Probabilistic modeling of multiperiod service levels

This study investigates multiperiod service level (MSL) policies in supply chains facing a stochastic customer demand. The objective of the supply chains is to construct integrated replenishment plans that satisfy strict stockout-oriented performance measures which apply across a multiperiod planning horizon. We formulate the stochastic service level constraints for the fill rate, ready rate, and conditional expected stockout MSL policies. The modeling approach is based on the concept of service level trajectory and provides reformulations of the stochastic planning problems associated with each MSL policy that can be efficiently solved with off-the-shelf optimization solvers. The approach enables the handling of correlated and non-stationary random variables, and is flexible enough to accommodate the implementation of fair service level policies, the assignment of differentiated priority levels per products, or the introduction of response time requirements. We use an earthquake disaster management case study to show the applicability of the approach and derive practical implications about service level policies.     

拟Bent函数的性质和构造

本文将基本2-群中拟Bent函数的概念推广到一般的有限Abel群中,统一了目前几乎所有的Bent函数概念,完全刻画了一类拟Bent函数和Bent函数的本质联系,给出了几种拟Bent函数的构造方法,拟Bent函数和相对差集的一种关系以及一种用拟Bent函数构造Bent函数的方法.最后,利用Galois环和组合集,找到一类拟Bent函数.     

CM分担两个小函数且IM分担另一个小函数的亚纯函数

本文研究了两个亚纯函数共享两个CM小函数和一个I M小函数,并存在第四个小函数和一定条件下的唯一性.利用构造辅助函数方法,得到一个亚纯函数是另一个亚纯函数的拟分式线性变换.     

Ribbon Schur Functions

We present a new determinantal expression for Schur functions. Previous expressions were due to Jacobi, Trudi, Giambelli and others (see [7]) and involved elementary symmetric functions or hook functions. We give, in Theorem 1.1, a decomposition of a Schur function into ribbon functions (also called skew hook functions, new functions by MacMahon, and MacMahon functions by others). We provide two different proofs of this result in Sections 2 and 3. In Section 2, we use Bazin's formula for the minors of a general matrix, as we already did in [6], to decompose a skew Schur function into hooks. In Section 3, we show how to pass from hooks to ribbons and conversely. In Section 4, we generalize to skew Schur functions. In Section 5, we give some applications, and show how such constructions, in the case of staircase partitions, generalize the classical continued fraction for the tangent function due to Euler.     

Function Decompositions Related to the Luzin N-property

We introduce a class of continuous completely regular functions satisfying the N-property. We obtain a decomposition of an arbitrary continuous function into the sum of two functions the first of which is completely regular and the second does not enjoy the N-property. We define a class of strongly regular Borel functions for which we prove the Luzin N-property. We demonstrate that the image of every Lebesgue measurable set of a strongly regular function is measurable. From an arbitrary Borel function we extract a strongly regular function and a function that does not enjoy the N-property.     

An addition formula for the Jacobian theta function and its applications

In this paper, we prove an addition formula for the Jacobian theta function using the theory of elliptic functions. It turns out to be a fundamental identity in the theory of theta functions and elliptic function, and unifies many important results about theta functions and elliptic functions. From this identity we can derive the Ramanujan cubic theta function identity, Winquist's identity, a theta function identities with five parameters, and many other interesting theta function identities; and all of which are as striking as Winquist's identity. This identity allows us to give a new proof of the addition formula for the Weierstrass sigma function. A new identity about the Ramanujan cubic elliptic function is given. The proofs are self contained and elementary.     

Generalization of the weighted voting method using penalty functions constructed via faithful restricted dissimilarity functions

In this paper we present a generalization of the weighted voting method used in the exploitation phase of decision making problems represented by preference relations. For each row of the preference relation we take the aggregation function (from a given set) that provides the value which is the least dissimilar with all the elements in that row. Such a value is obtained by means of the selected penalty function. The relation between the concepts of penalty function and dissimilarity has prompted us to study a construction method for penalty functions from the well-known restricted dissimilarity functions. The development of this method has led us to consider under which conditions restricted dissimilarity functions are faithful. We present a characterization theorem of such functions using automorphisms. Finally, we also consider under which conditions we can build penalty functions from Kolmogoroff and Nagumo aggregation functions. In this setting, we propose a new generalization of the weighted voting method in terms of one single variable functions. We conclude with a real, illustrative medical case, conclusions and future research lines.     

Partitionable variational inequalities with applications to network and economic equilibria

In this paper, we describe a useful class of finite-dimensional variational inequalities which we call partitionable. These variational inequalities are characterized by state functions which can be thought of as nonlinear separable functions added to antisymmetric linear functions. In the case of partitionable variational inequalities, questions of the monotonicity and coercivity of the state function can be addressed by considering the monotonicity and coercivity of a series of lower-dimensional functions. These functions are generally simpler to investigate than the state function. In the applications, these lower-dimensional functions are usually the natural functions to consider. To demonstrate, we conclude the paper by reviewing several models in the recent literature which give rise to partitionable variational inequalities.     

Radiant Separation Theorems and Minimum-Type Subdifferentials of Calm Functions

Applying minimum-type functions and plus-cogauges, we construct a closed, convex cone in order to separate a boundary point of a radiant set from its interior. Abstract convexity of positively homogeneous functions is studied as well. Since a locally Lipschitz function is degree-one calm, the class of degree-one calm functions is large. We study degree-one calm functions and investigate how these functions can be generated by a class of min-type functions. Then, we derive a method to find an element of the subdifferential of a non-negative, lower semicontinuous and degree-one calm function with respect to the class of min-type functions.     

