statistical mechanics of complex systems for pattern identification this paper presents a statistical mechanics concept for identification of behavioral patterns in complex systems based on measurements e g time series data of macroscopically observable parameters and their operational characteristics the tools of statistical mechanics which provide a link between the microscopic i e detailed and macroscopic i e aggregated properties of a complex system are used to capture the emerging information and to identify the quasi stationary evolution of behavioral patterns the underlying theory is built upon thermodynamic formalism of symbol sequences in the setting of a generalized ising model gim of lattice spin systems in this context transfer matrix analysis facilitates construction of pattern vectors from observed sequences the proposed concept is experimentally validated on a richly instrumented laboratory apparatus that is operated under oscillating load for identification of evolving microstructural changes in polycrystalline alloys

boundary value problems on infinite intervals and semiconductor devices the nonlinear differential equation y f x y y 0 x f satisfying bernstein type growth conditions we also examine an important application which occurs in the theory of semiconductor devices

gauge theory of self similar system abstract on the basis of a dilatation invariant lagrangian equations governing probability density and gauge potential of the non stationary self similar stochastic system are determined it is shown that an automodel regime is realized at small time interval determined by the tsallis parameter q 1 an exponential decay occurs at large time where the dilatation parameter and the partial scale tend to constant values

discrete systems on infinite intervals abstract we study superlinear boundary value problems for a discrete system which in particular includes the prototype equation x k 1 f k x k equations with finite as well as infinite delays equations of neutral type and the discrete integral equations of volterra type

focal boundary value problems for nonlinear difference equations ii on considere l unicite des solutions impliquant l existence des solutions de problemes aux valeurs limites de type focal pour l equation aux differences non lineaire d ordre n u t n f t u t u t n 1 ou f a r n r est continue et l equation u n 1 f t u 1 u n peut etre resolue pour u 1 comme fonction continue des variables t u 2 u u 1

multifractal spectrum of phase space related to generalized thermostatistics abstract we consider a self similar phase space with specific fractal dimension d being distributed with spectrum function f d related thermostatistics is shown to be governed by the tsallis formalism of the non extensive statistics where the non additivity parameter equals to q 1 q 1 and the multifractal function q q d q f d q is the specific heat determined with multifractal parameter q 1 at that the equipartition law is shown to take place optimization of the multifractal spectrum function f d arrives at the relation between the statistical weight and the system complexity it is shown that the statistical weight exponent q can be modeled by hyperbolic tangent deformed in accordance with both tsallis and kaniadakis exponential functions to describe arbitrary multifractal phase space explicitly the spectrum function f d is proved to increase monotonically from minimum value f 1 at d 0 to maximum one f 1 at d 1 at the same time the number of monofractals increases with the growth of the phase space volume at small dimensions d and falls down in the limit d 1

tsallis entropy maximization procedure revisited abstract the proper way of averaging is an important question with regards to tsallis thermostatistics three different procedures have been thus far employed in the pertinent literature the third one i e the tsallis mendes plastino tmp physica a 261 1998 534 normalization procedure exhibits clear advantages with respect to earlier ones in this work we advance a distinct from the tmp one way of handling the lagrange multipliers involved in the extremization process that leads to tsallis statistical operator it is seen that the new approach considerably simplifies the pertinent analysis without losing the beautiful properties of the tsallis mendes plastino formalism

topological methods for some boundary value problems we establish existence of solutions for a finite difference approximation to y f x y y on 0 1 subject to nonlinear two point sturm liouville boundary conditions of the form g i y i y i 0 i 0 1 assuming s satisfies one sided growth bounds with respect to y c 2001 elsevier science ltd all rights reserved

d form sequences families of sequences with low correlation values and large linear spans large families of binary sequences with low correlation values and large linear span are critical for spread spectrum communication systems the author describes a method for constructing such families from families of homogeneous functions over finite fields satisfying certain properties he then uses this general method to construct specific families of sequences with optimal correlations and exponentially better linear span than no sequences no 1988

divisible difference sets relative difference sets and sequences with ideal autocorrelation abstract in this correspondence we consider the equivalent condition that a sequence possesses ideal autocorrelation function as we know for a binary sequence the equivalent condition is that the characteristic class of this sequence consists of two cyclic difference sets this paper proves that for a p ary sequence with d form property the equivalent condition is that its characteristic class consists of one cyclic divisible difference sets and p 1 relative difference sets moreover a new way to construct cyclic divisible difference sets is presented

