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n this paper we introduce the concepts of Wijsman ρ-statistical convergence of order α and Wijsman strongly ρ-convergence of order α. In addition, some inclusion theorems are also presented. [ABSTRACT FROM AUTHOR]

For the system of equations of the integral theory of a fire in a room with open embrasures, we obtain comparison theorems that permit one to obtain relationships between solutions corresponding to various ignition conditions and hence compare the values of dangerous factors arising in fires under such conditions. These results are used for the practical problem of the replacement of a complicated system of embrasures by a single rectangular embrasure without diminishing the level of the fire danger. [ABSTRACT FROM AUTHOR]

We give a new perspective on the homological characterisations of amenability given by Johnson & Ringrose in the context of bounded cohomology and by Block & Weinberger in the context of uniformly finite homology. We examine the interaction between their theories and explain the relationship between these characterisations. We apply these ideas to give a new proof of non-vanishing for the bounded cohomology of a free group. [ABSTRACT FROM AUTHOR]

We establish the spectral gap property for dense subgroups of SU.d(d 2), generated by finitely many elements with algebraic entries; this result was announced in [BG3]. The method of proof differs, in several crucial aspects, from that used in [BG] in the case of SU.2/. [ABSTRACT FROM AUTHOR]

In this paper we deal with analytic nonautonomous vector fields with a periodic time-dependency, that we study near an equilibrium point. In a first part, we assume that the linearized system is split in two invariant subspaces E and E. Under light diophantine conditions on the eigenvalues of the linear part, we prove that there is a polynomial change of coordinates in E allowing to eliminate up to a finite polynomial order all terms depending only on the coordinate $${u_0 \in E_0}$$ in the E component of the vector field. We moreover show that, optimizing the choice of the degree of the polynomial change of coordinates, we get an exponentially small remainder. In the second part, we prove a normal form theorem with exponentially small remainder. Similar theorems have been proved before in the autonomous case: this paper generalizes those results to the nonautonomous periodic case. [ABSTRACT FROM AUTHOR]

Thomassen [Combinatorica, 3 (1983), pp. 393--396] proved that every digraph with minimum out-degree at least three has two vertex disjoint cycles. There are examples of 3-regular digraphs where all pairs of vertex disjoint cycles have the same length. In this paper we raise the conjectures that all 3-regular bipartite digraphs and all digraphs with minimum degree at least four have two vertex disjoint cycles of different length. We give support for our conjectures by proving that all 4-regular digraphs do indeed have two vertex disjoint cycles of different length. We furthermore discuss consequences of our results and conjectures as well as arc-weighted versions of our conjecture [ABSTRACT FROM AUTHOR]

Abstract: In this short note, we present a general version of Carlson’s inequality for the Sugeno integral, which generalizes some recent results obtained by others. [Copyright &y& Elsevier]

Let ([InlineMediaObject not available: see fulltext.], d, μ) be a space of homogeneous type in the sense of Coifman and Weiss. In this paper, we consider the behavior on [InlineMediaObject not available: see fulltext.] × ⋯ × [InlineMediaObject not available: see fulltext.] for the m-linear singular integral operators with nonsmooth kernels which were first introduced by Duong, Grafakos and Yan. [ABSTRACT FROM AUTHOR]

In this paper, we shall study the uniqueness problems on meromorphic functions sharing nonzero finite value or fixed point. We have answered some questions posed by Dyavanal. Our results improve or generalize a few of known results. [ABSTRACT FROM AUTHOR]

We give short proofs of general theorems about optimal entry and exit problems in Lévy models, when payoff streams may have discontinuities and be nonmonotone. As applications, we consider exit and entry problems in the theory of real options and an entry problem with all embedded option to exit. [ABSTRACT FROM AUTHOR]

Abstract: This note is concerned with an efficient computation of integrals of products of a smooth function and Daubechies scale function with partial support by using a one-point quadrature rule. The error estimate is obtained. The rule is illustrated by considering an example from the literature. [Copyright &y& Elsevier]

Given an algebraic subvariety X of a multiplicative torus A over , we study the intersection of with the union A[m] of all algebraic subgroups of codimension . This is related to conjectures stated by Zilber and Pink and follows previous work by Bombieri, Masser and Zannier. Our main result can be stated as follows: if X is a nondegenerate subvariety of A, then for any subgroup of finite rank Γ of , the points lying in a height-theoretic cone with nonzero radius around ΓA[m] are not dense in X. The case Γ={1} was proved by Habegger in 2009 as a corollary to his bounded height theorem. We show here that the general case follows from a new Vojta-type height inequality on Xm. The proof of this inequality relies on diophantine approximation techniques coming from previous work by Vojta, Faltings, Bombieri, … , Rémond. It shows that the height inequality can be deduced from a lower bound on some intersection numbers coming from a family of blow-ups of a given compactification of Xm. Our main task is to establish this lower bound. For that purpose, we use homogeneity and positivity properties of the intersection numbers. They are proved here in an analytic setting, using integrals of Chern-like forms over suitably chosen desingularizations. [ABSTRACT FROM PUBLISHER]

