D. ; Nikiel, J.; Treybig, L. B.; Tuncali, H. M.; Tymchatyn, E. D.
A continuum is said to be Suslinian if it does not contain uncountably many mutually exclusive non-degenerate subcontinua. Fitzpatrick and Lelek have shown that a metric Suslinian continuum $X$ has the property that the set of points at which $X$ is connected im kleinen is dense in $X$. We extend their result to Hausdorff Suslinian continua and obtain a number of corollaries. In particular, we prove that a homogeneous, non-degenerate, Suslinian continuum is a simple closed curve and that each separable, non-degenerate, homogenous, Suslinian continuum is metrizable.
| A Note about Analytic Solvability of Complex Planar Vector Fields with Degeneracies
Dattori da Silva, Paulo L.
This paper deals with the analytic solvability of a special class of complex vector fields defined on the real plane, where they are tangent to a closed real curve, while off the real curve, they are elliptic.
| On an Identity due to Bump and Diaconis, and Tracy and Widom
Dehaye, Paul-Olivier
A classical question for a Toeplitz matrix with given symbol is how to compute asymptotics for the determinants of its reductions to finite rank. One can also consider how those asymptotics are affected when shifting an initial set of rows and columns (or, equivalently, asymptotics of their minors). Bump and Diaconis obtained a formula for such shifts involving Laguerre polynomials and sums over symmetric groups. They also showed how the Heine identity extends for such minors, which makes this question relevant to Random Matrix Theory. Independently, Tracy and Widom used the Wiener-Hopf factorization to express those shifts in terms of products of infinite matrices. We show directly why those two expressions are equal and uncover some structure in both formulas that was unknown to their authors. We introduce a mysterious differential operator on symmetric functions that is very similar to vertex operators. We show that the Bump-Diaconis-Tracy-Widom identity is a differentiated version of the classical Jacobi-Trudi identity.
| Sequential Order Under PFA
Dow, Alan
It is shown that it follows from PFA that there is no compact scattered space of height greater than $\omega$ in which the sequential order and the scattering heights coincide.
| Maximal Sublattices of Finite Distributive Lattices. III: A Conjecture from the 1984 Banff Conference on Graphs and Order
Farley, Jonathan David
Let $L$ be a finite distributive lattice. Let $\operatorname{Sub}_0(L)$ be the lattice $$ \{S\mid S\text{ is a sublattice of }L\}\cup\{\emptyset\} $$ and let $\ell_*[\operatorname{Sub}_0(L)]$ be the length of the shortest maximal chain in $\operatorname{Sub}_0(L)$. It is proved that if $K$ and $L$ are non-trivial finite distributive lattices, then $$ \ell_*[\operatorname{Sub}_0(K\times L)]=\ell_*[\operatorname{Sub}_0(K)]+\ell_*[\operatorname{Sub}_0(L)]. $$ A conjecture from the 1984 Banff Conference on Graphs and Order is thus proved.
| Surgery on $\widetilde{\mathbb{SL}} \times \mathbb{E}^n$-Manifolds
Hillman, J. A.; Roushon, S. K.
We show that closed $\widetilde{\mathbb{SL}} \times \mathbb{E}^n$-manifolds are topologically rigid if $n\geq 2$, and are rigid up to $s$-cobordism, if $n=1$.
| The Resultant of Chebyshev Polynomials
Jacobs, David P.; Rayes, Mohamed O.; Trevisan, Vilmar
Let $T_{n}$ denote the $n$-th Chebyshev polynomial of the first kind, and let $U_{n}$ denote the $n$-th Chebyshev polynomial of the second kind. We give an explicit formula for the resultant $\operatorname{res}( T_{m}, T_{n} )$. Similarly, we give a formula for $\operatorname{res}( U_{m}, U_{n} )$.
| Lie Powers and Pseudo-Idempotents
Johnson, Marianne; Stöhr, Ralph
We give a new factorisation of the classical Dynkin operator, an element of the integral group ring of the symmetric group that facilitates projections of tensor powers onto Lie powers. As an application we show that the iterated Lie power $L_2(L_n)$ is a module direct summand of the Lie power $L_{2n}$ whenever the characteristic of the ground field does not divide $n$. An explicit projection of the latter onto the former is exhibited in this case.
| Structure of the Set of Norm-attaining Functionals on Strictly Convex Spaces
Kurka, Ondřej
Let $X$ be a separable non-reflexive Banach space. We show that there is no Borel class which contains the set of norm-attaining functionals for every strictly convex renorming of $X$.
| Some Remarks Concerning the Topological Characterization of Limit Sets for Surface Flows
Marzougui, Habib
We give some extension to theorems of Jiménez López and Soler López concerning the topological characterization for limit sets of continuous flows on closed orientable surfaces.
| The Saddle-Point Method and the Li Coefficients
Mazhouda, Kamel
In this paper, we apply the saddle-point method in conjunction with the theory of the Nörlund-Rice integrals to derive precise asymptotic formula for the generalized Li coefficients established by Omar and Mazhouda. Actually, for any function $F$ in the Selberg class $\mathcal{S}$ and under the Generalized Riemann Hypothesis, we have $$ \lambda_{F}(n)=\frac{d_{F}}{2}n\log n+c_{F}n+O(\sqrt{n}\log n), $$ with $$ c_{F}=\frac{d_{F}}{2}(\gamma-1)+\frac{1}{2}\log(\lambda Q_{F}^{2}),\ \lambda=\prod_{j=1}^{r}\lambda_{j}^{2\lambda_{j}}, $$ where $\gamma$ is the Euler's constant and the notation is as below.
| Sur la borne inférieure du rang du 2-groupe de classes de certains corps multiquadratiques
Mouhib, A.
Soient $p_1,p_2,p_3$ et $q$ des nombres premiers distincts tels que $p_1\equiv p_2\equiv p_3\equiv -q\equiv 1 \pmod{4}$, $k = \mathbf{Q} (\sqrt{p_1}, \sqrt{p_2}, \sqrt{p_3}, \sqrt{q})$ et $\operatorname{Cl}_2(k)$ le $2$-groupe de classes de $k$. A. Fröhlich a démontré que $\operatorname{Cl}_2(k)$ n'est jamais trivial. Dans cet article, nous donnons une extension de ce résultat, en démontrant que le rang de $\operatorname{Cl}_2(k)$ est toujours supérieur ou égal à $2$. Nous démontrons aussi, que la valeur $2$ est optimale pour une famille infinie de corps $k$.
| Szegö's Theorem and Uniform Algebras
Nakazi, Takahiko
We study Szegö's theorem for a uniform algebra. In particular, we do it for the disc algebra or the bidisc algebra.
| The Haar System in the Preduals of Hyperfinite Factors
Potapov, D.; Sukochev, F.
