metrics on semistable and numerically effective higgs bundles we provide notions of numerical effectiveness and numerical flatness for higgs vector bundles on compact kahler manifolds in terms of fibre metrics we prove several properties of bundles satisfying such conditions and in particular we show that numerically flat higgs bundles have vanishing chern classes and that they admit filtrations whose quotients are stable flat higgs bundles we compare these definitions with those previously given in the case of projective varieties finally we study the relations between numerically effectiveness and semistability establishing semistability criteria for higgs bundles on projective manifolds of any dimension

hamilton jacobi equations in infinite dimensions i uniqueness of viscosity solutions soient un espace de banach v son dual v et des solutions d une equation h x u du 0 dans etablies dans un sous ensemble de v h v r v r est continue on demontre que des solutions classiques sont determinees de facon unique par leurs valeurs limites on montre que l extension de la notion de solutions viscosite aux espaces de banach reussit dans des espaces munis de la propriete de radon nikodym

generic solutions for some perturbed optimization problem in non reflexive banach spaces abstract let z be a closed boundedly relatively weakly compact nonempty subset of a banach space x and j z r a lower semicontinuous function bounded from below if x 0 is a convex subset in x and x 0 has approximatively z property k then the set of all points x in x 0 z for which there exists z 0 z such that j z 0 x z 0 x and every sequence z n z satisfying lim n j z n x z n x for x contains a subsequence strongly convergent to an element of z is a dense g subset of x 0 z moreover under the assumption that x 0 is approximatively z strictly convex we show more namely that the set of all points x in x 0 z for which there exists a unique point z 0 z such that j z 0 x z 0 x and every sequence z n z satisfying lim n j z n x z n x for x converges strongly to z 0 is a dense g subset of x 0 z here x inf j z x z z z these extend s cobzas s result j math anal appl 243 2000 344 356

numerical peak holomorphic functions on banach spaces abstract we introduce the notion of numerical strong peak function and investigate the denseness of the norm and numerical peak functions on complex banach spaces let a b b x x be the banach space of all bounded continuous functions f on the unit ball b x of a banach space x and their restrictions f b x to the open unit ball are holomorphic in finite dimensional spaces we show that the intersection of the set of all norm peak functions and the set of all numerical peak functions is a dense g subset of a b b x x we also prove that if x is a smooth banach space with the radon nikod m property then the set of all numerical strong peak functions is dense in a b b x x in particular when x l p 1 p or x l 1 it is shown that the intersection of the set of all norm strong peak functions and the set of all numerical strong peak functions is a dense g subset of a b b x x as an application the existence and properties of numerical boundary of a b b x x are studied finally the numerical peak function in a b b x x is characterized when x c k and some negative results on the denseness of numerical strong peak holomorphic functions are given

bergman kernels and the pseudoeffectivity of relative canonical bundles a criterion for the pseudoeffectivity of twisted relative canonical bundles of surjective projective maps

existence of viscosity solutions of hamilton jacobi equations abstract equations of hamilton jacobi type arise in many areas of application including the calculus of variations control theory and differential games recently m g crandall and p l lions trans amer math soc 277 1983 1 42 introduced the class of viscosity solutions of these equations and proved uniqueness within this class this paper discusses the existence of these solutions under assumptions closely related to the ones which guarantee the uniqueness

on holomorphic functions attaining their norms abstract we show that on a complex banach space x the functions uniformly continuous on the closed unit ball and holomorphic on the open unit ball that attain their norms are dense provided that x has the radon nikodym property we also show that the same result holds for banach spaces having a strengthened version of the approximation property but considering just functions which are also weakly uniformly continuous on the unit ball we prove that there exists a polynomial such that for any fixed positive integer k it cannot be approximated by norm attaining polynomials with degree less than k for x d 1 a predual of a lorentz sequence space we prove that the product of two polynomials with degree less than or equal two attains its norm if and only if each polynomial attains its norm

hamilton jacobi equations in infinite dimensions ii existence of viscosity solutions on demontre des resultats d existence generaux pour 2 problemes 1 le probleme de cauchy u t h x t u du 0 dans v 0 t u x 0 x dans v et 2 le probleme stationnaire u h x u du 0 dans v ou h et sont donnees

an exact transfer matrix formulation of plane sound wave transmission in inhomogeneous ducts abstract the impedance or the reflection coefficient of plane sound waves in inhomogeneous ducts satisfies a riccati equation the present paper shows that the duct impedance matrix or the scattering matrix can be related explicitly to the solutions of the associated linear equation of the riccati equation for duct impedance or reflection coefficient respectively new exact analytical scattering matrix solutions which follow as consequences of this connection are given for two significant duct acoustics problems namely the sound transmission in non uniform ducts carrying an incompressible subsonic low mach number mean flow transmission of sound in uniform ducts with a full quadratic axial mean temperature gradient

on longitudinal acoustic propagation in convergent and divergent nozzle flows abstract the longitudinal propagation of sound in quasi one dimensional low mach number nozzle flow is considered in section 1 the solution in the ray approximation section 2 1 is used to transform the wave equation into a schrodinger form which is studied for the family of power law ducts including as a particular case the conical nozzle it is shown that the coincidence of flow sources sinks with sound sources can lead to appearance of essential singularities section 2 2 which can be removed by using a riccati transformation section 2 4 the exact solutions of the acoustic equations for the parabolic figure 1 and hyperbolic figure 2 nozzles are obtained in terms of bessel functions section 2 3 respectively of complex order and argument the general formulas together with limiting forms in the compactness ray and asymptotic approximations section 3 1 are used to establish properties of the acoustic velocity and pressure section 3 2 kinetic and compression energies and energy flux and wave action section 3 3 for example it is shown that the equipartition of energies for moderate variations in cross section gives way table 2 to a predominance of kinetic compression energies respectively near blockages openings the effects of non uniform mean flow table 1 are discussed by comparing horns with nozzles section 3 4 e g it is shown that the duality principle in three alternative forms does not extend from horn to nozzles and the acoustic equations have no elementary solutions for the latter in contrast with the former

