Geometry of lightlike hypersurfaces of an indefinite Sasakian manifold

In this paper, we study the geometry of lightlike hypersurfaces of an indefinite Sasakian manifold. The main result is to prove three characterization theorems for such a lightlike hypersurface. In addition to these main theorems, we study the geometry of totally geodesic lightlike hypersurfaces of an indefinite Sasakian manifold.     

The algebraic structure of left semi-trusses

The distributive laws of ring theory are fundamental equalities in algebra. However, recently in the study of the Yang-Baxter equation, many algebraic structures with alternative “distributive” laws were defined. In an effort to study these “left distributive” laws and the interaction they entail on the algebraic structures, Brzeziński introduced skew left trusses and left semi-trusses. In particular the class of left semi-trusses is very wide, since it contains all rings, associative algebras and distributive lattices. In this paper, we investigate the subclass of left semi-trusses that behave like the algebraic structures that came up in the study of the Yang-Baxter equation. We study the interaction of the operations and what this interaction entails on their respective semigroups. In particular, we prove that in the finite case the additive structure is a completely regular semigroup. Secondly, we apply our results on a particular instance of a left semi-truss called an almost left semi-brace, introduced by Miccoli to study its algebraic structure. In particular, we show that one can associate a left semi-brace to any almost left semi-brace. Furthermore, we show that the set-theoretic solutions of the Yang-Baxter equation originating from almost left semi-braces arise from this correspondence.     

Comparisons Between Largest Order Statistics from Multiple-outlier Models with Dependence

We study stochastic comparisons between the largest order statistics from samples which may contain outliers. The data in each sample can also be dependent. Under these assumptions we study three cases. In the first one we consider the general case without additional assumptions. In the second we assume that the data come from two different distributions. In the third one we assume that the data come from a proportional hazard rates model. The results obtained here can be applied to compare parallel systems. Some illustrative examples are provided.     

Relative asymptotics for orthogonal matrix polynomials

In this paper we study sequences of matrix polynomials that satisfy a non-symmetric recurrence relation. To study this kind of sequences we use a vector interpretation of the matrix orthogonality. In the context of these sequences of matrix polynomials we introduce the concept of the generalized matrix Nevai class and we give the ratio asymptotics between two consecutive polynomials belonging to this class. We study the generalized matrix Chebyshev polynomials and we deduce its explicit expression as well as we show some illustrative examples. The concept of a Dirac delta functional is introduced. We show how the vector model that includes a Dirac delta functional is a representation of a discrete Sobolev inner product. It also allows to reinterpret such perturbations in the usual matrix Nevai class. Finally, the relative asymptotics between a polynomial in the generalized matrix Nevai class and a polynomial that is orthogonal to a modification of the corresponding matrix measure by the addition of a Dirac delta functional is deduced.     

Qualitative Properties of Eigenvectors Related to Multivalued Operators and some Existence Results

In this work, we study a class of nonlinear eigenvalue problems related to fully discontinuous operators. In particular, we prove the existence of a critical point for two distinct problems. Connected with this problem, we also study a minimization problem with constraint, and we investigate the existence of solutions for a resonant case near zero. Moreover, we give some estimates and qualitative properties of solutions by using the relative rearrangement theory.     

Generating functions for ternary algebras and ternary trees

The main object of study are ternary algebras, i.e., algebras with a trilinear operation. In this class we study finitely generated algebras and their growth, as well as the growth of codimensions of absolutely free algebras and some other varieties. For these purposes we use ordinary generating functions and exponential generating functions (the complexity functions). In the classes of absolutely free, free symmetric, free antisymmetric, and some other algebras we study left nilpotent and completely left nilpotent algebras and varieties. The obtained results are equivalent to the enumeration of ternary trees which contain no forbidden subtrees of a special kind. As the main result, we prove that the complexity functions of the varieties of completely left nilpotent and left nilpotent ternary algebras are algebraic.     

