the periodic boundary value problem for semilinear elastic beam equations the resonance case this paper discusses the existence of generalized solutions to periodic boundary value problems for semilinear elastic beam equations under a resonance condition the argument presented makes use of the global inverse theorem and galerkin s method

forced vibrations of superquadratic hamiltonian systems on etudie l existence des solutions t periodiques ter t 0 du systeme hamiltonien suivant z gh z f t ou g est la matrice asymetrique standard

free vibrations for a semilinear wave equation abstract existence and regularity of nontrivial time periodic solutions are proved for semilinear wave equations under mild smoothness monotonicity and superlinearity assumptions the forced vibration case is also treated

weight monodromy conjecture for p adically uniformized varieties the aim of this paper is to prove the weight monodromy conjecture deligne s conjecture on the purity of monodromy filtration for varieties p adically uniformized by the drinfeld upper half spaces of any dimension the ingredients of the proof are to prove a special case of the hodge standard conjecture and apply a positivity argument of steenbrink m saito to the weight spectral sequence of rapoport zink as an application by combining our results with the results of schneider stuhler we compute the local zeta functions of p adically uniformized varieties in terms of representation theoretic invariants we also consider a p adic analogue by using the weight spectral sequence of mokrane

a new proof and an extension of a theorem of p rabinowitz concerning nonlinear wave equations abstract in 1978 p rabinowitz proved a theorem concerned with the existence of a nontrivial periodic solution of a nonlinear wave equation with a continuous increasing superlinear nonlinear term in this paper we present a new and simpler proof of this theorem and relax an assumption on the nonlinear term which is a discontinuous nondecreasing function author

abstract critical point theorems and applications to some nonlinear problems with strong resonance at infinity critical point theorems and applications to some nonlinear problems with strong resonance at infinity p bartolo and v benci istituto di matematica applicata via re david x0 bari ital and istituto di analisi matematica palazzo ateneo l ia scolai 2 bari italy received in revised form 20 december 1952

adapting a classification rule to local and global shift when only unlabelled data are available abstract for evolving populations the training data and the test data need not follow the same distribution thus the performance of a prediction model will deteriorate over the course of time this requires the re estimation of the prediction model after some time however in many applications e g credit scoring new labelled data are not available for re estimation due to verification latency i e label delay thus methods which enable a prediction model to adapt to distributional changes by using only unlabelled data are highly desirable a shift adaptation method for binary classification is presented here the model is based on mixture distributions the conditional feature distributions are determined at the time where labelled data are available and the unconditional feature distribution is determined at the time where new unlabelled data are accessible these mixture distributions provide information on the old and the new positions of subpopulations a transition model then describes how the subpopulations of each class have drifted to form the new unconditional feature distribution assuming that the conditional distributions are reorganised using a minimum of energy a two step estimation procedure results first for a given class prior distribution the transfer of probability mass is estimated such that the energy required to obtain the new unconditional distribution by a local transfer of the old conditional distributions is a minimum since the optimal solution of the resulting transportation problem measures the distance between the old and the new distributions the change of the class prior distribution is found in a second step by solving the transportation problem for varying class prior distributions and selecting the value for which the objective function is a minimum using the solution of the transportation problem and the component parameters of the unconditional feature distribution the new conditional feature distribution can be determined this thus allows for a shift adaptation of the classification rule the performance of the proposed model is investigated using a large real world dataset on default rates in danish companies the results show that the shift adaptation improves classification results

nonlinear problems with strong resonance at infinity an abstract theorem and applications on considere l equation au n u u e ou a est un operateur lineaire n avec c 1 e r et e est un espace de hilbert on suppose que n a une derivee a l infini n et que o appartient au spectre de a n on demontre un theoreme pour la multiplicite des solutions

periodic and quasi periodic solutions of nonlinear wave equations via kam theory in this paper the nonlinear wave equation u u u xx v x u x t varepsilon u 3 x t 0 is studied it is shown that for a large class of potentials v x one can use kam methods to construct periodic and quasi periodic solutions in time for this equation

existence of infinitely many periodic solutions for the radially symmetric wave equation with resonance abstract in this paper we consider the periodic dirichlet problem for a forced nonlinear wave equation with resonance u t t u u a t x u p 1 u in a n dimensional ball under some suitable assumptions on p and a t x we prove the existence of infinitely many radially symmetric time periodic solutions for the problem by variational methods

