Aggregation of a Distributed Source in Morphogen Gradient Formation

In the development of a biological entity, ligands (such as Decapentaplegic (Dpp) along the anterior–posterior axis of the Drosophila wing imaginal disc) are synthesized at a localized source and transported away from the source for binding with cell surface receptors to form concentration gradients of ligand–receptor complexes for cell signaling. Generally speaking, activities such as diffusion and reversible binding with degradable receptors also take place in the region of ligand production. The effects of such morphogen activities in the region of localized distributed ligand source on the ligand–receptor concentration gradient in the entire biological entity have been modeled and analyzed as System F in [ 1 ]. In this paper, we deduce from System F, a related end source model (System A) in which the effects of the distributed ligand source is replaced by an idealized point stimulus at the border between the (posterior) chamber and the ligand production region that simulates the average effects of the ligand activities in the production zone. This aggregated end source model is shown to adequately reproduce the significant implications of System F and to contain the corresponding ad hoc point source model, System R of [ 2 ], as a special case. Because of its simpler mathematical structure and the absence of any limitation on the ligand synthesis rate for the existence of steady-state gradients, System A type models are expected to be used widely. An example of such application is the recent study of the inhibiting effects of the formation of nonsignaling ligand–nonreceptor complexes [ 3 ].     

Large and moderate deviation principles for susceptible-infected-removed epidemic in a random environment

We are concerned with SIR epidemics in a random environment on complete graphs, where edges are assigned with i.i.d. weights. Our main results give large and moderate deviation principles of sample paths of this model. Our results generalize large and moderate deviation principles of the classic SIR models given by E. Pardoux and B. Samegni-Kepgnou [J. Appl. Probab., 2017, 54: 905-920] and X. F. Xue [Stochastic Process. Appl., 2019, 140: 49-80].     

Stochastic nonhomogeneous incompressible Navier-Stokes equations

We construct solutions for 2- and 3-D stochastic nonhomogeneous incompressible Navier-Stokes equations with general multiplicative noise. These equations model the velocity of a mixture of incompressible fluids of varying density, influenced by random external forces that involve feedback; that is, multiplicative noise. Weak solutions for the corresponding deterministic equations were first found by Kazhikhov [A.V. Kazhikhov, Solvability of the initial and boundary-value problem for the equations of motion of an inhomogeneous viscous incompressible fluid, Soviet Phys. Dokl. 19 (6) (1974) 331-332; English translation of the paper in: Dokl. Akad. Nauk SSSR 216 (6) (1974) 1240-1243]. A stochastic version with additive noise was solved by Yashima [H.F. Yashima, Equations de Navier-Stokes stochastiques non homogènes et applications, Thesis, Scuola Normale Superiore, Pisa, 1992].The methods here extend the Loeb space techniques used to obtain the first general solutions of the stochastic Navier-Stokes equations with multiplicative noise in the homogeneous case [M. Capiński, N.J. Cutland, Stochastic Navier-Stokes equations, Applicandae Math. 25 (1991) 59-85]. The solutions display more regularity in the 2D case. The methods also give a simpler proof of the basic existence result of Kazhikhov.     

On the structure of kripke models of heyting arithmetic

Since in Heyting Arithmetic (HA) all atomic formulas are decidable, a Kripke model for HA may be regarded classically as a collection of classical structures for the language of arithmetic, partially ordered by the submodel relation. The obvious question is then: are these classical structures models of Peano Arithmetic (PA)? And dually: if a collection of models of PA, partially ordered by the submodel relation, is regarded as a Kripke model, is it a model of HA? Some partial answers to these questions were obtained in [6], [3], [1] and [2]. Here we present some results in the same direction, announced in [7]. In particular, it is proved that the classical structures at the nodes of a Kripke model of HA must be models of IΔ₁ (PA^- with induction for provably Δ₁ formulas) and that the relation between these classical structures must be that of a Δ₁-elementary submodel. MSC: 03F30, 03F55.     

李代数$W(2,2)$上的Poisson结构

Poisson代数是指同时具有代数结构和李代数结构的一类代数,其乘法和李代数乘法满足Leibniz法则.李代数W(2,2)在权为2的向量生成的顶点算子代数的分类中起着重要作用.文章主要确定了李代数W(2,2)上的Poisson结构,并得到了Virasoro代数上一般的非结合的Poisson结构,改进了文[姚裕丰.Witt代数和Virasoro代数上的Poisson代数结构[J].数学年刊,2013,34A(1):111-128]的部分结果.     

