hascasl integrated higher order specification and program development we lay out the design of hascasl a higher order extension of the algebraic specification language casl that serves both as a wide spectrum language for the rigorous specification and development of software in particular but not exclusively in modern functional programming languages and as an expressive standard language for higher order logic distinctive features of hascasl include partial higher order functions higher order subtyping shallow polymorphism and an extensive type class mechanism moreover hascasl provides dedicated specification support for monad based functional imperative programming with generic side effects including a monad based generic hoare logic

positive periodic solutions of singular systems with a parameter abstract the existence and multiplicity of positive periodic solutions for second order non autonomous singular dynamical systems are established with superlinearity or sublinearity assumptions at infinity for an appropriately chosen parameter our results provide a unified treatment for the problem and significantly improve several results in the literature the proof of our results is based on the krasnoselskii fixed point theorem in a cone

nonlinear periodic boundary value problems with sign changing green s function abstract we study the existence and nonexistence of positive solutions of nonlinear periodic boundary value problems u a t u b t f u a e t 0 t u 0 u t u 0 u t where b 0 a 0 and the green s function g t s of the linear problem u a t u 0 a e t 0 t u 0 u t u 0 u t may change sign on 0 t 0 t

multiple positive solutions to superlinear repulsive singular impulsive differential equations the existence of multiple positive solutions to superlinear repulsive singular impulsive differential equations is discussed in this paper the proof relies on a nonlinear alternative of leray schauder type and on krasnoselskii fixed point theorem on compression and expansion of cone

optimal constants in a nonlocal boundary value problem we give improved results on the existence of positive solutions for a nonlinear differential equation with nonlocal boundary conditions that arise as a model of a thermostat we obtain some optimal criteria for the existence of one positive solution which involve the principal eigenvalue of a related linear operator we also determine optimal values of some other constants that are useful in obtaining existence of multiple positive solutions

numerical algorithm for solving two point second order periodic boundary value problems for mixed integro differential equations in this study the numerical solution of fredholm volterra integro differential equations for two point second order periodic boundary value problems is discussed in a reproducing kernel hilbert space a reproducing kernel hilbert space is constructed in which the periodic boundary conditions of the problem are satisfied the exact solution u x is represented in the form of series in the space w 2 3 in the mean time the n term approximate solution u n x is obtained and is proved to converge to the exact solution u x furthermore we present an iterative method for obtaining the solution in the space w 2 3 some examples are displayed to demonstrate the validity and applicability of the proposed method the numerical result indicates that the proposed method is straightforward to implement efficient and accurate for solving linear and nonlinear equations

multiplicity of positive periodic solutions to superlinear repulsive singular equations abstract in this paper we study positive periodic solutions to the repulsive singular perturbations of the hill equations it is proved that such a perturbation problem has at least two positive periodic solutions when the anti maximum principle holds for the hill operator and the perturbation is superlinear at infinity the proof relies on a nonlinear alternative of leray schauder type and on krasnoselskii fixed point theorem on compression and expansion of cones

r s method for unevenly sampled time series application to detecting long term temporal dependence of droplets transiting through a fixed spatial point in gas liquid two phase turbulent jets abstract we perform rescaled range analysis upon the signals measured by a dual particle dynamical analyzer in gas liquid two phase turbulent jets a novel rescaled range analysis is proposed to investigate these unevenly sampled signals the hurst exponents of velocity and other passive scalars in the bulk of spray are obtained to be 0 59 0 02 and the fractal dimension is hence 1 41 0 02 which is in remarkable agreement with and much more precise than previous results these scaling exponents are found to be independent of the configuration and dimensions of the nozzle and the fluid flows therefore such type of systems form a universality class with invariant scaling properties

numerical investigations for systems of second order periodic boundary value problems using reproducing kernel method the reproducing kernel method is a numerical as well as analytical technique for solving a large variety of ordinary and partial differential equations associated to different kind of boundary conditions and usually provides the solutions in term of rapidly convergent series in the appropriate hilbert spaces with components that can be elegantly computed the aim of the present analysis is to implement a relatively recent computational method reproducing kernel hilbert space for obtaining the solutions for systems of second order differential equations with periodic boundary conditions a reproducing kernel space is constructed in which the periodic conditions of the systems are satisfied whilst the smooth kernel functions are used throughout the evolution of the method to obtain the required grid points an efficient construction is given to obtain the approximate solutions for the systems together with an existence proof of the exact solutions is proposed based upon the reproducing kernel theory convergence analysis and error behavior of the presented method are also discussed in this approach computational results of some numerical examples are presented to illustrate the viability simplicity and applicability of the algorithm developed

