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In this note we offer some criticism on the paper “On an identity for zeros of Bessel functions” by Baricz et al. [3] . The paper gives identities of type Stieltjes–Calogero for the sums of reciprocals of differences of fourth powers of zeros of Bessel functions. Although interesting in principle, by containing one too many sums of similar complexity the identities fail to convey the true spirit of the work of Stieltjes and Calogero. We rectify this by providing what we think is the correct type of identity for the above-said sums, in the general setup of entire functions of order

In 1903, Epstein published his proof of meromorphic continuation and a functional equation for Dirichlet series associated with quadratic forms, now called Epstein zeta-functions. However, already in 1889 (or even earlier) Hurwitz was aware of these results as his mathematical diaries and some unpublished notes (in an almost final form) found in his estate at the ETH Zurich show. In this article we present and analyze Hurwitz's notes and compare his reasoning with Epstein's paper in detail.

We would like to present the ideas of Makoto Matsumoto and Andras Rapcsak in the projective theory of Finsler spaces. Finally, we give some remarks using of Matsumoto–Rapcsak Theorem.

In this paper, we first point out a gap in Yang (2012). Next, strong convergence theorem for the common solution for a finite family of ? -strongly accretive operator equations in Banach spaces is established without any bounded assumption, and we also give an example to show universality of the result of this paper, which improve and extend some recent results.

We complete a gap in the proof that exceptional polynomials are complete orthogonal systems in the associated Hilbert spaces.

In this paper, we introduce some notions of invariancy for the Ricci tensor on real hypersurfaces in complex two-plane Grassmannians G 2 ( C m + 2 ) , namely, F -invariant and invariant Ricci tensor. Using these notions, we give non-existence theorem and characterization for the special case among the real hypersurfaces of Type ( A ) in G 2 ( C m + 2 ) , respectively. Here the distribution F is defined by F = [ ξ ] ∪ D ⊥ where D ⊥ = Span { ξ 1 , ξ 2 , ξ 3 } and [ ξ ] = Span { ξ } .

In this paper we introduce a notion of a t-filter on residuated lattices which is a generalization of several special types of filters. We provide some basic properties of t-filters and show how particular results about special types of filters (e.g. Extension property, Triple of equivalent characteristics, and Quotient characteristics) are uniformly covered by this simple general framework.

We show that paper folding words contain arbitrarily large abelian powers.

In this paper, some sufficient conditions are established for the oscillation of second-order neutral differential equations(r(t)@j(x(t))|Z^'(t)|^@a^-^1Z^'(t))^'+q(t)f(x(@s(t)))=0,t>=t"0>0, where Z(t)=x(t)+p(t)x(t-@t) and @a>0,0==t"0>0, where @!"t"""0^~dtr(t)

The aim of this paper is twofold: First, we characterize an essentially optimal class of boundary operators $\Theta$ which give rise to self-adjoint Laplacians $-\Delta_{\Theta, \Omega}$ in $L^2(\Omega; d^n x)$ with (nonlocal and local) Robin-type boundary conditions on bounded Lipschitz domains $\Omega\subset\bbR^n$, $n\in\bbN$, $n\geq 2$. Second, we extend Friedlander's inequalities between Neumann and Dirichlet Laplacian eigenvalues to those between nonlocal Robin and Dirichlet Laplacian eigenvalues associated with bounded Lipschitz domains $\Omega$, following an approach introduced by Filonov for this type of problems., Comment: 23 pages, added Remark 5.4

Given a propositional theory T and a proposition q , a sufficient condition of q is one that will make q true under T , and a necessary condition of q is one that has to be true for q to be true under T . In this paper, we propose a notion of strongest necessary and weakest sufficient conditions. Intuitively, the strongest necessary condition of a proposition is the most general consequence that we can deduce from the proposition under the given theory, and the weakest sufficient condition is the most general abduction that we can make from the proposition under the given theory. We show that these two conditions are dual ones, and can be naturally extended to arbitrary formulas. We investigate some computational properties of these two conditions and discuss some of their potential applications.

This third and last part of a series of position papers on triangular norms (for Parts I and II see (E.P. Klement, R. Mesiar, E. Pap, Triangular norms, Position paper I: basic analytical and algebraic properties, Fuzzy Sets and Systems, in press; E.P. Klement, R. Mesiar, E. Pap, Triangular norms. Position paper II: general constructions and parameterized families, submitted for publication) presents the representation of continuous Archimedean t-norms by means of additive generators, and the representation of continuous t-norms by means of ordinal sums with Archimedean summands, both with full proofs. Finally some consequences of these representation theorems in the context of comparison and convergence of continuous t-norms, and of the determination of continuous t-norms by their diagonal sections are mentioned.