Thue inequalities with a small number of primitive solutions

Several upper bounds are known for the numbers of primitive solutions (x; y) of the Thue equation (1) j F(x; y) j = m and the more general Thue inequality (3) 0 < j F(x; y) j m. A usual way to derive such an upper bound is to make a distinction between "small" and "large" solutions, according as max( j x j ; j y j ) is smaller or larger than an appropriate explicit constant Y depending on F and m; see e.g. [1], [11], [6] and [2]. As an improvement and generalization of some earlier results we give in Section 1 an upper bound of the form cn for the number of primitive solutions (x; y) of (3) with max( j x j ; j y j )Y0 , wherec 25 is a constant and n denotes the degree of the binary form F involved (cf. Theorem 1). It is important for applications that our lower bound Y0 for the large solutions is much smaller than those in [1], [11], [6] and [4], and is already close to the best possible in terms of m. ByusingTheorem1 we establish in Section 2 similar upper bounds for the total number of primitive solutions of (3), provided that the height or discriminant of F is suficiently large with respect to m (cf. Theorem 2 and its corollaries). These results assert in a quantitative form that, in a certain sense, almost all inequalities of the form (3) have only few primitive solutions. Theorem 2 and its consequences are considerable improvements of the results obtained in this direction in [3], [6], [13] and [4]. The proofs of Theorems 1 and 2 are given in Section 3. In the proofs we use among other things appropriate modifications and refenements of some arguments of [1] and [6].     

An effective transformation in ranking using l1-norm in data envelopment analysis

Jahanshahloo et al. [G. R. Jahanshahloo, F. Hosseinzadeh Lotfi, N. Shoja, G. Tohidi, S. Razavyan, Ranking using l₁-norm in data envelopment analysis, Applied Mathematics and Computation, 153 (2004) 215-224] present a method for ranking extremely efficient decision making units (DMUs) in data envelopment analysis (DEA) by exploiting the leave-one-out idea and l₁-norm. It is shown that the proposed method is able to remove the existing difficulties in some methods. This paper suggests an effective procedure to transfer the proposed model from the nonlinear programming form into a linear programming form. We show that the model with this transformation is equivalent to the nonlinear model, while it is much easier to solve than the treatment in [1].     

Global stability for a discrete epidemic model for disease with immunity and latency spreading in a heterogeneous host population

In this paper, we propose a discrete epidemic model for disease with immunity and latency spreading in a heterogeneous host population, which is derived from the continuous case by using the well-known backward Euler method and by applying a Lyapunov function technique, which is a discrete version of that in the paper by Prüss et al. [J. Prüss, L. Pujo-Menjouet, G.F. Webb, R. Zacher, Analysis of a model for the dynamics of prions, Discrete Contin. Dyn. Syst. Ser. B 6 (2006) 225-235]. It is shown that the global dynamics of this discrete epidemic model with latency are fully determined by a single threshold parameter.     

Estimating market shares in each market segment using the information entropy concept

Sales data of a certain product for the various competitors are usually available at the aggregate level. However these data give no clue to the heterogeneities in the sales pattern across different market segments. Heterogeneities are caused by different purchasing behavior in each market segment; as a purchaser in a segment will be attracted to the attributes of the product most important to that segment. This concept can be formalized via a simple attraction model that utilizes an elasticity measure for each quality or price attribute [G.S. Carpenter, L.G. Cooper, D.M. Hanssens, D.F. Midgley, Modeling asymmetric competition, Marketing Science 7 (4) (1998) 393–412]. Assessment of these elasticities is not difficult since customer response – in each market segment – to perception of quality and price is tracked by most firms [J. Ross, D. Georgoff, A survey of productive and quality issues in manufacturing. The state of the industry, Industrial Management 3 (5) (1991) 22–25]. This paper attempts to formulate a generic framework based on the information entropy concept that utilizes such an attraction model to estimate competitors’ sales in each market segment.     