We shall present examples of Schauder bases in the preduals to the hyperfinite factors of types~$\hbox{II}_1$, $\hbox{II}_\infty$, $\hbox{III}_\lambda$, $0 < \lambda \leq 1$. In the semifinite (respectively, purely infinite) setting, these systems form Schauder bases in any associated separable symmetric space of measurable operators (respectively, in any non-commutative $L^p$-space).
| Lyapunov Theorems for the Asymptotic Behavior of Evolution Families on the Half-Line
Preda, Ciprian; Preda, Petre
Two theorems regarding the asymptotic behavior of evolution families are established in terms of the solutions of a certain Lyapunov operator equation.
| Manifold-Valued Holomorphic Approximation
Stout, Edgar Lee
This note considers the problem of approximating continuous maps from sets in complex spaces into complex manifolds by holomorphic maps.
| A Short Note on the Higher Level Version of the Krull--Baer Theorem
Velušček, Dejan
Klep and Velu\v{s}\v{c}ek generalized the Krull--Baer theorem for higher level preorderings to the non-commutative setting. A $n$-real valuation $v$ on a skew field $D$ induces a group homomorphism $\overline{v}$. A section of $\overline{v}$ is a crucial ingredient of the construction of a complete preordering on the base field $D$ such that its projection on the residue skew field $k_v$ equals the given level $1$ ordering on $k_v$. In the article we give a proof of the existence of the section of $\overline{v}$, which was left as an open problem by Klep and Velu\v{s}\v{c}ek, and thus complete the generalization of the Krull--Baer theorem for preorderings.
| Irreducible Representations of Inner Quasidiagonal $C^*$-Algebras
Blackadar, Bruce; Kirchberg, Eberhard
It is shown that a separable $C^*$-algebra is inner quasidiagonal if and only if it has a separating family of quasidiagonal irreducible representations. As a consequence, a separable $C^*$-algebra is a strong NF algebra if and only if it is nuclear and has a separating family of quasidiagonal irreducible representations. We also obtain some permanence properties of the class of inner quasidiagonal $C^*$-algebras.
| Parabolic Geodesics in Sasakian $3$-Manifolds
Cho, Jong Taek; Inoguchi, Jun-ichi; Lee, Ji-Eun
We give explicit parametrizations for all parabolic geodesics in 3-dimensional Sasakian space forms.
| Operator Algebras with Unique Preduals
Davidson, Kenneth R.; Wright, Alex
We show that every free semigroup algebra has a (strongly) unique Banach space predual. We also provide a new simpler proof that a weak-$*$ closed unital operator algebra containing a weak-$*$ dense subalgebra of compact operators has a unique Banach space predual.
| Two Conditions on the Structure Jacobi Operator for Real Hypersurfaces in Complex Projective Space
Pérez, Juan de Dios; Suh, Young Jin
We classify real hypersurfaces in complex projective space whose structure Jacobi operator satisfies two conditions at the same time.
| Complete Families of Linearly Non-degenerate Rational Curves
DeLand, Matthew
We prove that every complete family of linearly non-degenerate rational curves of degree $e > 2$ in $\mathbb{P}^{n}$ has at most $n-1$ moduli. For $e = 2$ we prove that such a family has at most $n$ moduli. The general method involves exhibiting a map from the base of a family $X$ to the Grassmannian of $e$-planes in $\mathbb{P}^{n}$ and analyzing the resulting map on cohomology.
| Nondegeneracy for Lie Triple Systems and Kantor Pairs
García, Esther; Lozano, Miguel Gómez; Neher, Erhard
We study the transfer of nondegeneracy between Lie triple systems and their standard Lie algebra envelopes as well as between Kantor pairs, their associated Lie triple systems, and their Lie algebra envelopes. We also show that simple Kantor pairs and Lie triple systems in characteristic $0$ are nondegenerate.
| On Operator Sum and Product Adjoints and Closures
Gustafson, Karl
We comment on domain conditions that regulate when the adjoint of the sum or product of two unbounded operators is the sum or product of their adjoints, and related closure issues. The quantum mechanical problem PHP essentially selfadjoint for unbounded Hamiltonians is addressed, with new results.
| A Characterization of the Compound-Exponential Type Distributions
Hwang, Tea-Yuan; Hu, Chin-Yuan
In this paper, a fixed point equation of the compound-exponential type distributions is derived, and under some regular conditions, both the existence and uniqueness of this fixed point equation are investigated. A question posed by Pitman and Yor can be partially answered by using our approach.
| A Semiregularity Map Annihilating Obstructions to Deforming Holomorphic Maps
Iacono, Donatella
We study infinitesimal deformations of holomorphic maps of compact, complex, Kähler manifolds. In particular, we describe a generalization of Bloch's semiregularity map that annihilates obstructions to deform holomorphic maps with fixed codomain.
| Some Properties Associated with Adequate Transversals
Kong, Xiangjun
In this paper, another relationship between the quasi-ideal adequate transversals of an abundant semigroup is given. We introduce the concept of a weakly multiplicative adequate transversal and the classic result that an adequate transversal is multiplicative if and only if it is weakly multiplicative and a quasi-ideal is obtained. Also, we give two equivalent conditions for an adequate transversal to be weakly multiplicative. We then consider the case when $I$ and $\Lambda$ (defined below) are bands. This is analogous to the inverse transversal if the regularity condition is adjoined.
| On the Adjoint and the Closure of the Sum of Two Unbounded Operators
Mortad, Mohammed Hichem
We prove, under some conditions on the domains, that the adjoint of the sum of two unbounded operators is the sum of their adjoints in both Hilbert and Banach space settings. A similar result about the closure of operators is also proved. Some interesting consequences and examples "spice up" the paper.
| On the Canonical Solution of the Sturm-Liouville Problem with Singularity and Turning Point of Even Order
Neamaty, A.; Mosazadeh, S.
In this paper, we are going to investigate the canonical property of solutions of systems of differential equations having a singularity and turning point of even order. First, by a replacement, we transform the system to the Sturm-Liouville equation with turning point. Using of the asymptotic estimates provided by Eberhard, Freiling, and Schneider for a special fundamental system of solutions of the Sturm-Liouville equation, we study the infinite product representation of solutions of the systems. Then we transform the Sturm-Liouville equation with turning point to the equation with singularity, then we study the asymptotic behavior of its solutions. Such representations are relevant to the inverse spectral problem.
| Erratum: Cartan Subalgebras of $\mathrm{gl}_\infty$
Neeb, K. H.; Penkov, I.
We correct an oversight in the the paper Cartan Subalgebras of $\mathrm{gl}_\infty$, Canad. Math. Bull. 46(2003), no. 4, 597-616. doi: 10.4153/CMB-2003-056-1
| Simple Helices on Fano Threefolds
Polishchuk, A.
Building on the work of Nogin, we prove that the braid group $B_4$ acts transitively on full exceptional collections of vector bundles on Fano threefolds with $b_2=1$ and $b_3=0$. Equivalently, this group acts transitively on the set of simple helices (considered up to a shift in the derived category) on such a Fano threefold. We also prove that on threefolds with $b_2=1$ and very ample anticanonical class, every exceptional coherent sheaf is locally free.
| On the Dichotomy of the Evolution Families: A Discrete-Argument Approach
Preda, Ciprian; Sipos, Ciprian
We establish a discrete-time criteria guaranteeing the existence of an exponential dichotomy in the continuous-time behavior of an abstract evolution family. We prove that an evolution family ${\cal U}=\{U(t,s)\}_{t \geq s\geq 0}$ acting on a Banach space $X$ is uniformly exponentially dichotomic (with respect to its continuous-time behavior) if and only if the corresponding difference equation with the inhomogeneous term from a vector-valued Orlicz sequence space $l^\Phi(\mathbb{N}, X)$ admits a solution in the same $l^\Phi(\mathbb{N},X)$. The technique of proof effectively eliminates the continuity hypothesis on the evolution family (i.e., we do not assume that $U(\,\cdot\,,s)x$ or $U(t,\,\cdot\,)x$ is continuous on $[s,\infty)$, and respectively $[0,t]$). Thus, some known results given by Coffman and Schaffer, Perron, and Ta Li are extended.
| On the Horizontal Monotonicity of $|\Gamma(s)|$
Srinivasan, Gopala Krishna; Zvengrowski, P.
