singular solutions of perturbed logistic type equations abstract we are concerned with the qualitative analysis of positive singular solutions with blow up boundary for a class of logistic type equations with slow diffusion and variable potential we establish the exact blow up rate of solutions near the boundary in terms of karamata regular variation theory this enables us to deduce the uniqueness of the singular solution

nonlinear state estimation indistinguishable states and the extended kalman filter it has been shown by judd and smith that it is impossible to determine the state of a nonlinear dynamical system from noisy observations of the system even with perfect knowledge of the system dynamics and unlimited prior observation there is always a set of states indistinguishable from the true state however a new simple method to assimilate data into a model and estimate the state is suggested this method is related to a dynamical systems approach to nonlinear filtering that is the use of shadowing trajectories in nonlinear noise reduction in this paper the performance of this new method of state estimation is compared with that of the extended kalman filter it is found that the new method performs better largely owing to it taking into account the nonlinearity of the system

bifix codes and sturmian words we prove new results concerning the relation between bifix codes episturmian words and subgroups of free groups we study bifix codes in factorial sets of words we generalize most properties of ordinary maximal bifix codes to bifix codes maximal in a recurrent set f of words f maximal bifix codes in the case of bifix codes contained in sturmian sets of words we obtain several new results let f be a sturmian set of words defined as the set of factors of a strict episturmian word our results express the fact that an f maximal bifix code of degree d behaves just as the set of words of f of length d an f maximal bifix code of degree d in a sturmian set of words on an alphabet with k letters has k 1 d 1 elements this generalizes the fact that a sturmian set contains k 1 d 1 words of length d moreover given an infinite word x if there is a finite maximal bifix code x of degree d such that x has at most d factors of length d in x then x is ultimately periodic our main result states that any f maximal bifix code of degree d on the alphabet a is the basis of a subgroup of index d of the free group on a

horizontal visibility graphs exact results for random time series networks this procedure allows us to apply methods of complex network theory for characterizing time series in this work we present the horizontal visibility algorithm a geometrically simpler and analytically solvable version of our former algorithm focusing on the mapping of random series series of independent identically distributed random variables after presenting some properties of the algorithm we present exact results on the topological properties of graphs associated with random series namely the degree distribution the clustering coefficient and the mean path length we show that the horizontal visibility algorithm stands as a simple method to discriminate randomness in time series since any random series maps to a graph with an exponential degree distribution of the shape pk 1 32 3 k 2 independent of the probability distribution from which the series was generated accordingly visibility graphs with other pk are related to nonrandom series numerical simulations confirm the accuracy of the theorems for finite series in a second part we show that the method is able to distinguish chaotic series from independent and identically distributed i i d theory studying the following situations i noise free low dimensional chaotic series ii low dimensional noisy chaotic series even in the presence of large amounts of noise and iii high dimensional chaotic series coupled map lattice without needs for additional techniques such as surrogate data or noise reduction methods finally heuristic arguments are given to explain the topological properties of chaotic series and several sequences that are conjectured to be random are analyzed

parameter identification in noisy extended systems a hydrodynamic case abstract this paper is concerned with the robustness of parameter identification methods with respect to the noise levels typically found in experiments more precisely we focus on the case of an extended nonlinear system a system of coupled local maps akin to a discretized complex ginzburg landau equation modeling a wake experiment after a brief description of this hydrodynamic experiment as well as of the associated cost function and synthetic data generation we introduce two inversion methods a one time step approach and a more sophisticated n time step optimization procedure solved by a backpropagation method the one time step approach reduces to a small linear system for the unknown parameters while the n time step approach involves a backpropagation equation for a set of lagrage multipliers the sensitivity of each method with respect to noise is then discussed while the n time step method is very robust even with large amounts of noise the one time step approach is shown to be affected by small noise levels

on the density of lyndon roots in factors this work takes another look at the number of runs that a string may contain and provides an alternative proof for the bound we also propose another stronger conjecture that states the following for a fixed order on the alphabet within every factor of a word there are at most as many occurrences of lyndon roots corresponding to runs in the word as the length of the factor only first occurrences of roots in each run are considered

existence and uniqueness of positive solutions of semilinear elliptic equations with coulomb potentials on bf r 3 we study the positive solutions of a semilinear equation with a coulomb potential on 3 we give a new uniqueness theorem for the positive radial solutions of such an equation and we apply these results to the thomas fermi dirac von weizsacker equation without electrostatic repulsion