existence and multiplicity of non negative solutions for systems of perturbed hammerstein integral equations abstract we study the existence of positive solutions for a system of perturbed hammerstein integral equations our setting is quite general and covers a wide class of systems of boundary value problems the main ingredient in our theory is the classical fixed point index theory for compact maps

existence of one signed periodic solutions of some second order differential equations via a krasnoselskii fixed point theorem this paper is devoted to study the existence of periodic solutions of the second order equation x 00 f t x where f is a caratheodory function by combining some new properties of green s function together with krasnoselskii fixed point theorem on compression and expansion of cones as applications we get new existence results for equations with jumping nonlinearities as well as equations with a repulsive or attractive singularity in this latter case our results cover equations with weak singularities and are compared with some recent results by i rachunkova m tvrdyand i vrkoc r 2002 elsevier science usa all rights reserved

solvability of singular second order m point boundary value problems abstract let f 0 1 r 2 r be a function satisfying caratheodory s conditions and 1 t e t l 1 0 1 let i 0 1 a i r i 1 m 2 0 1 2 m 2 1 be given this paper is concerned with the problem of existence of a c 1 0 1 solution for the m point boundary value problem x f t x t x t e t 0 t 1 0 1 x 0 0 x 1 i 1 m 2 a i x i the proof of our main result is based upon the leray schauder continuation theorem

detrending moving average algorithm for multifractals the detrending moving average dma algorithm is a widely used technique to quantify the long term correlations of nonstationary time series and the long range correlations of fractal surfaces which contains a parameter ensuremath theta determining the position of the detrending window we develop multifractal detrending moving average mfdma algorithms for the analysis of one dimensional multifractal measures and higher dimensional multifractals which is a generalization of the dma method the performance of the one dimensional and two dimensional mfdma methods is investigated using synthetic multifractal measures with analytical solutions for backward ensuremath theta 0 centered ensuremath theta 0 5 and forward ensuremath theta 1 detrending windows we find that the estimated multifractal scaling exponent ensuremath tau q and the singularity spectrum f ensuremath alpha are in good agreement with the theoretical values in addition the backward mfdma method has the best performance which provides the most accurate estimates of the scaling exponents with lowest error bars while the centered mfdma method has the worse performance it is found that the backward mfdma algorithm also outperforms the multifractal detrended fluctuation analysis the one dimensional backward mfdma method is applied to analyzing the time series of shanghai stock exchange composite index and its multifractal nature is confirmed

multiple positive solutions to superlinear periodic boundary value problems with repulsive singular forces abstract the existence of multiple positive solutions to superlinear periodic boundary value problems with repulsive singular forces is discussed in this paper our nonlinearity may be singular in its dependent variable and our analysis relies on a nonlinear alternative of leray schauder type and on a fixed point theorem in cones

positive solutions of neumann problems with singularities abstract in this paper we study the existence of positive solutions to second order singular equations with neumann boundary conditions the proof of the main result relies on a nonlinear alternative principle of leray schauder together with a truncation technique

nodal solutions for second order m point boundary value problems with nonlinearities across several eigenvalues abstract we study the existence of nodal solutions of the m point boundary value problem u f u 0 0 t 1 u 0 0 u 1 i 1 m 2 i u i where i q i 1 2 m 2 with 0 1 2 m 2 1 and i r i 1 2 m 2 with i 0 and 0 i 1 m 2 i 1 we give conditions on the ratio f s s at infinity and zero that guarantee the existence of nodal solutions the proofs of our main results are based upon bifurcation techniques