Writing $s = \sigma + it$ for a complex variable, it is proved that the modulus of the gamma function, $|\Gamma(s)|$, is strictly monotone increasing with respect to $\sigma$ whenever $|t| > 5/4$. It is also shown that this result is false for $|t| \leq 1$.
| Positive Definite Measures with Discrete Fourier Transform and Pure Point Diffraction
Strungaru, Nicolae
In this paper we characterize the positive definite measures with discrete Fourier transform. As an application we provide a characterization of pure point diffraction in locally compact Abelian groups.
| Cyclic Surgery Between Toroidal Surgeries
Teragaito, Masakazu
We show that there is an infinite family of hyperbolic knots such that each knot admits a cyclic surgery $m$ whose adjacent surgeries $m-1$ and $m+1$ are toroidal. This gives an affirmative answer to a question asked by Boyer and Zhang.
| A Note on Toric Varieties Associated with Moduli Spaces
Uren, James J.
In this note we give a brief review of the construction of a toric variety $\mathcal{V}$ coming from a genus $g \geq 2$ Riemann surface $\Sigma^g$ equipped with a trinion, or pair of pants, decomposition. This was outlined by J. Hurtubise and L.~C. Jeffrey. A. Tyurin used this construction on a certain collection of trinion decomposed surfaces to produce a variety $DM_g$, the so-called Delzant model of moduli space, for each genus $g.$ We conclude this note with some basic facts about the moment polytopes of the varieties $\mathcal{V}.$ In particular, we show that the varieties $DM_g$ constructed by Tyurin, and claimed to be smooth, are in fact singular for $g \geq 3.$
| Non-uniform Randomized Sampling for Multivariate Approximation by High Order Parzen Windows
Zhou, Xiang-Jun; Shi, Lei; Zhou, Ding-Xuan
We consider approximation of multivariate functions in Sobolev spaces by high order Parzen windows in a non-uniform sampling setting. Sampling points are neither i.i.d. nor regular, but are noised from regular grids by non-uniform shifts of a probability density function. Sample function values at sampling points are drawn according to probability measures with expected values being values of the approximated function. The approximation orders are estimated by means of regularity of the approximated function, the density function, and the order of the Parzen windows, under suitable choices of the scaling parameter.
| Erratum: The Duality Problem For The Class of AM-Compact Operators On Banach Lattices
Aqzzouz, Belmesnaoui
It is proved that if a positive operator $S: E \rightarrow F$ is AM-compact whenever its adjoint $S': F' \rightarrow E'$ is AM-compact, then either the norm of F is order continuous or $E'$ is discrete.
| Kiguradze-type Oscillation Theorems for Second Order Superlinear Dynamic Equations on Time Scales
Baoguo, Jia; Erbe, Lynn; Peterson, Allan
Consider the second order superlinear dynamic equation \begin{equation*} (*)\qquad x^{\Delta\Delta}(t)+p(t)f(x(\sigma(t)))=0\tag{$*$} \end{equation*} where $p\in C(\mathbb{T},\mathbb{R})$, $\mathbb{T}$ is a time scale, $f\colon\mathbb{R}\rightarrow\mathbb{R}$ is continuously differentiable and satisfies $f'(x)>0$, and $xf(x)>0$ for $x\neq 0$. Furthermore, $f(x)$ also satisfies a superlinear condition, which includes the nonlinear function $f(x)=x^\alpha$ with $\alpha>1$, commonly known as the Emden--Fowler case. Here the coefficient function $p(t)$ is allowed to be negative for arbitrarily large values of $t$. In addition to extending the result of Kiguradze for \eqref{star1} in the real case $\mathbb{T}=\mathbb{R}$, we obtain analogues in the difference equation and $q$-difference equation cases.
| Stability of Real $C^*$-Algebras
Boersema, Jeffrey L.; Ruiz, Efren
We will give a characterization of stable real $C^*$-algebras analogous to the one given for complex $C^*$-algebras by Hjelmborg and Rørdam. Using this result, we will prove that any real $C^*$-algebra satisfying the corona factorization property is stable if and only if its complexification is stable. Real $C^*$-algebras satisfying the corona factorization property include AF-algebras and purely infinite $C^*$-algebras. We will also provide an example of a simple unstable $C^*$-algebra, the complexification of which is stable.
| Lightness of Induced Maps and Homeomorphisms
Camargo, Javier
An example is given of a map $f$ defined between arcwise connected continua such that $C(f)$ is light and $2^{f}$ is not light, giving a negative answer to a question of Charatonik and Charatonik. Furthermore, given a positive integer $n$, we study when the lightness of the induced map $2^{f}$ or $C_n(f)$ implies that $f$ is a homeomorphism. Finally, we show a result in relation with the lightness of $C(C(f))$.
| Artinian and Non-Artinian Local Cohomology Modules
Dibaei, Mohammad T.; Vahidi, Alireza
Let $M$ be a finite module over a commutative noetherian ring $R$. For ideals $\mathfrak{a}$ and $\mathfrak{b}$ of $R$, the relations between cohomological dimensions of $M$ with respect to $\mathfrak{a}, \mathfrak{b}$, $\mathfrak{a}\cap\mathfrak{b}$ and $\mathfrak{a}+ \mathfrak{b}$ are studied. When $R$ is local, it is shown that $M$ is generalized Cohen-Macaulay if there exists an ideal $\mathfrak{a}$ such that all local cohomology modules of $M$ with respect to $\mathfrak{a}$ have finite lengths. Also, when $r$ is an integer such that $0\leq r< \dim_R(M)$, any maximal element $\mathfrak{q}$ of the non-empty set of ideals $\{\mathfrak{a} : \textrm{H}_\mathfrak{a}^i(M) $ is not artinian for some $ i, i\geq r \}$ is a prime ideal, and all Bass numbers of $\textrm{H}_\mathfrak{q}^i(M)$ are finite for all $i\geq r$.
| Mixed Norm Type Hardy Inequalities
Fiorenza, Alberto; Gupta, Babita; Jain, Pankaj
Higher dimensional mixed norm type inequalities involving certain integral operators are characterized in terms of the corresponding lower dimensional inequalities.
| An Extension of Craig's Family of Lattices
Flores, André Luiz; Interlando, J. Carmelo; Neto, Trajano Pires da Nóbrega
Let $p$ be a prime, and let $\zeta_p$ be a primitive $p$-th root of unity. The lattices in Craig's family are $(p-1)$-dimensional and are geometrical representations of the integral $\mathbb Z[\zeta_p]$-ideals $\langle 1-\zeta_p \rangle^i$, where $i$ is a positive integer. This lattice construction technique is a powerful one. Indeed, in dimensions $p-1$ where $149 \leq p \leq 3001$, Craig's lattices are the densest packings known. Motivated by this, we construct $(p-1)(q-1)$-dimensional lattices from the integral $\mathbb Z[\zeta _{pq}]$-ideals $\langle 1-\zeta_p \rangle^i \langle 1-\zeta_q \rangle^j$, where $p$ and $q$ are distinct primes and $i$ and $j$ are positive integers. In terms of sphere-packing density, the new lattices and those in Craig's family have the same asymptotic behavior. In conclusion, Craig's family is greatly extended while preserving its sphere-packing properties.
| Norm One Idempotent $cb$-Multipliers with Applications to the Fourier Algebra in the $cb$-Multiplier Norm
Forrest, Brian E.; Runde, Volker
For a locally compact group $G$, let $A(G)$ be its Fourier algebra, let $M_{cb}A(G)$ denote the completely bounded multipliers of $A(G)$, and let $A_{\mathit{Mcb}}(G)$ stand for the closure of $A(G)$ in $M_{cb}A(G)$. We characterize the norm one idempotents in $M_{cb}A(G)$: the indicator function of a set $E \subset G$ is a norm one idempotent in $M_{cb}A(G)$ if and only if $E$ is a coset of an open subgroup of $G$. As applications, we describe the closed ideals of $A_{\mathit{Mcb}}(G)$ with an approximate identity bounded by $1$, and we characterize those $G$ for which $A_{\mathit{Mcb}}(G)$ is $1$-amenable in the sense of B. E. Johnson. (We can even slightly relax the norm bounds.)
