generalized semi infinite programming theory and methods generalized semi infinite optimization problems gsip are considered the difference between gsip and standard semi infinite problems sip is illustrated by examples by applying the reduction ansatz optimality conditions for gsip are derived numerical methods for solving gsip are considered in comparison with methods for sip from a theoretical and a practical point of view it is investigated under which assumptions a gsip can be transformed into an sip

adaptive approximations and exact penalization for the solution of generalized semi infinite min max problems we develop an implementable algorithm for the solution of a class of generalized semi infinite min max problems to this end first we use exact penalties to convert a generalized semi infinite min max problem into a finite family of semi infinite min max min problems second the inner min function is smoothed and the semi infinite max part is approximated using discretization to obtain a three parameter family of finite min max problems under a calmness assumption we show that when the penalty is sufficiently large the semi infinite min max min problems have the same solutions as the original problem and that when the smoothing and discretization parameters go to infinity the solutions of the finite min max problems converge to solutions of the original problem provided the penalty parameter is sufficiently large our algorithm combines tests for adjusting the penalty the smoothing and the discretization parameters and makes use of a min max algorithm as a subroutine in effect the min max algorithm is applied to a sequence of gradually better approximating min max problems with the penalty parameter eventually stopping to increase but with the smoothing and discretization parameters driven to infinity a numerical example demonstrates the viability of the algorithm

systems of frequency distributions for water and environmental engineering abstract a wide spectrum of frequency distributions are used in hydrologic hydraulic environmental and water resources engineering these distributions may have different origins are based on different hypotheses and belong to different generating systems review of literature suggests that different systems of frequency distributions employed in science and engineering in general and environmental and water engineering in particular have been derived using different approaches which include 1 differential equations 2 distribution elasticity 3 genetic theory 4 generating functions 5 transformations 6 bessel function 7 expansions and 8 entropy maximization this paper revisits these systems of distributions and discusses the hypotheses that are used for deriving these systems it also proposes based on empirical evidence another general system of distributions and derives a number of distributions from this general system that are used in environmental and water engineering

streamflow record extension using power transformations and application to sediment transport to obtain a representative set of flow rates for a stream it is often desirable to fill in missing data or extend measurements to a longer time period by correlation to a nearby gage with a longer record linear least squares regression of the logarithms of the flows is a traditional and still common technique however its purpose is to generate optimal estimates of each day s discharge rather than the population of discharges for which it tends to underestimate variance maintenance of variance extension move equations hirsch 1982 were developed to correct this bias this study replaces the logarithmic transformation by the more general box cox scaled power transformation generating a more linear constant variance relationship for the move extension combining the box cox transformation with the move extension is shown to improve accuracy in estimating order statistics of flow rate particularly for the nonextreme discharges which generally govern cumulative transport over time this advantage is illustrated by prediction of cumulative fractions of total bed load transport

semi infinite programming theory methods and applications starting from a number of motivating and abundant applications in 2 including control of robots eigenvalue computations mechanical stress of materials and statistical design the authors describe a class of optimization problems which are referred to as semi infinite because their constraints bound functions of a finite number of variables on a whole region in 3 5 first and second order optimality conditions are derived for general nonlinear problems as well as a procedure for reducing the problem locally to one with only finitely many constraints another main effort for achieving simplification is through duality in 6 there algebraic properties of finite linear programming are brought to bear on duality theory in semi infinite programming section 7 treats numerical methods based on either discretization or local reduction with the emphasis on the design of superlinearly convergent sqp type methods taking this differentiable point of view this paper can be considered to be complementar

computational proof of the mackey formula for q 2 let g be a connected reductive group defined over a finite field with q elements we prove that the mackey formula for the lusztig induction and restriction holds in g whenever q 2 or g does not have a component of type e