an accelerated cyclic reduction based solvent method for solving quadratic eigenvalue problem of gyroscopic systems abstract the quadratic eigenvalue problem qep 2 m g k x 0 with m t m being positive definite k t k being negative definite and g t g is associated with gyroscopic systems in guo 2004 a cyclic reduction based solvent crs method was proposed to compute all eigenvalues of the above mentioned qep firstly the problem is converted to find a suitable solvent of the quadratic matrix equation qme m x 2 g x k 0 then using a cayley transformation and a proper substitution the qme is transformed into the nonlinear matrix equation nme z a t z 1 a q with a m k g and q 2 m k the problem finally can be solved by applying the cr method to obtain the maximal symmetric positive definite solution of the nme as long as the qep has no eigenvalues on the imaginary axis or for some cases where the qep has eigenvalues on the imaginary axis however when all eigenvalues of the qep are far away from or near the origin the cayley transformation seems not to be the best one and the convergence rate of the crs method proposed in guo 2004 might be further improved in this paper inspired by using a doubling algorithm to solve the qme we use a mobius transformation instead of the cayley transformation to present an accelerated crs acrs method for solving the qep of gyroscopic systems in addition we discuss the selection strategies of optimal parameter for the acrs method numerical results demonstrate the efficiency of our method

time dependent hurst exponent in financial time series abstract we calculate the hurst exponent h t of several time series by dynamical implementation of a recently proposed scaling technique the detrending moving average dma in order to assess the accuracy of the technique we calculate the exponent h t for artificial series simulating monofractal brownian paths with assigned hurst exponents h we next calculate the exponent h t for the return of high frequency tick by tick sampled every minute series of the german market we find a much more pronounced time variability in the local scaling exponent of financial series compared to the artificial ones the dma algorithm allows the calculation of the exponent h t without any a priori assumption on the stochastic process and on the probability distribution function of the random variables as happens for example in the case of the kitagawa grid and the extended kalmann filtering methods the present technique examines the local scaling exponent h t around a given instant of time this is a significant advance with respect to the standard wavelet transform or to the higher order power spectrum technique which instead operate on the global properties of the series by legendre or fourier transform of qth order moments

distribution of anomalous exponents of natural images recent studies of correlations of intensity in databases of natural images revealed a remarkable property the two point correlations are described in terms of power law behavior with an exponent which seems to be robust in the present letter we consider the statistical meaning of that result we study many individual images of one of the databases considered we find that the same law characterizing the correlations in the whole database governs also images randomly chosen from that database with one essential difference the exponent characterizing each image is specific and differs from the exponent characterizing the whole database the distribution of single image exponents has been measured and found to exhibit a rather heavy tail the database exponent cannot thus be considered as a statistical representative of a single image exponent possible reasons for the diversity in image exponents are discussed

on sign changing solution for some three point boundary value problems abstract in this paper an existence result of sign changing solution for some three point boundary value problems is obtained by using the fixed point index method

positive periodic solutions of singular systems of first order ordinary differential equations the existence and multiplicity of positive periodic solutions for first non autonomous singular systems are established with superlinearity or sublinearity assumptions at infinity for an appropriately chosen parameter the proof of our results is based on the krasnoselskii fixed point theorem in a cone

existence and nonexistence results for positive solutions of an integral boundary value problem abstract this paper deals with the existence and nonexistence of positive solutions for the integral boundary value problem a u b u g t f t u cos 0 u 0 sin 0 u 0 0 1 u d cos 1 u 1 sin 1 u 1 0 1 u d we provide sufficient conditions for the existence of either none or one or more positive solutions of the above problem the main tool used in the proofs of existence results is a fixed point theorem in a cone due to krasnoselskii and zabreiko the results presented substantially unify and extend the existing results in the literature

periodic solutions of lienard equations with singular forces of repulsive type in this paper we will use the coincidence degree to give an existence result of periodic solutions for the scalar lienard equations with singular forces of repulsive type the main result of this paper clearly describes what balance conditions between the singular force at the singularity and at the infinity should be imposed if the equation has a periodic solution as an application we will improve the results of ding ye and wang for the brillouin electron beam focusing system

relating casl with other specification languages the institution level in this work we investigate various specification languages and their relation to casl the recently developed common algebraic specification language in particular we consider the languages larch obj3 and functional cafeobj act one asf and hep theories as well as various sublanguages of casl all these languages are translated to an appropriate sublanguage of casl the translation mainly concerns the level of specification in the small the logics underlying the languages are formalized as institutions and representations among the institutions are developed however it is also considered how these translations interact with specification in the large thus we obtain on the one hand translations of any of the above mentioned specification languages to an appropriate sublanguage of casl this allows us to take libraries and case studies that have been developed for other languages and re use them in casl on the other hand we set up institution representations going from the casl institution and some of its subinstitutions to simpler subinstitutions given a theorem proving tool for such a simpler subinstitution with the help of a representation it can also be used for a more complex institution thus first order theorem provers and conditional term rewriting tools become usable for casl