Determination of effective properties for CFRP curing coupled to viscoleasticity based on a three-scale framework

Our work presents a three-scale model for temperature-dependent visco-elastic effects accompanied by curing, which are important phenomena in a resin transfer molding (RTM) process. The effective bulk quantities in dependence on the degree of cure are obtained by homogenization for a representative unit cell (micro-RVE) on the heterogeneous microscale. To this end, an analytic solution is derived by extension of the composite spheres model [1]. Voigt and Reuss bounds resulting from the assumption of a homogeneous matrix proposed in [2] are compared to the effective quantities. During curing, the periodic mesostructure defined by a visco-elastic polymeric matrix and linear-thermo-elastic fibres is taken into account as a representative unit cell (meso-RVE) subjected to thermo-mechanical loading on the mesoscale. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

SUFFICIENT CONDITIONS FOR OSCILLATION OF THE LIENARD EQUATION

1.IntroductionInthispaper,wegivesomesufficientconditionsfortheoscillationofallsolutionsofthegeneralizedLi6nardequationi~h(y)~F(x),gi~~g(x).(1.1)Throughoutthispaper,weassumeh(.),F(.),g(.)arecontinuousfunctionsonRandsatisfylocallyLipschitzcondition.MoreoverweassumeF(0)~0;ah(y)>0,y/0;xg(x)>0,x/0;h(y)isstrictlyincreasingandtimh(y)~boo,timG(x)~co,y-boolxl-cowhereG(x)~/".(.)d.,H(y)~l'h(.)d.,icg(u)du,H(y)~['h(u)du,H-'(.),G-'(.)areinversefunctionsofH(.)andG(.).Asolutionof(1.1)issaidtobeoscillato…     

Nonlinear versions of a vector maximal principle

Some nonlinear extensions of the vector maximality statement established by Goepfert et al. [A. Goepfert, C. Tammer, C. Z?linescu, On the vectorial Ekeland’s variational principle and minimal points in product spaces, Nonlinear Anal. 39 (2000) 909-922] are given. Basic instruments for these are the Brezis-Browder ordering principle [H. Brezis, F.E. Browder, A general principle on ordered sets in nonlinear functional analysis, Adv. Math. 21 (1976) 355-364] and its logical equivalent in Turinici [M. Turinici, Variational principles on semi-metric structures, Libertas Math. 20 (2000) 161-171].     

赋β-范空间中单位球面间的等距算子的线性延拓

本文得到了等距映射的线性延拓的一般结果:设E,F是赋范(或β-严格凸赋β-范)线性空间,若V_0:S_1(E)→S_1(F)是等距,且对任意的x,y∈S_1(E),有‖V_0x-|(?)|V_0y‖≤‖x-|(?)|y‖,(?)∈R,则V_0必可延拓到全空间上等距算子(或线性等距算子)。特别,当E,F是赋范线性空间,V_0是满射或F为严格凸空间时,则V_0必可延拓为全空间的线性等距算子,从而推广了文[3～5]中的相应结果。     

Tricyclic graphs with maximum Merrifield-Simmons index

It is well known that the graph invariant, ‘the Merrifield-Simmons index’ is important one in structural chemistry. The connected acyclic graphs with maximal and minimal Merrifield-Simmons indices are determined by Prodinger and Tichy [H. Prodinger, R.F. Tichy, Fibonacci numbers of graphs, Fibonacci Quart. 20 (1982) 16-21]. The sharp upper and lower bounds for the Merrifield-Simmons indices of unicyclic graphs are characterized by Pedersen and Vestergaard [A.S. Pedersen, P.D. Vestergaard, The number of independent sets in unicyclic graphs, Discrete Appl. Math. 152 (2005) 246-256]. The sharp upper bound for the Merrifield-Simmons index of bicyclic graphs is obtained by Deng, Chen and Zhang [H. Deng, S. Chen, J. Zhang, The Merrifield-Simmons index in (n,n+1)-graphs, J. Math. Chem. 43 (1) (2008) 75-91]. The sharp lower bound for the Merrifield-Simmons index of bicyclic graphs is determined by Jing and Li [W. Jing, S. Li, The number of independent sets in bicyclic graphs, Ars Combin, 2008 (in press)]. In this paper, we will consider the tricyclic graph, i.e., a connected graph with cyclomatic number 3. The tricyclic graph with n vertices having maximum Merrifield-Simmons index is determined.     