partial words and the critical factorization theorem revisited in this paper we consider one of the most fundamental results on the periodicity of words namely the critical factorization theorem given a word w and nonempty words u v satisfying w uv the minimal local period associated with the factorization u v is the length of the shortest square at position u 1 the critical factorization theorem shows that for any word there is always a factorization whose minimal local period is equal to the minimal period or global period of the word crochemore and perrin presented a linear time algorithm in the length of the word that finds a critical factorization from the computation of the maximal suffixes of the word with respect to two total orderings on words the lexicographic ordering related to a fixed total ordering on the alphabet and the lexicographic ordering obtained by reversing the order of letters in the alphabet here by refining crochemore and perrin s algorithm we give a version of the critical factorization theorem for partial words such sequences may contain do not know symbols or holes our proof provides an efficient algorithm which computes a critical factorization when one exists our results extend those of blanchet sadri and duncan for partial words with one hole a world wide web server interface at http www uncg edu mat research cft2 has been established for automated use of the program

semiclassical ground state solutions for critical schrodinger poisson systems with lower perturbations abstract in this paper we study the following singularly perturbed schrodinger poisson system e 2 u v x u u f u u 5 x r 3 e 2 u 2 x r 3 where e is a small positive parameter v c r 3 r and f c r r satisfies neither the usual ambrosetti rabinowitz type condition nor any monotonicity condition on f u u 3 by using some new techniques and subtle analysis we prove that there exists a constant e 0 0 determined by v and f such that for e 0 e 0 the above system admits a semiclassical ground state solution v e with exponential decay at infinity we also study the asymptotic behavior of v e as e 0 in particular our results can be applied to the nonlinearity f u u q 2 u for q 3 4 and extend the previous work that only deals with the case in which f u u q 2 u for q 4 6

noise robust estimates of correlation dimension and k2 entropy using gaussian kernels to define the correlation sum we derive simple formulas that correct the noise bias in estimates of the correlation dimension and k2 entropy of chaotic time series the corrections are only based on the difference of correlation dimensions for adjacent embedding dimensions and hence preserve the full functional dependencies on both the scale parameter and embedding dimension it is shown theoretically that the estimates which are derived for additive white gaussian noise are also robust for moderately colored noise simulations underline the usefulness of the proposed correction schemes it is demonstrated that the method gives satisfactory results also for non gaussian and dynamical noise

the analysis of chaotic time series data this paper presents a brief survey of time series analysis methods that are applicable to processes whose behavior can be described as low dimensional chaos the goal of these methods is to allow experimentalists to obtain local estimates of the dynamics directly from a set of data these estimates are often sufficiently accurate to attempt noise reduction prediction and control

gradient free descent shadowing and state estimation using limited derivative information shadowing trajectories can play an important role in assessing the reliability of forecasting models they can also play an important role in providing state estimates for ensemble forecasts gradient descent methods provide one approach for obtaining shadowing trajectories which have been shown to have many useful properties there remains the important question whether shadowing trajectories can be found in very high dimensional systems like weather and climate models the principle impediment is the need to compute the derivative or adjoint of the system dynamics in this paper we investigate gradient descent methods that use limited derivative information we demonstrate the methods with an application to a moderately high dimensional system using no derivative information at all

compressed suffix arrays and suffix trees with applications to text indexing and string matching the proliferation of online text such as found on the world wide web and in online databases motivates the need for space efficient text indexing methods that support fast string searching we model this scenario as follows consider a text t consisting of n symbols drawn from a fixed alphabet sigma the text t can be represented in n lg sigma bits by encoding each symbol with lg sigma bits the goal is to support fast online queries for searching any string pattern p of m symbols with t being fully scanned only once namely when the index is created at preprocessing time the text indexing schemes published in the literature are greedy in terms of space usage they require omega n lg n additional bits of space in the worst case for example in the standard unit cost ram suffix trees and suffix arrays need omega n memory words each of omega lg n bits these indexes are larger than the text itself by a multiplicative factor of omega smash lg sigma n which is significant when sigma is of constant size such as in textsc ascii or textsc unicode on the other hand these indexes support fast searching either in o m lg sigma time or in o m lg n time plus an output sensitive cost o mathit occ for listing the mathit occ pattern occurrences we present a new text index that is based upon compressed representations of suffix arrays and suffix trees it achieves a fast smash o m lg sigma n lg sigma epsilon n search time in the worst case for any constant 0 epsilon leq 1 using at most smash bigl epsilon 1 o 1 bigr n lg sigma bits of storage our result thus presents for the first time an efficient index whose size is provably linear in the size of the text in the worst case and for many scenarios the space is actually sublinear in practice as a concrete example the compressed suffix array for a typical 100 mb textsc ascii file can require 30 40 mb or less while the raw suffix array requires 500 mb our theoretical bounds improve emph both time and space of previous indexing schemes listing the pattern occurrences introduces a sublogarithmic slowdown factor in the output sensitive cost giving o mathit occ smash lg sigma epsilon n time as a result when the patterns are sufficiently long we can use auxiliary data structures in o n lg sigma bits to obtain a total search bound of o m lg sigma n mathit occ time which is optimal