on existence and multiplicity of positive solutions to periodic boundary value problems for singular nonlinear second order differential equations the existence and multiplicity of positive solutions are established to periodic boundary value problems for singular nonlinear second order ordinary differential equations the arguments are based only upon the positivity of the green s functions and the krasnosel skii fixed point theorem as an example a periodic boundary value problem is also considered which comes from the theory of nonlinear elasticity

performance of a high dimensional r s method for hurst exponent estimation abstract an extension of the r s method to estimate the hurst exponent of high dimensional fractals is proposed the method s performance was adequate when tested with synthetic surfaces having different preset hurst exponent values and different array sizes the two dimensional r s analysis is used to analyze three images from nature and experimental data revealing interesting scaling behavior with physical meaning

multifractal detrended cross correlation analysis of genome sequences using chaos game representation abstract we characterized the multifractal nature and power law cross correlation between any pair of genome sequence through an integrative approach combining 2d multifractal detrended cross correlation analysis and chaos game representation in this paper we have analyzed genomes of some prokaryotes and calculated fractal spectra h q and f from our analysis we observed existence of multifractal nature and power law cross correlation behavior between any pair of genome sequences cluster analysis was performed on the calculated scaling exponents to identify the class affiliation and the same is represented as a dendrogram we suggest this approach may find applications in next generation sequence analysis big data analytics etc

existence multiplicity and infinite solvability of positive solutions to a nonlinear fourth order periodic boundary value problem abstract the existence of n and infinitely many positive solutions is proved for the nonlinear fourth order periodic boundary value problem u 4 t u t u t f t u t 0 t 1 u i 0 u i 1 i 0 1 2 3 where n is an arbitrary natural number and 2 2 0 1 2 2 2 2 4 2 1 0 this kind of fourth order boundary value problems usually describes the equilibrium state of an elastic beam with periodic boundary condition the main results show that the problem may have n or infinitely many positive solutions provided the growth rates of nonlinear term f t l are appropriate on some bounded subsets of its domain

a relationship between the periodic and the dirichlet bvps of singular differential equations in this paper a relationship between the periodic and the dirichlet boundary value problems for second order ordinary differential equations with singularities is established this relationship may be useful in explaining the difference between the nonresonance of singular and nonsingular differential equations using this relationship we give in this paper an existence result of positive periodic solutions to singular differential equations when the singular forces satisfy some strong force condition at the singularity 0 and some linear growth condition at infinity

long term memory in stock market prices a test for long term memory that is robust to short range dependence is developed it is a modification of the r s statistic and the relevant asymptotic sampling theory is derived via functional central limit theory contrary to previous findings when applied to daily and monthly stock returns indexes over several time periods this test yields no evidence of long range dependence once short range dependence is accounted for monte carlo experiments show that the modified r s test has power against at least two specific models of long term memory suggesting that models with short range dependence may adequately capture the behavior of historical stock returns copyright 1991 by the econometric society

solving singular nonlinear second order periodic boundary value problems in the reproducing kernel space abstract in this paper we present a new method for solving a singular nonlinear second order periodic boundary value problem its analytical solution is represented in the form of series in the reproducing kernel space in the mean time the n term approximation u n x to the analytical solution u x is obtained and is proved to converge to the analytical solution some numerical examples are studied to demonstrate the accuracy of the present method results obtained by the method indicate the method is simple and effective

on the wavelet transformation of fractal objects the wavelet transformation is briefly presented it is shown how the analysis of the local scaling behavior of fractals can be transformed into the investigation of the scaling behavior of analytic functions over the half plane near the boundary of its domain of analyticity as an example a weierstrass like fractal function is considered for which the wavelet transform is related to a jacobi theta function some of the scalings of this theta function are analyzed and give some information about the scaling behavior of this fractal

