A Variational Approach to the Maximization of Preferences Without Numerical Representation

Journal of Optimization Theory and Applications - We introduce a variational approach to study a maximization problem of preferences that cannot be represented by a utility function. In such...     

Automorphisms of (B)-geometries

(B)-Geometries are incidence structures arising from permutation sets. The present paper studies the automorphism groups of (B)-Geometries. In certain cases these automorphisms yield examples of inversive planes and of subplanes which are embedded in Minkowski planes (chapter 2). In chapter 3 we describe the automorphism groups of the (B)-Geometries arising from the groups PL(2, pⁿ) and AL(1, pⁿ) in their natural representations on the points of the projective and affine line.Dedicated to Prof.Dr. Walter Benz on his 60th birthdayWork done within the activity of G.N.S.A.G.A. of C.N.R. and supported by the 40% grants of M.U.R.S.T.     

Stability conditions in families

Publications mathématiques de l'IHÉS - We develop a theory of Bridgeland stability conditions and moduli spaces of semistable objects for a family of varieties. Our approach is based...     

A symbolic treatment of Riordan arrays

We approach Riordan arrays and their generalizations via umbral symbolic methods. This new approach allows us to derive fundamental aspects of the theory of Riordan arrays as immediate consequences of the umbral version of the classical Abel?s identity for polynomials. In particular, we obtain a novel non-recursive formula for Riordan arrays and derive, from this new formula, some known recurrences and a new recurrence relation for Riordan arrays.     

Global sensitivity measures from given data

Simulation models support managers in the solution of complex problems. International agencies recommend uncertainty and global sensitivity methods as best practice in the audit, validation and application of scientific codes. However, numerical complexity, especially in the presence of a high number of factors, induces analysts to employ less informative but numerically cheaper methods. This work introduces a design for estimating global sensitivity indices from given data (including simulation input–output data), at the minimum computational cost. We address the problem starting with a statistic based on the L¹-norm. A formal definition of the estimators is provided and corresponding consistency theorems are proved. The determination of confidence intervals through a bias-reducing bootstrap estimator is investigated. The strategy is applied in the identification of the key drivers of uncertainty for the complex computer code developed at the National Aeronautics and Space Administration (NASA) assessing the risk of lunar space missions. We also introduce a symmetry result that enables the estimation of global sensitivity measures to datasets produced outside a conventional input–output functional framework.     

Infinitely many solutions for a class of discrete non-linear boundary value problems

The existence of infinitely many solutions for a discrete non-linear Dirichlet problem involving the p-Laplacian, under appropriate oscillating behaviours of the non-linear term, is established. The approach is based on the critical point theory.     

A note on Griffiths infinitesimal invariant for curves

Given a generic curve of genus $g\ge 4$ and a smooth point $L\in W_{g-1}^{1}(C)$ , whose linear system is base-point free, we consider the Abel–Jacobi normal function associated with $L^{\otimes 2}\otimes \omega _{C}^{-1}$ , when $(C,L)$ varies in moduli. We prove that its infinitesimal invariant reconstructs the couple $(C,L)$ . When $g=4$ , we obtain the generic Torelli theorem proved by Griffiths.     

Inner solvers for interior point methods for large scale nonlinear programming

This paper deals with the solution of nonlinear programming problems arising from elliptic control problems by an interior point scheme. At each step of the scheme, we have to solve a large scale symmetric and indefinite system; inner iterative solvers, with an adaptive stopping rule, can be used in order to avoid unnecessary inner iterations, especially when the current outer iterate is far from the solution. In this work, we analyse the method of multipliers and the preconditioned conjugate gradient method as inner solvers for interior point schemes. We discuss the convergence of the whole approach, the implementation details and report the results of numerical experimentation on a set of large scale test problems arising from the discretization of elliptic control problems. A comparison with other interior point codes is also reported. This research was supported by the Italian Ministry for Education, University and Research (MIUR) projects: FIRB Project: “Parallel Nonlinear Numerical Optimization PN ² O” (grant n. RBAU01JYPN, ) and COFIN/PRIN04 Project “Numerical Methods and Mathematical Software for Applications” (grant n. 2004012559, ).     

Character degree graphs that are complete graphs

Let be a finite group, and write for the set of degrees of irreducible characters of . We define to be the graph whose vertex set is , and there is an edge between and if . We prove that if is a complete graph, then is a solvable group.