On a model of electromagnetic field propagation in ferroelectric media

The Maxwell system in an anisotropic, inhomogeneous medium with non-linear memory effect produced by a Maxwell type system for the polarization is investigated under low regularity assumptions on data and domain. The particular form of memory in the system is motivated by a model for electromagnetic wave propagation in ferromagnetic materials suggested by Greenberg, MacCamy and Coffman [J.M. Greenberg, R.C. MacCamy, C.V. Coffman, On the long-time behavior of ferroelectric systems, Phys. D 134 (1999) 362-383]. To avoid unnecessary regularity requirements the problem is approached as a system of space-time operator equation in the framework of extrapolation spaces (Sobolev lattices), a theoretical framework developed in [R. Picard, Evolution equations as space-time operator equations, Math. Anal. Appl. 173 (2) (1993) 436-458; R. Picard, Evolution equations as operator equations in lattices of Hilbert spaces, Glasnik Mat. 35 (2000) 111-136]. A solution theory for a large class of ferromagnetic materials confined to an arbitrary open set (with suitably generalized boundary conditions) is obtained.     

Localization with respect to a class of maps I — Equivariant localization of diagrams of spaces

Homotopical localizations with respect to a set of maps are known to exist in cofibrantly generated model categories (satisfying additional assumptions) [4, 13, 24, 35]. In this paper we expand the existing framework, so that it will apply to not necessarily cofibrantly generated model categories and, more important, will allow for a localization with respect to a class of maps (satisfying some restrictive conditions). We illustrate our technique by applying it to the equivariant model category of diagrams of spaces [12]. This model category is not cofibrantly generated [8]. We give conditions on a class of maps which ensure the existence of the localization functor; these conditions are satisfied by any set of maps and by the classes of maps which induce ordinary localizations on the generalized fixed-points sets. During the preparation of this paper the author was a fellow of Marie Curie Training Site hosted by Centre de Recerca Matemàtica (Barcelona), grant no. HPMT-CT-2000-00075 of the European Commission.     

On the continuity of the feasible set in extremally linear problems

The purpose of this paper is to investigate continuity properties of the feasible set in extremally linear problems. Feasible sets of such problems are subsets of Fⁿ (the n-fold cartesian product of a fully ordered group (F,º)) and are described by a finite or an infinite number of inequalities or equalities, which are linear with respect to the operations ? and º. Thereby, the operation ? is induced by the fully-order in F by setting x?y = y iff x ≤ y for x, y in F. In particular, we derive conditions for the upper- and lower-semi-continuity of the feasible-set-mapping Z and investigate the structure of certain parameter sets. Especially, we show that the compactness of the feasible set, resp. the condition that the closure of the set of the strict feasible points is the feasible set, is sufficient for the upper-semi-continuity (u.s.c), resp. the lower-semi-continuity (l.s.c.) of Z, but - unlike to semi-infinite linear optimization - is not necessary for the u.s.c, resp. l.s.c. If we restrict Z on a certain subset of the parameter set, these conditions are also necessary. This paper is a continuation of the author's work in [6] and [7].     

关于(F,ρ)-不变凸性函数多目标规划的充分性条件

本文给出了一类更一般的广义凸性函数的定义:(F,ρ)-不变凸性函数,并论证了其多目标规划关于有效解的充分性条件.本文的一些主要结论是对文献[2]～[5]中相应结论的改进和推广.     

K. Saito's Conjecture for nonnegative eta products and analogous results for other infinite products

We prove that the Fourier coefficients of a certain general eta product considered by K. Saito are nonnegative. The proof is elementary and depends on a multidimensional theta function identity. The z=1 case is an identity for the generating function for p-cores due to Klyachko [A.A. Klyachko, Modular forms and representations of symmetric groups, J. Soviet Math. 26 (1984) 1879-1887] and Garvan, Kim and Stanton [F. Garvan, D. Kim, D. Stanton, Cranks and t-cores, Invent. Math. 101 (1990) 1-17]. A number of other infinite products are shown to have nonnegative coefficients. In the process a new generalization of the quintuple product identity is derived.     

Common fixed points of generalized contractions on partial metric spaces and an application

In this paper, common fixed point theorems for four mappings satisfying a generalized nonlinear contraction type condition on partial metric spaces are proved. Presented theorems extend the very recent results of I. Altun, F. Sola and H. Simsek [Generalized contractions on partial metric spaces, Topology and its applications 157 (18) (2010) 2778-2785]. As application, some homotopy results for operators on a set endowed with a partial metric are given.