a new kind of integral transform and its application to periodic solutions in this paper we suggest a new kind of integral transform and establish the main theorems of that this approach allows us to show some general existence theorems for periodic solutions to the semilinear wave equation with the forced term having double frequency a novelty of this transform is to prove the existence of a combination oscillation for the continuous system without the so called difficulty of small divisors by j j stoker nonlinear vibrations interscience new york 1950 in addition our integral transform can be applied to rather general reaction diffusion systems however as a concrete example we show that maginu s model f rothe j math biol 7 1979 375 384 has multiple nonconstant t periodic plane wave solutions

topological results on a certain class of functionals and application abstract we study in this paper problems of the type u u p 1 u x bounded r n u 0 i where x is given and where p 1 n 2 n 2 p 1 if n 2 our main result is that i has an infinite number of solutions for a residual set of in h 1 in particular for many n n there exists an open and dense subset of in h 1 such that i has n distinct solutions for such an this result is to be related to the conjecture developed in 1 of the existence of an infinite number of solutions to i the proof relies on a general characterization of level sets for a certain class of functionals when there are no critical value in a large enough interval in addition to the study of problem i we apply this characterization to give another proof using e g brouwer s fixed point theorem for some classical results about even functionals and saddle points

periodic solutions of symmetric wave equations this paper concerns the existence of solutions to the following nonautonomous wave equation gu uttu f 2 f x t is nondecreasing in and f x t 0 if and only if 0 our first result deals with the case where f is superlinear at theorem 1 let f 1 and f 2 be satisfied assume moreover that f satisfies f 3 there are r 0 and 2 such that

oscillatory phenomena associated to semilinear wave equations in one spatial dimension let g be a nonincreasing odd c function and i 0 we establish that for any solution u s c r hq 0 of the equation utt uxx g u 0 and any io 0 l the function t u t xo satisfies the following alternative either u t x0 0 vt g r or vo r there exist t and t2 in a a 21 such that u ti xo 0 and u t2 xo 0 we study the structure of the set of points satisf ing the first possibility we give analogous results for ux and for some other homogeneous boundary conditions

uber die lokale zetafunktion von shimuravarietaten monodromiefiltration und verschwindende zyklen in ungleicher charakteristik

periodic solutions for completely resonant nonlinear wave equations with dirichlet boundary conditions we consider the nonlinear string equation with dirichlet boundary conditions utt uxx u with u u3 o u5 odd and analytic 0 and we construct small amplitude periodic solutions with frequency for a large lebesgue measure set of close to 1 this extends previous results where only a zero measure set of frequencies could be treated the ones for which no small divisors appear the proof is based on combining the lyapunov schmidt decomposition which leads to two separate sets of equations dealing with the resonant and non resonant fourier components respectively the q and the p equations with resummation techniques of divergent powers series allowing us to control the small divisors problem the main difficulty with respect to the nonlinear wave equations utt uxx mu u m 0 is that not only the p equation but also the q equation is infinite dimensional

infinitely many periodic solutions for a semilinear wave equation in a ball in rn abstract in this paper we study the wave equation with sub linearity in a ball with periodic dirichlet conditions combining the minimax principle with an approximation argument we prove the existence of infinitely many time periodic solutions for the problem the proof also relies on the structure of the spectrum of the linearized problem

periodic solutions of nonlinear wave equations on obtient des conditions suffisantes pour l existence de solutions doublement periodiques de l equation d onde non lineaire u ts f t s u u t t s u t s u t s t ou f est une fonction continue donnee dans r 3 et f est t periodique en t et s

cantor families of periodic solutions for wave equations via a variational principle abstract we prove existence of small amplitude periodic solutions of completely resonant wave equations with frequencies in a cantor set of asymptotically full measure via a variational principle a lyapunov schmidt decomposition reduces the problem to a finite dimensional bifurcation equation variational in nature defined on a cantor set of non resonant parameters the cantor gaps are due to small divisors phenomena to solve the bifurcation equation we develop a suitable variational method in particular we do not require the typical arnold non degeneracy condition of the known theory on the nonlinear terms as a consequence our existence results hold for new generic sets of nonlinearities

