existence and bifurcation of solutions for an elliptic degenerate problem abstract we investigate the existence multiplicity and bifurcation of solutions of a model nonlinear degenerate elliptic differential equation x 2 u u u p 1 u in 0 1 u 0 u 1 0 this model is related to a simplified version of the nonlinear wheeler dewitt equation as it appears in quantum cosmological models we prove the existence of multiple positive solutions more precisely we show that there exists an infinite number of connected branches of solutions which bifurcate from the bottom of the essential spectrum of the corresponding linear operator nous etudions ici l existence multiplicite et proprietes de bifurcation des solutions d un probleme elliptique degenere x 2 u u u p 1 u in 0 1 u 0 u 1 0 ce probleme modele est proche d une version simplifiee et non lineaire de l equation de wheeler dewitt utilisee dans des modeles de cosmologie quantique nous prouvons l existence d une infinite de branches de solutions qui bifurquent a partir de l infimum du spectre continu de l operateur lineaire correspondant

dynamical model and nonextensive statistical mechanics of a market index on large time windows the shape and tails of partial distribution functions pdf for a financial signal i e the s and the turbulent nature of the markets are linked through a model encompassing tsallis nonextensive statistics and leading to evolution equations of the langevin and fokker planck type a model originally proposed to describe the intermittent behavior of turbulent flows describes the behavior of normalized log returns for such a financial market index for small and large time windows and both for small and large log returns these turbulent market volatility of normalized log returns distributions can be sufficiently well fitted with a ensuremath chi 2 distribution the transition between the small time scale model of nonextensive intermittent process and the large scale gaussian extensive homogeneous fluctuation picture is found to be at ca a 200 day time lag the intermittency exponent ensuremath kappa in the framework of the kolmogorov log normal model is found to be related to the scaling exponent of the pdf moments thereby giving weight to the model the large value of ensuremath kappa points to a large number of cascades in the turbulent process the first kramers moyal coefficient in the fokker planck equation is almost equal to zero indicating no restoring force a comparison is made between normalized log returns and mere price increments

two dimensional quantum random walk we analyze several families of two dimensional quantum random walks the feasible region the region where probabilities do not decay exponentially with time grows linearly with time as is the case with one dimensional qrw the limiting shape of the feasible region is however quite different the limit region turns out to be an algebraic set which we characterize as the rational image of a compact algebraic variety we also compute the probability profile within the limit region which is essentially a negative power of the gaussian curvature of the same algebraic variety our methods are based on analysis of the space time generating function following the methods of pemantle and wilson j comb theory ser a 97 1 129 161 2002

characterization of large price variations in financial markets statistics of drawdowns loss from the last local maximum to the next local minimum plays an important role in risk assessment of investment strategies as they incorporate higher two order correlations they offer a better measure of real market risks than the variance or other cumulants of daily or some other fixed time scale of returns previous results have shown that the vast majority of drawdowns occurring on the major financial markets have a distribution which is well represented by a stretched exponential while the largest drawdowns are occurring with a significantly larger rate than predicted by the bulk of the distribution and should thus be characterized as outliers eur phys j b 1 1998 141 j risk 2001 in the present analysis the definition of drawdowns is generalized to coarse grained drawdowns or so called e drawdowns and a link between such e outliers and preceding log periodic power law bubbles previously identified quantitative finance 1 2001 452 is established

on a criterion for discrete or continuous spectrum of p laplace eigenvalue problems with singular sign changing weights abstract in this paper we study the existence of spectrum for one dimensional p laplace eigenvalue problems with singular weights subject to dirichlet boundary condition for certain class of singular sign changing weights we prove the existence of discrete spectrum proofs are based on the c 1 0 1 regularity of solutions and construction of the first eigenvalue in a variational set up we also present an example of a weight for which the spectrum is continuous and any corresponding eigenfunction does not belong to c 1 0 1

analysis of the linearization around a critical point of an infinite dimensional hamiltonian system partial differential equations that conserve energy can often be written as infinite dimensional hamiltonian systems of the following general form du dt je u where j x x is a symplectic matrix i e jj 1 and e x r is a c 2 functional defined on some hilbert space x

