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Abstract In this paper, we discuss a method of constructing separable representations of the C ⁎ -algebras associated to strongly connected row-finite k -graphs Λ. We begin by giving an alternative characterization of the Λ-semibranching function systems introduced in an earlier paper, with an eye towards constructing such representations that are faithful. Our new characterization allows us to more easily check that examples satisfy certain necessary and sufficient conditions. We present a variety of new examples relying on this characterization. We then use some of these methods and a direct limit procedure to identify a faithful separable representation for any row-finite source-free k -graph. [ABSTRACT FROM AUTHOR]

This paper examines the Euler–Rodrigues formula in dual 3-space D 3 by analyzing its variations such as vectorial form, exponential map, point–line theory and quaternions which have some intrinsic relations. Contrary to the Euclidean case, dual rotation in dual 3-space corresponds to a screw motion in Euclidean 3-space. This paper begins by explaining dual motion in terms of the given dual axis and angle. It will then go on to express dual Euler–Rodrigues formula with algebraic methods. Furthermore, an application of dual Euler–Rodrigues formula to point–line geometry is accomplished and point–line displacement operator is obtained by dual Euler–Rodrigues formula. Finally, dual Euler–Rodrigues formula is presented with the help of dual Euler–Rodrigues parameters that is expressed as a dual quaternion. [ABSTRACT FROM AUTHOR]

In this paper we employ a C-algebra approach to the study of Fredholm properties of differential and pseudodifferential operators on the half line. The algebra investigated in this paper has compact commutators, so the Gelfand theory applies to the quotient algebra, and we obtain an explicit description of the corresponding maximal ideal space and necessary and sufficient conditions for Fredholmness of operators in the algebra. [ABSTRACT FROM AUTHOR]

The concept of a relatively weakly injective pair of operator systems is introduced and studied in this paper, motivated by relative weak injectivity in the C*-algebra category. E. Kirchberg [11] proved that the C\*-algebra C\*(F∞) of the free group F∞ on countably many generators characterises relative weak injectivity for pairs of C\*-algebras by means of the maximal tensor product. One of the main results of this paper shows that C\*(F∞) also characterises relative weak injectivity in the operator system category. A key tool is the theory of operator system tensor products [9,10]. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we extend the work of Kawamura, see [K. Kawamura, The Perron–Frobenius operators, invariant measures and representations of the Cuntz–Krieger algebras, J. Math. Phys. 46 (2005)], for Cuntz–Krieger algebras for infinite matrices A. We generalize the definition of branching systems, prove their existence for any given matrix A and show how they induce some very concrete representations of . We use these representations to describe the Perron–Frobenius operator, associated to a nonsingular transformation, as an infinite sum and under some hypothesis we find a matrix representation for the operator. We finish the paper with a few examples. [Copyright &y& Elsevier]

Abstract: In an earlier paper we extended Lai''s (1974) law of the single logarithm for delayed sums to a class of delayed sums of random fields. In this paper we allow for more general windows. [Copyright &y& Elsevier]

Abstract: Let X be a Banach space and Z a nonempty subset of X. Let be a lower semicontinuous function bounded from below and . This paper is concerned with the perturbed optimization problem of finding such that , which is denoted by . The notions of the J-strictly convex with respect to Z and of the Kadec with respect to Z are introduced and used in the present paper. It is proved that if X is a Kadec Banach space with respect to Z and Z is a closed relatively boundedly weakly compact subset, then the set of all for which every minimizing sequence of the problem has a converging subsequence is a dense -subset of , where is the set of all points such that z is a solution of the problem . If additionally and X is J-strictly convex with respect to Z, then the set of all for which the problem is well-posed is a dense -subset of . [Copyright &y& Elsevier]

Abstract: In this paper we complete a distributional Fourier analysis developed by Howell in a serie of papers. We investigate convolution operators in the corresponding distribution spaces. [Copyright &y& Elsevier]