This paper investigates the following question: when can one reliably infer the existence of an intersection point from a diagram presenting crossing curves or lines? Two cases are considered, one from Euclid's geometry and the other from basic real analysis. I argue for the acceptability of such an inference in the geometric case but against in the analytic case. Though this question is somewhat specific, the investigation is intended to contribute to the more general question of the extent and limits of reliable diagrammatic reasoning in mathematics. [ABSTRACT FROM PUBLISHER]

The article presents methods for solving the mass equidistribution for automomorphic forms of cohomological type on GL2l. The were methods used by Holowinsky and Soundararajan over Q. Theorems are provided before explaining the modifications applied. It discusses the generalisation of Holowinsky's method of shifted convolution sums, Soundrarajan's approach of triple product identities and subconvexity, and provides the main result and generalisation of Rudnick's theorem.

The Aitken Δ method for finding fixed points of scalar mappings is interpreted as a modification of the Wegstein method. Based on this approach, conditions for the quadratic convergence of this method are obtained for various situations of convergence/divergence of simple iteration. An algorithm for calculating fixed points that keeps track of these situations is presented. [ABSTRACT FROM AUTHOR]

We give an alternative definition of integral at the generality of the Perron integral and propose an exposition of the foundations of integral theory starting from this new definition. Both definition and proofs needed for the development are unexpectedly simple. We show how to adapt the definition to cover the multidimensional and Stieltjes case and prove that our integral is equivalent to the Henstock-Kurzweil(-Stieltjes) integral. [ABSTRACT FROM AUTHOR]

There is a confusing situation in geostatistical literature: Some authors write variogram, and some authors write semivariogram. Based on a formula for the empirical variance that relates to pairwise differences, it is shown that the values depicted in a variogram are entire variances of observations at a given spatial separation (lag). Therefore, they should not be called semivariances, and the term semivariogram should also be avoided. To name a variogram value, we suggest the use of the term gammavariance instead of the misleading semivariance. [ABSTRACT FROM AUTHOR]

We will prove learning theorems that could explain, if only a little, how some organisms generalize information that they get from their senses. [ABSTRACT FROM AUTHOR]

In this short paper we study the game of cops and robbers, which is played on the vertices of some fixed graph G. Cops and a robber are allowed to move along the edges of G, and the goal of cops is to capture the robber. The cop number c(G) of G is the minimum number of cops required to win the game. Meyniel conjectured a long time ago that O(√n) cops are enough for any connected G on n vertices. Improving several previous results, we prove that the cop number of an n-vertex graph is at most n2-(1+0(1))√log n.A similar result independently and slightly before us was also obtained by Lu and Peng. [ABSTRACT FROM AUTHOR]

A finite set H in Rd is called an acute set if any angle determined by three points of H is acute. We examine the maximal cardinality α(d) of a d-dimensional acute set. The exact value of α(d) is known only for d ≤ 3. For each d ≥ 4 we improve on the best known lower bound for α(d). We present different approaches. On one hand, we give a probabilistic proof that α(d) > c ⋅ 1.2d. (This improves a random construction given by Erdõs and Füredi.) On the other hand, we give an almost exponential constructive example which outdoes the random construction in low dimension (d ≤ 250). Both approaches use the small dimensional examples that we found partly by hand (d = 4, 5) and partly by computer (6 ≤ d ≤ 10). We also investigate the following variant of the above problem: what is the maximal size κ(d) of a d-dimensional cubic acute set (that is, an acute set contained in the vertex set of a d-dimensional hypercube)? We give an almost exponential constructive lower bound, and we improve on the best known upper bound. [ABSTRACT FROM AUTHOR]

It was conjectured that a permutation matrix with bandwidth can be written as a product b of no more than 2b - 1 permutation matrices of bandwidth 1. In this note, two proofs are given to affirm the conjecture. [ABSTRACT FROM AUTHOR]

Let L(G) denote the set of all odd cycle lengths of a graph G. Gyárfás gave an upper bound for χ(G) depending on the size of this set: if |L(G)| = k ≥ 1, then χ(G) ≤ 2k + 1 unless some block of G is a K2k+2, in which case χ(G) = 2k + 2. This bound is generally tight, but when investigating L(G) of special forms, better results can be obtained. Wang completely analyzed the case L(G) = {3, 5} Camacho proved that if L(G) = {k, k + 2}, k ≥ 5, then χ(G) ≤ 4. We show that L(G) = {5, 7} implies χ(G) = 3. [ABSTRACT FROM AUTHOR]

The article examines the probability and integral solutions to the fixed Kolmogorov equation, L*μ = 0. It analyzes the circumstances that probability solutions are given unique integral solution up to multiplication by a constant. It notes that the uniqueness in the class of probability solutions and the uniqueness in the class of integrable solutions are varied constructs that are already in dimension d = 1. It considers the validity of the given theorems, asserting that theorems 3 and 5 need additional conditions on the manifold.