scaling and memory in volatility return intervals in financial markets abstract for both stock and currency markets we study the return intervals between the daily volatilities of the price changes that are above a certain threshold q we find that the distribution function pq scales with the mean return interval as the scaling function f x is similar in form for all seven stocks and for all seven currency databases analyzed and f x is consistent with a power law form f x x with 2 we also quantify how the conditional distribution pq 0 depends on the previous return interval 0 and find that small or large return intervals are more likely to be followed by small or large return intervals this clustering of the volatility return intervals is a previously unrecognized phenomenon that we relate to the long term correlations known to be present in the volatility econophysics fluctuations extreme values long term correlations long term memory

schrodinger operators with boundary singularities hardy inequality pohozaev identity and controllability results abstract the aim of this paper is two folded firstly we study the validity of a pohozaev type identity for the schrodinger operator a x 2 r in the situation where the origin is located on the boundary of a smooth domain r n n 1 showing some applications to semi linear elliptic equations the problem we address is very much related to optimal hardy poincare inequalities with boundary singularities which have been investigated in the recent past in various papers in view of that the proper functional framework is described and explained secondly we use the pohozaev identity to derive the method of multipliers and we apply it to study the exact boundary controllability for the wave and schrodinger equations corresponding to the singular operator a in particular this complements and extends well known results by vancostenoble and zuazua 2009 38 who discussed the same issue in the case of interior singularity

bifurcation points of a singular boundary value problem on 0 1 abstract following earlier work on some special cases 11 17 and on the analogous problem in higher dimensions 10 20 we make a more thorough investigation of the bifurcation points for a nonlinear boundary value problem of the form a x u x f x u x u x for 0 x 1 0 1 a x u x 2 d x and u 1 0 where for all r and x 0 1 f x 0 0 0 and 3 f x 0 0 v x and 4 f x 0 0 0 so that the formal linearization about a trivial solution u 0 is a x v x v x v x v x for 0 x 1 even when f is a smooth function of all its variables standard bifurcation theory does not apply to the problem and the results differ from the usual conclusions this is because we deal with the case where the coefficient a has a critical degeneracy as x 0 in the sense that a c 0 1 with a x 0 for x 0 1 and lim x 0 a x x 2 a 0 it was observed in 11 17 that if the exponent 2 is replaced by a value less than 2 then classical bifurcation theory can be used to treat the problem the paper 17 deals with the case f x s t sin s whereas 11 covers the more general form f x s t f s here we admit a much broader class of nonlinearities and some new phenomena appear in particular we encounter situations where bifurcation does not occur at a simple eigenvalue of the linearization lying below the essential spectrum

oscillation criteria for pde with p laplacian via the riccati technique abstract the conditions on the function c x r n r are derived which ensure that the pde div u p 2 u c x u p 2u 0 p 1 is oscillatory i e belongs to the closure of the set of zeros of every solution defined on the domain x r n x 1 the main tool is the riccati technique combined with suitable a priori bounds

existence of positive solutions for singular boundary value problems involving the one dimensional p laplacian this paper studies the existence of positive solutions for singular dirichlet boundary value problems these results are obtained by using the global continuation theorem fixed point index theory and approximate method

existence of the second positive radial solution for a p laplacian problem we investigate the existence nonexistence and multiplicity of positive radial solutions for the p laplacian problem with boundary parameters for proofs we mainly use a combination of a fixed point theorem the method of upper and lower solutions and fixed point index theory in the frame of the ordinary differential equation ode technique

inverse statistics and information content abstract inverse statistics analysis studies the distribution of investment horizons to achieve a predefined level of return this distribution provides a maximum investment horizon which determines the most likely horizon for gaining a specific return there exists a significant difference between inverse statistics of financial market data and a fractional brownian motion fbm as an uncorrelated time series which is a suitable criteria to measure information content in financial data in this paper we perform this analysis for the djia and s p500 as two developed markets and tehran price index tepix as an emerging market we also compare these probability distributions with fbm probability to detect when the behavior of the stocks are the same as fbm

on the existence and multiplicity of solutions for a class of singular elliptic problems abstract in this paper we prove the existence and multiplicity of solutions for a class of elliptic problems with singular coefficients we also prove the existence of a sign changing solution for a brezis nirenberg type problem with hardy potential and singular coefficients our proofs are based on the krasnoselskii genus the concentration compactness principle of lions and the linking theorem