fidos a generalized fisher based feature extraction method for domain shift traditional pattern recognition techniques often assume that the data sets used for training and testing follow the same distribution however this assumption is usually not true for many real world problems as data from the same classes but different domains e g data are collected under different conditions may show different characteristics we introduce fidos a generalized fisher based method for domain shift problem that aims at learning invariant features across domains in a supervised manner different from classical fisher feature extraction fidos aims to minimize not only the within class scatter but also the difference in distributions between domains therefore the subspace constructed by fidos reduces the drift in distributions among different domains and at the same time preserves the discriminants across classes another advantage of fidos over classical fisher is that fidos extracts more features when multiple source domains are available in the training set this is essential for a good classification especially when the number of classes is small experimental results on both artificial and real data and comparisons with other methods demonstrate the efficiency of our method in classifying objects under domain shift situations

a property of exponential stability in nonlinear wave equations near the fundamental linear mode abstract we consider the nonlinear wave equation utt c2uxx u u t 0 u t 0 where is an analytic function satisfying 0 0 and 00 0 for each value of the harmonic energy e i e energy when 0 we consider the closed curve e which is the phase space trajectory of the linear mode with lowest frequency if the perturbation parameter and the harmonic energy e are small enough then near e we construct by means of a suitable simplified equation a closed curve e with the following property provided the distance between the initial datum and such a curve is small enough the corresponding solution remains close to e up to times exponentially long with 1 eve cannot expect the curves e to be trajectories of solutions of such curves depend smoothly on the parameters e and the above result is deduced from a general theorem on generic hamiltonian perturbations of completely resonant linear systems

free vibrations for an asymmetric beam equation the existence of nontrivial solutions for the beam equations is proved in two cases the superlinearity case and the jump nonlinearity case

nonlinear vibration of a beam where u cu k enexzujke jkr sinjx z and n denote the integer set and the positive integer set respectively the domain of a is given by d a u e l q iau e t q let w q be the completion of d a j under the graph norm i l4tr o l4lt2 l q then the space w2 q can be characterized by the fourier series u c ujk eik sinjx c 1 j2 lk iujk12 it is easy to see that the imbedding w12 b l q is compact c a

subclass discriminant analysis over the years many discriminant analysis da algorithms have been proposed for the study of high dimensional data in a large variety of problems each of these algorithms is tuned to a specific type of data distribution that which best models the problem at hand unfortunately in most problems the form of each class pdf is a priori unknown and the selection of the da algorithm that best fits our data is done over trial and error ideally one would like to have a single formulation which can be used for most distribution types this can be achieved by approximating the underlying distribution of each class with a mixture of gaussians in this approach the major problem to be addressed is that of determining the optimal number of gaussians per class i e the number of subclasses in this paper two criteria able to find the most convenient division of each class into a set of subclasses are derived extensive experimental results are shown using five databases comparisons are given against linear discriminant analysis lda direct lda dlda heteroscedastic lda hlda nonparametric da nda and kernel based lda k lda we show that our method is always the best or comparable to the best

on p adic intermediate jacobians for an algebraic variety of dimension with totally degenerate reduction over a adic field definition recalled below and an integer with we define a rigid analytic torus together with an abel jacobi mapping to it from the chow group of codimension algebraic cycles that are homologically equivalent to zero modulo rational equivalence these tori are analogous to those defined by griffiths using hodge theory over we compare and contrast the complex and adic theories finally we examine a special case of a adic analogue of the generalized hodge conjecture

covariate shift adaptation by importance weighted cross validation a common assumption in supervised learning is that the input points in the training set follow the same probability distribution as the input points that will be given in the future test phase however this assumption is not satisfied for example when the outside of the training region is extrapolated the situation where the training input points and test input points follow different distributions while the conditional distribution of output values given input points is unchanged is called the covariate shift under the covariate shift standard model selection techniques such as cross validation do not work as desired since its unbiasedness is no longer maintained in this paper we propose a new method called importance weighted cross validation iwcv for which we prove its unbiasedness even under the covariate shift the iwcv procedure is the only one that can be applied for unbiased classification under covariate shift whereas alternatives to iwcv exist for regression the usefulness of our proposed method is illustrated by simulations and furthermore demonstrated in the brain computer interface where strong non stationarity effects can be seen between training and test sessions

