Optimal contracts and the manufacturer’s pricing strategies in a supply chain with an inequity-averse retailer

Studies in the supply chain literature have typically focused on profit or revenue maximization and assumed that agents within the supply chain are self-interested and only care about their own monetary payoffs. Research in these areas, however, rarely considers an important phenomenon called inequity aversion in which the object pursued by agents within the supply chain is not only their own profit maximization but also the equity of profit allocation. In fact, when agents within a supply chain collaborate with each other to serve a market, the scheme of profit allocation between them usually plays a determinate role in cooperation. Taking into account the impact of agents’ behavior of inequity aversion on the coordination of the supply chain, this paper investigates the optimal contracts and the manufacturer’s pricing strategies in a single-manufacturer and single-retailer supply chain. In this way, we obtain two interesting results: (1) the retailer’s equity aversion largely affects the manufacturer’s decision making, which is not always bad for the manufacturer; and (2) the retailer’s inequity aversion as well as the consumer’s price-sensitive coefficient plays a dominant role in the manufacturer’s decision making.     

The boundary-value problem for the Lavrent’ev-Bitsadze equation with unknown right-hand side

We study the inverse problem for the Lavrent’ev-Bitsadze equation in a rectangular domain. We construct its solution as a series of eigenfunctions for the corresponding problem on eigenvalues and establish a criterion for its uniqueness. We also prove the stability of the obtained solution.     

Sturm-Liouville’s problem with discontinuous nonlinearity

We establish a theorem on the existence of solutions of the Sturm-Liouville problem with nonlinearity discontinuous in the phase variable. By way of application, we consider a one-dimensional analog of the Gol’dshtik model of separated flows of an incompressible fluid.     

Waring’s problem with digital restrictions

The aim of this paper is to consider an analogue of Waring’s problem with digital restrictions. In particular, we prove the following result. Lets _q (n) be theq-adic sum of digits function and leth,m be fixed positive integers. Then fors>2 ^k there existsn ₀∈ℕ such that each integern≥n ₀ has a representation of the form We will even give an asymptotic formula for the number of representations ofn in this way. The result is shown with help of the circle method in combination with a “digital” version of Weyl’s Lemma. Dedicated to Professor Hillel Furstenberg The first author was supported by the Austrian Science Foundation project S8310. The second author was supported by the Austrian Science Foundation project S8308.     

Coupon collector’s problems with statistical applications to rankings

Some new exact distributions on coupon collector’s waiting time problems are given based on a generalized Pólya urn sampling. In particular, usual Pólya urn sampling generates an exchangeable random sequence. In this case, an alternative derivation of the distribution is also obtained from de Finetti’s theorem. In coupon collector’s waiting time problems with $m$ kinds of coupons, the observed order of $m$ kinds of coupons corresponds to a permutation of $m$ letters uniquely. Using the property of coupon collector’s problems, a statistical model on the permutation group of $m$ letters is proposed for analyzing ranked data. In the model, as the parameters mean the proportion of the $m$ kinds of coupons, the observed ranking can be intuitively understood. Some examples of statistical inference are also given.     

On mockenhoupt’s conjecture in the Hardy-Littlewood majorant problem

The Hardy-Littlewood majorant problem has a positive answer only for even integer exponents p, while there are counterexamples for all p {ie91-1} 2?. Montgomery conjectured that even among the idempotent polynomials there must exist counterexamples, i.e. there exist a finite set of characters and some ± signs with which the signed character sum has larger p ^th norm than the idempotent obtained with all the signs chosen + in the character sum. That conjecture was proved recently by Mockenhaupt and Schlag. However, Mockenhaupt conjectured that even the classical {ie91-2} three-term character sums, used for p = 3 and k = 1 already by Hardy and Littlewood, should work in this respect. That remained unproved, as the construction of Mockenhaupt and Schlag works with four-term idempotents. In our previous work we proved this conjecture for k = 0, 1, 2, i.e. in the range 0 < p < 6, p {ie91-3} 2?. Continuing this work here we demonstrate that even k = 3, 4 cases hold true. Several refinement in the technical features of our approach include improved fourth order quadrature formulae, finite estimation of G′²/G (with G being the absolute value square function of an idempotent), valid even at a zero of G, and detailed error estimates of approximations of various derivatives in subintervals, chosen to have accelerated convergence due to smaller radius of the Taylor approximation     

Nirenberg’s problem on domains in the 2-sphere

In this article, we consider the problem of prescribing Gaussian curvature on domains in the unit 2-sphere. We obtain the existence result for any domain with area between (2π, 4π) and having at least 2 boundary components.     

Cooperation in an evolutionary prisoner’s dilemma game with probabilistic strategies

In this work, we investigate an evolutionary prisoner’s dilemma game in structured populations with probabilistic strategies instead of the pure strategies of cooperation and defection. We explore the model in details by considering different strategy update rules and different population structures. We find that the distribution of probabilistic strategies patterns is dependent on both the interaction structures and the updating rules. We also find that, when an individual updates her strategy by increasing or decreasing her probabilistic strategy a certain amount towards that of her opponent, there exists an optimal increment of the probabilistic strategy at which the cooperator frequency reaches its maximum.     

Waring’s problem in prime numbers

The existence of a constant V(n) such that any sufficiently large natural number can be represented as a sum of nth degrees of primes in total quantity not exceeding this constant is proved.     

Parametric stability in Robe’s problem

In this work we have given a Hamiltonian formulation to Robe’s problem, obtaining again the classic results. We have computed the resonances existing in the circular case and obtained some information with regard to the linear stability of the central equilibrium of Robe’s problem in the elliptic case. In some critical cases we have constructed, in the parameter plane, the boundary curves that separate the regions of stability and instability.     

Stability in an overdetermined problem for the Green’s function

In the plane, we consider the problem of reconstructing a domain from the normal derivative of its Green’s function (with fixed pole) relative to the Dirichlet problem for the Laplace operator. By means of the theory of conformal mappings, we derive stability estimates of Hölder type.     

Nonlinear Stefan problem with convective boundary condition in Storm’s materials

We consider a nonlinear one-dimensional Stefan problem for a semi-infinite material x > 0, with phase change temperature T_f. We assume that the heat capacity and the thermal conductivity satisfy a Storm’s condition, and we assume a convective boundary condition at the fixed face x = 0. A unique explicit solution of similarity type is obtained. Moreover, asymptotic behavior of the solution when \({h\rightarrow + \infty}\) is studied.     

Maximizing the profit in customer’s order acceptance and scheduling problem with weighted tardiness penalty

The customer’s order acceptance and scheduling problem in a single machine environment has long been an appealing research subject. In this paper, a situation where a pool of customers exists and each customer tends to place all his orders to a single company is addressed. Hence, the customer’s orders will be entirely either accepted or rejected. In this work, decisions on rejection or acceptance of customers and sequencing of the accepted orders are simultaneously considered. The goal is to maximize the total net profit obtained from accepted orders revenues contributed by tardiness penalty. In response to the computational complexity of the problem, a heuristic algorithm and two optimal branch and bound procedures with upper bound, lower bound, and dominance rules are developed. Computational results demonstrate that the proposed methods perform well in a timely manner.     

Doob’s optional sampling theorem in Riesz spaces

The notions of stopping times and stopped processes for continuous stochastic processes are defined and studied in the framework of Riesz spaces. This leads to a formulation and proof of Doob’s optional sampling theorem.