Abstract: In this paper some new properties and applications of modified Chebyshev polynomials and Morgan–Voyce polynomials will be presented. The aim of the paper is to complete the knowledge about all of these types of polynomials. [Copyright &y& Elsevier]

Abstract: Let be a polynomial of degree 4 with four distinct real roots . Let be the critical points of p, and define the ratios , . For notational convenience, let , , and . is called the ratio vector of p. We prove necessary and sufficient conditions for to be a ratio vector of a polynomial of degree 4 with all real roots. Most of the necessary conditions were proven in an earlier paper. The main results of this paper involve using the theory of Groebner bases to prove that those conditions are also sufficient. [Copyright &y& Elsevier]

Abstract: In this paper and in a forthcoming one, we study difference equations in of the types which are linked to families of conics, cubics and quartics, respectively. These equations generalize Lyness'' one studied in several papers, whose behavior was completely elucidated in [G. Bastien, M. Rogalski, in press] through methods which are transposed in the present paper for the study of (1) and (2), and in the forthcoming one for (3). In particular we prove in the present paper a form of chaotic behavior for solutions of difference equations (1) and (2), and find all the possible periods for these solutions. [Copyright &y& Elsevier]

The paper presents a formula for the γ-interior of a set under special conditions for γ :expX→expX, more general than those in the previous paper [Acta Math. Hungar. 80 (1998) 89–93]. There are also some applications. [Copyright &y& Elsevier]

In this paper we investigate the behavior of powers of operators with spectrum contained in the Cantor sets. As consequence we show that the Cantor sets satisfy spectral synthesis in a large class of weighted Beurling algebras. [ABSTRACT FROM AUTHOR]

By a labeled graph C ⁎ -algebra we mean a C ⁎ -algebra associated to a labeled space ( E , L , E ) consisting of a labeled graph ( E , L ) and the smallest normal accommodating set E of vertex subsets. Every graph C ⁎ -algebra C ⁎ ( E ) is a labeled graph C ⁎ -algebra and it is well known that C ⁎ ( E ) is simple if and only if the graph E is cofinal and satisfies Condition (L). Bates and Pask extend these conditions of graphs E to labeled spaces, and show that if a set-finite and receiver set-finite labeled space ( E , L , E ) is cofinal and disagreeable, then its C ⁎ -algebra C ⁎ ( E , L , E ) is simple. In this paper, we show that the converse is also true. [ABSTRACT FROM AUTHOR]

Following Schachermayer, a subset B of an algebra A of subsets of Ω is said to have the N-property if a B -pointwise bounded subset M of b a ( A ) is uniformly bounded on A , where b a ( A ) is the Banach space of the real (or complex) finitely additive measures of bounded variation defined on A . Moreover B is said to have the strong N-property if for each increasing countable covering ( B m ) m of B there exists B n which has the N -property. The classical Nikodym–Grothendieck's theorem says that each σ -algebra S of subsets of Ω has the N-property . The Valdivia's theorem stating that each σ -algebra S has the strong N -property motivated the main measure-theoretic result of this paper: We show that if ( B m 1 ) m 1 is an increasing countable covering of a σ -algebra S and if ( B m 1 , m 2 , … , m p , m p + 1 ) m p + 1 is an increasing countable covering of B m 1 , m 2 , … , m p , for each p , m i ∈ N , 1 ⩽ i ⩽ p , then there exists a sequence ( n i ) i such that each B n 1 , n 2 , … , n r , r ∈ N , has the strong N -property. In particular, for each increasing countable covering ( B m ) m of a σ -algebra S there exists B n which has the strong N -property, improving mentioned Valdivia's theorem. Some applications to localization of bounded additive vector measures are provided. [ABSTRACT FROM AUTHOR]

In this paper we give a new characterization of when a Banach space E has the Schur property in terms of the disk algebra. We prove that E has the Schur property if and only if A ( D , E ) = A ( D , E w ) . [ABSTRACT FROM AUTHOR]