how the character comparison order shapes the shift function of on line pattern matching algorithms string matching is the problem of finding all occurrences of a string 0 m 1 of length m called a pattern in a longer string 0 n 1 of length n called a text several string matching algorithms have been designed to solve the problem in linear time most of them work in two steps called pattern preprocessing and text search step the paper addresses the definition and computation of the shift function in the pattern preprocessing step of on line string matching algorithms the shift function depends essentially on the order the pattern characters are compared with the corresponding text characters we consider a family of algorithms that do not change the character comparison order j during execution and we present a uniform definition of shift function j for such algorithms via a function iminj the definition allows one to compute j in o m log log m time in the worst case given iminj but sufficient conditions to compute j in o m time are provided computing iminj requires o m2 comparisons in general we introduce the class of compact orders which is the generalization of knuth morris pratt boyer moore and crochemore perrin character comparison orders and we give algorithms to compute both function iminj and shift function j in o m time for all compact orders we show that given the order j and the pattern there exists a set c of equivalent orders such that the function imink can be computed in linear time given iminj for all orders k c moreover we characterize two orders in the set c that respectively minimize and maximize the values of the shift function and we show that for both those orders the shift function can be computed in linear time given iminj

positive solutions for some non autonomous schrodinger poisson systems abstract in this paper we study the schrodinger poisson system sp u u k x x u a x u p 1 u x r 3 k x u 2 x r 3 with p 3 5 assuming that a r 3 r and k r 3 r are nonnegative functions such that lim x a x a 0 lim x k x 0 and satisfying suitable assumptions but not requiring any symmetry property on them we prove the existence of positive solutions

multiplicity of concentrating positive solutions for schrodinger poisson equations with critical growth abstract in this paper we deal with a nonlinear schrodinger poisson equation involving critical sobolev exponent under a local condition imposed on the potential we relate the number of positive solutions with the topology of the set where the potential attains its minimum values in the proofs we apply szulkin and weth s generalized nehari manifold methods penalization techniques and ljusternik schnirelmann theory

phase space embedding of electrocardiograms we study properties of the human electrocardiogram under the working hypothesis that fluctuations beyond the regular structure of single cardiac cycles are unpredictable against this background we discuss the possibility of using the phase space embedding method for this kind of signal in particular the specific nature of the stochastic or high dimensional component allows us to use phase space embeddings for certain signal processing tasks as practical applications we discuss noise filtering fetal ecg extraction and the automatic detection of clinically relevant features the main purpose of the paper is to connect results of embedding theory that have not been previously applied in practice and practical applications that have not yet been justified theoretically

multiple positive solutions to a class of modified nonlinear schrodinger equations abstract this paper is concerned with the existence and multiplicity of positive solutions of the following equation u u 2 u 2 u a x u p 2 u k x u where u h 1 r we will prove that the modified term 2 u 2 u is helpful to find multiple positive solutions in the case of the nonlinearity with sign changing coefficient a x surprisingly we do not need a sign condition r n a x e 1 p d x 0 which has been proven to be a necessary condition to the existence of positive solutions for semilinear elliptic equations with sign changing nonlinearity alama and tarantello 1993 1

testing predictability of symbolic sequences using time delay embedding a criterion is proposed to determine the embedding dimension from symbolic sequences several artificial and dna sequences are tested by using this criterion and the likelihood of determinism in those sequences are investigated based on the results of the time delay embedding some interesting numerical results have been obtained

noise reduction in chaotic time series data a survey of common methods this paper surveys some of the methods that have been suggested for reducing noise in time series data whose underlying dynamical behavior can be characterized as low dimensional chaos although the procedures differ in details all of them must solve three basic problems how to reconstruct an attractor from the data how to approximate the dynamics in various regions on the attractor and how to adjust the observations to satisfy better the approximations to the dynamics all current noise reduction methods have similar limitations but the basic problems are reasonably well understood the methods are an important tool in the experimentalist s repertoire for data analysis in our view they should be used more widely particularly in studies of attractor dimension lyapunov exponents prediction and control

two way string matching a new string matching algorithm is presented which can be viewed as an intermediate between the classical algorithms of knuth morris and pratt on the one hand and boyer and moore on the other hand the algorithm is linear in time and uses constant space as the algorithm of galil and seiferas it presents the advantage of being remarkably simple which consequently makes its analysis possible the algorithm relies on a previously known result in combinatorics on words called the critical factorization theorem which relates the global period of a word to its local repetitions of blocks

on the planar schrodinger poisson system with the axially symmetric potential abstract in this paper we develop some new variational and analytic techniques to prove that the following planar schrodinger poisson system u v x u u f u x r 2 u 2 x r 2 admits a nontrivial solution and a ground state solution possessing the least energy in the axially symmetric functions space where v x is axially symmetric our results improve and extend the ones in the case v 1 and f u u p 2 u with 2 p 6 in particular we use the assumption that 2 v x v x x is bounded from below instead of the usually one that lim x v x 1 moreover v x is even admitted to be unbounded