power spectrum and detrended fluctuation analysis application to daily temperatures the variability measures of fluctuation analysis fa and detrended fluctuation analysis dfa are expressed in terms of the power spectral density and of the autocovariance of a given process the diagnostic potential of these methods is tested on several model power spectral densities in particular we find that both fa and dfa reveal an algebraic singularity of the power spectral density at small frequencies corresponding to an algebraic decay of the autocovariance a scaling behavior of the power spectral density in an intermediate frequency regime is better reflected by dfa than by fa we apply fa and dfa to ambient temperature data from the 20th century with the primary goal to resolve the controversy in literature whether the low frequency behavior of the corresponding power spectral densities are better described by a power law or a stretched exponential as a third possible model we suggest a weibull distribution however it turns out that neither fa nor dfa can reliably distinguish between the proposed models

periodic solutions for second order differential equations with a singular nonlinearity abstract this paper deals with the existence of positive t periodic solutions for the following differential equation x a t x f t x c t where a c l 1 0 t and f car 0 t r r the existence results are obtained by using a fixed point theorem in cones

three nonnegative solutions for fractional differential equations with integral boundary conditions in this paper we study multiple nonnegative solutions for the fractional differential equation with integral boundary conditions cd ax t f t x t 0 email protected 0 1 x 0 email protected 0 1g 0 s x s ds x 1 email protected 0 1g 1 s x s ds x k 0 email protected 0 1g k s x s ds k 2 3 a by means of leggett williams fixed point theorem some new results on the existence of at least three nonnegative solutions are obtained

existence of multiple solutions for some nonlinear boundary value problems abstract by imposing one sided conditions on the nonlinearity where neither regularity nor uniformity is required we prove the existence of either a nonnegative or a nonpositive solution for first and second order ordinary differential equations with periodic neumann or dirichlet boundary conditions positone and nonpositone problems are considered some nonexistence results are also obtained when using generalized ambrosetti prodi type conditions we get the existence of nonnegative and nonpositive solutions for first and second order periodic or neumann boundary value problems our method of proof makes use of topological degree arguments in cones

dependence of the unique solution of a periodic boundary value problem on the parameter abstract in this paper we study the dependence of the unique positive solution of the periodic boundary value problem u 2 u w t u s 0 s 1 and 0 u 0 u 1 u 0 u 1 on the parameter as 0 we show that this solution u t is infinitely differentiable in and has singularity in the order of with 2 1 s as 0 furthermore the graph of u t has fluctuation in t only of the order o 2 this will help us to determine the location of the solution in numerical computations to study the behavior of the solution when is sufficiently close to 0

hurst exponent footprints from activities on a large structural system abstract this paper presents hurst exponent footprints from pseudo dynamic measurements of significantly varied activities on a damaged bridge structure during rehabilitation through continuous monitoring the system is interesting due to associated uncertainty in large scale structures and significant presence of human intervention arising from fundamentally different processes investigations into the variation of computed hurst exponents on time series of limited lengths are carried out in this regard the hurst exponents are compared with respect to specific events during the rehabilitation as well as with the data collection locations the variations of local hurst exponents about the values computed for each activity are presented the scaling of hurst exponents for different activities is also investigated these are representative of the extent of multifractality for each event the extent of multifractality is assessed along with its source and time dependency

positive solutions for nonlinear discrete periodic boundary value problems we are concerned with the nonlinear discrete periodic boundary value problem p d p t 1 du t 1 q t u t rg t f u t t 1 t z u 0 u t p 0 du 0 p t du t where r is a positive parameter optimal interval will be given to the parameter r to ensure that p has at least one positive solution

bifurcation from interval and positive solutions for second order periodic boundary value problems we give a global description of the branches of positive solutions of second order periodic boundary value problemsu q t u lf t u 0 0

the sampling properties of hurst exponent estimates abstract the classical rescaled adjusted range r s statistic is a popular and robust tool for identifying fractal structures and long term dependence in time series data subsequent to mandelbrot and wallis water resour res 4 1968 909 who proposed the statistic be measured over several subseries contained within the whole series length the use overlapping vs contiguous subseries has been a source of some debate amongst r s theorists this study examines the distributional characteristics of rescaled adjusted range and hurst exponent estimates derived using overlapping vs contiguous subseries henceforth closing debate on the issue of relative bias due to either technique confidence intervals for the statistical significance of the hurst exponent are also determined