We investigate structural properties of the reduced cross-sectional algebra C r ⁎ ( B ) of a Fell bundle B over a discrete group G . Conditions allowing one to determine the ideal structure of C r ⁎ ( B ) are studied. Notions of aperiodicity, paradoxicality and B -infiniteness for the Fell bundle B are introduced and investigated by themselves and in relation to the partial dynamical system dual to B . Several criteria of pure infiniteness of C r ⁎ ( B ) are given. It is shown that they generalize and unify corresponding results obtained in the context of crossed products, by the following duos: Laca, Spielberg [34] ; Jolissaint, Robertson [21] ; Sierakowski, Rørdam [47] ; Giordano, Sierakowski [18] and Ortega, Pardo [39] . For exact, separable Fell bundles satisfying the residual intersection property primitive ideal space of C r ⁎ ( B ) is determined. The results of the paper are shown to be optimal when applied to graph C ⁎ -algebras. Applications to a class of Exel–Larsen crossed products are presented. [ABSTRACT FROM AUTHOR]

In this paper we consider the projection lifting from the corona algebra of C ( X ) ⊗ B where X is a compact, Hausdorff, finite dimensional space and B is either the algebra of compact operators on a separable infinite dimensional Hilbert space or a stable Kirchberg algebra whose multiplier algebra has real rank zero. Assuming a geometric condition on the projection, we suggest a new approach to the projection lifting using major classification results of continuous fields of C ⁎ -algebras. [ABSTRACT FROM AUTHOR]

A face of a convex polyhedral set can be investigated on the basis of only the maximal descriptor index set for it. This helps us reduce difficulties and computational efforts in solving many problems. In this paper, we consider a multiple objective linear programming (MOLP) problem in which the constraint polyhedron may have no extreme points and the variables may be negative. First we deal with determining the maximal descriptor index set for an arbitrary face of the constraint polyhedron, then we apply the maximal descriptor index sets for faces to compare descriptor sets for the faces and find all maximal efficient faces for the MOLP problem. The methods known so far compare descriptor sets at large computational cost (in terms of computing times and storage) because they require finding all extreme points and directions of them. Known top-down search methods have been devised to find the efficient set of the MOLP problem but they may fail to find all maximal efficient faces and the computational cost is considerable. We propose a new method to compare descriptor sets and a new top-down search method which finds all maximal efficient faces and requires less computational cost. A numerical example is given to illustrate how the method works. [ABSTRACT FROM AUTHOR]

In this paper, we prove that the Jordan–Kinderlehrer–Otto scheme for a family of linear parabolic equations on the flat torus converges uniformly in space. [ABSTRACT FROM AUTHOR]

In this paper, some Hardy and Rellich type inequalities on complete non-compact smooth metric measure spaces have been established. Moreover, based on the main results about the Hardy and Rellich type inequalities, several inequalities of the Hardy–Poincaré type or the Heisenberg–Pauli–Weyl type can also be given as byproducts. [ABSTRACT FROM AUTHOR]

When a locally compact group acts on a C ⁎ -correspondence, it also acts on the associated Cuntz–Pimsner algebra in a natural way. Hao and Ng have shown that when the group is amenable the Cuntz–Pimsner algebra of the crossed product correspondence is isomorphic to the crossed product of the Cuntz–Pimsner algebra. In this paper, we have a closer look at this isomorphism in the case where the group is not necessarily amenable. We also consider what happens at the level of Toeplitz algebras. [ABSTRACT FROM AUTHOR]

Generalized B\*-algebras (shortly, GB\*-algebras) are generalizations of C\*-algebras and belong to the class of abstract unbounded operator algebras. These algebras have interesting applications in mathematical physics and this gives a strong impetus for studying them. To our knowledge, up to now, there is nothing in the literature about tensor products of GB\*-algebras. For this reason, this paper is devoted to the investigation of this subject matter. [ABSTRACT FROM AUTHOR]

