Search

The proofs of Theorem 2.2 of K. J. Dykema and M. Rørdam, Purely infinite simple C*-algebras arising from free product constructions, Canad. J. Math. 50 (1998), 323–341 and of Theorem 3.1 of K J. Dykema, Purely infinite simple C*-algebras arising from free product constructions, II,Math. Scand. 90 (2002), 73–86 are corrected.

In this note, we give a counterexample for Theorem 2.3 of the above mentioned paper that is a generalization of the Grothendieck non-vanishing theorem to a class of modules larger than finitely generated modules.

n/a

In this short paper, generally, we define a family of functions fk depends on the Eisenstein series with weight 2k, for k ( N. More detail, by considering the function fk, we define a derivative formula for generating weakly modular forms with weight 12. As a result for this, we claim that this formula gives an advantage to find the special solutions of some differential equations.

near a point solution xi ai (i 1, 1 *, n) when certain conditions are satisfied. In the present paper these conditions are replaced by less stringent ones; the methods of proof of certain existence theorems are very similar to those employed in the first paper, and these proofs are given here in an abbreviated forin. In addition, the asymptotic properties of certain trajectories are discussed by an extension of the methods of Bohl. On account of the more complicated form of certain quadratic forms which occur here, it has been convenient to leave undetermined certain constants which are determined explicitly in the first paper; this procedure, together with the algebraic method of transforming the canonical equations, reduces to a small amount the results common to both papers.

Wahl recently proved that the homology of the non-orientable mapping class group stabilizes as the genus increases. In this short paper we analyse the situation where the underlying non-orientable surfaces have marked points.

The purpose of this short paper is to provide a proof of a local observability criterion for invariant systems on Lie groups and coset spaces. The criterion was originally presented with an ad hoc proof based on Lie theoretic arguments. The alternative proof presented here shows that the criterion essentially comes from the classical observability results involving the observability codistribution and its properties. In this way it unifies the two approaches and extends the application field of the classical results.

In this short paper I describe special situations where a local ring is normally flat along a divisorial prime ideal.

In this paper, we establish coincidence point and common fixed point theorems involving two pairs of weakly compatible mapping satisfying contraction condition with complex coefficient are proved in complex valued metric space. The presented theorems generalize, extend and improve many existing results in the literature. An example is given at the end of the paper.

In this paper our aim is to show some new inequalities of the Redheffer type for Bessel and modified Bessel functions of the first kind. The key tools in our proofs are some classical results on the monotonicity of quotients of differentiable functions as well as on the monotonicity of quotients of two power series. We also use some known results on the quotients of Bessel and modified Bessel functions of the first kind, and by using the monotonicity of the Dirichlet eta function we prove a sharp inequality for the tangent function. At the end of the paper a conjecture is stated, which may be of interest for further research.

In the authors' first paper, Beurling-Rudin-Korenbljum type characterization of the closed ideals in a certain algebra of holomorphic functions was used to describe the lattice of invariant subspaces of the shift plus a complex Volterra operator. Current work is an extension of the previous work and it describes the lattice of invariant subspaces of the shift plus a positive integer multiple of the complex Volterra operator on the Hardy space. Our work was motivated by a paper by Ong who studied the real version of the same operator., We deleted a proposition and a corollary from section 4, and simplified the proof of the main theorem. **The article has been published in Archiv der Mathematik**

In this paper, the authors first construct a dynamical system which is strongly mixing but has no weak specification property. Then the authors introduce two new concepts which are called the quasi-weak specification property and the semi-weak specification property in this paper, respectively, and the authors prove the equivalence of quasi-weak specification property, semi-weak specification property and strongly mixing.