the ionization conjecture in thomas fermi dirac von weizsacker theory we prove that in thomas fermi dirac von weizsacker theory a nucleus of charge z 0 can bind at most z c electrons where c is a universal constant this result is obtained through a comparison with thomas fermi theory which as a by product gives bounds on the screened nuclear potential and the radius of the minimizer a key ingredient of the proof is a novel technique to control the particles in the exterior region which also applies to the liquid drop model with a nuclear background potential c 2017 wiley periodicals inc

from molecular models to continuum mechanics we present here a limiting process allowing us to write some continuum mechanics models as a natural asymptotic of molecular models the approach is based on the hypothesis that the macroscopic displacement is equal to the microscopic one we carry out the corresponding calculations in the case of two body energies including higher order terms and also in the case of thomas fermi type models

normalized solutions for schrodinger poisson equations with general nonlinearities abstract in this paper we prove the existence of normalized solutions to the following schrodinger poisson equation u x 1 u 2 u f u u x r 3 r where f c r r satisfies more general conditions which cover the case f u u q 2 u with q 3 10 3 10 3 6 especially some new analytical techniques are presented to overcome the difficulties due to the presence of three terms in the corresponding energy functional which scale differently

upper and lower bounds for eigenvalues of nonlinear elliptic equations i the lowest eigenvalue we give a method for finding bounds for the lowest eigenvalue of nonlinear elliptic equations with monotone local nonlinearities this is an extension to nonlinear problems of barta s method for linear elliptic operators

classification of positive solitary solutions of the nonlinear choquard equation in this paper we settle the longstanding open problem concerning the classification of all positive solutions to the nonlinear stationary choquard equation delta u u 2u left frac 1 x u 2 right 0 quad u in h 1 mathbb r 3 which can be considered as a certain approximation of the hartree fock theory for a one component plasma as explained in lieb and lieb simon s papers starting from 1970s we first prove that all the positive solutions of this equation must be radially symmetric and monotone decreasing about some fixed point interestingly to use the new method of moving planes introduced by chen li ou we deduce the problem into an elliptic system as a key step we transform this differential system into a system of integral equations with the help of riesz and bessel potentials and then use the method of a moving plane in an integral form next using radial symmetry we deduce the uniqueness result from lieb s work our argument can be adapted well to study the radial symmetry of positive solutions of the equation in the generalized form u k 1 f left u k 2 u right

a proof of the extended duval s conjecture we give a short and elementary proof of the following stronger version of duval s conjecture let u be an unbordered word and v a word of length u such that v is not a prefix of u then uv contains an unbordered word of length at least u 1

on maximal suffixes and constant space linear time versions of kmp algorithm constant space linear time string matching algorithms are usually very sophisticated most of them consist of two phases very technical preprocessing phase and searching phase an exception is one phase crochemore s algorithm theoret comput sci 92 1992 33 it is an on line version of knuth morris pratt algorithm kmp with on the fly computation of pattern shifts as approximate periods in this paper we explore further crochemore s approach and construct alternative algorithms which are differently structured in crochemore s algorithm the approximate period function is restarted from inside which means that several internal variables of this function are changing globally also crochemore s algorithm strongly depends on the concrete implementation of approximate periods computation we present a simple modification of kmp algorithm which works in o 1 space o n time for any function which computes periods or approximate periods in o 1 space and linear time the approximate period function can be treated as a black box we identify class of patterns self maximal words which are especially well suited for crochemore style string matching a new o 1 space string matching algorithm maxsuffix matching is proposed in the paper which gives yet another example of applicability of maximal suffixes

dynamics from multivariate time series abstract multivariate time series data are common in experimental and industrial systems if the generating system has nonlinear dynamics we may be able to construct a model that reproduces the dynamics and can be used for control and other purposes in principle multivariate time series are not necessary for recovering dynamics according to the embedding theorem only one time series should be needed however for real data there may be large gains in using all of the measurements in this paper we examine the issues of how to use multiple data streams most effectively for modeling and prediction for example perhaps the data are redundant in that only a subset of the data streams is useful and how should we embed the data if indeed embedding is required at all we show how these questions can be answered and describe some numerical experiments which show that using multivariate time series can significantly improve predictability we also demonstrate a somewhat surprising synchronization between different reconstructions

higher order finite difference formulation of periodic orbital free density functional theory we present a real space formulation and higher order finite difference implementation of periodic orbital free density functional theory of dft specifically utilizing a local reformulation of the electrostatic and kernel terms we develop a generalized framework for performing of dft simulations with different variants of the electronic kinetic energy in particular we propose a self consistent field scf type fixed point method for calculations involving linear response kinetic energy functionals in this framework evaluation of both the electronic ground state and forces on the nuclei are amenable to computations that scale linearly with the number of atoms we develop a parallel implementation of this formulation using the finite difference discretization we demonstrate that higher order finite differences can achieve relatively large convergence rates with respect to mesh size in both the energies and forces additionally we establish that the fixed point iteration converges rapidly and that it can be further accelerated using extrapolation techniques like anderson s mixing we validate the accuracy of the results by comparing the energies and forces with plane wave methods for selected examples including the vacancy formation energy in aluminum overall the suitability of the proposed formulation for scalable high performance computing makes it an attractive choice for large scale of dft calculations consisting of thousands of atoms