growth conditions for oscillation of nonlinear differential equations with p laplacian abstract in this paper oscillation criteria are established for all solutions of second order nonlinear differential equations of the form p x 1 t p g x 0 t 0 here p y is the one dimensional p laplacian operator and g x satisfies the signum condition x g x 0 if x 0 but is not assumed to be monotone the equation naturally includes the famous euler differential equation and half linear differential equations the main purpose is to examine the influence of certain growth conditions of the nonlinear term g x on the oscillation of solutions the conditions are shown to be sharp some of differential inequalities play important roles to prove our results a simple example is included to illustrate the main result a conjecture on the inverse problem is also given finally elliptic equations with p laplacian operator are discussed as an application to our results

one dimensional p laplacian with a strong singular indefinite weight i eigenvalue abstract in this paper we prove the existence of eigenvalues for the problem p u t h t p u t 0 a e in 0 1 u 0 u 1 0 where p s s p 2 s p 1 is a real parameter and the indefinite weight h is a nonnegative measurable function on 0 1 which may be singular at 0 and or 1 and h 0 on any compact subinterval in 0 1 we derive similar properties of eigenvalues as known in linear case p 2 or continuous case h c 0 1 if h satisfies 0 1 t p 1 1 t p 1 h t d t when 1 p 2 and 0 1 2 p 1 s 1 2 h d d s 1 2 1 p 1 1 2 s h d d s when p 2 respectively for the result we establish the c 1 regularity of all solutions at the boundary for the above problem as well as the following problem p u t h t f u t 0 a e in 0 1 u 0 u 1 0 where f c r r s f s 0 for s 0 f is odd and f s p s is bounded above as s 0

weighted hardy inequalities and ornstein uhlenbeck type operators perturbed by multipolar inverse square potentials abstract in this paper our main results are the multipolar weighted hardy inequality c i 1 n r n 2 x a i 2 d r n 2 d k r n 2 d c c o where the functions belong to a weighted sobolev space h 1 and the proof of the optimality of the constant c o c o n n 2 2 2 the gaussian probability measure d is the unique invariant measure for ornstein uhlenbeck type operators this estimate allows us to get necessary and sufficient conditions for the existence of positive solutions to a parabolic problem corresponding to the kolmogorov operators defined on smooth functions and perturbed by a multipolar inverse square potential l u v u u u i 1 n c x a i 2 u x r n c 0 a 1 a n r n

application of multifractal measures to tehran price index we report an empirical study of tehran price index tepix to analyze our data we use various methods like as rescaled range analysis r s modified rescaled range analysis lo s method detrended fluctuation analysis dfa and generalized hurst exponents analysis based on numerical results the scaling range of tepix returns is specified long memory effect or long range correlation property in this market is investigated characteristic exponent for probability distribution function of tepix returns is derived and finally the stage of development in tehran stock exchange is determined

inverse statistics in economics the gain loss asymmetry abstract inverse statistics in economics is considered we argue that the natural candidate for such statistics is the investment horizons distribution this distribution of waiting times needed to achieve a predefined level of return is obtained from often detrended historic asset prices such a distribution typically goes through a maximum at a time called the optimal investment horizon since this defines the most likely waiting time for obtaining a given return by considering equal positive and negative levels of return we report on a quantitative gain loss asymmetry most pronounced for short horizons it is argued that this asymmetry reflects the market dynamics and we speculate over the origin of this asymmetry

existence and bifurcation theorems for nonlinear elliptic eigenvalue problems on unbounded domains abstract we consider nonlinear elliptic eigenvalue problems on unbounded domains g r n using an extended ljusternik schnirelman theory we prove the existence of infinitely many eigenfunctions on every sphere in l 2 g moreover we establish that the infimum of the spectrum of the linearized problem l is always a bifurcation point in addition there is an infinity of branches emanating at from the trivial line of solutions if belongs to the essential spectrum of l

on schrodinger operators with multipolar inverse square potentials abstract positivity essential self adjointness and spectral properties of a class of schrodinger operators with multipolar inverse square potentials are discussed in particular a necessary and sufficient condition on the masses of singularities for the existence of at least a configuration of poles ensuring the positivity of the associated quadratic form is established