Abstract: This paper is devoted to derivations on the algebra of all measurable operators affiliated with a finite von Neumann algebra . We prove that if is a finite von Neumann algebra with a faithful normal semi-finite trace , equipped with the locally measure topology , then every -continuous derivation is inner. A similar result is valid for derivation on the algebra of -measurable operators equipped with the measure topology . [Copyright &y& Elsevier]

Abstract: Let be a locally compact group and . Let denote the Figà-Talamanca–Herz algebra and its pointwise multiplier algebra. In this paper, we shall introduce two new spaces of multipliers of , defined as coefficient functions of certain representations of on some interpolation couples. Then we shall show that, in the amenable case, the Fourier–Stieltjes algebra is dense in , and that , as an ordered space, is a complete invariant for . [Copyright &y& Elsevier]

Abstract: Let be a Hilbert space and be the algebra of all bounded linear operators on . In this paper we obtain a structure theorem of maps preserving the -Jordan-triple zero product on . Then this is applied to give a full characterization of a surjective map satisfying . [Copyright &y& Elsevier]

Abstract: In this paper, we continue to investigate the value distribution of some difference polynomials, which can be considered as difference counterparts of some classic results of Hayman. [Copyright &y& Elsevier]

Abstract: In this paper, we discuss the nonlinear functional spaces based on triangular conorms. Particularly, we discuss the properties of the upper-closures of the regular subspaces of the nonlinear functional space based on a continuous triangular conorm. Furthermore, we prove that with respect to a strict triangular conorm, a subset of the nonlinear functional space is an upper-complete normal subspace if and only if the family of all sets whose characteristic functionals are contained in the given subset of the nonlinear functional space is a sigma-algebra. [Copyright &y& Elsevier]

Abstract: In this paper, we prove that anisotropic homogeneous Besov spaces are gentle spaces, for all parameters and all anisotropies . Using the Littlewood–Paley decomposition, we study their completeness, separability, duality and homogeneity. We then define the notion of anisotropic orthonormal wavelet basis of , and we show that the homogeneous version of Triebel families of anisotropic orthonormal wavelet bases associated to the tensor product of Lemarié–Meyer (resp. Daubechies) wavelets are particular examples. We characterize the spaces using Lemarié–Meyer wavelets. In fact, we show that these bases will be either unconditional bases or unconditional -weak bases of , depending on whether is separable or not. By introducing an anisotropic version of the class of almost diagonal matrices related to anisotropic orthonormal wavelet bases, we prove that these spaces are stable under changes of anisotropic orthonormal wavelet bases. As a consequence, we extend the characterization of using Daubechies wavelets. [Copyright &y& Elsevier]

Abstract: The main aim of this paper is the investigation of conditions under which a locally convex quasi ⁎-algebra attains sufficiently many -continuous ⁎-representations in , to separate its points. Having achieved this, a usual notion of bounded elements on rises. On the other hand, a natural order exists on related to the topology τ, that also leads to a kind of bounded elements, which we call “order bounded”. What is important is that under certain conditions the latter notion of boundedness coincides with the usual one. Several nice properties of order bounded elements are extracted that enrich the structure of locally convex quasi ⁎-algebras. [Copyright &y& Elsevier]

Abstract: In this paper, the authors prove some inequalities for the generalized elliptic integrals with respect to Hölder means. [Copyright &y& Elsevier]

Abstract: In this paper we exploit the algebraic structure of the soliton equations and find solutions in terms of neutral free fermion particles. We show how pfaffians arise naturally in the fermionic approach to soliton equations. We write the τ-function for neutral free fermions in terms of pfaffians. Examples of how to get soliton, rational and dromion solutions from τ-functions for the various soliton equations are given. [Copyright &y& Elsevier]

Abstract: Toric degenerations of toric varieties and toric ideals are important both in theory and in applications. In this paper, we study the correspondence between degenerations of toric variety and of toric ideal when the weight admits a regular subdivision. [Copyright &y& Elsevier]