existence of nontrivial periodic solutions for a nonlinear second order periodic boundary value problem abstract in this paper we study the existence of nontrivial periodic solutions to the following nonlinear differential equation u t a t u t f t u t t r u 0 u u 0 u where a r r is an periodic continuous function with a t 0 f r r r is continuous may take negative values and can be sign changing without making any nonnegative assumption on nonlinearity by using the first eigenvalue corresponding to the relevant linear operator and the topological degree the existence of nontrivial periodic solutions to the above periodic boundary value problem is established finally three examples are given to demonstrate the validity of our main results

algorithm to estimate the hurst exponent of high dimensional fractals we propose an algorithm to estimate the hurst exponent of high dimensional fractals based on a generalized high dimensional variance around a moving average low pass filter as working examples we consider rough surfaces generated by the random midpoint displacement and by the cholesky levinson factorization algorithms the surrogate surfaces have hurst exponents ranging from 0 1 to 0 9 with step 0 1 and different sizes the computational efficiency and the accuracy of the algorithm are also discussed

direct determination approach for the multifractal detrending moving average analysis in the canonical framework we propose an alternative approach for the multifractal analysis based on the detrending moving average method mf dma we define a canonical measure such that the multifractal mass exponent q is related to the partition function and the multifractal spectrum f can be directly determined the performances of the direct determination approach and the traditional approach of the mf dma are compared based on three synthetic multifractal and monofractal measures generated from the one dimensional p model the two dimensional p model and the fractional brownian motions we find that both approaches have comparable performances to unveil the fractal and multifractal nature in other words without loss of accuracy the multifractal spectrum f can be directly determined using the new approach with less computation cost we also apply the new mf dma approach to the volatility time series of stock prices and confirm the presence of multifractality

detrended fluctuation analysis for fractals and multifractals in higher dimensions one dimensional detrended fluctuation analysis dfa and multifractal detrended fluctuation analysis mfdfa are widely used in the scaling analysis of fractal and multifractal time series because they are accurate and easy to implement in this paper we generalize the one dimensional dfa and mfdfa to higher dimensional versions the generalization works well when tested with synthetic surfaces including fractional brownian surfaces and multifractal surfaces the two dimensional mfdfa is also adopted to analyze two images from nature and experiment and nice scaling laws are unraveled

global structure of positive solutions for superlinear second order periodic boundary value problems in this paper we consider the nonlinear eigenvalue problems gather u lambda h t f u 0 quad 0 0 for i 1 ldots m 2 with sum i 1 m 2 alpha i eta i 0 for t 0 in 0 1 f in c 0 infty 0 infty and f s 0 for s 0 and f 0 infty where f 0 lim s rightarrow 0 f s s we investigate the global structure of positive solutions by using the nonlinear krein rutman theorem

positive solutions of even order system periodic boundary value problems we study a class of even order system boundary value problems with periodic boundary conditions a series of criteria are obtained for the existence of one two any arbitrary number and even a countably infinite number of positive solutions criteria for the nonexistence of positive solutions are also derived as for the second order case our results extend improve and supplement those in the literature for scalar and system boundary value problems several examples are given to demonstrate the applications moreover we obtain conditions for system periodic boundary value problems of a different form to have nontrivial solutions by transforming our main results to such problems

existence multiplicity and dependence on a parameter for a periodic boundary value problem the authors consider the boundary value problem y 2 y g t f y 0 0 t 2 y 0 y 2 y 0 y 2

a sharper condition for the solvability of a three point second order boundary value problem letf 0 1 r2 rbe a function satisfying caratheodory s conditions ande t l1 0 1 let 0 1 r 1 1 be given this paper is concerned with the problem of existence of a solution for the three point boundary value problem formula omitted this problem was studied earlier by gupta ntouyas and tsamatos when 1 and when 1 with 1 in the general case this problem was studied by gupta as a multi point boundary value problem in this paper sharper existence conditions are obtained for the solvability of the above boundary value problem in the general case

nontrivial solutions of singular sublinear sturm liouville problems abstract the singular superlinear sturm liouville problems l x h x f x 0 x 1 r 1 1 0 1 0 0 r 2 2 1 2 1 0 are considered under some conditions concerning the first eigenvalues corresponding to the relevant linear operators where l x p x x q x x and h x is allowed to be singular at both x 0 and x 1 in particular f is not necessary to be nonnegative the existence results of nontrivial solutions and positive solutions are given by means of the topological degree theory