the level crossing and inverse statistic analysis of german stock market index dax and daily oil price time series a b s t r a c t the level crossing and inverse statistics analysis of dax and oil price time series are given we determine the average frequency of positive slope crossings where t 1 is the average waiting time for observing the level again we estimate the probability p k which provides us the probability of observing k times of the level with positive slope in time scale t for analyzed time series we found that maximum k is about 6 we show that by using the level crossing analysis one can estimate how the dax and oil time series will develop we carry out the same analysis for the increments of dax and oil price log returns which is known as inverse statistics and provide the distribution of waiting times to observe some level for the increments 2011 elsevier b v all rights reserved stochastic processes occur in many natural and man made phenomena ranging from various indicators of economic activities in the stock market velocity fluctuations in turbulent flows and heartbeat dynamics etc 1 the level crossing analysis of stochastic processes has been introduced by rice 1944 1945 2 26 and used to describe the turbulence 16 rough surfaces 27 stock markets 28 burgers turbulence and kardar parisi zhang equation 29 30 the level crossing analysis of the data set has the advantage that it gives important global properties of the time series and do not need the scaling feature the almost of the methods in time series analysis are using the scaling features of time series and their applications are restricted to the time series with scaling properties our goal with the level crossing analysis is to characterize the statistical properties of the data set with the hope to better understand the underlying stochastic dynamics and provide a possible tool to estimate its dynamics the level crossing and inverse statistics analysis can be viewed as the complementary method to the other well known methods such as detrended fluctuation analysis dfa 31 detrended moving average dma 32 wavelet transform modulus maxima wtmm 33 rescaled range analysis r s 34 scaled windowed variance swv 35 langevin dynamics 36 detrended cross correlation analysis 37 multifactor analysis of

gap bifurcation for nonlinear perturbations of hill s equation keywords bifurcation nonlinear hill s equation testfunctions reference ana article 1990 002view record in web of science record created on 2008 12 10 modified on 2016 08 08

how to quantify deterministic and random influences on the statistics of the foreign exchange market it is shown that price changes of the u s dollar german mark exchange rates upon different delay times can be regarded as a stochastic marcovian process furthermore we show how kramers moyal coefficients can be estimated from the empirical data finally we present an explicit fokker planck equation which models very precisely the empirical probability distributions in particular their non gaussian heavy tails

algebraic unimodular counting we study algebraic algorithms for expressing the number of non negative integer solutions to a unimodular system of linear equations as a function of the right hand side our methods include todd classes of toric varieties via grobner bases and rational generating functions as in barvinok s algorithm we report polyhedral and computational results for two special cases counting contingency tables and kostant s partition function

the number of bound states for a discrete schrodinger operator on bb z n n geq1 lattices we consider the discrete schrodinger operator in in the case of a potential with negative part in an appropriate l space decays with an appropriate rate we present a discrete analog of the method of li and yau 1983 commun math phys 88 309 18 proving an explicit upper estimate on the number of bound states which is independent of the dimension of the lattice this is a major difference with the continuous counterpart estimate which is not valid when n 1 2 as a consequence a dimension independent smallness criterion for the existence of bound states is derived in contrast to the continuous case as well as to the discrete case of vanishing potential a short comment is made on possible applications of the results to the study of the dynamics of some particular spatially discrete nonlinear systems

markov analysis and kramers moyal expansion of nonstationary stochastic processes with application to the fluctuations in the oil price we describe a general method for analyzing a nonstationary stochastic process x t which unlike many of the previous analysis methods does not require x t to have any scaling feature the method is used to study the fluctuations in the daily price of oil it is shown that the returns time series y t ln x t 1 x t is a stationary and markov process characterized by a markov time scale t m the coefficients of the kramers moyal expansion for the probability density function p y tmid r y 0 t 0 are computed p y tmid r y 0 t 0 satisfies a fokker planck equation which is equivalent to a langevin equation for y t that provides quantitative predictions for the oil price over times that are of the order of t m also studied is the average frequency of positive slope crossings nu alpha p y i alpha y i 1 alpha for the returns where t alpha 1nu alpha is the average waiting time for observing y t alpha again

asymptotic properties of free monoid morphisms abstract motivated by applications in the theory of numeration systems and recognizable sets of integers this paper deals with morphic words when erasing morphisms are taken into account cobham showed that if an infinite word w g f a is the image of a fixed point of a morphism f under another morphism g then there exist a non erasing morphism and a coding such that w b based on the perron theorem about asymptotic properties of powers of non negative matrices our main contribution is an in depth study of the growth type of iterated morphisms when one replaces erasing morphisms with non erasing ones we also explicitly provide an algorithm computing and from f and g

