on the existence of positive solution for second order multi points boundary value problems here we are concerned with the existence of positive solution for autonomous and nonautonomous second order systems with multi points boundary conditions for nonautonomous systems we use the schauder s fixed point theorem in a suitable banach space while for autonomous ones using fixed point theorems is usually useless because of the existence of trivial solution and for this we employed a method based on the implicit function theorem and topological degree in order to verify the obtained results we have considered some definite systems to verify the results numerically

universal statistics of the scattering coefficient of chaotic microwave cavities we consider the statistics of the scattering coefficient s of a chaotic microwave cavity coupled to a single port we remove the nonuniversal effects of the coupling from the experimental s data using the radiation impedance obtained directly from the experiments we thus obtain the normalized scattering coefficient whose probability density function pdf is predicted to be universal in that it depends only on the loss quality factor of the cavity we compare experimental pdfs of the normalized scattering coefficients with those obtained from random matrix theory rmt and find excellent agreement the results apply to scattering measurements on any wave chaotic system

statistics of transmitted power in multichannel dissipative ergodic structures we use the random matrix theory rmt to study the probability distribution function and moments of the wave power transmitted inside systems with ergodic wave motion the results describe either open multichannel systems or their closed counterparts with local in space internal dissipation we concentrate on the regime of broken time reversal invariance and employ two different analytical approaches the exact supersymmetry method and a simpler technique that uses rmt eigenstatistics for closed nondissipative systems as an input the results of the supersymmetric method were confirmed by numerical simulation the simpler method is found to be adequate for closed systems with uniform dissipation or in the limit of a large number of weak local dampers

combined effects of concave and convex nonlinearities in some elliptic problems abstract this paper deals with a class of semilinear elliptic dirichlet boundary value problems where the combined effects of a sublinear and a superlinear term allow us to establish some existence and multiplicity results

existence and comparison results for operator and differential equations in abstract spaces in this paper we apply the chain methods developed in heikkila and lakshmikantham 1994 to obtain new fixed point theorems and new existence and comparison results for operator equations in partially ordered sets these results are then applied to discontinuous implicit functional differential equations in ordered banach spaces

existence results for operator and differential equations and inclusions abstract this paper contains a brief summary of existence results for operator and differential equations and inclusions derived recently via a recursion method and generalized iteration methods introduced in 11 12 23

first principles model of time dependent variations in transmission through a fluctuating scattering environment fading is the time dependent variation in transmitted signal strength through a complex medium due to interference or temporally evolving multipath scattering in this paper we use random matrix theory rmt to establish a first principles model for fading including both universal and nonuniversal effects this model provides a more general understanding of the most common statistical models rayleigh fading and rice fading and provides a detailed physical basis for their parameters we also report experimental tests on two ray chaotic microwave cavities the results show that our rmt model agrees with the rayleigh and rice models in the high loss regime but there are strong deviations in low loss systems where the rmt approach describes the data well

on extremal solutions of inclusion problems with applications to game theory abstract a recursion principle generalized iteration methods and the axiom of choice are applied to prove the existence of extremal fixed points of set valued mappings in posets extremal solutions of an inclusion problem and extremal nash equilibria for a normal form game

positive solutions of a nonlinear m point boundary value problem let ai 0 for i 1 m 3 and am 2 0 let i satisfy 0 1 2 m 2 1 and m 2i 1 ai i 1 we study the existence of positive solutions to the boundary value problem where a c 0 1 0 and f c 0 0 we show the existence of at least one positive solution if f is either superlinear or sublinear by applying a fixed point theorem in cones

universal properties of two port scattering impedance and admittance matrices of wave chaotic systems statistical fluctuations in the eigenvalues of the scattering impedance and admittance matrices of two port wave chaotic systems are studied experimentally using a chaotic microwave cavity these fluctuations are universal in that their properties are dependent only upon the degree of loss in the cavity we remove the direct processes introduced by the nonideally coupled driving ports through a matrix normalization process that involves the radiation impedance matrix of the two driving ports we find good agreement between the experimentally obtained marginal probability density functions pdfs of the eigenvalues of the normalized impedance admittance and scattering matrix and those from random matrix theory rmt we also experimentally study the evolution of the joint pdf of the eigenphases of the normalized scattering matrix as a function of loss experimental agreement with the theory by brouwer and beenakker for the joint pdf of the magnitude of the eigenvalues of the normalized scattering matrix is also shown

on the existence of periodic solutions for the quasi linear third order differential equation abstract in this paper we consider the nonlinear third order quasi linear differential equation x k 2 x f x x x and obtain some simple conditions for the existence of a periodic solution for it in so doing we use the implicit function theorem to prove a theorem about the existence of periodic solutions and consider one example to show the realizability of the conditions the validity of the conditions for the parameter free problem x k 2 x f x x x also is considered