| Admissible Sequences for Twisted Involutions in Weyl Groups
Haas, Ruth; G. Helminck, Aloysius
Let $W$ be a Weyl group, $\Sigma$ a set of simple reflections in $W$ related to a basis $\Delta$ for the root system $\Phi$ associated with $W$ and $\theta$ an involution such that $\theta(\Delta) = \Delta$. We show that the set of $\theta$-twisted involutions in $W$, $\mathcal{I}_{\theta} = \{w\in W \mid \theta(w) = w^{-1}\}$ is in one to one correspondence with the set of regular involutions $\mathcal{I}_{\operatorname{Id}}$. The elements of $\mathcal{I}_{\theta}$ are characterized by sequences in $\Sigma$ which induce an ordering called the Richardson-Springer Poset. In particular, for $\Phi$ irreducible, the ascending Richardson-Springer Poset of $\mathcal{I}_{\theta}$, for nontrivial $\theta$ is identical to the descending Richardson-Springer Poset of $\mathcal{I}_{\operatorname{Id}}$.
| Quasi-isometry and Plaque Expansiveness
Hammerlindl, Andy
We show that a partially hyperbolic diffeomorphism is plaque expansive (a form of structural stability for its center foliation) if the strong stable and unstable foliations are quasi-isometric in the universal cover. In particular, all partially hyperbolic diffeomorphisms on the 3-torus are plaque expansive.
| $2$-Local Isometries on Spaces of Lipschitz Functions
Jiménez-Vargas, A.; Villegas-Vallecillos, Moisés
Let $(X,d)$ be a metric space, and let $\mathop{\textrm{Lip}}(X)$ denote the Banach space of all scalar-valued bounded Lipschitz functions $f$ on $X$ endowed with one of the natural norms $ \| f\| =\max \{\| f\| _\infty ,L(f)\}$ or $\|f\| =\| f\| _\infty +L(f), $ where $L(f)$ is the Lipschitz constant of $f.$ It is said that the isometry group of $\mathop{\textrm{Lip}}(X)$ is canonical if every surjective linear isometry of $\mathop{\textrm{Lip}}(X) $ is induced by a surjective isometry of $X$. In this paper we prove that if $X$ is bounded separable and the isometry group of $\mathop{\textrm{Lip}}(X)$ is canonical, then every $2$-local isometry of $\mathop{\textrm{Lip}}(X)$ is a surjective linear isometry. Furthermore, we give a complete description of all $2$-local isometries of $\mathop{\textrm{Lip}}(X)$ when $X$ is bounded.
| Stratified Subcartesian Spaces
Lusala, Tsasa; Śniatycki, Jędrzej
We show that if the family $\mathcal{O}$ of orbits of all vector fields on a subcartesian space $P$ is locally finite and each orbit in $\mathcal{O}$ is locally closed, then $\mathcal{O}$ defines a smooth Whitney A stratification of $P$. We also show that the stratification by orbit type of the space of orbits $M/G$ of a proper action of a Lie group $G$ on a smooth manifold $M$ is given by orbits of the family of all vector fields on $M/G$.
| Nonconstant Continuous Functions whose Tangential Derivative Vanishes along a Smooth Curve
Moonens, Laurent
We provide a simple example showing that the tangential derivative of a continuous function $\phi$ can vanish everywhere along a curve while the variation of $\phi$ along this curve is nonzero. We give additional regularity conditions on the curve and/or the function that prevent this from happening.
| Symplectic Lie-Rinehart-Jacobi Algebras and Contact Manifolds
Okassa, Eugène
We give a characterization of contact manifolds in terms of symplectic Lie-Rinehart-Jacobi algebras. We also give a sufficient condition for a Jacobi manifold to be a contact manifold.
| Auerbach Bases and Minimal Volume Sufficient Enlargements
Ostrovskii, M. I.
Let $B_Y$ denote the unit ball of a normed linear space $Y$. A symmetric, bounded, closed, convex set $A$ in a finite dimensional normed linear space $X$ is called a sufficient enlargement for $X$ if, for an arbitrary isometric embedding of $X$ into a Banach space $Y$, there exists a linear projection $P\colon Y\to X$ such that $P(B_Y)\subset A$. Each finite dimensional normed space has a minimal-volume sufficient enlargement that is a parallelepiped; some spaces have ``exotic'' minimal-volume sufficient enlargements. The main result of the paper is a characterization of spaces having ``exotic'' minimal-volume sufficient enlargements in terms of Auerbach bases.
| The Infimum in the Metric Mahler Measure
Samuels, Charles L.
Dubickas and Smyth defined the metric Mahler measure on the multiplicative group of non-zero algebraic numbers. The definition involves taking an infimum over representations of an algebraic number $\alpha$ by other algebraic numbers. We verify their conjecture that the infimum in its definition is always achieved, and we establish its analog for the ultrametric Mahler measure.
| On the Distribution of Irreducible Trinomials
Shparlinski, Igor E.
We obtain new results about the number of trinomials $t^n + at + b$ with integer coefficients in a box $(a,b) \in [C, C+A] \times [D, D+B]$ that are irreducible modulo a prime $p$. As a by-product we show that for any $p$ there are irreducible polynomials of height at most $p^{1/2+o(1)}$, improving on the previous estimate of $p^{2/3+o(1)}$ obtained by the author in 1989.
| Cancellation of Cusp Forms Coefficients over Beatty Sequences on $\textrm{GL}(m)$
Sun, Qingfeng
Let $A(n_1,n_2,\dots,n_{m-1})$ be the normalized Fourier coefficients of a Maass cusp form on $\textrm{GL}(m)$. In this paper, we study the cancellation of $A (n_1,n_2,\dots,n_{m-1})$ over Beatty sequences.


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The 5 x 7' slate X-Drop Background System from Westcott is a lightweight package that is good for travel. This kit can be used for headshots, product photography, weddings or general commercial photography in the studio or on location. The 100% polyester fabric comes with grommet holes on the top and bottom, making for easy hanging and eliminating the need to establish a top or bottom orientation. When it gets dirty, it's readily machine washable in cold water and tumble dried on "low".
The background support stand contains telescoping arms and legs and is characterized by quick setup and tear down capability. It's lightweight and will hold the fabric taut. The expandable carrying case is capable of holding the X-Drop System as well as up to three backdrops.
|5.0 x 7.0' (1.5 x 2.1 m)
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Best of...
If you want to take home the pot on this Shoot Out - enter your best images ~ of any type or subject.
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Hoops for Hope Gala
The Petersen Events Center at the University of Pittsburgh served as more than just an athletic arena when it played host to the inaugural Hoops for Hope Gala. Pittsburgh Coaches vs. Cancer, comprised of the six Division I college basketball coaches in the region and 350 American Cancer Society patrons gathered in their best black-tie attire to support the Society's mission to increase funding for cancer research. The event raised more than $200,000 — double the projected sum of $100,000. Photography by David Bachman.Read More


text:
Kingdom, The (US - BD RA)
Gabe takes a belated look at this Jamie Foxx and Jennifer Garner political thriller
FBI special agent and loving family man Ronald Fleury (Jamie Foxx) leads an elite team into Saudi Arabia to find the terrorists who attacked American employees working in the Middle East, including one of his best friends. Fleury and his team, including forensics expert Janet Mayes (Jennifer Garner), explosives guru Grant Sykes (Chris Cooper), and intelligence analyst Adam Leavitt (Jason Bateman), are now in hostile territory, and are given a five day deadline. Their only real assistance comes from their Saudi liaison, Colonel Faris Al Ghazi (Ashraf Barhom), who proves a valuable ally in the war ahead.