Abstract: In this paper, we present results on the existence of positive stationary solutions for a diffusive variable-territory prey–predator model in heterogeneous environment, which improve and extend those of Wang and Pang (2009). In addition, the asymptotic behavior of solutions is also analyzed. [Copyright &y& Elsevier]

Abstract: For Liénard systems , with and real polynomials of degree m and n respectively, in [H. Zoladek, Algebraic invariant curves for the Liénard equation, Trans. Amer. Math. Soc. 350 (1998) 1681–1701] the author showed that if and there always exist Liénard systems which have a hyperelliptic limit cycle. Llibre and Zhang [J. Llibre, Xiang Zhang, On the algebraic limit cycles of Liénard systems, Nonlinearity 21 (2008) 2011–2022] proved that the Liénard systems with and have no hyperelliptic limit cycles and that there exist Liénard systems with and which do have hyperelliptic limit cycles. So, it is still an open problem to characterize the Liénard systems which have an algebraic limit cycle in cases and . In this paper we will prove that there exist Liénard systems with and which have hyperelliptic limit cycles. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we establish some results relating star, left-star, right-star, minus ordering and the reverse order law under certain conditions on Moore–Penrose invertible elements of -algebras. [Copyright &y& Elsevier]

Abstract: In this paper, we try to attack a conjecture of Araujo and Jarosz that every bijective linear map θ between -algebras, with both θ and its inverse preserving zero products, arises from an algebra isomorphism followed by a central multiplier. We show it is true for CCR -algebras with Hausdorff spectrum, and in general, some special -algebras associated to continuous fields of -algebras. [Copyright &y& Elsevier]

Abstract: Fernández Sare and Rivera [H.D. Fernández Sare, J.E. Muñoz Rivera, Stability of Timoshenko systems with past history, J. Math. Anal. Appl. 339 (1) (2008) 482–502] considered the following Timoshenko-type system where g is a positive differentiable exponentially decaying function. They established an exponential decay result in the case of equal wave-speed propagation and a polynomial decay result in the case of nonequal wave-speed propagation. In this paper, we study the same system, for g decaying polynomially, and prove polynomial stability results for the equal and nonequal wave-speed propagation. Our results are established under conditions on the relaxation function weaker than those in [H.D. Fernández Sare, J.E. Muñoz Rivera, Stability of Timoshenko systems with past history, J. Math. Anal. Appl. 339 (1) (2008) 482–502]. [Copyright &y& Elsevier]

Abstract: Let be a polynomial of degree n and for any real or complex number α, let denote the polar derivative of the polynomial with respect to α. In this paper, we obtain inequalities for the polar derivative of a polynomial having all its zeros inside or outside a circle. Our results shall generalize and sharpen some well-known polynomial inequalities. [Copyright &y& Elsevier]

Abstract: This paper considers two problems on the Fock type spaces (). Firstly, it is shown that on the space (), the identity representation of is a boundary representation for the Banach subalgebra , while on the space , it is not. Secondly, it is shown that all the submodules of are rigid. [Copyright &y& Elsevier]

Abstract: Let and be polynomials of degree respectively n and less than n such that A result due to Q.I. Rahman states that In this paper, we slightly improve the above inequality and discuss several sharpness aspects, including all cases of equality. [Copyright &y& Elsevier]

Abstract: This paper concerns normed algebras whose product is free of the requirement of associativity. For these algebras, a very natural notion of spectrum is provided and basic spectral properties of (associative) Banach algebras are extended to this general non-associative setting. These results are applied to generalize Rickart''s dense-range homomorphism theorem. Our approach sheds some light on the classical associative theory. [Copyright &y& Elsevier]

Abstract: The self-affine measure corresponding to the expanding integer matrix is supported on the generalized three-dimensional Sierpinski gasket , where p is odd. In the present paper we show that there exist at most 7 mutually orthogonal exponential functions in . This generalizes the result of Dutkay and Jorgensen [D.E. Dutkay, P.E.T. Jorgensen, Analysis of orthogonality and of orbits in affine iterated function systems, Math. Z. 256 (2007) 801–823] on the non-spectral self-affine measure problem. By using the same method, we also obtain that for self-affine measure corresponding to the expanding integer matrix where p is odd, there exist at most 5 mutually orthogonal exponential functions in . [Copyright &y& Elsevier]