effect of short ray trajectories on the scattering statistics of wave chaotic systems in many situations the statistical properties of wave systems with chaotic classical limits are well described by random matrix theory however applications of random matrix theory to scattering problems require introduction of system specific information into the statistical model such as the introduction of the average scattering matrix in the poisson kernel here it is shown that the average impedance matrix which also characterizes the system specific properties can be expressed in terms of classical trajectories that travel between ports and thus can be calculated semiclassically theoretical results are compared with numerical solutions for a model wave chaotic system

scattering reflection and impedance of waves in chaotic and disordered systems with absorption we review recent progress in analysing wave scattering in systems with both intrinsic chaos and or disorder and internal losses when the scattering matrix is no longer unitary by mapping the problem onto a nonlinear supersymmetric model we are able to derive closed form analytic expressions for the distribution of reflection probability in a generic disordered system one of the most important properties resulting from such an analysis is statistical independence between the phase and the modulus of the reflection amplitude in every perfectly open channel the developed theory has far reaching consequences for many quantities of interest including local green functions and time delays in particular we point out the role played by absorption as a sensitive indicator of mechanisms behind the anderson localization transition we also provide a random matrix based analysis of s matrix and impedance correlations for various symmetry classes as well as the distribution of transmitted power for systems with broken time reversal invariance completing previous works on the subject the results can be applied in particular to the experimentally accessible impedance and reflection in a microwave or an ultrasonic cavity attached to a system of antennas

a parallel method for linear equations with tridiagonal toeplitz coefficient matrices abstract there are many articles on symmetric tridiagonal toeplitz and circulant systems such systems in areas including numerical methods for solving boundary value differential equations and in graph theory these matrices can often be written as the product of bidiagonal matrices in this article nonsymmetric toepliz systems and nonsymmetric circulant systems are examined the coefficient matrix is split into two bidiagonal matrices and the efficient solution of the resulting systems is considered

on generalized methods of successive approximations abstract there are several generalized methods of monotone successive approximations in ordered sets a which generalize the usual sequences of the iterative of a point a of a under a selfmapping f on a to some well ordered subsets of a these are smallest admissible set containing a by buber and kirk the set w a by abian and brown well ordered chain of f iterations of a by heikkila and smallest complete f chain containing a by fuchssteiner the well ordered chains of f iterations were compared by heikkila in 1999 with the admissible sets we compare here all of the above four methods our study is based on a notion of a generalized orbit which is a generalization of the one which was introduced by the author in 1988 as an answer to a problem posed by banaschewski in 1992 we use in our proofs a minimum of tools in particular we assume that the relation is only asymmetric we do not use the transitivity postulated for orderings and use only extensionality pairing union and separation axioms of zermelo s set theory

elliptic problems with lack of compactness via a new fixed point theorem abstract this paper provides a new fixed point theorem for increasing self mappings g b b of a closed ball b x where x is a banach semilattice which is reflexive or has a weakly fully regular order cone x by means of this fixed point theorem we are able to establish existence results of elliptic problems with lack of compactness

universal and nonuniversal properties of wave chaotic scattering systems prediction of the statistics of scattering in typical wave chaotic systems requires combining system specific information with universal aspects of chaotic scattering as described by random matrix theory this rapid communication shows that the average impedance matrix which characterizes such system specific properties can be semiclassically calculated in terms of ray trajectories between ports theoretical predictions are compared with experimental results for a microwave billiard demonstrating that the theory successfully uncovered universal statistics of wave chaotic scattering systems

random matrix theory of multi antenna communications the ricean channel the use of multi antenna arrays in wireless communications through disordered media promises huge increases in the information transmission rate it is therefore important to analyse the information capacity of such systems in realistic situations of microwave transmission where the statistics of the transmission amplitudes channel may be coloured here we present an approach that provides analytic expressions for the statistics i e the moments of the distribution of the mutual information for general gaussian channel statistics the mathematical method applies tools developed originally in the context of coherent wave propagation in disordered media such as random matrix theory and replicas although it is valid formally for large antenna numbers this approach produces extremely accurate results even for arrays with as few as two antennas we also develop a method to analytically optimize over the input signal distribution which enables us to calculate analytic capacities when the transmitter has knowledge of the statistics of the channel the emphasis of this paper is on elucidating the novel mathematical methods used we do this by analysing a specific case when the channel matrix is a complex gaussian with arbitrary mean and unit covariance which is usually called the ricean channel