periodic solutions for an asymptotically linear wave equation with resonance abstract in this paper we study the existence and multiplicity of nontrivial periodic solutions for an asymptotically linear wave equation with resonance both at infinity and at zero the main features are using morse theory for the strongly indefinite functional and the precise computation of critical groups under conditions which are more general

on the k theory of local fields in this paper we establish a connection between the quillen k theory of certain local fields and the de rham witt complex of their rings of integers with logarithmic poles at the maximal ideal the fieldsk we consider are complete discrete valuation fields of characteristic zero with perfect residue field k of characteristic p 2 when k contains the pth roots of unity the relationship between the k theory with z p coefficients and the de rham witt complex can be described by a sequence

computations of critical groups and applications to asymptotically linear wave equation and beam equation in this paper by using the morse index theory for strongly indefinite functionals developed in nonlinear anal tma in press we compute precisely the critical groups at the origin and at infinity respectively the abstract theorems are used to study the existence multiplicity of nontrivial periodical solutions for asymptotically wave equation and beam equation with resonance both at infinity and at zero

asymptotic approach for non linear periodical vibrations of continuous structures abstract an asymptotic approach for determining periodic solutions of non linear vibration problems of continuous structures such as rods beams plates etc is proposed starting with the well known perturbation technique the independent displacement and frequency is expanded in a power series of a natural small parameter it leads to infinite systems of interconnected non linear algebraic equations governing the relationships between modes amplitudes and frequencies a non trivial asymptotic technique based on the introduction of an artificial small parameter is used to solve the equations an advantage of the procedure is the possibility to take into account a number of vibration modes as examples free longitudinal vibrations of a rod and lateral vibrations of a beam under cubically non linear restoring force are considered resonance interactions between different modes are investigated and asymptotic formulae for corresponding backbone curves are derived

standing waves on an infinitely deep perfect fluid under gravity the existence of two dimensional standing waves on the surface of an infinitely deep perfect fluid under gravity is established when formulated as a second order equation for a real valued function w on the 2 torus and a positive parameter the problem is fully nonlinear the highest order x derivative appears in the nonlinear term but not in the linearization at 0 and completely resonant there are infinitely many linearly independent eigenmodes of the linearization at 0 for all rational values of the parameter moreover for any prescribed order of accuracy there exists an explicit approximate solution of the nonlinear problem in the form of a trigonometric polynomial using a nash moser method to seek solutions of the nonlinear problem as perturbations of the approximate solutions the existence question can be reduced to one of estimating the inverses of linearized operators at non zero points after changing coordinates these operators become first order and non local in space and second order in time after further changes of variables the main parts become diagonal with constant coefficients and the remainder is regularizing or quasi one dimensional in the sense of 22 the operator can then be inverted for two reasons first the explicit formula for the approximate solution means that restricted to the infinite dimensional kernel of the linearization at zero the inverse exists and can be estimated second the small divisor problems that arise on the complement of this kernel can be overcome by considering only particular parameter values selected according to their diophantine properties a parameter dependent version of the nash moser implicit function theorem now yields the existence of a set of unimodal standing waves on flows of infinite depth corresponding to a set of values of the parameter 1 which is dense at 1 unimodal means that the term of smallest order in the amplitude is cos x cos t which is one of many eigenfunctions of the completely resonant linearized problem

linear dimensionality reduction via a heteroscedastic extension of lda the chernoff criterion we propose an eigenvector based heteroscedastic linear dimension reduction ldr technique for multiclass data the technique is based on a heteroscedastic two class technique which utilizes the so called chernoff criterion and successfully extends the well known linear discriminant analysis lda the latter which is based on the fisher criterion is incapable of dealing with heteroscedastic data in a proper way for the two class case the between class scatter is generalized so to capture differences in co variances it is shown that the classical notion of between class scatter can be associated with euclidean distances between class means from this viewpoint the between class scatter is generalized by employing the chernoff distance measure leading to our proposed heteroscedastic measure finally using the results from the two class case a multiclass extension of the chernoff criterion is proposed this criterion combines separation information present in the class mean as well as the class covariance matrices extensive experiments and a comparison with similar dimension reduction techniques are presented

periodic solutions to nonlinear one dimensional wave equation with dependent coefficients this paper deals with t periodicity and regularity of solutions to the one dimensional nonlinear wave equation with x dependent coefficients