It is well-known that dyadic martingale transforms are a good model for Calderon–Zygmund singular integral operators. In this paper we extend some results on weighted norm inequalities to vector-valued functions. We prove that if W is an A 2 matrix weight, then the weighted L 2 -norm of a Calderon–Zygmund operator with cancellation has the same dependence on the A 2 characteristic of W as the weighted L 2 -norm of an appropriate matrix martingale transform. Thus the question of the dependence of the norm of matrix-weighted Calderon–Zygmund operators on the A 2 characteristic of the weight is reduced to the case of dyadic martingales and paraproducts. We also show a slightly different proof for the special case of Calderon–Zygmund operators with even kernel, where only scalar martingale transforms are required. We conclude the paper by proving a version of the matrix-weighted Carleson Embedding Theorem. Our method uses a Bellman function technique introduced by S. Treil to obtain the right estimates for the norm of dyadic Haar shift operators. We then apply the representation theorem of T. Hytonen to extend the result to general Calderon–Zygmund operators.

This paper studies vanishing of Ext modules over Cohen–Macaulay local rings. The main result of this paper implies that the Auslander–Reiten conjecture holds for maximal Cohen–Macaulay modules of rank one over Cohen–Macaulay normal local rings. It also recovers a theorem of Avramov–Buchweitz–Şega and Hanes–Huneke, which shows that the Tachikawa conjecture holds for Cohen–Macaulay generically Gorenstein local rings.

This paper suggests new types of weak nonexpansive mappings defined from normed space X into its Cartesian product X × X, studies the main features of the fixed points for those mappings and extends the concept of (C)-contractivity condition introduced in some previous research papers. On other side, it introduces new types of contraction mappings with a mixed monotone property; the {a, b, c} M-first type and the {a, b, c} M-second type contractions, these types are defined from the Cartesian product space X × X into X, where X is a sequentially ordered Banach space, proves the existence of first-anti-second and second-anti-first couple fixed points of such types and generalizes some of the results given before.

In this paper, we consider a class of generalized operator equilibrium problems and derive a Minty type lemma for this class of problems. Further, we establish some existence theorems for the generalized operator equilibrium problems. The theorems presented in this paper generalize and unify many well-known results in the literature.

In the paper under review, we analyze various types of degenerate abstract Volterra integrodifferential equations in sequentially complete locally convex spaces. From the theory of non-degenerate equations, it is well known that the class of (a,k)-regularized C-resolvent families provides an efficient tool for dealing with abstract Volterra integro-differential equations of scalar type. Following the approach of T.-J. Xiao and J. Liang [41]-[43], we introduce the class of degenerate exponentially equicontinuous (a,k)- regularized C-resolvent families and discuss its basic structural properties. In the final section of paper, we will look at generation of degenerate fractional resolvent operator families associated with abstract differential operators.

In this paper, we present a refinement of the global Langlands correspondence for discrete symplectic motives of rank 2n over Q. To such a motive Langlands conjecturally associates a generic, automorphic representation of the split orthogonal group SO2n+1 over Q, which appears with multiplicity one in the cuspidal spectrum. Using the local theory of generic representations of odd orthogonal groups, we define a new vector F in this representation, which is the tensor product of local test vectors for the Whittaker functionals [9]. I hope that the defining properties ofF will make it easier to investigate the Langlands correspondence computationally, especially for the cohomology of algebraic curves. Our refinement is similar to the refinement that Weil [24] proposed for the conjecture that elliptic curves over Q are modular. Namely, Weil proposed that such a curve should be associated with a homomorphic newform F = P anq n of weight 2 on 0(N), where N is equal to the conductor of the curve. This paper expands on a letter that I wrote to Serre in 2010. It was motivated by a question Serre posed at my 60th birthday conference, and a suggestion Brumer made of a family of discrete subgroups generalizing 0(N). I would like to thank them, and to thank Deligne for his comments.

In this paper, we study the Lp mapping properties of certain class of maximal oscillatory singular integral operators. We prove a general theorem for a class of maximal functions along surfaces. As a consequence of such theorem, we establish the Lp boundedness of various maximal oscillatory singular integrals provided that their kernels belong to the natural space Llog L(Sn−1). Moreover, we highlight some additional results concerning operators with kernels in certain block spaces. The results in this paper substantially improve previously known results.