inverse statistics in stock markets universality and idiosyncracy abstract investigations of inverse statistics a concept borrowed from turbulence in stock markets exemplified with filtered dow jones industrial average sp physica a 324 2003 338 343 int j mod phys b 17 2003 4003 4012 we have performed extensive analyses based on unfiltered daily indices and stock prices as well as high frequency 5 min records in numerous stock markets all over the world our analysis confirms that the power law distribution of exit times with an exponent of about 1 5 is universal for all the data sets analyzed in addition all data sets show that the power law scaling in the optimal investment horizon holds but with idiosyncratic exponents specifically 1 5 for the daily data in most of the developed stock markets and the 5 min high frequency data while the values for the daily indexes and stock prices in emerging markets are significantly less than 1 5 we show that there is little chance that the discrepancy in is due to the difference in sample sizes of the two kinds of stock markets

the distribution of the number of node neighbors in random hypergraphs hypergraphs the generalization of graphs in which edges become conglomerates of r nodes called hyperedges of rank r 2 are excellent models to study systems with interactions that are beyond the pairwise level for hypergraphs the node degree number of hyperedges connected to a node and the number of neighbors k of a node differ from each other in contrast to the case of graphs where counting the number of edges is equivalent to counting the number of neighbors in this paper i calculate the distribution of the number of node neighbors in random hypergraphs in which hyperedges of uniform rank r have a homogeneous equal for all hyperedges probability p to appear this distribution is equivalent to the degree distribution of ensembles of graphs created as projections of hypergraph or bipartite network ensembles where the projection connects any two nodes in the projected graph when they are also connected in the hypergraph or bipartite network the calculation is non trivial due to the possibility that neighbor nodes belong simultaneously to multiple hyperedges node overlaps from the exact results the traditional asymptotic approximation to the distribution in the sparse regime small p where overlaps are ignored is rederived and improved the approximation exhibits poisson like behavior accompanied by strong fluctuations modulated by power law decays in the system size n with decay exponents equal to the minimum number of overlapping nodes possible for a given number of neighbors it is shown that the dense limit cannot be explained if overlaps are ignored and the correct asymptotic distribution is provided the neighbor distribution requires the calculation of a new combinatorial coefficient qr 1 k which counts the number of distinct labeled hypergraphs of k nodes hyperedges of rank r 1 and where every node is connected to at least one hyperedge some identities of qr 1 k are derived and applied to the verification of normalization and the calculation of moments of the neighbor distribution

complete monotonicity for inverse powers of some combinatorially defined polynomials we prove the complete monotonicity on 0 infty n for suitable inverse powers of the spanning tree polynomials of graphs and more generally of the basis generating polynomials of certain classes of matroids this generalizes a result of szeg and answers among other things a long standing question of lewy and askey concerning the positivity of taylor coefficients for certain rational functions our proofs are based on two ab initio methods for proving that p beta is completely monotone on a convex cone c the determinantal method and the quadratic form method these methods are closely connected with harmonic analysis on euclidean jordan algebras or equivalently on symmetric cones we furthermore have a variety of constructions that given such polynomials can create other ones with the same property among these are algebraic analogues of the matroid operations of deletion contraction direct sum parallel connection series connection and 2 sum the complete monotonicity of p beta for some beta 0 can be viewed as a strong quantitative version of the half plane property hurwitz stability for p and is also related to the rayleigh property for matroids

inverse statistics in the foreign exchange market abstract we investigate intra day foreign exchange fx time series using the inverse statistic analysis developed by simonsen et al eur phys j 27 2002 583 and jensen et al physica a 324 2003 338 specifically we study the time averaged distributions of waiting times needed to obtain a certain increase decrease in the price of an investment the analysis is performed for the deutsch mark dm against the us for the full year of 1998 but similar results are obtained for the japanese yen against the us with high statistical significance the presence of resonance peaks in the waiting time distributions is established such peaks are a consequence of the trading habits of the market participants as they are not present in the corresponding tick business waiting time distributions furthermore a new stylized fact is observed for the normalized waiting time distribution in the form of a power law pdf this result is achieved by rescaling of the physical waiting time by the corresponding tick time thereby partially removing scale dependent features of the market activity

multiple positive solutions to a singular boundary value problem for a superlinear emden fowler equation a multiplicity result for the singular ordinary differential equation y x 2y 0 posed in the interval 0 1 with the boundary conditions y 0 0 and y 1 where 1 0 and 0 are real parameters is presented using a logarithmic transformation and an integral equation method we show that there exists 0 2 such that a solution to the above problem is possible if and only if 1 for 0 1 there are multiple positive solutions while if 1 1 1 the problem has a unique positive solution which is monotonic increasing the asymptotic behavior of y x as x 0 is also given which allows us to establish the absence of positive solution to the singular dirichlet elliptic problem u d x 2u in where rn n 2 is a smooth bounded domain and d x dist x