existence of nontrivial solutions for a nonlinear sturm liouville problem with integral boundary conditions abstract this paper deals with the existence of nontrivial solutions for a nonlinear singular sturm liouville problem with integral boundary conditions

solvability of an m point boundary value problem for second order ordinary differential equations let 0 1 r2 r be a function satisfying caratheodory s conditions and e t l1 0 1 let i 0 1 ai r all of the ai s having the same sign i 1 2 m 2 0 1 2 m 2 1 be given this paper is concerned with the problem of existence of a solution for the m point boundary value problem x t t x t x t e t t 0 1 e formula conditions for the existence of a solution for the above boundary value problem are given using the leray schauder continuation theorem

free objects and equational deduction for partial conditional specifications abstract partial conditional specifications consist of conditional axioms with equalities in the possibly infinite set of premises and in the consequence which are interpreted in partial algebras equalities may be existential e or strong t e t holds in an algebra iff both t and t are defined and equal while t t holds in an algebra iff either t e t holds or both t and t are undefined contrary to the well explored case of positive conditional axioms only existential equalities in the premises general partial conditional specifications do not always admit free models and the related theory is much more subtle in this paper we fully investigate and solve the problem of existence of free and initial models giving necessary and sufficient conditions first from a model theoretical and then from a logical deduction viewpoint in particular we present a deduction system which is complete w r t strong equalities between open terms since positive conditional partial specifications and conditional total specifications are special cases of the paradigm investigated here the presented theory generalizes the related results about free models and the birkhoff like deduction theory the system we exhibit handles also the case of infinitary conjunctions as premises of the axioms it reduces to a classical one for the positive conditional case by just dropping one rule and finally it solves the empty carrier problem without using explicit quantification the theory presented here also gives the basis for solving via the usual first order reduction the problem of the existence of free and initial models for partial higher order specifications of term generated extensional models

existence of nonnegative and nonpositive solutions for second order periodic boundary value problems we are interested in nonnegative and nonpositive solutions of the boundary value problem u f t u u 0 u 1 u 0 u 1 where f fulfils the caratheodory conditions on 0 1 r we generalize the results reached by m n nkashama j santanilla and l sanchez and present estimates for solutions in addition we apply our existence theorems to periodic boundary value problems for nonlinear duffing equations whose right hand sides have a repulsive or attractive singularity at the origin we extend or generalize existence results by a c lazer and s solimini and other authors moreover we get some multiplicity results and in the case of a repulsive singularity we also admit a weak singularity in constrast to the previous papers on this subject our proofs are based on the method of lower and upper functions and topological degree arguments and the results are tested on examples

positive solutions for singular non linear third order periodic boundary value problems abstract in this paper we are concerned with the problem of the existence of positive solutions for non linear third order periodic boundary value problem u 3 u f t u 0 t 2 u i 0 u i 2 i 0 1 2 here 0 1 3 is a positive constant and our non linearity f t u may be singular at u 0 the proof relies on a non linear alternative of leray schauder type and on krasnoselskii fixed point theorem on compression and expansion of cones

on nonlinear boundary conditions satisfying certain asymptotic behavior abstract in this paper we consider a second order boundary value problem of the form y t a t g y t y 0 y y 1 0 we demonstrate that if the nonlinear functional y satisfies certain asymptotic behavior then the problem will possess at least one positive solution these results generalize and improve on some recent results in the literature on boundary value problems with nonlocal nonlinear boundary conditions and we provide some examples which illustrate these generalizations and improvements

on the existence of periodic solutions for certain differential equations here we are concerned with the problem of the existence of periodic solution for certain second and third order nonlinear differential equations our method here is to consider the problem as an eigenvalue problem and treat it by the topological degree theory in particular we establish the conditions of the existence of periodic solution first for a simpler system which is homotopic to the original system and then generalize the obtained results for the focal system the method employed here is applicable also for a system of nonlinear differential equations just with simple modifications finally we present some specific examples numerically to show that the results are valid and realizable

