Belief structures,weight generating functions and decision-making

We describe the Dempster–Shafer belief structure and provide some of its basic properties. We introduce the plausibility and belief measures associated with a belief structure. We note that these are not the only measures that can be associated with a belief structure. We describe a general approach for generating a class of measures that can be associated with a belief structure using a monotonic function on the unit interval, called a weight generating function. We study a number of these functions and the measures that result. We show how to use weight-generating functions to obtain dual measures from a belief structure. We show the role of belief structures in representing imprecise probability distributions. We describe the use of dual measures, other then plausibility and belief, to provide alternative bounding intervals for the imprecise probabilities associated with a belief structure. We investigate the problem of decision making under belief structure type uncertain. We discuss two approaches to this decision problem. One of which is based on an expected value of the OWA aggregation of the payoffs associated with the focal elements. The second approach is based on using the Choquet integral of a measure generated from the belief structure. We show the equivalence of these approaches.     

Existence and structure results on almost periodic solutions of difference equations

We study the almost periodic solutions of Euler equations and of some more general Difference Equations. We consider two different notions of almost periodic sequences, and we establish some relations between them. We build suitable sequences spaces and we prove some properties of these spaces. We also prove properties of Nemytskii operators on these spaces. We build a variational approach to establish existence of almost periodic solutions as critical points, We obtain existence theorems fornonautonomous linear equations and for an Euler equation with a concave and coercive Lagrangian. We also use a Fixed Point approach to obtain existence results for quasi-linear Difference Equations.     

The personalization of security selection: An application of fuzzy set theory

We apply the theory of fuzzy subsets to the multiple objective decision problem of stock selection. We allow our objectives to have varying degrees of importance. We discuss various criteria used in selecting stocks. We indicate some procedures for subjectively evaluating the membership functions associated with these criteria.     

A free boundary problem for the Laplacian with a constant Bernoulli-type boundary condition

We study a free boundary problem for the Laplace operator, where we impose a Bernoulli-type boundary condition. We show that there exists a solution to this problem. We use A. Beurling’s technique, by defining two classes of sub- and super-solutions and a Perron argument. We try to generalize here a previous work of A. Henrot and H. Shahgholian. We extend these results in different directions.     

Comatrix Coring Generalized and Equivalences of Categories of Comodules

We extend the comatrix coring to the case of a quasi-finite bicomodule. We also generalize some of its interesting properties. We study equivalences between categories of comodules over rather general corings. We particularize to the case of the adjoint pair of functors associated to a morphism of corings over different base rings. We apply our results to corings coming from entwining structures and graded structures, and we obtain new results in the setting of entwining structures and in the graded ring theory.     

Formulations and Valid Inequalities for the Heterogeneous Vehicle Routing Problem

We consider the vehicle routing problem where one can choose among vehicles with different costs and capacities to serve the trips. We develop six different formulations: the first four based on Miller-Tucker-Zemlin constraints and the last two based on flows. We compare the linear programming bounds of these formulations. We derive valid inequalities and lift some of the constraints to improve the lower bounds. We generalize and strengthen subtour elimination and generalized large multistar inequalities.     

Supersymmetry, Witten Complex and Asymptotics for Directional Lyapunov Exponents in Zd

. We study the long distance asymptotic for random walks in random potentials. We use the analytical formulation. We relate the problem to Witten Laplacians via using supersymmetry. We obtain the asymptotic for the directional Lyapunov exponents.     

Poisson algebras associated to quasi-Hopf algebras

We define admissible quasi-Hopf quantized universal enveloping (QHQUE) algebras by ?-adic valuation conditions. We show that any QHQUE algebra is twist-equivalent to an admissible one. We prove a related statement: any associator is twist-equivalent to a Lie associator. We attach a quantized formal series algebra to each admissible QHQUE algebra and study the resulting Poisson algebras.     

Relaxing support vectors for classification

We introduce a novel modification to standard support vector machine (SVM) formulations based on a limited amount of penalty-free slack to reduce the influence of misclassified samples or outliers. We show that free slack relaxes support vectors and pushes them towards their respective classes, hence we use the name relaxed support vector machines (RSVM) for our method. We present theoretical properties of the RSVM formulation and develop its dual formulation for nonlinear classification via kernels. We show the connection between the dual RSVM and the dual of the standard SVM formulations. We provide error bounds for RSVM and show it to be stable, universally consistent and tighter than error bounds for standard SVM. We also introduce a linear programming version of RSVM, which we call RSVMLP. We apply RSVM and RSVMLP to synthetic data and benchmark binary classification problems, and compare our results with standard SVM classification results. We show that relaxed influential support vectors may lead to better classification results. We develop a two-phase method called RSVM² for multiple instance classification (MIC) problems, where RSVM formulations are used as classifiers. We extend the two-phase method to the linear programming case and develop RSVMLP². We demonstrate the classification characteristics of RSVM² and RSVMLP², and report our classification results compared to results obtained by other SVM-based MIC methods on public benchmark datasets. We show that both RSVM² and RSVMLP² are faster and produce more accurate classification results.     