asymptotics of multivariate sequences part iii quadratic points abstract we consider a number of combinatorial problems in which rational generating functions may be obtained whose denominators have factors with certain singularities specifically there exist points near which one of the factors is asymptotic to a nondegenerate quadratic we compute the asymptotics of the coefficients of such a generating function the computation requires some topological deformations as well as fourier laplace transforms of generalized functions we apply the results of the theory to specific combinatorial problems such as aztec diamond tilings cube groves and multi set permutations

existence and nonexistence results for higher order semilinear evolution inequalities with critical potential we prove nonexistence results for higher order semilinear evolution equations and inequalities of the form ku tk u x 2u u qin rn 0 where n 22 2 this problem can be seen as a higher order evolution version of the nonlinear wheeler de witt equation which appears in the theory of quantum cosmology in order to show that our result is sharp in the parabolic case we establish the existence of positive solutions to the semilinear equation u t u x 2u uqin rn 0 for 0 the nonexistence results are based on the test function method developed by mitidieri pohozaev tesei and veron the existence result is established by the construction of an explicit global solution of the semilinear parabolic inequality

twenty combinatorial examples of asymptotics derived from multivariate generating functions let a bf r bf r in mathbb n d be a d dimensional array of numbers for which the generating function f bf z sum bf r a bf r bf z bf r is meromorphic in a neighborhood of the origin for example f may be a rational multivariate generating function we discuss recent results that allow the effective computation of asymptotic expansions for the coefficients of f our purpose is to illustrate the use of these techniques on a variety of problems of combinatorial interest the survey begins by summarizing previous work on the asymptotics of univariate and multivariate generating functions next we describe the morse theoretic underpinnings of some new asymptotic techniques we then quote and summarize these results in such a way that only elementary analyses are needed to check hypotheses and carry out computations the remainder of the survey focuses on combinatorial applications such as enumeration of words with forbidden substrings edges and cycles in graphs polyominoes and descents in permutations after the individual examples we discuss three broad classes of examples namely functions derived via the transfer matrix method those derived via the kernel method and those derived via the method of lagrange inversion these methods have the property that generating functions derived from them are amenable to our asymptotic analyses and we describe further machinery that facilitates computations for these classes of examples

null controllability for a heat equation with a singular inverse square potential involving the distance to the boundary function this article is devoted to the analysis of control properties for a heat equation with a singular potential 2 defined on a bounded c2 domain rn where is the distance to the boundary function more precisely we show that for any 1 4 the system is exactly null controllable using a distributed control located in any open subset of while for 1 4 there is no way of preventing the solutions of the equation from blowing up the result is obtained applying a new carleman estimate

nodal properties and bifurcation from the essential spectrum for a class of nonlinear sturm liouville problems is taken as the boundary condition at infinity our interest in this problem derives from the fact that it provides an example of bifurcation from the essential spectrum the terms bifurcation from the essential spectrum or singular bifurcation have recently been used to describe the following situation suppose a is a self adjoint hilbert space operator arising from a singular elliptic boundary value problem so that the essential spectrum of a may be non empty when a is perturbed by a nonlinearity f such that f u vanishes of higher order for u 0 the points of the essential spectrum of a are candidates for bifurcation points of the nonlinear eigenvalue problem

uniqueness and bifurcation for solutions of nonlinear sturm liouville eigenvalue problems a class of nonlinear sturm liouville problems is considered these problems admit zero as a trivial solution and the nonlinear operator linearized about zero has a purely continuous spectrum 0 uniqueness of solutions with a prescribed number of nodes is obtained by a shooting argument moreover combining with the previous existence results we prove there are infinitely many continua of solutions which are distinguished by nodal properties bifurcate from the line of trivial solutions at the lowest point of the continuous spectrum

scaling behaviors in differently developed markets scaling properties of four di erent stock market indices are studied in terms of a generalized hurst exponent approach we nd that the deviations from pure brownian motion behavior are associated with the degrees of development of the markets and we observe strong di erentiations in the scaling properties of markets at di erent development stage c