In this paper we introduce a new subclass of analytic functions defined through Convolution. We obtain the sharp upper bounds for the coefficient functional corresponding to the k th root transformation for the function in this class. Similar problems are investigated for the Inverse function and .The results of this paper generalise the work of earlier researchers in this direction.

We study etale extensions of rings that have FIP., Comment: The paper entitled FIP and FCP products of ring morphisms (arXiv: 1312.1250 [math.AC]) is now split into three papers. The present paper contains the last section of the original paper and many other results on etale FIP extensions

This is a follow-up to a paper with the same title and by the same authors. In that paper, all groups were assumed to be abelian, and we are now aiming to generalize the results to nonabelian groups. The motivating point is Pedersen's theorem, which does hold for an arbitrary locally compact group $G$, saying that two actions $(A,\alpha)$ and $(B,\beta)$ of $G$ are outer conjugate if and only if the dual coactions $(A\rtimes_{\alpha}G,\widehat\alpha)$ and $(B\rtimes_{\beta}G,\widehat\beta)$ of $G$ are conjugate via an isomorphism that maps the image of $A$ onto the image of $B$ (inside the multiplier algebras of the respective crossed products). We do not know of any examples of a pair of non-outer-conjugate actions such that their dual coactions are conjugate, and our interest is therefore exploring the necessity of latter condition involving the images, and we have decided to use the term "Pedersen rigid" for cases where this condition is indeed redundant. There is also a related problem, concerning the possibility of a so-called equivariant coaction having a unique generalized fixed-point algebra, that we call "fixed-point rigidity". In particular, if the dual coaction of an action is fixed-point rigid, then the action itself is Pedersen rigid, and no example of non-fixed-point-rigid coaction is known., Comment: Minor revision. To appear in Internat. J. Math

In this paper, we study some uniqueness problems of meromorphic functions when certain nonlinear differential polynomials generated by them share a nonconstant polynomial. The results of the paper improve the concerning results due to Xu et al. (Mat Vesnik 64:1–16, 2012).

In the present paper, necessary conditions for the metric and topological projectivity of closed ideals of Banach algebras are given. In the case of commutative Banach algebras, a criterion for the metric and topological projectivity of ideals admitting a bounded approximate identity is obtained. The main result of the paper is as follows: a closed ideal of an arbitrary C*-algebra is metrically or topologically projective if and only if it admits a self-adjoint right identity.

In this paper we consider the following critical nonlocal problem { − L K u = λ u + | u | 2 ⁎ − 2 u in Ω u = 0 in R n ∖ Ω , where s ∈ ( 0 , 1 ) , Ω is an open bounded subset of R n , n > 2 s , with continuous boundary, λ is a positive real parameter, 2 ⁎ : = 2 n / ( n − 2 s ) is the fractional critical Sobolev exponent, while L K is the nonlocal integrodifferential operator L K u ( x ) : = ∫ R n ( u ( x + y ) + u ( x − y ) − 2 u ( x ) ) K ( y ) d y , x ∈ R n , whose model is given by the fractional Laplacian − ( − Δ ) s . Along the paper, we prove a multiplicity and bifurcation result for this problem, using a classical theorem in critical points theory. Precisely, we show that in a suitable left neighborhood of any eigenvalue of − L K (with Dirichlet boundary data) the number of nontrivial solutions for the problem under consideration is at least twice the multiplicity of the eigenvalue. Hence, we extend the result got by Cerami, Fortunato and Struwe in [14] for classical elliptic equations, to the case of nonlocal fractional operators.