To call The Kingdom a generic political thriller would be a bit unfair of me, but it's not the same as calling it a bad political thriller. The Kingdom is kind of generic, with its current events espionage, its ever roving camera, its deathly serious tone, its 'stuff blowing up' scenes. It's actually very much like a Paul Greengrass/Ridley Scott inspired Jack Ryan movie, only Jack Ryan (Jason Bateman's character) isn't really the lead protagonist, Mr. Serious FBI Guy is (Jamie Foxx's character). There is more to it than that, of course, but as far as memorability goes, that's how it's gonna go down for most viewers.
The script is a standard model, with some less than successful character moments (though there's a nice nighttime ritual montage smack in the middle of the film), but the mystery solving bits are above average. For his part director Peter Berg keeps the pacing expeditious and tight (minus one really bad cut-away during the opening). There is a thick sense of tenseness throughout the film that loosens a bit (ironically enough) when the threat becomes more tangible. Berg is careful enough to avoid too much heavy handed patriotism, and also plays it safe with the Saudi stereotypes, which is preferable, but prevents that gut tickling reaction broad war movies sometimes ensure. The hands get a little heavier at the very end when the film's moral rears its little head. Still, it all feels pretty authentic, at least until the show stopping later third where people start shooting and throwing grenades at each other.
As Berg's style has developed throughout his films, it has become very assured and exciting, but it's really starting to look a little too much like another Tony and Ridley Scott clone. A lot about The Kingdom looks a lot like Black Hawk Down. He's also started over-cutting his action, something he deftly avoided with his underrated action comedy The Rundown. Still, Berg is a solid storyteller, and his skills, along with some good actors, inevitably overcomes what amounts to a pretty average script.
Director Peter Berg and his DP Mauro Fiore mostly aim for a hyper-realistic look, which ends up being a nice workout for the Blu-ray's hi-def abilities. The lighting is often dulled, or entirely source based, so the transfer can't hide behind stylized colours, or high contrast light and dark play. Indoor and nighttime sequences aren't going to impress most giant TV owners, but the general lack of grain and noise is pretty impressive. Details aren't mind blowing, but surely sharper than standard definition. The daytime scenes are beautifully bright and blown-out, featuring sharper details, and some cool Scott-esque high contrast black bits floating about. Still, the look is very realist, and even the daylight scenes are duller in colour than many of us may have come to expect from the format.
The Kingdom sounds fantastic in 5.1 channels of DTS-HD Master Audio goodness. The surround channel extras get a little bit silly with filler, but post-bombing there would be a lot of construction noise, and it's reasonably realistic. Through all the noise of life (which is quite immersive, don't get me wrong) the dialogue track is consistently understandable, without losing a realistic volume in the mix. The movie's big car chase and guns action scene is pretty much reference level stuff. The guns all have their own special sound, locations of carnage is never in question (audibly at least), and the explosions burst with bassy goodness. Danny Elfman's score is atrociously mawkish, and sounds as if it were made-for-TV on a budget. It may be the worst score in the composer's entire collection.
We begin with Peter Berg's commentary track. Berg isn't a rapid fire speaker, but he chooses his words well, and his thoughts on the film are generally intriguing, so long as he's not just talking about how great his cast and crew are. Berg addresses some of his critics with grace, and makes some good suggestions for further viewing, including a mention of Hany Abu-Assad's incendiary Paradise Now. The director runs out of steam pretty early, but overall it's a solid track.
The Universal U-Control options are mostly unwatchable on my Profile 1.0 player, including the PiP option and the 'Mission Dossier: Surveillance' option. Fortunately, the 'Surveillance' option shows up elsewhere on the disc. The standard Mission Dossier is a text based option that states both pointless facts about the in-film mission, and interesting facts about the real Saudi Arabia. The 'Character by Character' option during the shoot-out allows the viewer to watch the entire scene, unedited, from four different points of view.
Next up is a selection of deleted scenes, presented in hi-def video, but stereo sound. There is unfortunately no menu option for the scenes, they play as a reel. Fortunately the reel is divided into chapters. Most of the scenes would be better described as extended rather than deleted, and total about eleven minutes.
'Constructing the Freeway Sequence' is a hi-def look at the films biggest action scene. The featurette is made up of interview footage on and off the set, a computer generated pre-viz, a toy car test, footage of a cheaper cars being destroyed as tests, behind the scenes footage, and, of course, footage from the final scene. The whole thing runs about 18 minutes.
'Creating the Kingdom' is an eight part featurette, with a nice 'play all' option sitting at the top of the menu. The doc mostly consists of on-set, and post film interviews, but it also runs down the early stages of pre-production. The raw set footage is well cut with the final product footage, and all in all the doc has good pace when watched in a clump. As an ex-Arizonian it's fun to recall landmarks from around the sets during the set production section. In all the featurettes run about thirty-five minutes.
'History of The Kingdom' is an interactive timeline option, running the history of modern Saudi Arabia all the way back to 1932. This starts as a mostly text based extra, but there is news footage included later in the timeline. Here viewers will find some valuable information about one of the most interesting and volatile international relationships in American history.
The disc finishes out with the 'Mission Dossier: Surveillance' option I couldn't get to work during U-Control. Surprisingly no trailers can be found anywhere on the disc.
Despite some exceedingly generic trailers The Kingdom manages to satisfy most of my political thriller needs, and I regret not seeing it earlier. It's not a memorable movie, but it's quite entertaining, and actor turned director Peter Berg continues proving his talents, even if his imagery is a bit on the cribbed side this time around. The Blu-ray disc meets expectations on an audio/visual level, and even features a few fun extras not found on the original DVD release.
*Note: The images on this page are not representative of the Blu-ray release.
Review by Gabriel Powers
Mr.White Member Join Date: November 2005 Location: United States Posts: 143
Great Review, I'll have to finally give this a watch.
Fabricio De Zuasnabar Member Join Date: July 2005 Location: United States Posts: 1,350
this isnt one of the best movies... not even on my top list... but sure it's a good one...
nice review
nice review
bored Member Join Date: May 2008 Location: Bahrain Posts: 59
the score is his worst in my opinion. he's my hero and it hurts to say that but it was a disapointing score.
but he bounced back though, I still think Hellboy 2 is one of his finest even if I'm the only soul in the world that thinks so
but he bounced back though, I still think Hellboy 2 is one of his finest even if I'm the only soul in the world that thinks so
Under 17 requires accompanying parent or adult guardian
Disc Details
Release Date: 25th November 2008
Discs: 1
Disc Type: Blu-ray Disc
RCE: No
Video: 1080p
Aspect: 2.35:1
Anamorphic: No
Colour: Yes
Audio: DTS-HD Master Audio 5.1 English, DTS 5.1 French, DTS 5.1 Spanish
Subtitles: English SDH, French, Spanish, Portuguese
Extras: Director Commentary, U-Control Options, Deteleted Scenes, 'Constructing the Freeway Sequence', 'Creating the Kingdom', 'History of the Kingdom', 'Mission Dossier: Surveillance'
Easter Egg: No
Feature Details
Director: Peter Berg
Cast: Jamie Foxx, Chris Cooper, Jennifer Garner, Jason Bateman, Ashraf Barhom
Genre: Action and Thriller
Length: 110 minutes
6Review Guide
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Steady job growth boosts US consumer confidence despite economy's slowdown
WASHINGTON – Strong job growth lifted U.S. consumer confidence this month, as Americans looked past the economy's dismal first quarter performance.