error covariance matrix estimation of noisy and dynamically coupled time series we estimate the covariance matrix of the errors in several dynamically coupled time series corrupted by measurement errors we say that several scalar time series are dynamically coupled if they record the values of measurements of the state variables of the same smooth dynamical system the estimation of the covariance matrix of the errors is made using a noise reduction algorithm that efficiently exploits the information contained jointly in the dynamically coupled noisy time series the method is particularly powerful for short length time series with high uncertainties

boundary blow up and degenerate equations let r2 be a bounded domain of class c2 0 1 we show that if u is the solution of u 4exp 2u which tends to as x y then the hyperbolic radius v exp u is also of class c2 up to the boundary the proof relies on new schauder estimates for degenerate elliptic equations of fuchsian type

an aperiodic phenomenon of the extended kalman filter in filtering noisy chaotic signals in this correspondence we report an interesting behavior of the extended kalman filter ekf when it is used to filter a chaotic system we show both theoretically and experimentally that the gain of the ekf does not converge or diverge but oscillates aperiodically more precisely when a nonlinear system is periodic the kalman gain and error covariance of the ekf converge to zero however when the system is chaotic they either converge to a fixed point with magnitude larger than zero or oscillate our theoretical analyses are verified using monte carlo simulations based on some popular chaotic systems

parameter estimation in chaotic noise the problem of parameter estimation in chaotic noise is considered in this paper since a chaotic signal is inherently deterministic a new complexity measure called the phase space volume psv is introduced for estimation instead of using the conventional probabilistic measures we show that the unknown parameters of a signal embedded in chaotic noise ran be obtained by minimizing the psv mpsv of the output of an inverse filter of the received signal in a reconstructed phase space monte carlo simulations are carried out to analyze the efficiency of the mpsv method for parameter estimation in chaotic noise to illustrate the usefulness of the mpsv technique in solving real life problems the problem of sinusoidal frequency estimation in real radar clutter unwanted radar backscatters is considered modeling radar clutter as a chaotic process we apply the mpsv technique to estimate the sinusoidal frequencies by estimating the coefficients of an autoregressive ar spectrum the results show that the frequency estimates generated by the mpsv method are more accurate than those obtained by the standard least square ls technique

homoclinic tangencies and non normal jacobians effects of noise in nonhyperbolic chaotic systems abstract a general study of the effects of noise interacting with the deterministic dynamics of nonhyperbolic chaotic 2 d maps and 3 flows is presented noise in these systems can have dramatic effects on the invariant measure of the system in regions of homoclinic tangencies perturbations are transported away from the neighborhood of the attractor leading to deformations which can be one to two orders of magnitude larger than the noise level a qualitative understanding is attained by a study of the universal properties of the unstable and stable foliation of the phase space in the vicinity of homoclinic tangencies through the investigation of nontrivial structures of the tangent space at homoclinic tangencies related to the non normal jacobians we obtain a quantitative description of these noise induced deformations of the attractor local expansion rates which are much larger than the maximal lyapunov exponent can be used as a measure of the system s structural instability under perturbations we exemplify our general results on the henon ikeda and duffing system a new and effective algorithm to calculate the homoclinic tangencies in the entire phase space based on the results of this paper is presented

transducers and repetitions the factor transducer of a word associates to each of its factors or subwords their first occurrence optimal bounds on the size of minimal factor transducers together with an algorithm for building them are given analogue results and a simple algorithm are given for the case of subsequential suffix transducers algorithms are applied to repetition searching in words le transducteur des facteurs d un mot associe a chacun de ses facteurs leur premiere occurrence on donne des bornes optimales sur la taille du transducteur minimal d un most ainsi qu un algorithme pour sa construction on donne des resultats analogues et un algorithme simple dans le cas du transducteur sous sequentiel des suffixes d un mot on donne une application a la detection de repetitions dans les mots

nonlinear elliptic equations with a jumping reaction abstract we study a nonlinear nonhomogeneous dirichlet problem driven by the sum of a p laplacian and a laplacian 2 p and a jumping nonlinearity under very general conditions on the reaction and without using the fucik spectrum we show that the problem has at least three nontrivial solutions and we provide sign information for all of them our approach uses critical point theory truncation and comparison techniques and morse theory

linear computation of unbordered conjugate on unordered alphabet we present an algorithm that given a word w of length n on an unordered alphabet computes one of its unbordered conjugates if such a conjugate does not exist the algorithm computes one of its conjugates that is a power of an unbordered word the time complexity of the algorithm is o n the number of comparisons between letters of w is bounded by 4n