In view of the fact that there are not appropriate frame operators of frames in Banach spaces, this paper considers a class of sequences satisfying certain conditions in Banach spaces which is called as the $\sigma$-frame, and the corresponding concept of frame operators is given. The $\sigma$-frames and $\sigma$-frame operators are natural generalizations of frames and frame operators in Hilbert spaces. This paper illustrates that $\sigma$-frame operators are positive, self-adjoint and they can be decomposed through $l_2$. The perturbation result under operators of $\sigma$-frame is obtained. This paper also shows that the kind of $\sigma$-frames contains two other kinds of frames in Banach space---$p$-frames ($1＜p\leq 2$) and $\sigma {\rm HS}$ frames which are a kind of frames according to the definition of the Hilbert-Schauder frames. The perturbation results under operators of $p$-frames ($1＜p\leq 2$) and $\sigma {\rm HS}$ frames are obtained.

For an arbitrary local field K (a finite extension of the field Qp) and an arbitrary formal group law F over K, we consider an analog cF of the classical Hilbert pairing. A theorem by S.V. Vostokov and I.B. Fesenko says that if the pairing cF has a certain fundamental symbol property for all Lubin–Tate formal groups, then cF = 0. We generalize the theorem of Vostokov–Fesenko to a wider class of formal groups. Our first result concerns formal groups that are defined over the ring OK of integers of K and have a fixed ring O0 of endomorphisms, where O0 is a subring of OK. We prove that if the symbol cF has the above-mentioned symbol property, then cF = 0. Our second result strengthens the first one in the case of Honda formal groups. The paper consists of three sections. After a short introduction in Section 1, we recall basic definitions and facts concerning formal group laws in Section 2. In Section 3, we state and prove two main results of the paper (Theorems 1 and 2). Refs. 8.

In the paper, using the concept of weakly weighted sharing and relaxed weighted sharing, we investigate the uniqueness problems of certain type of difference polynomials that share a small function. The results of the paper improve and extend some recent results due to C. Meng [Math. Bohem., 139(2014), 89–97] and the present first author [Commun. Math. Stat., 3(2015), 227–238].

Some version of the statement of the Fundamental Theorem of Algebra first appeared early in the 17th century in the writings of several mathematicians, including Peter Roth, Albert Girard, and Rene Descartes. The first proof of the Fundamental Theorem was published by Jean Le Rond d’Alembert in 1746 [2], but his proof was not very rigorous. Carl Friedrich Gauss is often credited with producing the first correct proof in his doctoral dissertation of 1799 [15], although this proof also had gaps. (For a comparison of these two proofs, see [26, pp. 195–200].) Today there are many known proofs of the Fundamental Theorem of Algebra, including proofs using methods of algebra, analysis, and topology. (The references include many papers and books containing proofs of the Fundamental Theorem; [14] alone contains 11 proofs.) Our focus in this paper will be on the use of pictures to see why the theorem is true. Of course, if we want to use pictures to display the behavior of polynomials defined on the complex numbers, we are immediately faced with a difficulty: the complex numbers are two-dimensional, so it appears that a graph of a complex-valued function on the complex numbers will require four dimensions. Our solution to this problem will be to use color to represent some dimensions. We begin by assigning a color to every number in the complex plane. Figure 1 is a picture of the complex plane in which every point has been assigned a different color. The origin is colored black. Traveling counterclockwise around a circle centered at the origin, we go through the colors of a standard color wheel: red, yellow, green, cyan, blue, magenta, and back to red. Points near the origin have dark colors, with the color assigned to a complex number z approaching black as z approaches 0. Points far from the origin are light, with the color of z approaching white as |z| approaches infinity. Every complex number has a different color in this picture, so a complex number can be uniquely specified by giving its color. We can now use this color scheme to draw a picture of a function f : C → C as follows: we simply color each point z in the complex plane with the color corresponding to the value of f(z). From such a picture, we can read off the value of f(z), for any complex number z, by determining the color of the point z in the picture, and then consulting Figure 1 to see what complex number is represented by that color.