The University of Michigan says that its index of consumer sentiment rose slightly to 82.5 in June from 81.9 in May. That is still below April's reading of 84.1, which had been the highest in almost a year.
The reading suggests consumers shrugged off the economy's first quarter contraction. Still, the survey was conducted before the government said the economy shrank much more than previously estimated, at an annual rate of 2.9 percent rather than 1 percent.
And better confidence hasn't yet translated into more spending.
Steady hiring is improving American's finances, the survey found. Forty percent of respondents said their finances had improved in June, the most in seven years.


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Phone: 601-923-1688 EXT - 1688Email: firstname.lastname@example.com
Dr. Elias dos Santos Medeiros has been an ordained minister of the Gospel since January 1975. While in Brazil he worked in pioneer church planting in the Amazon region and in Recife (rural and urban). He also taught at several theological institutions in Brazil, including the Presbyterian Seminary of the North, and was Dean at the Evangelical Missions Center. He is a member of the Lausanne Global Diaspora Network Advisory Board and of the Brazilian Evangelical Diaspora movement. In addition to numerous articles and essays, he has written Teaching Them to Make Disciples of All Nations (D.Min), Missiology as an Academic Discipline in Theological Education (D.Miss), and The Reformers' Commitment to the Propagation of the Gospel to all Nations from 1555 to 1654 (Ph.D). Dr. Medeiros is deeply committed to evangelism through every member of the body of Christ. He has published: Evangelização e Ministério Pastoral (Evangelization and Pastoral Ministry)
Listen to a Fall 2014 Chapel Message by Dr. Medeiros, from Matthew 4:12-17, entitled Don't Waste Your Theo-graphy.
Whether you're a prospective student, current student, alumnus, donor, or friend of RTS, we would love to hear from you.


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GRAHAM � The Alamance County Board of Commissioners could get a new chairman on Monday.
The board is scheduled to elect a new chair and vice-chair during its regular December morning meeting. Commissioner Tom Manning currently serves as chair while Commissioner Bill Lashley serves as vice-chair.
Commissioners Tim Sutton and Bill Lashley said Friday they plan to nominate Commissioner David Smith to serve as the next chairman. Once a person is nominated, then a formal vote is taken by the board on whether to elect the nominee.
Smith said Friday he would be willing to serve as the next chair. Commissioner Linda Massey said Friday she would not support Smith�s nomination for chairman.
�I will not vote for him,� Massey said.
Sutton said at first he planned to support Manning to continue as chair before he realized that Smith was interested in the job. Sutton said he plans to support Smith becoming chair because he believes that while they don�t agree about everything, their political views are more aligned.
Lashley said he doesn�t plan to support Manning to continue to serve as chair because he believed Manning was too liberal. Lashley said he would like to continue to serve as vice-chair.
Smith and Sutton said they supported Lashley�s bid to continue as vice-chair. Massey said she didn�t care either way about Lashley serving another year as vice-chair.
Several messages were left with Manning on Friday by the Times-News regarding the issue with no response.
ANOTHER ISSUE BEING considered by the board Monday is a proposed ordinance �prohibiting the carrying of deadly weapons in Alamance County buildings, and permitting the posting of signs to prohibit the carrying of deadly weapons in Alamance County buildings.�
On Nov. 18, Sheriff Terry Johnson advised the commissioners regarding recent incidents in which customers paying their taxes carried handguns strapped on their sides into the tax office.
Johnson said the incidents scared the county employees working in the tax office, and he sought direction from the commissioners on how to proceed on increasing security.
The county�s current policy prohibits the public from carrying concealed weapons into all county buildings. There is no current county ordinance against carrying guns openly into county buildings.
Since the board meeting Nov. 18, a proposed ordinance was drafted by County Attorney Clyde Albright to be considered by board.
The proposed ordinance states, �Concealed or Open Carrying of deadly weapons, as they are defined in NCGS 14-269, in or on Alamance County buildings now or hereafter owned, leased, as lessee, operated, occupied, managed, or controlled by Alamance County is prohibited.�
Sutton, Lashley, Smith and Massey said Friday they don�t plan to support the proposed ordinance. Manning was not available for comment.
Sutton called the decision by the county to draft the proposed ordinance a �knee-jerk reaction� and that those individuals who carried firearms openly strapped to their sides into the tax office had done nothing wrong. Sutton said also that he would like to see the county allow people to carry concealed firearms into county buildings, a practice currently prohibited by the county.
Lashley said he had received at least 100 emails from the public regarding the issue. Lashley said he, too, would like to see the county reverse course and allow concealed firearms along with open firearms to be carried into county buildings.
Smith said he believed the public has a �right� to be allowed to carry weapons openly, and that he didn�t want to �tinker with the Second Amendment.�
The board meeting is scheduled to be held at 9 a.m. Monday at 124 W. Elm St. in Graham.


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|Home Software category Just in softwares Submit a program Contact us
Home > Others::Others > ZSKSoft Synchronizer 2.2
ZSKSoft Synchronizer 2.2
Intellectual folder synchronizer between laptop, remote computer, FTP, etc.Company: ZSKSoft Lab
Platform: Win95,Win98,WinME,WinXP,WinNT 4.x,Windows2000,Windows2003
Size: 1549 KB
Price: USD $39.95
Release Date: 2005-05-12
Screenshot: http://www.zsksoft.com/Images/zsync-screenshot.gif
Category: Others::Others
Intellectual folder synchronizer that monitors actual changes. Efficient: supports regular folders, laptop, remote computer, FTP, etc. Clearly displays current state, what has changed, and what action is suggested - displaying the action buttons in the corresponding places. Accurate: highlights suspicious changes, prevents conflicts. Convenient: unnecessary files can be simply dragged to the "off" category. Powerful. Reliable. Good-looking.
Related keywords:
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ZSKSoft Synchronizer Related Titles:Fix for Cisco VPN Client x64 3.6 - Cisco VPN Client Windows 8 and 10 Fix
Fix for Cisco VPN Client x64 3.6 - Cisco VPN Client Windows 8 and 10 Fix
iMyFone D-Port for Mac 2.0.0 - Selectively extract iPhone data and iTunes/iCloud backup to computer
Fort Myers video production 1.0 - Kean Eye Video Services are the premier Fort Myers video production.
Barcode Software 0.0.0.0 - Our Barcode helps to create barcode images and labels
Online Car Insurance Quotes 2.1 - There are many people that claim to have the inside scoop when it comes to...
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Things to do in vietnam - Aeon Mall 1.0 - Today I go visit a vietnamese shopping center called Aeon mall. Its the biggest.
Akumal Real Estate 3.0 - BuyPlaya Akumal - Your Real Estate Experts in the Riviera Maya.
Asset management Asia 3.0 - Asiya Investments is a premier Emerging Asia specialist investment firm...
Asset management Asia 3.0 - Asiya Investments is a premier Emerging Asia specialist investment firm...
We buy any car 2.0 - Keep an eye on your childrens internet activity with our FREE keylogger!