Abstract: Let be the set of all polynomials of degree n with all roots in the unit disk, and define to be the maximum of the distances from each of the roots of a polynomial P to that root''s nearest critical point. In this notation, Sendov''s conjecture asserts that is at most 1 for every P in . Define P in to be locally extremal if is at least for all nearby Q in . In this paper, we determine sufficient conditions for real polynomials of degree n with a root strictly between 0 and 1 and a real critical point of order to be locally extremal, and we use these conditions to find locally extremal polynomials of this form of degrees 8, 9, 12, 13, 14, 15, 19, 20, and 26. [Copyright &y& Elsevier]

Abstract: The self-affine measure associated with an iterated function system and a weight is uniquely determined. The problem of determining whether a self-affine measure is absolutely continuous or singular has been studied extensively in recent years. In the present paper we consider the singularity of certain self-affine measures. We obtain a sufficient condition for such measures being singular. Two applications of this result are given, which extend several known results in a simple manner. [Copyright &y& Elsevier]

Abstract: Let be a fractional Brownian motion of Hurst index with values in , and let be the local time process at zero of a strictly stable Lévy process of index independent of . The α-stable local time fractional Brownian motion is defined by . The process is self-similar with self-similarity index and is related to the scaling limit of a continuous time random walk with heavy-tailed waiting times between jumps [P. Becker-Kern, M.M. Meerschaert, H.P. Scheffler, Limit theorems for coupled continuous time random walks, Ann. Probab. 32 (2004) 730–756; M.M. Meerschaert, H.P. Scheffler, Limit theorems for continuous time random walks with infinite mean waiting times, J. Appl. Probab. 41 (2004) 623–638]. However, does not have stationary increments and is non-Gaussian. In this paper we establish large deviation results for the process . As applications we derive upper bounds for the uniform modulus of continuity and the laws of the iterated logarithm for . [Copyright &y& Elsevier]

Abstract: In this paper we establish the strong Fréchet differentiability of maps from the set of initial values and forcing terms into the set of solutions for semilinear second order evolution equations. Also, under the weaker conditions of nonlinear terms we establish the strong Gâteaux differentiability of the solution maps. An application of results to semilinear strongly damped wave equations is given. [Copyright &y& Elsevier]

Abstract: In this paper we obtain some characterizations of Besov spaces and α-Bloch spaces on the unit ball of , which extend some results in the settings of the unit disk. [Copyright &y& Elsevier]

Abstract: Let S be a pre-Hilbert space. We study quasi-splitting subspaces of S and compare the class of such subspaces, denoted by , with that of splitting subspaces . In [D. Buhagiar, E. Chetcuti, Quasi splitting subspaces in a pre-Hilbert space, Math. Nachr. 280 (5–6) (2007) 479–484] it is proved that if S has a non-zero finite codimension in its completion, then . In the present paper it is shown that if S has a total orthonormal system, then implies completeness of S. In view of this result, it is natural to study the problem of the existence of a total orthonormal system in a pre-Hilbert space. In particular, it is proved that if every algebraic complement of S in its completion is separable, then S has a total orthonormal system. [Copyright &y& Elsevier]

Abstract: The aim of this paper is to provide a new approach concerning the characterization of exponential dichotomy of difference equations by means of admissible pair of sequence spaces. We classify the classes of input and output spaces, respectively, and deduce necessary and sufficient conditions for exponential dichotomy applicable for a large variety of systems. By an example we show that the obtained results are the most general in this topic. As an application we deduce a general lower bound for the dichotomy radius of difference equations in terms of input–output operators acting on sequence spaces which are invariant under translations. [Copyright &y& Elsevier]