a unipotent support for irreducible representations 1 1 let g f be the group of fq rational points of a connected reductive algebraic group g defined over a finite field f throughout this paper we shall assume that the characteristic of the ground field is large the following is part of problem ii in l9 let p be an irreducible complex character of g f show that there is a unique umpotent class c in g which has the property that cga c cfqi p g 0 and has maximal dimension among classes with this property one of the results of this paper is a solution of this problem we also prove the following refinement if g e gf is such that tr g p 0 then the unipotent part of g lies in c or in a conjugacy class of dimension dim c we call c the unipotent support of p another map from the set of irreducible representations of gf to unipotent classes in g has been defined in l8 13 43 this was the composition of two maps one from irreducible representations of gf to a set of parameters in the langlands dual of g and one from this set of parameters to unipotent classes in g another conjectural definition of this map which did not pass through the langlands dual has been proposed by kawanaka kl k2 k3 in terms of generalized gelfand graev representations in analogy with real lie groups he uses the name wave front set for the unipotent class attached to a representation one of the results of this paper is a proof see section 11 of kawanaka s conjecture that his wave front set is well defined and that it coincides with the one defined in l8 this has been known earlier from the work of kawanaka in certain special cases we also show that the unipotent support of an irreducible representation coincides with the wave front set of the dual representation

green functions and character sheaves purely combinatorial way using earlier ideas of p hall in the general case they were introduced 3 in terms of l adic cohomology as values of certain virtual representations of r o t is a maximal torus defined over fq at unipotent elements the characters of rg 0 at arbitrary elements were then expressible in a simple form in terms of green functions of g and of smaller groups one drawback of the definition of 3 was that it did not allow one to compute the green functions except in some simple cases another definition of green functions was proposed by springer first in terms of trigonometric sums on the lie algebra and later in geometrical terms 17 this definition was applicable only in large characteristic and in that case it was identified with the definition in 3 by springer 17 and kazhdan 10 in 12 i observed that green functions for gln can be redefined in terms of intersection cohomology this led me to a new definition of green functions

some generalized functions for the size distribution of income many distributions have been used as descriptive models for the size distribution of income this paper considers two generalized beta distributions which include many of these models as special or limiting cases these generalized distributions have not been used as models for the distribution of income and provide a unified method of comparing many models previously considered

some characterizations of the weil representations of the symplectic and unitary groups abstract let g be a finite symplectic or unitary group we characterize the weil representations of g via their restriction to a standard subgroup then we complete the determination of complex representations of g with specific minimal polynomials of certain elements by showing that they coincide with the weil representations

systems of frequency curves generated by transformations of logistic variables abstract the lognormal s sub l s sub b and s sub u systems of frequency curves are obtained by three simple transformations of the normal curve by applying the same transformations to the logistic systems l sub l l sub b and l sub u are obtained some properties of these systems and their relation to the s systems are set out tables to facilitate fitting l sub u curves by moments are presented author

generalized semi infinite optimization a first order optimality condition and examples we consider a generalized semi infinite optimization problem gsip of the form gsip min f x xem where m x n hi x 0i l m g x y 0 y y x and all appearing functions are continuously differentiable furthermore we assume that the sety x is compact for allx under consideration and the set valued mappingy is upper semi continuous the difference with a standard semi infinite problem lies in thex dependence of the index sety we prove a first order necessary optimality condition of fritz john type without assuming a constraint qualification or any kind of reduction approach moreover we discuss some geometrical properties of the feasible setm

generalized semi infinite programming a tutorial this tutorial presents an introduction to generalized semi infinite programming gsip which in recent years became a vivid field of active research in mathematical programming a gsip problem is characterized by an infinite number of inequality constraints and the corresponding index set depends additionally on the decision variables there exist a wide range of applications which give rise to gsip models some of them are discussed in the present paper furthermore geometric and topological properties of the feasible set and in particular the difference to the standard semi infinite case are analyzed by using first order approximations of the feasible set corresponding constraint qualifications are developed then necessary and sufficient first and second order optimality conditions are presented where directional differentiability properties of the optimal value function of the so called lower level problem are used finally an overview of numerical methods is given

on the estimation of long tailed skewed distributions with actuarial applications abstract very long tailed skewed distributions often arise in practice in particular we find that size of loss distributions in casualty insurance are mainly of this type compounding explains why many of these losses have approximate pareto generalized pareto burr and log t distributions an adaptation of the empirical mean residual life function helps the statistician select the correct model to fit in these cases it is then discovered that minimum distance estimates in particular that of cramer von mises and minimum chi square estimates are extremely valuable and easy to use in the case of grouped data two substantial examples are given one involving hurricane losses and the other dealing with malpractice claims