Minimizing the Difference of Dual Functions of Two Coradiant Functions

In this article, we solve the problem of minimizing the difference of dual functions of two coradiant functions. We do this by applying a type of duality, that is used in microeconomic theory. Indeed, the dual function of a co-radiant function is decreasing and inverse coradiant. So, we first give various characterizations for the maximal elements of the support sets of this class of functions. Next, by using these results, we obtain the necessary and sufficient conditions for the global minimizers of the difference of two decreasing and inverse coradiant functions. Finally, as an application, we present the necessary and sufficient conditions for the global minimizers of the difference of dual functions of two co-radiant functions.     

On the Riesz constants for systems of integer translates

In this paper, one-parameter families of integer translates of the Gaussian and Lorentz functions are studied. For a Lorentz function, we obtain formulas for the coefficients of the series defining node functions and show that the limit value of node functions is given by a sample function. For systems of translates generated by the Gaussian and Lorentz functions as well as by the node functions related to them, we obtain explicit expressions for the Riesz constants and study the parameter-dependent behavior of these constants. While proving some of the results of this paper, we establish the monotonicity of a special ratio of two Jacobi theta functions, a fact which is of interest in itself.     

Second order linear difference equations

We provide the explicit solution of a general second order linear difference equation via the computation of its associated Green function. This Green function is completely characterized and we obtain a closed expression for it using functions of two–variables, that we have called Chebyshev functions due to its intimate relation with the usual one–variable Chebyshev polynomials. In fact, we show that Chebyshev functions become Chebyshev polynomials if constant coefficients are considered.     

On Differentiability of Volume Time Functions

We show differentiability of a class of Geroch’s volume functions on globally hyperbolic manifolds. Furthermore, we prove that every volume function satisfies a local anti-Lipschitz condition over causal curves, and that locally Lipschitz time functions which are locally anti-Lipschitz can be uniformly approximated by smooth time functions with timelike gradient. Finally, we prove that in stably causal space-times Hawking’s time function can be uniformly approximated by smooth time functions with timelike gradient.     

A Conic Trust-Region Method for Nonlinearly Constrained Optimization

Trust-region methods are powerful optimization methods. The conic model method is a new type of method with more information available at each iteration than standard quadratic-based methods. Can we combine their advantages to form a more powerful method for constrained optimization? In this paper we give a positive answer and present a conic trust-region algorithm for non-linearly constrained optimization problems. The trust-region subproblem of our method is to minimize a conic function subject to the linearized constraints and the trust region bound. The use of conic functions allows the model to interpolate function values and gradient values of the Lagrange function at both the current point and previous iterate point. Since conic functions are the extension of quadratic functions, they approximate general nonlinear functions better than quadratic functions. At the same time, the new algorithm possesses robust global properties. In this paper we establish the global convergence of the new algorithm under standard conditions.     

Optimality functions in stochastic programming

Optimality functions define stationarity in nonlinear programming, semi-infinite optimization, and optimal control in some sense. In this paper, we consider optimality functions for stochastic programs with nonlinear, possibly nonconvex, expected value objective and constraint functions. We show that an optimality function directly relates to the difference in function values at a candidate point and a local minimizer. We construct confidence intervals for the value of the optimality function at a candidate point and, hence, provide a quantitative measure of solution quality. Based on sample average approximations, we develop an algorithm for classes of stochastic programs that include CVaR-problems and utilize optimality functions to select sample sizes.     

A new class of complementarity functions for symmetric cone complementarity problems

A popular approach to solving the complementarity problem is to reformulate it as an equivalent equation system via a complementarity function. In this paper, we propose a new class of functions, which contains the penalized natural residual function and the penalized Fischer–Burmeister function for symmetric cone complementarity problems. We show that this class of functions is indeed a class of complementarity functions. We finally prove that the merit function of this new class of complementarity functions is coercive.     

A function class of strictly positive definite and logarithmically completely monotonic functions related to the modified Bessel functions

In this paper, we give some conditions for a class of functions related to Bessel functions to be positive definite or strictly positive definite. We present some properties and relationships involving logarithmically completely monotonic functions and strictly positive definite functions. In particular, we are interested with the modified Bessel functions of the second kind. As applications, we prove the logarithmically monotonicity for a class of functions involving the modified Bessel functions of second kind and we established new inequalities for this function.     

模糊子模函数与模糊秩函数

讨论模糊集合的一些性质;再以一般子模函数为蓝本,定义模糊子模函数,研究模糊子模函数和模糊秩函数的性质;然后利用这些性质推广通过模糊秩函数确定模糊拟阵的一个重要定理。     

Cauchy-Stieltjes积分和面积平均p叶函数

本文研究由Cauchy-Stieltjes积分形成的函数空间Fα.首先给出这个空间的一个等价定义,然后研究面积平均p叶函数的对数函数和这个函数空间的关系,最后对单叶函数的情形做进一步的讨论.根据这种研究,我们得到了有界单叶函数的系数增长估计,这是目前最好的结果.     

Properties of Restricted NCP Functions for Nonlinear Complementarity Problems

In this paper, we study restricted NCP functions which may be used to reformulate the nonlinear complementarity problem as a constrained minimization problem. In particular, we consider three classes of restricted NCP functions, two of them introduced by Solodov and the other proposed in this paper. We give conditions under which a minimization problem based on a restricted NCP function enjoys favorable properties, such as equivalence between a stationary point of the minimization problem and the nonlinear complementarity problem, strict complementarity at a solution of the minimization problem, and boundedness of the level sets of the objective function. We examine these properties for three restricted NCP functions and show that the merit function based on the restricted NCP function proposed in this paper enjoys favorable properties compared with those based on the other restricted NCP functions.