Advertising a new product in a segmented market

We bring some market segmentation concepts into the statement of the “new product introduction” problem with Nerlove-Arrow’s linear goodwill dynamics. In fact, only a few papers on dynamic quantitative advertising models deal with market segmentation, although this is a fundamental topic of marketing theory and practice. In this way we obtain some new deterministic optimal control problems solutions and show how such marketing concepts as “targeting” and “segmenting” may find a mathematical representation. We consider two kinds of situations. In the first one, we assume that the advertising process can reach selectively each target group. In the second one, we assume that one advertising channel is available and that it has an effectiveness segment-spectrum, which is distributed over a non-trivial set of segments. We obtain the explicit optimal solutions of the relevant problems.     

On a bi-layer shallow-water problem

In this paper, we prove an existence and uniqueness result for a bi-layer shallow water model in depth-mean velocity formulation. Some smoothness results for the solution are also obtained. In a previous work we proved the same results for a one-layer problem. Now the difficulty arises from the terms coupling the two layers. In order to obtain the energy estimate, we use a special basis which allows us to bound these terms.     

Inverses and pseudo-inverses of a strong endomorphism of a graph

In this paper, we explicitly describe all the inverses and pseudo-inverses of a strong endomorphism of a graph. The number of them is determined. In addition, we give a characterization of a strong endomorphism whose pseudo-inverse set coincides with its inverse set. The graph, each strong endomorphism of which has this property, is also investigated.     

Every integer can be written as a square plus a squarefree

In the paper we can prove that every integer can be written as the sum of two integers, one perfect square and one squarefree. We also establish the asymptotic formula for the number of representations of an integer in this form. The result is deeply related with the divisor function. In the course of our study we get an independent result about it. Concretely we are able to deduce a new upper bound for the divisor function fully explicit.     

Unfolding of a Quadratic Integrable System with a Homoclinic Loop

In this paper, we make a complete study of the unfolding of a quadratic integrable system with a homoclinic loop. Making a Poincaré transformation and using some new techniques to estimate the number of zeros of Abelian integrals, we obtain the complete bifurcation diagram and all phase portraits of systems corresponding to different regions in the parameter space. In particular, we prove that two is the maximal number of limit cycles bifurcation from the system under quadratic non-conservative perturbations. Received July 16, 1999, Revised March 15, 2001, Accepted May 25, 2001     

Optimal stability criterion for a wall in a ferromagnetic wire in a magnetic field

In this paper, we study a one dimensional asymptotic model of ferromagnetic nanowire submitted to a magnetic field. We address the stability of the wall configuration for the Landau-Lifschitz equation, thus we determine the stability domain improving a result of Carbou-Labbé.     

紧度量空间上的连续在上映射是粘合映射

本文讨论了有关粘合映射的一个问题 ,证明了 ,如果X是紧致度量空间 ,Y是度量空间 ,则由X到Y的连续在上映射是粘合映射 .并给出了一个反例 ,说明 :如果去掉紧致性条件 ,则定理的结论不再成立 .     

Various inverses of a strong endomorphism of a graph

In this paper, we first give a characterization of a completely regular strong endomorphism of a graph. Then we explicitly exhibit its various inverses. The enumerations of them are also derived.     

一类lpp-半群的结构

本文研究含左正则lpp-断面的lpp-半群的结构．特别地，给出了合右理想左正则lpp-断面的lpp-半群的一个结构．另外，还把这个结构用于一些特殊情况。     

Diffraction of a plane wave by a circular disk

In this paper we solve the problem of diffraction of a normally incident plane wave by a circular disk. We treat both the hard and soft disk. In each case we obtain the solution as a series which converges when the product of the wave number and the radius of the disk is large. Our construction leads directly to asymptotic approximations to the solution for large wave number.     

一类逐段决定风险模型罚金函数的期望

本文主要考虑了一类逐段决定的风险模型的罚金函数．利用建立的积分一微分方程,我们得出了此类风险模型罚金函数期望的一般解．     

一类逐段决定风险模型罚金函数的期望(英)

本文主要考虑了一类逐段决定的风险模型的罚金函数.利用建立的积分-微分方程,我们得出了此类风险模型罚金函数期望的一般解.     

Green's Function of a Hartree-Type Equation with a Quadratic Potential

Using the complex WKB–Maslov method, we consider a solution of the Cauchy problem for a Hartree-type equation with a quadratic potential in the class of semiclassically supported functions. In this class, we obtain the evolution operator explicitly. We find parametric families of symmetry operators of the Hartree-type equation. Using the symmetry operators, we construct a family of exact solutions of this equation.     

Minimizing a differentiable function over a differential manifold

To generalize the descent methods of unconstrained optimization to the constrained case, we define intrinsically the gradient field of the objective function on the constraint manifold and analyze descent methods along geodesics, including the gradient projection and reduced gradient methods for special choices of coordinate systems. In particular, we generalize the quasi-Newton methods and establish their superlinear convergence; we show that they only require the updating of a reduced size matrix. In practice, the geodesic search is approximated by a tangent step followed by a constraints restoration or by a simple arc search again followed by a restoration step.A first draft of this paper was first presented at the 10th International Symposium on Mathematical Programming, Montreal, Canada, 1979. The present version has been prepared while the author was visiting the Department of Engineering-Economic Systems at Stanford University, partially supported by AFOSR Grant No. 77-3141.     

Mountain pass theorem in the problem on a nontrivial solution of a quasilinear equation with a parameter

In the present paper, we consider a quasilinear elliptic equation with a parameter whose values lie in a neighborhood of an eigenvalue of the linear problem. To prove the existence of a nontrivial solution, we use a modification of the conditional mountain pass theorem.     

Diffraction of a pulse by a strip

In this paper we consider the problem of diffraction of a normally incident plane pulse by a strip. We use the method of Laplace transformation. By applying results on the asymptotic behavior of solutions of the reduced wave equation, we are able to establish the rate of decay as t → ∞ of the solution of our problem.     

含公共开支的R&D模型

本文给出了一个含公共开支的R&D模型 ,并对模型进行了均衡分析及动态分析 ,得出在一定的条件下 ,模型存在局部稳定的均衡点     

The Hicks property for a variational problem on a graph

In this paper we use the Hicks property for a variational problem on a graph. For an elastic system defined on a graph we state a well-posed problem which implies the definition and the study of the influence function.     

On a nonlinear renewal equation with diffusion

In this paper, we consider a nonlinear age structured McKendrick–von Foerster population model with diffusion term. Here we prove existence and uniqueness of the solution of the equation. We consider a particular type of nonlinearity in the renewal term and prove Generalized Relative Entropy type inequality. Longtime behavior of the solution has been addressed for both linear and nonlinear versions of the equation. In linear case, we prove that the solution converges to the first eigenfunction with an exponential rate. In nonlinear case, we have considered a particular type of nonlinearity that is present in the mortality term in which we can predict the longtime behavior. Copyright © 2015 John Wiley & Sons, Ltd.     

Solving a continuous local access network design problem with a stabilized central column generation approach

In this paper, we focus on a variant of the multi-source Weber problem. In the multi-source Weber problem, the location of a fixed number of concentrators, and the allocation of terminals to them, must be chosen to minimize the total cost of links between terminals and concentrators. In our variant, we have a third hierarchical level, two categories of link costs, and the number of concentrators is unknown. To solve this difficult problem, we propose several heuristics, and use a new stabilized column generation approach, based on a central cutting plane method, to provide lower bounds.