Audio & Multimedia Business Communications Desktop Development Education Dwg Converter Games & Entertainment Graphic Apps Home & Hobby Network & Internet News Security & Privacy Servers System Utilities Web Development Others
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text: Bunny Snuggle Comforter and Pram Blanket Set Bunny Snuggle Comforter and Pram Blanket Set Bunny Snuggle Comforter and Pram Blanket Set £30.00 Quantity: at £30.00 each Add To Basket The price is per item set ¨¨¨°º©©º°¨¨¨¨¨¨°º©©º°¨¨¨¨¨¨°º©©º°¨¨¨¨¨¨°º©©º°¨¨¨¨¨¨°º©©º° All our crocheted items are made using premium acrylic yarns. And poly stuffing which comply with EU and UK selling standards. *Spitspot animals are not toys, this item is (as are all my makes) a keepsake/collectors item, and would prefer to be treasured and looked at, rather than played with, though the eyes are fitted with saftey eyes and cannot be removed once put in place, no child should be left unsupervised with a bunny. These are made to order and shipping can take up to 7 working days. While we try to replicate the bunny exactly, it may differ slightly to the image in the listing, this is part of the handmade charm.* Text and images Copyright ©2016 by Spitspot Loves, all rights reserved. No pattern may be reproduced or distributed — mechanically, electronically, or by any other means, including photocopying, without written permission. Finished products created with this pattern may be used for commercial sale


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"Sex and the City" star Cynthia Nixon and partner Christine Marinoni are parents to a baby boy, Nixon's rep told People.
Marinoni, a 43-year-old education activist, gave birth to Max Ellington Nixon-Marinoni on Feb. 7, People reported.
"Christine and baby are doing great," Nixon's rep told the gossip mag.
The couple of six years announced their engagement at a rally in support gay marriage in New York in 2009, according to The Advocate.
Nixon, 44, has two children from a previous 15-year relationship with photographer Danny Mozes, according to the gay-interest magazine. Nixon and Mozes split in 2003.
Selected Reading: Advocate, People, Reuters


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8:30 pm
Idaho Reports Election Special 2012 "Ballot Measures" Host Greg Hahn explores issues surrounding propositions 1, 2 and 3 on the November ballot - the educational reform measures. State Superintendent Tom Luna, an opposition spokesperson, a panel of journalists, and political analyst Jim Weatherby put the questions in context.G
9:00 pm
Midsomer Murders "Judgement Day, Part 2" In a town still hoping to win the Perfect Village competition, DCI Barnaby finds there is no shortage of suspects for the pitchfork murder of a local thief and womanizer. Then too, there are the murders of two of the competition judges to solve. Part 2 of 2G
10:00 pm
Billy Connolly's Route 66 The Scottish comedian and actor begins in Chicago on his journey to the Pacific Coast along the storied route. He points out distinctive aspects of the Chicago Tribune Building, meets the Route 66 "Pie Man," sees Abraham Lincoln's home, and the Chain of Rocks bridge. He paces a horse-drawn carriage with his low-rider motor-trike at an Amish community. Part 1 of 4G
11:00 pm
Charlie Rose NULL


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Not All Asian People Are Tech Experts
You think you're living in the year "2011," when America has long since left its ugly legacy of racism behind, until you read something like this: companies are still using Asian people as "tech experts," in commercials. Free your minds!
This lengthy rundown of all the commercials recently starring Asian actors portraying technologically savvy employees is enough to make one choke on one's ironic "Chop Suey" dish. Are Asians supposed to feel better, just because the "martial arts expert" stereotype has been replaced with the "IT expert" stereotype? This AmeriKKKan mind sickness has gotten so strong that it's even infecting the Asian community itself, according to a recent study:
Result: Asian American consumers were more favorably disposed toward the tech products when they were endorsed by the Asian models. They also liked the non-tech products more when they were endorsed by Caucasian models.
A stereotype is no less insidious simply because some people perceive it to be positive. Stereotypes have the effect of making us judge others based on superfluous concerns, rather than the content of characters. Whether positive or negative, stereotypes throttle humanity's fundamental freedom of will; they wall us into preconceived worlds and stifle our imaginations; they erode the souls of both their subject and their object. It is no exaggeration to say that all stereotypes are tragedies.
Besides, those natural math skills could be used for engineering, teaching, architecture—any number of fields besides technology.


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Answers to your questions about diabetes mellitus
Editor's note: We asked Dr. Cook to address a few questions we've received from readers concerning diabetic regulation in their patients. Here are her responses.
Insulin resistance and infection
Q. What's the mechanism behind chronic infections causing insulin resistance?
How high is too high?
Q. I have a patient named Sandy who is a 10-year-old spayed female terrier mix. She was diagnosed with diabetes mellitus in November 2009. At the time, she was a slightly obese dog (BCS 6.5/9), but she is now 25 lb (BCS 5/9) and receiving 8 U NPH twice a day.
I have been monitoring her glucose concentrations (every seven to 10 days the first two times and then every three to four weeks), usually five to six hours after the morning insulin dose. According to the owner, Sandy does not have polyuria, polydipsia or polyphagia; does not have an urgency to urinate during the night; and is doing well in general. The last glucose concentration was 333 mg/dl, which, again, was measured five to six hours after the last insulin dose. Unfortunately, she is a very aggressive patient.
A glucose concentration of 333 mg/dl is still high, but I am hesitant to change the dose because of the owner's good subjective opinion about signs of glucose control and the dog's stable physical examination findings. Should I increase the insulin dose until the glucose concentration decreases, regardless of the clinical signs? Measuring a fructosamine concentration is not an option because of financial limitations. And I think performing a glucose curve in the clinic is not an option either. If I do not increase the insulin dose, will the dog have significant complications from having a glucose concentration higher than ideal?
A. I would not feel comfortable increasing an insulin dose based on a single glucose measurement. The reason for this is that you do not know what the true nadir (true lowest value) was, and there is a real risk of an overdose. In addition, it is always important to look at the whole patient for signs of good regulation or poor regulation. If the owner reports minimal clinical signs, and body weight is holding on target, then I would certainly not increase the insulin dose based on this one reading. This dog may be a good candidate for at-home monitoring, and it would be an inexpensive way to get a lot more information. Your client can review several great web resources.
Q. I have a feline patient with a glucose concentration of 409 mg/dl (measurement obtained four to six hours after the morning insulin dose) that is doing well according to the owner. Since this is a high concentration, should I increase the insulin dose?
A. With feline patients, glucose concentrations measured in the hospital are often a poor representation of glucose concentrations in the home. Stress can trigger massive sustained hyperglycemia in cats, so it is always important to look at the whole picture. Again, checking glucose concentrations at home is often a great option. Otherwise, I would look at clinical signs (including weight) and consider measuring a fructosamine concentration. If this is on target, you have good evidence of acceptable glycemic control.


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"Shell's world-wide LNG supply position and customer base means we are uniquely positioned to add value to Repsol's LNG portfolio, including through Shell's trading capabilities," said Chief Executive Officer Peter Voser. "By optimising the combined portfolios we will increase our ability to bring LNG to areas that need it the most, adding value for Shell, our partners and our customers."
The acquisition will add a new dynamic to Shell's portfolio, namely LNG capacity in the West Atlantic from Atlantic LNG in Trinidad & Tobago, and in the East Pacific from Peru LNG. These additions will complement Shell's existing LNG capacity in Africa, Asia, Australia, the Middle East and Russia. The acquisition should add some 7.2 million tonnes per annum (mtpa) of LNG volumes through long-term off-take agreements, including some 4 mtpa of equity LNG plant capacity.
Shell expects to add value to this portfolio by optimizing the new LNG flows in our world-wide customer base. Subject to successful completion, the new portfolio is expected to immediately provide additional cash flow to Shell, with limited on-going capital expenditure requirements.
The transaction, which has an effective date of 1 October 2012, is expected to close in the second half of 2013 or early 2014, subject to regulatory approvals and other conditions precedent.