This paper considers certain neutral differential equation with the distributed delayddt[x(t)+c(t)x([email protected])]+p(t)x(t)+q(t)x([email protected])+r(t)@!"t"-"@d^tx(s)ds=0.Without imposing a nonnegative restriction on coefficients of the equation, we establish a delay-dependent asymptotic stability condition for the equation by introducing a new Lyapunov function. The condition presented here is different from that of Park [J.H. Park, LMI optimization approach to asymptotic stability of certain neutral delay differential equation with time-varying coefficients, Appl. Math. Comput. 160 (2005) 355-361] in the sense that it is dependent on all delays of the equation. Numerical examples illustrate effectiveness and sharpness of our theoretical result.

We associate to a good cell decomposition of a manifold M a quadratic algebra and show that the Koszulity of the algebra implies a restriction on the Euler characteristic of M . For a two-dimensional manifold M the algebra is Koszul if and only if the Euler characteristic of M is two.

In this paper we construct a family of circle-like continua, each admitting a finest monotone map onto S 1 such that there exists a subset of point inverses which is homeomorphic to the Cantor set cross an interval. We then show how to realize some members of this family as the boundaries ∂U of bounded irreducible local Siegel disks U . These boundaries are geometrically rigid in the following sense: there exist arbitrarily small periodic homeomorphisms of the sphere, conformal on U , which keep U invariant. The embedding portion of this paper follows a flexible construction of Herman. These results provide a partial answer to a question of Rogers and a complete answer to a question of Brechner, Guay, and Mayer.

Huang and Zhang reviewed cone metric spaces in 2007 [Huang Long-Guang, Zhang Xian, Cone metric spaces and fixed point theorems of contractive mappings, J. Math. Anal. Appl. 332 (2007) 1468–1476]. We shall prove that there are no normal cones with normal constant M 1 and for each k > 1 there are cones with normal constant M > k . Also, by providing non-normal cones and omitting the assumption of normality in some results of [Huang Long-Guang, Zhang Xian, Cone metric spaces and fixed point theorems of contractive mappings, J. Math. Anal. Appl. 332 (2007) 1468–1476], we obtain generalizations of the results.

Complementing the work of T.-S. Liu and A.C.M. van Rooij we show that the existence of non-zero translation invariant operators between certain function spaces on a locally compact group implies its amenability.

We prove oscillation and nonoscillation theorems for the second order linear differential equation (E) y″+q(t)y=0, where q(t)⩾0 and locally integrable on [t∗,∞). These results are extensions of earlier results of Huang [J. Math. Anal. Appl. 210 (1997) 712–723]. Furthermore, we show that the oscillation criterion established for Eq. (E) can be extended to the delayed differential equation y″+q(t)y(σ(t))=0, where σ(t)⩽t and limt→∞σ(t)=∞.

Recently, Broyden [Optim. Methods Software 8 (3-4) (1998) 185-199] proved a property of orthogonal matrices from which he derived Farkas' lemma and some related results. It is shown that Broyden's result straightforwardly follows from well-known theorems of the alternative, like Motzkin's transposition theorem and Tucker's theorem, which are all logically equivalent to Farkas' lemma; we also answer the question of Broyden on how to efficiently compute the sign matrix of an orthogonal matrix. Finally, we raise some related questions about possible generalizations of Broyden's result.

In this note, we will modify several gaps in Chidume and Ofoedu [C.E. Chidume, E.U. Ofoedu, A new iteration process for generalized Lipschitz pseudo-contractive and generalized Lipschitz accretive mappings, Nonlinear Anal. (2006), in press ( doi:10.1016/j.na.2006.05.012 )].

In their 1993 paper, W. Goh and J. Wimp derive interesting asymptotics for the moments cn(?) ? cn = ?10tnd?(t), n = 0, 1, 2, ..., of some singular distributions ? (with support ? 0, 1]), which contain oscillatory terms. They suspect, that this is a general feature of singular distributions and that this behavior provides a striking contrast with what happens for absolutely continuous distributions. In the present note, however, we give an example of an absolutely continuous measure with asymptotics of moments containing oscillatory terms, and an example of a singular measure having very regular asymptotic behavior of its moments. Finally, we give a short proof of the fact that the drop-off rate of the moments is exactly the local measure dimension about 1 (if it exists).

Lemma 4.1 in [Comm. Math. Phys.91(1983)] by Ron Diperna pertaining to the vacuum case for an existence proof of polytropic gas dynamics using compensated compactness is incomplete as given. Here we give a quick fix of the lemma plus some generalization.

It is asserted in Definition 4.2 in [1] that the random operators U ( t ) defined there are unitary. As was pointed out to the author by Shizan Fang, it is clear that U ( t ) is an isometry but it is not obvious that U ( t ) is surjective. The purpose of this note is to fill this gap.