scaling and memory of intraday volatility return intervals in stock markets we study the return interval tau between price volatilities that are above a certain threshold q for 31 intraday data sets including the standard and poor s 500 index and the 30 stocks that form the dow jones industrial index for different threshold q the probability density function pq tau scales with the mean interval tau as formula see text similar to that found in daily volatilities since the intraday records have significantly more data points compared to the daily records we could probe for much higher thresholds and still obtain good statistics we find that the scaling function f x is consistent for all 31 intraday data sets in various time resolutions and the function is well approximated by the stretched exponential f x similar to e ax gamma with gamma 0 38 0 05 and a 3 9 0 5 which indicates the existence of correlations we analyze the conditional probability distribution pq tau tau0 for tau following a certain interval tau0 and find pq tau tau0 depends on tau0 which demonstrates memory in intraday return intervals also we find that the mean conditional interval tau tau0 increases with tau0 consistent with the memory found for pq tau tau0 moreover we find that return interval records in addition to having short term correlations as demonstrated by pq tau tau0 have long term correlations with correlation exponents similar to that of volatility records

existence of solutions for quasilinear elliptic equations with hardy potential in this paper we consider the following quasilinear elliptic equation with hardy potential and dirichlet boundary condition i j 1ndj aij x u diu 12 i j 1ndsai j x u diudju x 2u f x u in where n n 3 is a smooth bounded domain di xi dsaij x s saij x s and 0 n 22 2 and x 2 is called the hardy potential by using the perturbation method we prove the existence of infinitely many solutions for the above problem

sturmian comparison and oscillation theorems for a class of half linear elliptic equations abstract sturmian comparison theorems are established for a class of half linear elliptic equations via the picone identity and oscillation results are derived on the basis of comparison results obtained

solvability of nonlinear equations in spectral gaps of the linearization keywords strongle indefinite nonlinear hill s equation reference ana article 1992 002doi 10 1016 0362 546x 92 90116 vview record in web of science record created on 2008 12 10 modified on 2016 08 08

distribution of the first return time in fractional brownian motion and its application to the study of on off intermittency herein the term fractional brownian motion is used to refer to a class of random walks with long range correlated steps where the mean square displacement of the walker at large time t is proportional to mathit t 2 mathit h with 0h1 for ordinary brownian motion we obtain h 1 2 let t denote the time at which the random walker starting at the origin first returns to the origin the purpose of this paper is to show that the probability distribution of t scales with t as p t ensuremath sim mathit t mathit h mathrm ensuremath 2 theoretical arguments and numerical simulations are presented to support the result additional issues explored include modification to the power law distribution when the random walk is biased and the application of the result to the characterization of on off intermittency a recently proposed mechanism for bursting

multidimensional residues generating functions and their application to queueing networks this paper has two goals the first is to introduce applied mathematicians to a new technique involving several complex variable residue theory this is a multidimensional extension of a well known result for functions of one complex variable p griffiths and j harris principles of algebraic geometry john wiley and sons new york 1978 that yields useful asymptotic information when applied to generating functions the authors begin by reviewing the residue theory of one complex variable noting that there are useful sets of relationships between the residues of certain rational functions they use the one dimensional theory to rederive and extend a well known result of koenigsberg p g harrison oper res 33 1985 pp 464 468 these relationships to a degree can be found for residues of the analogous rational functions of several complex variables the second goal is to apply these tools to the study of product form queueing networks it is well known that for generating functions of a single v

central and local limit theorems applied to asymptotic enumeration iv multivariate generating functions abstract flajolet and soria 1989 1990 discussed some general combinatorial structures in which central limit theorem and exponential tail results hold in this paper we shall use flajolet and odlyzko s transfer theorems 1990 to extend bender and richmond s 1983 central and local limit theorems to a wider class of generating functions which will cover the above mentioned combinatorial structures the local limit theorem provides more accurate asymptotic information and implies the superexponential tail results

existence and multiplicity results for nonlinear boundary value problems this paper studies the existence of positive solutions for a class of boundary value problems of elliptic degenerate equations by using bifurcation and fixed point index theories in the frame of approximation arguments the criteria of the existence multiplicity and nonexistence of positive solutions are established

a global branch of solutions to a semilinear equation on an unbounded interval keywords semilinear second order differential equation bifurcation asymptotic bifurcation neumann problem global branch reference ana article 1985 001view record in web of science record created on 2008 12 10 modified on 2016 08 08