We use a transformation due to Bekenstein to relate the ADM and Bondi masses of asymptotically-flat solutions of the Einstein equations with, respectively, scalar sources and conformal-scalar sources. Although the conformal-scalar energy-momentum tensor does not satisfy the Dominant Energy Condition one may, by this means, still conclude that the ADM mass is positive. [ABSTRACT FROM AUTHOR]

The article presents a discussion on Greek philosopher Aristotle's book "Metaphysica." In section 1051a21-33 of "Metapyhsica," Aristotle stressed that geometrical proofs are discovered through supplementary constructions. An example of the theory in section 1051a26-9, however, presents difficulties for scholars. Reasons behind the problem include the ambiguity of a mathematical argument presumed by the example, and disputes in the interpretation of the text.

We propose the minimal representation of an element in a pseudocomplemented modular lattice satisfying the descending chain condition and prove that the minimal representation of an element is unique. Then we give necessary and sufficient conditions under which a sequence can be the spectrum of a modular lattice and a distributive lattice, respectively. These results settle two problems raised by G. Grätzer, D. S. Gunderson and R. W. Quackenbush in 2009. [ABSTRACT FROM AUTHOR]

We classify the real and strongly real conjugacy classes in GL n( q) and SL n( q). In each case we give a formula for the number of real, and the number of strongly real, conjugacy classes. This paper is the first of two that together classify the real and strongly real classes in GL n( q), SL n( q), PGL n( q), PSL n( q), and all quasi-simple covers of PSL n( q). [ABSTRACT FROM AUTHOR]

Using combinatorics and character theory, we determine the imprimitive faithful complex characters, i.e., the irreducible faithful complex characters which are induced from proper subgroups, of the Schur covers of the symmetric and alternating groups. Furthermore, for every imprimitive character we establish all its minimal block stabilizers. As a corollary, we also determine the monomial faithful characters of the Schur covers. [ABSTRACT FROM AUTHOR]

The article discusses the problem from the context of the classical problem in extremal hypergraph theory. It explains that the bounds proved for the problem differ for different relations between the parameters as it relies on two parameters. It outlines the formulation of the problem's results and shows its theorem. However, it points out that there is uncertainty on whether or not the theorem can be improved. The equations, theorem, as well as the proof for the bound of the problem are also presented.

The article investigates the optimality conditions in optimal control problems with state constraints through the use of Pontryagin's maximum principle (MP). It presents an MP in the form of Gamkrelidze without considering a priori assumption on the regularity of optimal trajectory. It notes the non-restrictiveness of the assumption on the compatibility of state constraints with the terminal ones. It reveals the theorem which explains that nontriviality condition in the MP can be strengthened in a regular optimal process. The necessary optimality conditions in control problem is also presented.

We have characterized the spaces X for which the smallest z-ideal containing C∞(X) is prime. It turns out that C C∞ (X) is a z-ideal in C(X) if and only if every zero-set contained in an open locally compact σ-compact set is compact. Some interesting ideals related to C C∞ (X) are introduced and corresponding to the relations between these ideals and C C∞ (X), topological spaces X are characterized. Some compactness concepts are explicitly stated in terms of ideals related to C C∞ (X). Finally we have shown that a σ-compact space X is Baire if and only if every ideal containing C C∞ (X) is essential. [ABSTRACT FROM AUTHOR]

We treat the classical notion of convexity in the context of hard real analysis. Definitions of the concept are given in terms of defining functions and quadratic forms, and characterizations are provided of different concrete notions of convexity. This analytic notion of convexity is related to more classical geometric ideas. Applications are given both to analysis and geometry. [ABSTRACT FROM AUTHOR]

In this paper, we obtain some applications of first order differential subordination and superordination results involving a linear operator and other linear operators for certain normalized analytic functions. Some of our results generalize previously known results. [ABSTRACT FROM AUTHOR]

We give a version in characteristic p > 0 of Mumford's theorem characterizing a smooth complex germ of surface ( X, x) by the triviality of the topological fundamental group of U = X\{ x}. [ABSTRACT FROM AUTHOR]