In 1.9 of the paper [A. Hahn, A Hermitian Morita theorem for algebras with anti-structure, J. Algebra 93 (1985) 215–235], End P A should be replaced by ( End P A ) o . This leads to minor changes in the rest of the paper where the ring should be replaced by its opposite and vice versa.

Gaemer's technique for recovering a function ⨍(x) from its power moments μ n = ∝ 1 0 ⨍(x)x n dx specified at n = 0, 1, 2,…N, is rederived using an expansion in Chebyshev polynomials of the second kind. Advantages of the present derivation over the original one are pointed out.

In this note we show that a multivalued bounded quasimonotone operator of type ( M ) between a reflexive Banach space and its dual is pseudomonotone. Hence we deduce that a result of Su Ke and He Zhen [Su Ke, He Zhen, Solutions of nonlinear evolution inclusions, J. Math. Anal. Appl. 313 (2006) 84–97] follows from a theorem of Bian and Webb [W. Bian, J.R.L. Webb, Solutions of nonlinear evolution inclusions, Nonlinear Anal. 37 (1999) 915–932].

A nonoscillation criterion for a second-order linear difference equation is established correcting a result in [1].

In a recent paper, Little et al. point out that certain terms in the eigenvector expansion of a nonsymmetric stochastic matrix are unbounded. This appears to throw doubt on the usual assumption that only terms associated with the largest eigenvalues contribute significantly to high powers of the matrix. In this note we show that although individual terms can be unbounded, their sum is always well behaved, and since this is the relevant quantity, the eigenvalue criterion is still valid. An explicit bound on the sum is obtained for a 3 × 3 case, and for the general N × N case it is shown that the factors causing the unboundedness cancel.

We show that slight technical changes in the definition transform the probability of fuzzy events introduced by R. R. Yager [16] into a new concept of such probabilities having nice properties, both from an intuitive and from a mathematical point of view: monotonicity, additivity, and continuity.

The proof of one of the main results of C. N. Friedman, Perturbations of the Schroedinger equation by potentials with small support ( J. Functional Analysis 10 (1972), 346–360) is modified basing it on a more general existence theorem. A proof of this existence theorem is provided.

In this short paper we find that the Sobolev inequality 1 p − 2 ∫ f p d μ 2 p − ∫ f 2 d μ ≤ C ∫ | ∇ f | 2 d μ ( p ≥ 0 ) is equivalent to the exponential convergence of the Markov diffusion semigroup ( P t ) to the invariant measure μ , in some Φ -entropy. We provide the estimate of the exponential convergence in total variation and a bounded perturbation result under the Sobolev inequality. Finally in the one-dimensional case we get some two-sided estimates of the Sobolev constant by means of the generalized Hardy inequality.

In this short paper, we generalize the cyclotomic constructions of zero-difference balanced (ZDB) functions proposed by Zha and Hu [7] to generate ZDB functions with higher definition domain.

Recently, Adachi, Iyama and Reiten [1] introduced support τ -tilting modules which is an interesting generalization of classical tilting modules and showed that they have close relations with silting complexes and cluster-tilting objects. In this short paper, we prove that support τ -tilting modules over artin algebras are just quasi-tilting modules in sense of Colpi, D'Este and Tonolo [6] .

In this short paper, it is proved that every pair of large positive even integers satisfying some necessary conditions can be represented in the form of a pair of quadratic equations in prime variables and k powers of 2. In particular, we have k = 584 . We also consider the similar result for cubic equations.

It has recently been shown that the symmetric gauge functions on the canonical (principal) angles give a family of unitarily invariant metrics between linear subspaces of the same dimension. In this short paper, we extend such metrics to subspaces of possibly different dimensions. This extension is necessary in addressing some perturbation analysis problems involving subspaces with different dimensions. Examples of such perturbation analysis problems are also studied in this paper using the extended metrics.

In this short paper we prove a conjecture of Martelli–Sparks–Yau regarding the isometry group of a Sasaki–Einstein metric.

This short paper outlines the basic topological features of two new fuzzy Kahler manifolds in duality. Relation to E-infinity theory of the compactified Klein modular space in connection with ’t Hooft holographic principles is briefly discussed.

In this short paper we propose a definition of flatness for systems not necessarily given in input/state/output representation. A flat system is a system for which there exists a mapping such that the manifest system behavior is equal to the image of this mapping, and such that the latent variable appearing in this image representation can be written as a function of the manifest variable and its derivatives up to some order. For linear differential systems, flatness is equivalent to controllability. We will generalize the main theorem of Levine and Nguyen (Systems Control Lett. 48 (2003) 69) to general linear differential systems.