The Stokes phenomenon in the confluence of the hypergeometric equation using Riccati equation

In this paper we study the confluence of two regular singular points of the hypergeometric equation into an irregular one. We study the consequence of the divergence of solutions at the irregular singular point for the unfolded system. Our study covers a full neighborhood of the origin in the confluence parameter space. In particular, we show how the divergence of solutions at the irregular singular point explains the presence of logarithmic terms in the solutions at a regular singular point of the unfolded system. For this study, we consider values of the confluence parameter taken in two sectors covering the complex plane. In each sector, we study the monodromy of a first integral of a Riccati system related to the hypergeometric equation. Then, on each sector, we include the presence of logarithmic terms into a continuous phenomenon and view a Stokes multiplier related to a 1-summable solution as the limit of an obstruction that prevents a pair of eigenvectors of the monodromy operators, one at each singular point, to coincide.     

Advertising Events in a Competitive Framework

We study the problem of how to minimize the advertising costs for a one-time entertainment event taking competition into account. Using the concept of Nerlove-Arrow goodwill, we describe a market where two single players organize two different events. A single-player instance of the same problem has been analyzed already in the literature using both the Nerlove-Arrow dynamics and the Bass dynamics, but without considering a competitive framework. In this work, starting from a linear-quadratic model, we consider competition in the market and we study the problem in the settings of linear-quadratic deterministic and stochastic differential games. The analytical tractability of the problem allows us to characterize the Nash equilibria and to study the new features of the competitive scenario. In the deterministic instance of the model, we show that competition decreases efficiency. On the other hand, when the goodwill evolution is stochastic, competition may even increase efficiency by a diversification effect.     

Sub-semigroups determined by the zero-divisor graph

In this paper we study sub-semigroups of a finite or an infinite zero-divisor semigroup S determined by properties of the zero-divisor graph Γ(S). We use these sub-semigroups to study the correspondence between zero-divisor semigroups and zero-divisor graphs. In particular, we discover a class of sub-semigroups of reduced semigroups and we study properties of sub-semigroups of finite or infinite semilattices with the least element. As an application, we provide a characterization of the graphs which are zero-divisor graphs of Boolean rings. We also study how local property of Γ(S) affects global property of the semigroup S, and we discover some interesting applications. In particular, we find that no finite or infinite two-star graph has a corresponding nil semigroup.     

与Gauss测度有关的椭圆方程比较结果中等号成立的条件

In this paper, we deal with a Dirichlet problem for linear elliptic equations related to Gauss measure. For this problem, we study the converse of some inequalities proved by other authors, in the sense that we study the case of equalities and show that equalities are achieved only in the ＂symmetrized＂ situations. In addition, under other assumptions, we give a different form of comparison results and discuss the corresponding case of equalities.     

Beliefs and beyond: hows and whys in the teaching of proof

In this paper, we report on a study aimed at describing the way secondary school teachers treat proof and at understanding which factors may influence such a treatment. This study is part of a wider project on proof carried out for many years. In our theoretical framework, we combine references from research on proof with those from research on teachers in relation to their beliefs. The study was carried out through interviews with secondary school teachers aimed at learning how they describe their work with proof in the classroom, and to elicit beliefs and other factors that shape this work. Through the interviews we were able to detect reasons behind teachers’ choices in planning their work in the classroom. In the present paper, we concentrate on four cases that, among other factors, offer elements suitable to unravel the problem of inconsistencies using the construct of leading beliefs, i.e., beliefs (whose nature may vary from teacher to teacher) that seem to drive the way each teacher treats proof.     

Ginzburg‐Landau vortex dynamics driven by an applied boundary current

In this paper we study the time‐dependent Ginzburg‐Landau equations on a smooth, bounded domain Ω ? ?², subject to an electrical current applied on the boundary. The dynamics with an applied current are nondissipative, but via the identification of a special structure in an interaction energy, we are able to derive a precise upper bound for the energy growth. We then turn to the study of the dynamics of the vortices of the solutions in the limit ε → 0. We first consider the original time scale in which the vortices do not move and the solutions undergo a “phase relaxation.” Then we study an accelerated time scale in which the vortices move according to a derived dynamical law. In the dynamical law, we identify a novel Lorentz force term induced by the applied boundary current. © 2010 Wiley Periodicals, Inc.     