wg a family of stream ciphers with designed randomness properties in this paper we present a family of stream ciphers which generate a keystream with ideal two level autocorrelation the design also guarantees other randomness properties i e balance long period ideal tuple distribution and high and exact linear complexity we discuss how these properties are achieved by the proposed design and show how to select various parameters to obtain an efficient stream cipher for the desired security level we also show that the proposed generators are secure against time memory data tradeoff attacks algebraic attacks and correlation attacks finally we present wg 128 as a concrete example of a wg stream cipher with a key size of 128bits

nagumo type existence results for second order nonlinear dynamic bvps abstract in this paper we present a nagumo condition for time scales equations that includes as a particular case a type of the classical one for differential equations involving a certain restriction the established nagumo condition further allows us to prove the existence of at least one solution lying between a pair of lower and upper solutions of a nonlinear second order dynamic equation with nonlinear functional boundary value conditions

new nonbinary sequences with ideal two level autocorrelation we find new families of nonbinary sequences of period p sup n 1 with symbols from a finite field f sub p for any prime p spl ges 3 the sequences have two level ideal autocorrelation and are generalizations of previously found ternary sequences with ideal autocorrelation difference sets with parameters p sup n 1 p 1 p sup n 1 1 p 1 p sup n 2 1 p 1 can also be derived from these sequences in a natural way

new cyclic relative difference sets constructed from d homogeneous functions with difference balanced property for a prime power q we show that a cyclic relative difference set with parameters q sup n 1 q 1 q 1 q sup n 1 q sup n 2 can be constructed from a d homogeneous function from f sub q sup n spl bsol 0 onto f sub q with difference balanced property where f sub q sup n is the finite field with q sup n elements this construction method enables us to construct several new cyclic relative difference sets with parameters p sup n 1 p sup l 1 p sup l 1 p sup n l p sup n 2l from p ary sequences of period p sup n 1 with ideal autocorrelation property introduced by helleseth and gong using a lifting idea other new cyclic relative difference sets can be constructed from the helleseth gong hg sequences also the 3 ranks and the trace representation of the characteristic sequences of cyclic relative difference sets from a specific class of ternary hg sequences and ternary lin sequences are derived

chaos or noise difficulties of a distinction in experiments the dynamical behavior of systems is reflected in time series due to the finiteness of the observational data set it is not possible to reconstruct the invariant measure up to an arbitrarily fine resolution and an arbitrarily high embedding dimension these restrictions limit our ability to distinguish between signals generated by different systems such as regular chaotic or stochastic ones when analyzed from a time series point of view we propose to classify the signal behavior without referring to any specific model as stochastic or deterministic on a certain scale of the resolution ensuremath epsilon according to the dependence of the ensuremath epsilon ensuremath tau entropy h ensuremath epsilon ensuremath tau and the finite size lyapunov exponent ensuremath lambda ensuremath epsilon on ensuremath epsilon

effective temperature of self similar time series analytical and numerical developments abstract within both slightly non extensive statistics and a related numerical model a picture is elaborated to treat self similar time series as a thermodynamic system thermodynamic type characteristics relevant to temperature pressure entropy internal and free energies are introduced and tested predictability conditions of time series analysis are discussed on the basis of van der waals model maximal magnitude for time interval and minimal resolution scale of the value under consideration are found and analyzed in details the statistics developed is shown to be governed by effective temperature being an exponential measure of the fractal dimension of the time series testing of the analytical consideration is based on numerical scheme of non extensive random walk a statistical scheme is introduced to present the numerical model as a grand canonical ensemble for which entropy and internal energy are calculated as functions of particle number effective temperature is found numerically to show that its value is reduced to averaged energy per one degree of freedom

boundary value problems for general discrete systems on infinite intervals this paper continues the study of boundary value problems for a discrete system which in particular includes the prototype equation x k 1 f k x k equations with finite as well as infinite delays equations of neutral type and the discrete integral equations of volterra type while the finite discrete interval case regular as well as at resonance has been discussed in 1 2 in the present paper the infinite interval case will be addressed

the role of constraints within generalized nonextensive statistics the gibbs jaynes path for introducing statistical mechanics is based on the adoption of a specific entropic form sand of physically appropriate constraints for instance for the usual canonical ensemble one adopts i ii ipi 1 and iii ei eigenvalues of the hamiltonian u1 internal energy equilibrium consists in optimizing s1 with regard to pi in the presence of constraints ii and iii within the recently introduced nonextensive statistics i is generalized into sq k 1 ipiq q 1 q 1 reproduces s1 ii is maintained and iii is generalized in a manner which might involve piq in the present effort we analyze the consequences of some special choices for iii and their formal and practical implications for the various physical systems that have been studied in the literature to illustrate some mathematically relevant points we calculate the specific heat respectively associated with a nondegenerate two level system as well as with the classical and quantum harmonic oscillators