Additional information:
Shell has agreed to acquire from several Repsol subsidiaries which own key LNG businesses of Repsol. Upon completion, after securing regulatory approvals and meeting other conditions precedent, the transaction will add:
a) Net 4.2 mtpa equity LNG plant capacity comprising:
- ALNG trains 1-4 14.6 mtpa capacity, on a 100% basis (20-25% equity per train); operated by Atlantic LNG Company of Trinidad and Tobago
- Peru LNG 4.45 mtpa capacity, on a 100% basis (acquisition: 20% equity; 100% offtake); operated by Peru LNG Company
- BBE power plant in Spain (25%, 800MW); operated by Bahía de Bizkaia Electricidad S.L.
- A fleet of LNG carriers, comprising both long term and short term time charters.
b) A material LNG marketing and trading operation, with 7.2 mtpa of LNG volumes through long-term off-take agreements.
c) As part of this agreement, Shell has committed to supply around 0.1 mtpa of LNG to Repsol's Canaport LNG terminal in Canada over a period of 10 years.
Shell Media Relations
International +44 207 934 5550
Americas +1 713 241 4544
Shell Investor Relations
International +31 70 377 4540
North America +1 713 241 1042
Cautionary note
The companies in which Royal Dutch Shell plc directly and indirectly owns investments are separate entities. In this announcement "Shell", "Shell Group" and "Royal Dutch Shell" are sometimes used for convenience where references are made to Royal Dutch Shell plc and its subsidiaries in general. Likewise, the words "we", "us" and "our" are also used to refer to subsidiaries in general or to those who work for them. These expressions are also used where no useful purpose is served by identifying the particular company or companies. "Subsidiaries", "Shell subsidiaries" and "Shell companies" as used in this announcement refer to companies in which Shell either directly or indirectly has control, by having either a majority of the voting rights or the right to exercise a controlling influence. The companies in which Shell has significant influence but not control are referred to as "associated companies" or "associates" and companies in which Shell has joint control are referred to as "jointly controlled entities". In this announcement, associates and jointly controlled entities are also referred to as "equity-accounted investments". The term "Shell interest" is used for convenience to indicate the direct and/or indirect (for example, through our 23 per cent shareholding in Woodside Petroleum Ltd.) ownership interest held by Shell in a venture, partnership or company, after exclusion of all third-party interest.
This announcement contains forward looking statements concerning the financial condition, results of operations and businesses of Shell and the Shell Group. All statements other than statements of historical fact are, or may be deemed to be, forward-looking statements. Forward-looking statements are statements of future expectations that are based on management's current expectations and assumptions and involve known and unknown risks and uncertainties that could cause actual results, performance or events to differ materially from those expressed or implied in these statements. Forward-looking statements include, among other things, statements concerning the potential exposure of Shell and the Shell Group to market risks and statements expressing management's expectations, beliefs, estimates, forecasts, projections and assumptions. These forward looking statements are identified by their use of terms and phrases such as "anticipate", "believe", "could", "estimate", "expect", "goals", "intend", "may", "objectives", "outlook", "plan", "probably", "project", "risks", "seek", "should", "target", "will" and similar terms and phrases. There are a number of factors that could affect the future operations of Shell and the Shell Group and could cause those results to differ materially from those expressed in the forward looking statements included in this announcement, including (without limitation): (a) price fluctuations in crude oil and natural gas; (b) changes in demand for Shell's products; (c) currency fluctuations; (d) drilling and production results; (e) reserves estimates; (f) loss of market share and industry competition; (g) environmental and physical risks; (h) risks associated with the identification of suitable potential acquisition properties and targets, and successful negotiation and completion of such transactions; (i) the risk of doing business in developing countries and countries subject to international sanctions; (j) legislative, fiscal and regulatory developments including regulatory measures addressing climate change; (k) economic and financial market conditions in various countries and regions; (l) political risks, including the risks of expropriation and renegotiation of the terms of contracts with governmental entities, delays or advancements in the approval of projects and delays in the reimbursement for shared costs; and (m) changes in trading conditions. All forward looking statements contained in this announcement are expressly qualified in their entirety by the cautionary statements contained or referred to in this section. Readers should not place undue reliance on forward looking statements. Additional factors that may affect future results are contained in Shell's 20-F for the year ended 31 December 2011 (available at www.shell.com/investor and www.sec.gov). These factors also should be considered by the reader. Each forward looking statement speaks only as of the date of this announcement, 26 February 2013. Neither Shell nor any of its subsidiaries nor the Shell Group undertake any obligation to publicly update or revise any forward looking statement as a result of new information, future events or other information. In light of these risks, results could differ materially from those stated, implied or inferred from the forward looking statements contained in this announcement.


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All pictures are under the ownership and copyright FirdausMahadi Photography. No photograph may be reproduced, downloaded, copied, stored, manipulated, or used whole or in part of a derivative work, without my permission. If you'd like to use one of my images for any reason, please contact me.
© FirdausMahadi Photography • captures the spiritual beauty of creation itself • All Rights Reserved
Aerial View
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Nearly three dozen homes evacuated after large landslide
Photo: AP
An aerial photo shows a landslide near Coupeville, Wash. on Whidbey Island, Wednesday, March 27, 2013. The slide severely damaged one home and isolated or threatened more than 30 on the island, about 50 miles north of Seattle in Puget Sound. No one was reported injured in the slide, which happened at about 4 a.m. Wednesday. (AP Photo/Ted S. Warren)


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product description
Related Products:
Rader, Michael, M.S.
Carbon Steel
Fixed Blade Knives
Work by Mastersmiths
Artisan Made
Carbon Steel - 52100
Chef Knives & Santoku
Integral Guard
Japanese/Asian Knives
Wood - Box Elder
Wood - Koa
Maker: Michael Rader, M.S. (click to see more by this maker)
Item num: 91676
*** This is handmade and one-of-a-kind ***Blade length: 10.50 in.Total length: 15.20 in.Blade height (at heel): 2.20 in.Blade thickness (near bolster): 0.10 in.Item weight: 10.15 oz.Blade: Marquenched, hand forged 52100 carbon steel for high performance edge retentionBolster: Integral 52100 carbon steel with G10 and copper spacersHandle: Curly mango with box elder burl accent and curly koa cap
Description: Michael Rader, who was honored as a Mastersmith June 2010, is best known for creating dramatic swords, daggers and chef's knives -- in each case with woodwork that is beyond compare. His understanding of chef's knives is exceptional and results in perfect balance and geometry.
The European chef's knife (known as a gyuto in Japan) is well suited for use as a general purpose knife in the kitchen -- from chopping, to slicing and dicing -- from fruits to vegetables and meats, the chef's knife is a great choice. The long blade is needed for the sawing motion required to cut meat and vegetables while the tall blade provides plenty of finger clearance when working over a cutting board.
The blade has been antiqued. This attractive finish helps prevent rust and makes the knife easy to maintain. The blade and bolster are formed from 52100 carbon steel. Many knifemakers and collectors feel that this steel is among the best steels currently used for knives due to its exceptional edge holding and sharpness. Because this knife is forged from carbon steel, we recommend using camellia oil to prevent rust. The bolster is integral -- a technique that, while common in production knives, is very rare in handmade knives due to the difficulty of implementation. Like his hunting knives, this chef's knife was pre-tested for edge flex and cutting ability before assembly.
The handle is formed from curly mango with lighter box elder burl and curly koa wood accents. By using stabilized woods, Michael is able to combine the beauty of natural wood with durability. Alternating copper and G10 spacers highlight warm tones in the natural wood. The knife has perfect balance and feels exceptional in the hand.
Availability: Not currently available