Instability of Hopf vector fields on Lorentzian Berger spheres

In this work, we study the stability of Hopf vector fields on Lorentzian Berger spheres as critical points of the energy, the volume and the generalized energy. In order to do so, we construct a family of vector fields using the simultaneous eigenfunctions of the Laplacian and of the vertical Laplacian of the sphere. The Hessians of the functionals are negative when they act on these particular vector fields and then Hopf vector fields are unstable. Moreover, we use this technique to study some of the open problems in the Riemannian case.     

Feedback control variables to restrain the Babesiosis disease

In this paper, we complete the study of the dynamics of a recognized continuous‐time model for the Babesiosis disease. The local and global asymptotic stability of the endemic state are established theoretically and experimentally. In addition, to restrain the disease in the original model when the endemic state exists, we propose and study the continuous model with feedback controls. The global stability of the boundary‐equilibrium point of this model is analyzed by means of rigorous mathematical methods. As an important consequence of this result, we propose a strategy to select feedback control variables in order to restrain the disease in the original model. This strategy allows us to make the disease vanish completely. In other words, the feedback controls are specially effective for restraining disease in the model. The validity of the established theoretical result is supported by a set of numerical simulations.     

Selfdecomposable Fields

In the present paper, we study selfdecomposability of random fields, as defined directly rather than in terms of finite-dimensional distributions. The main tools in our analysis are the master Lévy measure and the associated Lévy-Itô representation. We give the dilation criterion for selfdecomposability analogous to the classical one. Next, we give necessary and sufficient conditions (in terms of the kernel function) for a Volterra field driven by a Lévy basis to be selfdecomposable. In this context, we also study the so-called Urbanik classes of random fields. We follow this with the study of existence and selfdecomposability of integrated Volterra fields. Finally, we introduce infinitely divisible field-valued Lévy processes, give the Lévy-Itô representation associated with them and study stochastic integration with respect to such processes. We provide examples in the form of Lévy semistationary processes with a Gamma kernel and Ornstein–Uhlenbeck processes.     

Indefinite functions on commutative groups

The purpose of this paper is to study indefinite functions of orderk on commutative locally compact groups. In section 3 we establish some fundamental properties of these functions. Using the results of this section we get a characterization for indefinite functions of order one (section 4). In section 5 we give a decomposition of measurable indefinite functions.     

Limits of relaxed dirichlet problems involving a non symmetric dirichlet form

In this paper we study the convergence of solutions of a sequence of relaxed Dirichlet problems relative to non-symmetric Dirichlet forms. The techniques rely on the study of the behaviour of the solutions of the adjoint problems, as suggested by G. Dal Maso and A. Garroni in [16] in the case of linear elliptic operators of second order with bounded measurable coefficients. In particular we prove a compactness results due to Mosco [31] in the symmetric case. Entrata in Redazione il 18 gennaio 1999     

Coefficient estimates for a certain family of analytic functions involving a q-derivative operator

The Ramanujan Journal - In this paper, we study the coefficient estimates for a class of analytic functions defined by using the q-Ruscheweyh derivative operator. In particular, we investigate the...     

Global existence and large-time behavior of a parabolic phase-field model with Neumann boundary conditions

In this paper, we continue to study an initial boundary value problems to a model describing the evolution in time of diffusive phase interfaces in sea ice growth. In a previous paper, the global existence and the large-time behavior of weak solutions in one space was studied under Dirichlet boundary conditions. Here, we show that the global existence of weak solutions and the large-time behavior are also studied under Neumann boundary condition. In this paper, we study in space dimension lower than or equal to 3.     

Non-Archimedean Pseudodifferential Operators and Feller Semigroups

In this article we study a large class of non-Archimedean pseudodifferential operators whose symbols are negative definite functions.We prove that these operators extend to generators of Feller semigroups. In order to study these operators, we introduce a new class of anisotropic Sobolev spaces, which are the natural domains for the operators considered here.We also study the Cauchy problem for certain pseudodifferential equations.