a complex frobenius theorem multiplier ideal sheaves and hermitian einstein metrics on stable bundles a complex frobenius theorem is proved for subsheaves of a holomorphic vector bundle satisfying a finite generation condition and a differential inclusion relation a notion of multiplier ideal sheaf for a sequence of hermitian metrics is defined the complex frobenius theorem is applied to the multiplier ideal sheaf of a sequence of metrics along donaldson s heat flow to give a construction of the destabilizing subsheaf appearing in the donaldson uhlenbeck yau theorem in the case of algebraic surfaces

plane wave analysis of conical and exponential pipes with incompressible mean flow the general equation for one dimensional wave propagation at low flow mach numbers m less than or equals slant0 2 is derived and is solved analytically for conical and exponential shapes the transfer matrices are derived and shown to be self consistent comparison is also made with the relevant data available in the literature the transmission loss behaviour of conical and exponential pipes and mufflers involving these shapes are studied analytical expressions of the same are given for the case of a stationary medium the mufflers involving conical and exponential pipes are shown to be inferior to simple expansion chambers of similar dimensions at higher frequencies from the point of view of noise abatement as was observed earlier experimentally

on the one dimensional acoustic propagation in conical ducts with stationary mean flow this paper proposes a direct time domain calculation of the time domain responses of anechoic conical tubes with steady weak mean flow the starting point is the approximated linear one dimensional wave equation governing the velocity potential for the case of steady flow with low mach number a traveling solution with general space dependent propagation velocity is then proposed from which the inward and outward pressure and velocity impulse responses can be obtained the results include the well known responses of conical and cylindrical ducts with zero mean flow

optimization and differentiation in banach spaces abstract we show that some old ideas of smulian can be used to give another proof of a theorem of bourgain we characterize subsets of banach spaces having the radon nikodym property by means of optimization results

on existence and uniqueness of solutions of hamilton jacobi equations abstract the theory of scalar first order nonlinear partial differential equations has been enjoying a rapid development in the last few years this development occurred because the authors established uniqueness criteria for generalized solutions called viscosity solutions which correctly identify the solutions sought in areas of application including control theory differential games and the calculus of variations the concept of viscosity solutions is relatively easy to work with and many formally heuristic or difficult proofs have been made rigorous or simple using this concept a feedback process has begun and the experience recently gained in working with viscosity solution has suggested new existence and uniqueness results the current paper continues this interaction by establishing new existence ane uniqueness results in a natural generality suggested by earlier proofs it is also felt that the presentation of the comparison results which imply uniqueness continuous dependence and are used to estimate moduli of continuity has something to offer over earlier presentations in special cases author

on stegall s smooth variational principle abstract assume that every coercive continuous and bounded below function defined on a real banach space attains after a suitable linear perturbation a not necessarily strong minimum then the space is dentable

the influence of a liquid flow on sound fields confined by conical walls abstract sound propagation in conical waveguides is analyzed for the case where a background flow is maintained through the cone and points along the radial co ordinate r only a general expression for the acoustic pressure is derived and the perturbations of the acoustic field accommodated by the presence of a background flow are found by use of the green function method in the second part of this paper flow measurement properties are discussed the designation of propagation constants such as the wave number and phase speed lose much of their intuitive meaning in a conical waveguide instead the so called pseudo guide wave number and pseudo phase speed are introduced as they are well defined in the cone case and simplifies to the wave number and phase speed in the cylinder case respectively it is shown that changes due to a background flow in pseudo guide wave number pseudo phase speed and zero point crossing times all exhibit an oscillatory behavior as a function of the r co ordinate this is in contrast to the case of a cylinder where such changes become a linear function of the distance from the transmitter the oscillatory behavior in the changes in zero point crossing times as a function of r does not hamper flow measurement in the cone case since the only requirement to be fulfilled is in principle that a one to one correspondence between measured output changes in zero point crossing times and actual flow determined by v 0 at a specific receiver location exists it is shown that this requirement is fulfilled as changes in zero point crossing times depend linearly on the flow coefficient v 0 at a given r co ordinate there are however certain discrete r co ordinate values where this is not the case namely those where changes in zero point crossing times become zero for any value of v 0 in other words if the receiver is positioned near r co ordinates where zero point crossing times are at a maximum or a minimum for a given value of v 0 the truncated cone flow meter sensor is able to measure flow unambiguiosly by detection of changes in zero point crossing times induced by a background flow

some properties of viscosity solutions of hamilton jacobi equations abstract recently m g crandall and p l lions introduced the notion of viscosity solutions of scalar nonlinear first order partial differential equations viscosity solutions need not be differentiable anywhere and thus are not sensitive to the classical problem of the crossing of characteristics the value of this concept is established by the fact that very general existence uniqueness and continuous dependence results hold for viscosity solutions of many problems arising in fields of application the notion of a viscosity solution admits several equivalent formulations here we look more closely at two of these equivalent criteria and exhibit their virtues by both proving several new facts and reproving various known results in a simpler manner moreover by forsaking technical generality we hereby provide a more congenial introduction to this subject than the original paper author

generic existence of solutions for some perturbed optimization problems abstract let x be a real banach space z a closed nonvoid subset of x and j z r a lower semicontinuous function bounded from below if x is reflexive and has the kadets property then the set of all x x for which there exists z0 z such that j z0 x z0 inf j z x z z z is g and dense in x this extends a result of k s lau 1978 indiana univ math j 27 791 795 on nearest points the case j 0