Exponentially damped operators for a harmonic oscillator linearly coupled to a heat bath

We consider the problem of the dissipative dynamics of a harmonic oscillator linearly coupled to a heat bath. We demonstrate that in addition to the mean energy, there exists an infinite series of quantities exponentially decreasing in time that are means of polynomials of the system Hamiltonian. We obtain the spectrum of the corresponding relaxation times. We propose a method for representing the time characteristics of the system in terms of operators corresponding to the exponentially damped observables. We obtain a recurrence relation for these operators.     

Reduction and construction of exact solutions for a nonlinear system of the parabolic type

We study a system of two equations of the parabolic type with two nonlinearities depending on the sum of squares of two unknown functions. We derive conditions under which the system can be reduced to a single equation. We indicate conditions under which this equation can be reduced to a linear heat equation or to semilinear equations. We construct parametric families of exact solutions defined by elementary functions. We derive a control law providing the existence of a wide class of functions that can be realized as exact solutions.     

An Interactive Algorithm for Multi-objective Route Planning

We address the route selection problem for Unmanned Air Vehicles (UAV) under multiple objectives. We consider a general case for this problem, where the UAV has to visit several targets and return to the base. We model this problem as a combination of two combinatorial problems. First, the path to be followed between each pair of targets should be determined. We model this as a multi-objective shortest path problem. Additionally, we need to determine the order of the targets to be visited. We model this as a multi-objective traveling salesperson problem (MOTSP). The overall problem is a combination of these two problems, which we define as a generalized MOTSP. We develop an exact interactive approach to identify the best paths and the best tour of a decision maker under a linear utility function.     

Scheduling and lot sizing models for the single-vendor multi-buyer problem under consignment stock partnership

We consider a centralized supply chain composed of a single vendor serving multiple buyers and operating under consignment stock arrangement. Solving the general problem is hard as it requires finding optimal delivery schedule to the buyers and optimal production lot sizes. We first provide a nonlinear mixed integer programming formulation for the general scheduling and lot sizing problem. We show that the problem is NP-hard in general. We reformulate the problem under the assumption of ‘zero-switch rule’. We also provide a simple sequence independent lower bound to the solution of the general model. We then propose a heuristic procedure to generate a near-optimal delivery schedule. We assess the cost performance of that heuristic by conducting sensitivity analysis on the key model parameters. The results show that the proposed heuristic promises substantial supply-chain cost savings that increase as the number of buyers increases.     

Complex classical fields: An example

We study complex, classical, scalar fields within a new framework introduced in a previous work. We replace the usual functional integral by a complex functional arising from a boosted Hamiltonian. We generalize the Feynman–Kac relation to this setting, and use it to establish the spectral condition on a cylinder. We consider also positive-temperature states.     

Towards higher topology

We categorify the adjunction between locales and topological spaces, this amounts to an adjunction between (generalized) bounded ionads and topoi. We show that the adjunction is idempotent. We relate this adjunction to the Scott adjunction, which was discussed from a more categorical point of view in [21]. We hint that 0-dimensional adjunction inhabits the categorified one.     

An optimal stocking problem to minimize the expected time to sellout

We consider an assortment planning problem where the objective is to minimize the expected time to sell all items in the assortment. We provide several structural results for the optimal assortment. We present a heuristic policy, which we prove is asymptotically optimal. We also show that there are alternate objective criteria under which the problem simplifies considerably.     

Proximal Point Algorithms for Convex Multi-criteria Optimization with Applications to Supply Chain Risk Management

We study a class of convex multi-criteria optimization problems with convex objective functions under linear constraints. We use a non-scalarization method—namely, two implementable proximal point algorithms—to obtain the Pareto optimum under multi-criteria optimization. We show that the algorithms are globally convergent. We apply the algorithms to a supply chain risk management problem under multi-criteria considerations.     

Global existence and blow-up phenomena for a weakly dissipative 2-component Camassa–Holm system

We study the Cauchy problem of a weakly dissipative 2-component Camassa–Holm system. We first establish local well-posedness for a weakly dissipative 2-component Camassa–Holm system. We then present a global existence result for strong solutions to the system. We finally obtain several blow-up results and the blow-up rate of strong solutions to the system.     

Complexification of Multilinear Mappings and Polynomials

We study various methods of complexifying real normed spaces. We see how the notions of duality and complexification are interchangeable. We obtain estimates for the norms of complexified multilinear mappings and polynomials. We see how polynomials can be complexified without reference to the associated multilinear mappings.