Under the restriction of finite order, we prove two uniqueness theorems of nonconstant meromorphic functions sharing three values with their difference operators, which are counterparts of Theorem 2.1 in (6) for a finite-order meromorphic function and its shift operator. 1. Introduction and main results In this paper, by meromorphic functions we will always mean meromorphic functions in the complex plane. We adopt the standard notations of the Nevan- linna theory of meromorphic functions as explained in (5), (10) and (16). It will be convenient to let E denote any set of positive real numbers of finite lin- ear measure, not necessarily the same at each occurrence. For a nonconstant meromorphic function h, we denote by T(r,h) the Nevanlinna characteristic of h and by S(r,h) any quantity satisfying S(r,h) = o(T(r,h)), as r → ∞,r 6∈E. Let f and g be two nonconstant meromorphic functions, and let a be a value in the extended plane. We say that f and g share the value a CM, provided that f and g have the same a-points with the same multiplicities. We say that f and g share the value a IM, provided that f and g have the same a-points ignoring multiplicities (cf. (16)). Throughout this paper, we denote by �(f) the order of f (cf. (5), (10) and (16)). We also need the following two definitions: Definition 1.1 ((15)). Let f be a nonconstant meromorphic function. We define difference operators of f as

In the 1960s Bers showed how to uniformize simultaneously two Riemann surfaces of the same finite analytic type by using a single quasi-Fuchsian group of the first kind. In this paper, we show how to uniformize simultaneously two uniformly quasisymmetric circle endomorphisms of the same degree by a unique normalized branched covering of the Riemann sphere of the same degree such that this branched covering has a unique normalized quasicircle as an invariant limit set. We use this simultaneous uniformization to define a transformation between their spaces of probability invariant measures and formulate several equivalent conjectures to the uniqueness conjecture for symmetric invariant probability measures. In a subsequent paper, we study these conjectures.

In this paper we investigate nilpotenct and probabilistically nilpotent Hopf algebras. We define nilpotency via a descending chain of commutators and give a criterion for nilpotency via a family of central invertible elements. These elements can be obtained from a commutator matrix A A which depends only on the Grothendieck ring of H . H. When H H is almost cocommutative we introduce a probabilistic method. We prove that every semisimple quasitriangular Hopf algebra is probabilistically nilpotent. In a sense we thereby answer the title of our paper Are we counting or measuring anything? by Yes, we are.

Let X be a complex L1-predual, non-separable in general. We investigate extendability of complex-valued bounded homogeneous Baire-α functions on the set ext BX* of the extreme points of the dual unit ball BX* to the whole unit ball BX*. As a corollary we show that, given α ∈ [1, ω1), the intrinsic α-th Baire class of X can be identified with the space of bounded homogeneous Baire-α functions on the set ext BX* when ext BX* satisfies certain topological assumptions. The paper is intended to be a complex counterpart to the same authors’ paper: Baire classes of non-separable L1-preduals (2015). As such it generalizes former work of Lindenstrauss and Wulbert (1969), Jellett (1985), and ourselves (2014), (2015).

In the paper [Differ. Uravn., 2007, vol. 43, no. 2, pp. 191–202], we defined the noncoinciding irreducibility sets N 2(a, σ) and N 3(a, σ), σ ∈ (0, 2a], of all n-dimensional linear differential systems with piecewise continuous coefficient matrices A(t) bounded on the half-line [0,+∞) with norms ||A(t)|| ≤ a < +∞ for each of which there exists a linear differential system that cannot be reduced to it by Lyapunov transformations and whose coefficient matrix B(t) satisfies the condition ||B(t) - A(t)|| ≤ const × e −σt , t ≥ 0, or the more general condition that the Lyapunov exponent of the difference B(t) - A(t) does not exceed -σ, respectively. In the present paper, we study the properties of irreducibility sets treated as functions of the parameters σ and a.