noise level estimation of time series using coarse grained entropy we present a method of noise level estimation that is valid even for high noise levels the method makes use of the functional dependence of coarse grained correlation entropy k 2 ensuremath varepsilon on the threshold parameter ensuremath varepsilon we show that the function k 2 ensuremath varepsilon depends in a characteristic way on the noise standard deviation ensuremath sigma it follows that observing k 2 ensuremath varepsilon one can estimate the noise level ensuremath sigma although the theory has been developed for the gaussian noise added to the observed variable we have checked numerically that the method is also valid for the uniform noise distribution and for the case of langevin equation corresponding to the dynamical noise we have verified the validity of our method by applying it to estimate the noise level in several chaotic systems and in the chua electronic circuit contaminated by noise

blow up rate and uniqueness of singular radial solutions for a class of quasi linear elliptic equations we establish the uniqueness and the blow up rate of the large positive solution of the quasi linear elliptic problem pu up 1 b x h u in br x0 with boundary condition u on br x0 where br x0 is a ball centered at x0 rn with radius r n 3 2 p 0 are constants and the weight function b is a positive radially symmetrical function we only require h u to be a locally lipschitz function with h u up 1 increasing on 0 and h u uq 1 for large u with q p 1 our results extend the previous work z xie uniqueness and blow up rate of large solutions for elliptic equation u u b x h u j differential equations 247 2009 344 363 from case p 2 to case 2 p

the thomas fermi von weizsacker theory of atoms and molecules we place the thomas fermi von weizsacker model of atoms on a firm mathematical footing we prove existence and uniqueness of solutions of the thomas fermi von weizsacker equation as well as the fact that they minimize the thomas fermi von weizsacker energy functional moreover we prove the existence of binding for two very dissimilar atoms in the frame of this model

stochastic time series with strong correlated measurement noise markov analysis in n dimensions an extension and generalization of a recently presented approach for the analysis of langevin type stochastic processes in the presence of strong measurement noise is presented for a stochastic process in n dimensions which is superimposed with strong exponentially correlated gaussian distributed measurement noise it is possible to extract the strength and the correlation functions of the noise as well as polynomial approximations of the drift and diffusion functions of the underlying process

nonexistence of a minimizer for thomas fermi dirac von weizsacker model 1 x y dx dy a nonexistence result similar to theorem 1 also holds theorem 2 there exists constant v0 0 such that the variational problem 4 inf v e does not have a minimizer if v v0 if the coulomb term is not present in 1 and 3 a standard modica mortela type result establishes a link between the two functional through gamma convergence when the volume constraint m is large this is no longer valid for the energy functionals 1 and 3 due to the coulomb term the connection between the two functionals is just on the formal level

cancelling deterministic noise by constructing nonlinear inverses to linear filters abstract in this paper we propose a method of noise cancellation where the noise is deterministic that is it is generated by some possibly chaotic dynamical system the method exploits the fact that a time series measured from a nonlinear dynamical system can be used to reconstruct the phase space of the system and that this is still true if the time series is first passed through a linear fir filter since both filtered and unfiltered versions reconstruct the same system there is an invertible nonlinear mapping from the filtered time series to the unfiltered one which undoes the effect of the filter to perform signal separation we use a filter which stops the signal we wish to recover so that the output is a filtered version of the noise alone using the nonlinear mapping the unfiltered noise time series can be recovered and subtracted from the original noisy signal two examples of the recovery of simple signals from chaotic time series are given and one in which one chaotic signal is separated from another

large solutions for yamabe and similar problems on domains in riemannian manifolds we present a unifled approach to study large positive solutions i e u x 1 as x of the equation u hu i k u if in an arbitrary domain we assume u is convex and grows su ciently fast as u 1 equations of this type arise in geometry yamabe problem two dimensional curvature equation probability superdifiusion we prove that both existence and uniqueness are local properties of points of the boundary i e they depend only on properties of in arbitrary small neighborhood of each boundary point we also flnd several new necessary and su cient conditions for existence and uniqueness of large solutions including an existence theorem on domains with fractal boundaries

semi classical solutions for schrodinger poisson equations with a critical frequency abstract in this paper we study a system of schrodinger poisson equation e 2 v v x v k x v v p 2 v x r 3 e 2 k x v 2 x r 3 where p 4 6 the potentials v k c r 3 r and e 0 is a parameter under the critical frequency assumptions on v and k we investigate the existence and multiplicity of semi classical solutions for this system and exhibit the concentration behavior that such solutions converge to the least energy solutions of the associated limit problem as e 0

infinite time aggregation for the critical patlak keller segel model in ℝ2 we analyze the two dimensional parabolic elliptic patlak keller segel model in the whole euclidean space r2 under the hypotheses of integrable initial data with finite second moment and entropy we first show local in time existence for any mass of free energy solutions namely weak solutions with some free energy estimates we also prove that the solution exists as long as the entropy is controlled from above the main result of the paper is to show the global existence of free energy solutions with initial data as before for the critical mass 8 actually we prove that solutions blow up as a delta dirac at the center of mass when t keeping constant their second moment at any time furthermore all moments larger than 2 blow up as t if initially bounded