three dimensional wavelet based multifractal method the need for revisiting the multifractal description of turbulence dissipation data we generalize the wavelet transform modulus maxima wtmm method to multifractal analysis of 3d random fields this method is calibrated on synthetic 3d monofractal fractional brownian fields and on 3d multifractal singular cascade measures as well as their random function counterpart obtained by fractional integration then we apply the 3d wtmm method to the dissipation field issued from 3d isotropic turbulence simulations we comment on the need to revisit previous box counting analyses which have failed to estimate correctly the corresponding multifractal spectra because of their intrinsic inability to master nonconservative singular cascade measures

a comparative study of two dimensional multifractal detrended fluctuation analysis and two dimensional multifractal detrended moving average algorithm to estimate the multifractal spectrum multifractal detrended fluctuation analysis mfdfa and multifractal detrended moving average mfdma algorithm have been established as two important methods to estimate the multifractal spectrum of the one dimensional random fractal signal they have been generalized to deal with two dimensional and higher dimensional fractal signals this paper gives a brief introduction of the two dimensional multifractal detrended fluctuation analysis 2d mfdfa and two dimensional multifractal detrended moving average 2d mfdma algorithm and a detailed description of the application of the two dimensional fractal signal processing by using the two methods by applying the 2d mfdfa and 2d mfdma to the series generated from the two dimensional multiplicative cascading process we systematically do the comparative analysis to get the advantages disadvantages and the applicabilities of the two algorithms for the first time from six aspects such as the similarities and differences of the algorithm models the statistical accuracy the sensitivities of the sample size the selection of scaling range the choice of the q orders and the calculation amount the results provide a valuable reference on how to choose the algorithm from 2d mfdfa and 2d mfdma and how to make the schemes of the parameter settings of the two algorithms when dealing with specific signals in practical applications

analyzing exact fractal time series evaluating dispersional analysis and rescaled range methods precise reference signals are required to evaluate methods for characterizing a fractal time series here we use fgp fractional gaussian process to generate exact fractional gaussian noise fgn reference signals for one dimensional time series the average autocorrelation of multiple realizations of fgn converges to the theoretically expected autocorrelation two methods commonly used to generate fractal time series an approximate spectral synthesis ssm method and the successive random addition sra method do not give the correct correlation structures and should be abandoned time series from fgp were used to test how well several versions of rescaled range analysis r s and dispersional analysis disp estimate the hurst coefficient 0 0 9 r s detrended overestimates h for time series with h 0 7 estimates of h from all versions of disp usually have lower bias and variance than those from r s all versions of dispersional analysis disp now tested on fgp are better than we previously thought and are recommended for evaluating time series as long memory processes

multiple closed orbits of fixed energy forn body type problems with gravitational potentials abstract using the equivariant ljusternik schnirelmann theory and the estimates of the upper bound and lower bound of the critical values for the variational functional we obtain results in general concerning multiple geometrically distinct periodic solutions of fixed energy for a class of planarn body type problems

periodic solutions of second order non autonomous singular dynamical systems abstract in this paper we establish two different existence results of positive periodic solutions for second order non autonomous singular dynamical systems the first one is based on a nonlinear alternative principle of leray schauder and the result is applicable to the case of a strong singularity as well as the case of a weak singularity the second one is based on schauder s fixed point theorem and the result sheds some new light on problems with weak singularities and proves that in some situations weak singularities may help create periodic solutions recent results in the literature are generalized and significantly improved

nontrivial solutions of singular two point boundary value problems with sign changing nonlinear terms abstract the singular two point boundary value problem u t h t f u t t 0 1 u 0 u 1 0 is considered under some conditions concerning the first eigenvalue corresponding to the relevant linear problem where h is allowed to be singular at both t 0 and t 1 moreover f is a sign changing function and not necessarily bounded from below by computing the topological degree of an completely continuous field the existence results of nontrivial solutions are established

periodic solutions to some problems of n body type we prove the existence of at least one t periodic solution to a dynamical system of the type m i ddot u i sum limits j 1 j ne i n triangledown v ij u i u j text t 1 where the potentials v ij are t periodic in t and singular at the origin u i e r k i 1 n and k 3 we also provide estimates on the h 1 norm of this solution the proofs are based on a variant of the ljusternik schnirelman method the results here generalize to the n body problem some results obtained by bahri rabinowitz on the 3 body problem in 6