a generalization of coleman s p adic integration theory we associate to a scheme x smooth over a p adic ring a kind of cohomology group h i fp x j for proper x this cohomology has poincare duality hence gysin maps and cycle class maps which are reasonably explicit for zero cycles we show that the cycle class map is given by coleman integration the cohomology theory h fp is therefore interpreted as giving a generalization of coleman s theory we find an embedding h syn 2i x i h fp 2i x i where h syn is rigid syntomic cohomology our main result is an explicit description of the syntomic abel jacobi map in terms of generalized coleman integration

on strongly indefinite functionals with applications recently in their remarkable paper critical point theory for indefinite functionals v benci and p rabinowitz gave a direct approach avoiding finitedimensional approximationsto the existence theory for critical points of indefinite functionals in this paper we develop under weaker hypotheses a simpler but more general theory for such problems in the second part of the paper the abstract results are applied to a class of resonance problems of the landesman and lazer type and moreover they are illustrated by an application to a wave equation problem 0 introduction this paper is devoted to the critical point theory of strongly indefinite functionals in a real hilbert space h here a strongly indefinite functional is a cl map h r which is neither bounded from above or below not even modulo a finite dimensional subspace such functionals arise for example in the study of periodic solutions of the one dimensional wave equation in the study of periodic solutions of hamiltonian systems of ordinary differential equations in the existence theory for systems of elliptic equations etc to find the critical points of strongly indefinite functionals different methods were used for example rabinowitz studied the restrictions of the functional to finite dimensional subspaces 1 2 and then he tried to find the critical points of the original problem by passing to the limit for a suitable subsequence of the critical points of the restricted problems amann 3 reduced the indefinite functionals by means of a saddlepoint reduction to a finite dimensional problem of course this is only possible under some strong hypotheses under certain assumptions the functional can be replaced by a dual variational problem having some better properties see for example 4 or 5 the first direct approach was given by benci and rabinowitz 6 the essential in their paper is the observation that more detailed information about the special form of the deformations a substitute for the gradient flow associated to the functional is needed they constructed deformations having special representations by solving appropriate differential equations approximately by time discretisation this method has some disadvantages because one needs strong hypotheses in order to get the approximations uniformly on bounded sets a main part of our paper will be the construction of flows and deformations having special representations by solving appropriate differential equations exactly received by the editors march 30 1981 and in revised form november 30 1981 1980 mathematics subject classification primary 58e05 secondary 47h25 35l05

discriminative learning under covariate shift we address classification problems for which the training instances are governed by an input distribution that is allowed to differ arbitrarily from the test distribution problems also referred to as classification under covariate shift we derive a solution that is purely discriminative neither training nor test distribution are modeled explicitly the problem of learning under covariate shift can be written as an integrated optimization problem instantiating the general optimization problem leads to a kernel logistic regression and an exponential model classifier for covariate shift the optimization problem is convex under certain conditions our findings also clarify the relationship to the known kernel mean matching procedure we report on experiments on problems of spam filtering text classification and landmine detection

domain adaptation via transfer component analysis domain adaptation allows knowledge from a source domain to be transferred to a different but related target domain intuitively discovering a good feature representation across domains is crucial in this paper we first propose to find such a representation through a new learning method transfer component analysis tca for domain adaptation tca tries to learn some transfer components across domains in a reproducing kernel hilbert space using maximum mean miscrepancy in the subspace spanned by these transfer components data properties are preserved and data distributions in different domains are close to each other as a result with the new representations in this subspace we can apply standard machine learning methods to train classifiers or regression models in the source domain for use in the target domain furthermore in order to uncover the knowledge hidden in the relations between the data labels from the source and target domains we extend tca in a semisupervised learning setting which encodes label information into transfer components learning we call this extension semisupervised tca the main contribution of our work is that we propose a novel dimensionality reduction framework for reducing the distance between domains in a latent space for domain adaptation we propose both unsupervised and semisupervised feature extraction approaches which can dramatically reduce the distance between domain distributions by projecting data onto the learned transfer components finally our approach can handle large datasets and naturally lead to out of sample generalization the effectiveness and efficiency of our approach are verified by experiments on five toy datasets and two real world applications cross domain indoor wifi localization and cross domain text classification