In this paper we study the semicontinuity of the automor-phism groups of domains in multi-dimensional complex space. We giveexamples to show that known results are sharp (in terms of the requiredboundary smoothness). 1. IntroductionThepaper [4] wasthe firstworktostudy the semicontinuityofautomorphismgroups of domains in complex space. The main result there is as follows:Theorem 1.1. LetΩ ∗ ⊆ C n be a strongly pseudoconvex domain with smoothboundary. ThenthereisaneighborhoodU ofΩ ∗ intheC ∞ topologyondomains(thatistosay,U isacollectionofdomains) sothat,ifΩ ∈ U,thenAut(Ω) isasubgroupofAut(Ω ∗ ). Moreover, thereisaC ∞ mappingΨ fromΩ toΩ 0 sothatAut(Ω) ∋ ϕ −→ Ψ◦ϕ ◦Ψ −1 isaninjectivegrouphomomorphism fromAut(Ω) toAut(Ω ∗ ).Over the years, the hypothesis of smooth or C ∞ boundary in this theoremhas been weakened. In the paper [5], the hypothesis was weakened (using anentirely different argument) to C 2 boundary smoothness. In the paper [3],yet another approach to the C 2 boundary smoothness situation was described.The paper [2] treats the case of C

An SM domain is an integral domain which satisfies the as-cending chain condition on w-ideals. Then an SM domain also satisfiesthe descending chain condition on those chains of v-ideals whose intersec-tion is not zero. In this paper, a study is begun to extend these propertiesto commutative rings with zero divisors. A Q 0 -SM ring is defined to be aring which satisfies the ascending chain condition on semiregular w-idealsand satisfies the descending chain condition on those chains of semiregularv-ideals whose intersection is semiregular. In this paper, some propertiesof Q 0 -SM rings are discussed and examples are provided to show the dif-ference between Q 0 -SM rings and SM rings and the difference betweenQ 0 -SM rings and Q 0 -Mori rings. 1. IntroductionIn this paper, we assume that Ris a commutative ring with an identity andSis a multiplicatively closed set of R. Let Z(R) denote the set of zero divisorsof Rand let T(R) be the total quotient ring of R.Let I be an ideal of R. Then I is called a regular ideal if I contains aregular element and I is called a semiregular ideal of Rif I contains a finitelygenerated ideal I

The present paper gives several subordination results involving a generalized Srivastava–Attiya operator (defined below). Among the results presented in this paper include also a sufficiency condition for the convexity of the convolution of certain functions and a sharp result relating to the convolution structure. We also mention various useful special cases of the main results including those which are related to the Zeta function.

Let \(\Gamma \) be a closed co-compact subgroup of a second countable locally compact abelian (LCA) group \(G\). In this paper we study translation-invariant (TI) subspaces of \(L^2(G)\) by elements of \(\Gamma \). We characterize such spaces in terms of range functions extending the results from the Euclidean and LCA setting. The main innovation of this paper, which contrasts with earlier works, is that we do not require that \(\Gamma \) be discrete. As a consequence, our characterization of TI-spaces is new even in the classical setting of \(G=\mathbb {R}^n\). We also extend the notion of the spectral function in \(\mathbb {R}^n\) to the LCA setting. It is shown that spectral functions, initially defined in terms of \(\Gamma \), do not depend on \(\Gamma \). Several properties equivalent to the definition of spectral functions are given. In particular, we show that the spectral function scales nicely under the action of epimorphisms of \(G\) with compact kernel. Finally, we show that for a large class of LCA groups, the spectral function is given as a pointwise limit.

Let $R$ be a commutative (Noetherian) local ring of prime characteristic $p$ that is $F$-pure. This paper is concerned with comparison of three finite sets of radical ideals of $R$, one of which is only defined in the case when $R$ is $F$-finite (that is, is finitely generated when viewed as a module over itself via the Frobenius homomorphism). Two of the afore-mentioned three sets have links to tight closure, via test ideals. Among the aims of the paper are a proof that two of the sets are equal, and a proposal for a generalization of I. M. Aberbach's and F. Enescu's splitting prime., 17 pages. This paper has been accepted for publication in Acta Mathematica Vietnamica