nodal solutions for p 2 equations in this paper we study a nonlinear elliptic equation driven by the sum of a p laplacian and a laplacian p 2 equation with a caratheodory p 1 sub linear reaction using variational methods combined with morse theory we prove two multiplicity theorems providing precise sign information for all the solutions constant sign and nodal solutions in the process we prove two auxiliary results of independent interest

regularized local linear prediction of chaotic time series abstract local linear prediction based on the ordinary least squares ols approach is one of several methods that have been applied to prediction of chaotic time series apart from potential linearization errors a drawback of this approach is the high variance of the predictions under certain conditions here a different set of so called linear regularization techniques originally derived to solve ill posed regression problems are compared to ols for chaotic time series corrupted by additive measurement noise these methods reduce the variance compared to ols but introduce more bias a main tool of analysis is the singular value decomposition svd and a key to successful regularization is to damp the higher order svd components several of the methods achieve improved prediction compared to ols for synthetic noise corrupted data from well known chaotic systems similar results were found for real world data from the r r intervals of ecg signals good results are also obtained for real sunspot data compared to published predictions using nonlinear techniques

two positive solutions of a class of schrodinger poisson system with indefinite nonlinearity abstract we study the existence and multiplicity of positive solutions of a class of schrodinger poisson system u u l x u k x u p 2 u h x u in r 3 l x u 2 in r 3 where 4 p 6 k c r 3 k changes sign in r 3 and lim x k x k 0 we mainly prove the existence of at least two positive solutions in the case that 1 and near 1 where 1 is the first eigenvalue of i d in h 1 r 3 with weight function h whose corresponding eigenfunction is denoted by e 1 an interesting phenomenon is that we do not need the condition r 3 k x e 1 p d x 0 which has been shown to be a necessary condition to the existence of positive solutions for semilinear elliptic equations with indefinite nonlinearity see e g s alama g tarantello on semilinear elliptic equations with indefinite nonlinearities calc var partial differential equations 1 1993 439 475

augmented lagrangian formulation of orbital free density functional theory we present an augmented lagrangian formulation and its real space implementation for non periodic orbital free density functional theory of dft calculations in particular we rewrite the constrained minimization problem of of dft as a sequence of minimization problems without any constraint thereby making it amenable to powerful unconstrained optimization algorithms further we develop a parallel implementation of this approach for the thomas fermi von weizsacker tfw kinetic energy functional in the framework of higher order finite differences and the conjugate gradient method with this implementation we establish that the augmented lagrangian approach is highly competitive compared to the penalty and lagrange multiplier methods additionally we show that higher order finite differences represent a computationally efficient discretization for performing of dft simulations overall we demonstrate that the proposed formulation and implementation are both efficient and robust by studying selected examples including systems consisting of thousands of atoms we validate the accuracy of the computed energies and forces by comparing them with those obtained by existing plane wave methods

symmetry properties of the solutions to thomas fermi dirac von weizsacker type equations we consider a semilinear elliptic equation with a spherically symmetric potential specifically thomas fermi dirac von weizsacker type equations without electronic repulsion assuming some regularity properties of the solutions at the origin and at infinity we prove that the solutions have spherical symmetry

constant space string matching in sublinear average time given two strings pattern p of length m and text t of length n the string matching problem is to find all occurrences of the pattern p in the text t we present a string matching algorithms which works in o n average time and constant additional space for one dimensional texts and two dimensional arrays this is a first attempt to the small space string matching problem in which sublinear time algorithms are achieved we show that all occurrences of one or two dimensional patterns can be found in o n r average time with constant memory where r is the repetition size of p size of the longest repeated subword of p

linear time computation of local periods we present a linear time algorithm for computing all local periods of a given word this subsumes but is substantially more powerful than the computation of the global period of the word and on the other hand the computation of a critical factorization implied by the critical factorization theorem

existence of multiple positive solutions to nonhomogeneous schrodinger poisson system in this paper we consider the existence of multiple solutions to the following nonhomogeneous generalized schrodinger poisson system u ku q f u g u h x in r 3 2 qf u in r 3 where q 0 is a parameter 0 h x h x l 2 r 3 and g is asymptotically linear or superliner at infinity we show that there exists q 0 0 such that the system has at least two positive radial solutions for q 0 q 0

a remark on the uniqueness of positive solutions for some dirichlet problems abstract in this paper we prove the uniqueness of positive weak solutions to the problem p u g x u x u 0 x by a direct argument here is a bounded domain in r n n 3 with smooth boundary p denotes the p laplacian operator defined by p z div z p 2 z p 1 g x 0 0 for a e x and g x u is a caratheodory function we provide a direct uniqueness proof for this problem under certain conditions

