Showing papers in "Applied mathematical sciences in 2007"

On Some Properties of a High Order Fractional Differential Operator which is not in General Selfadjoint

Abstract: A fractional differential operator of order α ∈ R+ is introduced and some of its properties are studied. This operator is a generalization of the operators of Riesz-Feller, of Riemann-Liouville, of the fractional power of the Laplacian and of a class of the Jacob pseudodifferential operators. Mathematics Subject Classification: 26A33, 35S05, 60G52

m solutions good, m-1 solutions better

Abstract: One of the main objectives of theoretical research in computational complexity and feasibility is to explain experimentally observed difference in complexity. Empirical evidence shows that the more solutions a system of equations has, the more difficult it is to solve it. Similarly, the more global maxima a continuous function has, the more difficult it is to locate them. Until now, these empirical facts have been only partially formalized: namely, it has been shown that problems with two or more solutions are more difficult to solve than problems with exactly one solution. In this paper, we extend this result and show that for every m, problems with exactly m solutions are more difficult to solve than problems with m − 1 solutions. Rephrasing Orwell’s “Four legs good, two legs better”, we can describe this result as “m solutions good, m−1 solutions better”. Mathematics Subject Classification: 68Q17, 68Q15, 90C60, 65G20 2 L. Longpre, V. Kreinovich, W. Gasarch, G.W. Walster

Factor Demand Modelling: the Theory and the Practice

Abstract: Since the work of Cobb and Douglas [18], two main innovations have been introduced in applied factor demand analysis, i.e. the use of flexible functional forms and the modelling of dynamics, expectations, and the interrelatedness of the adjustment process. Recently, cointegration theory has provided an additional important contribution, yielding empirical content to the notion of equilibrium employed in economic analysis, encompassing both the idea of centre of gravity relationship, suggested by Classical economists, and the notion of market-clearing position, employed by Neoclassical economist. Also in the light of the most recent generalizations of the concept of cointegration, allowing for economic attractors changing over time, as the evolution of the structural features of the economy proceeds, this paper critically assess the key theoretical and empirical issues in factor demand analysis.

Bandwidth Allocation and QoS Routing for Heterogeneous Networks

Abstract: We present a bandwidth allocation scheme offering optimal solutions to the network optimization problem. The bandwidth allocation policy in class-based networks can be defined with the proportionally fair rule expressed by piecewise linear objective functions. This scheme is formulated as a mixed-integer linear programming (MILP) model, preparing a database identifying suitable paths upon each connection request. We also study the blocking probability of an end-to-end transmission system with predetermined optimal solutions. Mathematics Subject Classification: 90B10, 90B18, 90C11

Any (True) Statement Can Be Generalized So That It Becomes Trivial: A Simple Formalization of D. K. Faddeev's Belief

Abstract: In his unpublished lectures on general algebra, a well-known algebraist D. K. Faddeev expressed a belief that every true mathematical statement can be generalized in such a way that it becomes trivial. To the best of our knowledge, this belief has never been formalized before. In this short paper, we provide a simple formalization (and proof) of this belief.

A Note on Relations for Reliability Measures in Zero-Adjusted Models

Abstract: In this note we examine and study relations in zero-adjusted models. Relations for reliability measures in the adjusted and unadjusted models are established and appropriate comparisons including the relative error are presented. The relative error is shown to be a decreasing function of the counts. Some inequalities and comparisons for weighted zeroadjusted models are established. Mathematics Subject Classifications: 62N05, 60B10

The Recursive Fitting of Multivariate Complex Subset ARX Models

Abstract: In this paper we propose an innovative recursive learning algorithm to sequentially estimate multivariate complex subset autoregressive models with exogenous variables (VARX models), including full-order models. This paper suggests the use of the recursive fitting of multivariate complex subset ARX models in conjunction with order selection criteria to select an 'optimal' multivariate complex subset ARX model. The recursive procedure can be embedded in a tree algorithm. We fit the necessary models associated with the bottom stage, and then recursively fit models which include more variables, until finally we fit recursively the full order ARX model with maximum lags P and Q.

Large Sharpening Intertemporal Prospect Theory

Abstract: Prospect theory [4] of risky choices has been extended to encompass intertemporal choices [6]. Presentation of intertemporal prospect theory suffers from minor mistakes, however [2]. To clarify the theory we restate it and show further mistakes in current presentations ([6], [2]) of value and discount functions.

An Efficient Algorithm for Graph Bisection of Triangularizations

Abstract: Graph bisection is an elementary problem in graph theory. We consider the best known experimental algorithms and introduce a new algorithm called Longest-Path-Algorithm. Applying this algorithm to the cluster tree generation of hierarchical matrices, arising for example in discretizations of partial equations, we show that this algorithm outperforms previous algorithms.

Orthogonal Linear Regression in Roentgen Stereophotogrammetry

Abstract: Rooted in aerial reconnaissance, mathematical photogrammetry has evolved into a mainstay of biomedical image processing. The present paper develops an algorithm for Roentgen stereophotogrammetry, a method of imaging musculoskeletal systems both static and dynamic, which incorporates a number of novel features employing techniques from projective geometry, orthogonal regression and least squares approximation. Theoretical and numerical evidence is presented of the efficacy of the proposed procedure. Mathematics Subject Classifications: 51N15, 62J05, 92C55

Bounds and Comparisons for Weighted Renewal-Type Integral Equations

Abstract: In this note, inequalities and bounds for weighted renewal-type integral equations are presented. Some upper and lower bounds for the weighted renewal-type integral equations with monotone weight functions are derived. Some upper and lower bounds for the weighted renewal-type equations with monotone weight functions are derived. Bounds for the difference between two weighted renewal functions as well between the parent and weighted renewal functions are obtained in terms of the parent renewal reliability functions and their first and second moments. Relations for renewal-type integrals of the ruin probability are presented. Some inequalities, bounds and convergence results are also established. Mathematics Subject Classifications: 62N05, 62B10