The logical status of abstraction principles, and especially Hume’s Principle, has been long debated, but the best currently availeble tool for explicating a notion’s logical character—permutation invariance—has not received a lot of attention in this debate. This paper aims to fill this gap. After characterizing abstraction principles as particular mappings from the subsets of a domain into that domain and exploring some of their properties, the paper introduces several distinct notions of permutation invariance for such principles, assessing the philosophical significance of each. [ABSTRACT FROM PUBLISHER]

We prove that the obstruction bundle used to define the cup-product in Chen–Ruan cohomology has a simple representation-theoretic description. The key quantities in this description are the age gradings or degree-shifting numbers of the representations of the local groups of the orbifold. We obtain a Künneth Theorem for Chen–Ruan cohomology as a direct consequence of an elementary property of the age grading, and explain how several other results, including associativity of the cup product, can be proved in a similar way. [ABSTRACT FROM PUBLISHER]

We prove the analogue of Schanuel's conjecture for raising to the power of an exponentially transcendental real number. All but countably many real numbers are exponentially transcendental. We also give a more general result for several powers in a context which encompasses the complex case. [ABSTRACT FROM PUBLISHER]

We study the regularity of complex Monge–Ampère equation on Hermitian manifolds. Our main results give the C1 and C2 estimates for the solution of Equation (1.1). Moreover, we also give the gradient estimate for the geometric solution of complex Hessian Equations (1.4) and (1.6) when the background manifold is Hermitian. [ABSTRACT FROM PUBLISHER]

The main purpose of this paper is to studied the mean value properties of some new sequences, and give several mean value formulae and their applications. [ABSTRACT FROM AUTHOR]

A computer algebra system is used to derive a theorem on the existence of roots of a quadratic equation on any bounded real interval. This is extended to a cubic polynomial. We discuss how students could be led to derive and prove these theorems. [ABSTRACT FROM AUTHOR]

We present a convergence theorem for the Henstock-Kurzweil integral of functions taking values in a locally convex topological vector space, which is sequentially complete with respect to its weak topology. [ABSTRACT FROM AUTHOR]

In the whole article, the function is understood as the real valued function of real variables. It is well known that the construction of semicontinuous functions is possible either as a limit (in the sense of pointwise convergence) of the monotonous sequence of continuous functions or with assistance of the certain system of associated sets. In the first case a good understanding of the constructed function is obtained. However in the second case the Darboux property of semicontinuous function is assured when certain requirements on the system of associated sets are satisfied. Therefore the combination of both approaches seems to be the optimal method when a semicontinuous function with Darboux property is constructed. Such a combined method is used when the main theorem of this paper is proven. Later, the validity of the main theorem helps us to address the problem published by J. G. Ceder and T. L. Pearson in [2]. [ABSTRACT FROM AUTHOR]

We prove a theorem (for arbitrary ring varieties and, in a stronger form, for varieties of associative rings) which basically reduces the problem of a description of varieties with distributive subvariety lattice to the case of algebras over a finite prime field. [ABSTRACT FROM AUTHOR]

Green's relations and their generalizations on semigroups are useful in studying regular semigroups and their generalizations. In this paper, we first give a brief survey of this topic. We then give some examples to illustrate some special properties of generalized Green's relations which are related to completely regular semigroups and abundant semigroups. [ABSTRACT FROM AUTHOR]

The purpose of our article is to show two simpler and clearer methods of proving Stirling's formula than the traditional and conventional ones. The distinction of our method is to use the simple trapezoidal formula. [ABSTRACT FROM AUTHOR]

In this article, by using Rolle's theorem, we establish some results related to the mean value theorem for integrals. Our results are different from the set of integral mean value theorems which are given by Wayment [An integral mean value theorem, Math. Gazette 54 (1970), pp. 300-301] and Sahoo [Some results related to the integral mean value theorem, Int. J. Math. Ed. Sci. Tech. 38(6) (2007), pp. 818-822]. The importance of our results are illustrated by interesting examples. [ABSTRACT FROM AUTHOR]

Lexicographic product G ∘ H of two graphs G and H has vertex set V (G) x V (H) and two vertices (u1; v1) and (u2; v2) are adjacent whenever u1u2 ∊ E(G), or u1 = u2 and v1v2 ∊ E(H). If every matching of G of size k can be extended to a perfect matching in G, then G is called k-extendable. In this paper, we study matching extendability in lexicographic product of graphs. The main result is that the lexicographic product of an m-extendable graph and an n-extendable graph is (m + 1)(n + 1)-extendable. In fact, we prove a slightly stronger result. [ABSTRACT FROM AUTHOR]

We show that the nilpotency of the metacyclic subgroups of a hypercyclic group implies the hypercentrality of the whole group. We also construct a center-free metabelian group all of whose polycyclic subgroups are abelian. [ABSTRACT FROM AUTHOR]