multi bump solutions for the nonlinear schrodinger poisson system in this paper we study a kind of nonlinear schrodinger poisson system with a parameter e for any positive integer m we prove that there exists e m 0 such that for 0 e e m the equation has an m bump positive solution under some suitable conditions as a consequence the equation has more and more multi bump positive solutions as e 0

localized nodal solutions of higher topological type for nonlinear schrodinger poisson system abstract in this paper we focus our attention on following schrodinger poisson system e 2 u v x u u u p 2 u x r 3 e 2 u 2 u h 1 r 3 where 4 p 6 and e 0 are small positive parameters under a local condition imposed on the potential v we study above system and obtain an infinite sequence of localized sign changing solutions by applying the symmetric mountain pass theorem precisely these solutions are constructed as higher topological type critical points of the energy functional and concentrated at a local minimum set of the potential v our method follows the same spirit of chen and wang s method chen and wang 2017 which does not need any non degeneracy condition of the limiting equations but we cannot use it directly due to the presence of nonlocal term x 1 4 r 3 u 2 y x y d y we employ some new analytical skills to overcome the obstacles caused by the nonlocal term our results improve and extend some related ones in the literature

approach to block entropy modeling and optimization abstract this paper introduces an approach to the block entropy modeling of stationary signals the block entropies constructed according to the tsallis generalized formalism are optimized with respect to the block length and the partition of the signal value domain to appropriately measure the complexity of the signal the optimal partition is known to be addressed by the euclidean mean expressing the signal optimized level based on the least squares fitting method however this is valid only for random signal values following a symmetric distribution alternatively and within the framework of fitting methods based on non euclidean metrics we implement the q th order means to consistently describe the optimal signal level and to clearly present the difference between the optimal signal level and the optimal partition the signal optimization is utilized for detecting the distribution modes developing a technique being resistant to the noise corruption that can be useful for detecting the optimal partition moreover the mechanisms that affect the optimal partition are identified and thoroughly investigated we first consider random signals following an arbitrary distribution where the block entropy modeling reveals that the optimal partition is located at the median thereafter we consider persistent signals specifying a degree of determinism where the optimal partition is found to be driven far from the median and close to the persistent mode the existence of persistent modes of small hitting time is the key point of this dissertation highlighting their implications on the block entropy modeling finally efforts towards block entropy modeling of non stationary signals are discussed

on positive solutions for a second order differential system with indefinite weight in this paper we consider the existence of positive solutions for a second order differential system u a t u h t f u 0 t 1 b t u 0 t 1 u 0 u 1 0 0 1 0 where a t b t h t change sign the proof is based on the well known fixed point theorem of cone expansion and compression

spatio temporal chaos a solvable model abstract a solvable coupled map lattice model exhibiting spatio temporal chaos is studied exact expressions are obtained for the spectra of lyapunov exponents as a function of the model parameters although the model has spatio temporal structure the time series measured at a single lattice site are shown to consist of independent identically distributed samples for several values of the model parameters for these parameter values the spatial series measured at a fixed time also consist of independent identically distributed samples in these cases the information dimension density is 1 but the information entropy density depends on the model parameters thus the model is an example where the information entropy density can be obtained neither from a time series measured at a single lattice site nor from a spatial series measured at a fixed time we conclude that in studying only a time series or a spatial series without any knowledge of the system one could be easily led into thinking that there is no spatio temporal structure for a full characterization of the system structure in time and space will have to be considered simultaneously

finding the leftmost critical factorization on unordered alphabet we present a linear time and space algorithm computing the leftmost critical factorization of a given string on an unordered alphabet we consider algorithms computing the leftmost critical point on unordered alphabets we describe an o n log n time algorithm finding the leftmost critical point we investigate some combinatorial properties of strings related to our problem using found combinatorial facts we improve our first algorithm to o n algorithm

stability for the time dependent hartree equation with positive energy abstract in this paper we show that the h 1 solutions to the time dependent hartree equation i u t 1 2 u 2 x u u 2 1 x u on r 3 are stable under the perturbation of parameters we show that any sequence of h 1 solutions to the hartree equations with perturbed parameters admits a weakly convergent subsequence the weak limit of which is also an h 1 solution to the hartree equation to prove our stability result we need to deal with the terms involving the potential 1 x and new estimates will be employed

characteristic sturmian words are extremal for the critical factorization theorem we prove that characteristic sturmian words are extremal for the critical factorization theorem cft in the following sense if p x n denotes the local period of an infinite word x at point n we prove that x is a characteristic sturmian word if and only if p x n is smaller than or equal to n 1 for all n 1 and it is equal to n 1 for infinitely many integers n this result is extremal with respect to the cft since a consequence of the cft is that for any infinite recurrent word x either the function p x is bounded and in such a case x is periodic or p x n n 1 for infinitely many integers n as a byproduct of the techniques used in the paper we extend a result of harju and nowotka 2002 in 18 stating that any finite fibonacci word f n n 5 has only one critical point indeed we determine the exact number of critical points in any finite standard sturmian word