measuring the strangeness of strange attractors we study the correlation exponent v introduced recently as a characteristic measure of strange attractors which allows one to distinguish between deterministic chaos and random noise the exponent v is closely related to the fractal dimension and the information dimension but its computation is considerably easier its usefulness in characterizing experimental data which stem from very high dimensional systems is stressed algorithms for extracting v from the time series of a single variable are proposed the relations between the various measures of strange attractors and between them and the lyapunov exponents are discussed it is shown that the conjecture of kaplan and yorke for the dimension gives an upper bound for v various examples of finite and infinite dimensional systems are treated both numerically and analytically

applications of soft sets in ideal theory of bck bci algebras the notion of soft ideals and idealistic soft bck bci algebras is introduced and several examples are given relations between soft bck bci algebras and idealistic soft bck bci algebras are provided the intersection union and operation and or operation of soft ideals and idealistic soft bck bci algebras are established

soft sets and soft groups molodtsov introduced the concept of soft set theory which can be used as a generic mathematical tool for dealing with uncertainty in this paper we introduce the basic properties of soft sets and compare soft sets to the related concepts of fuzzy sets and rough sets we then give a definition of soft groups and derive their basic properties using molodtsov s definition of the soft sets

effects of fatigue on inter cycle variability in cross country skiing the aim of the study was to examine the inter cycle variability in cross country skiing gait and its evolution with fatigue both issues were investigated to understand the flexibility capabilities of the neuromuscular system four women and four men skied on a treadmill up to exhaustion the angular displacements of the arms and legs movements were obtained for 40s period at the beginning and end of the skiing test mean inter cycle standard deviation sd c largest lyapunov exponent lambda 1 and correlation dimension d c were computed for each time series and surrogate counterpart to evaluate the magnitude and nature of the variability for any experimental time series lambda 1 was positive d c greater than 1 and both were found to be different from their surrogate counterparts confirming that the temporal variations of the data had a deterministic origin more larger sd c d c and lambda 1 values were observed at the end of the test indicating more variability noise and local dynamic instability in the data with fatigue hence the fluctuations of limb angular displacements displayed a chaotic behavior which reflected flexibility of the neuromuscular system to adapt to possible perturbations during skiing however such chaotic behavior degraded with fatigue making the neuromuscular system less adaptable and more unstable

stability of explicit runge kutta methods abstract the classical theory of stability of explicit runge kutta methods is concerned with lipschitzian problems it is not useful for stable problems with large lipschitz constants the classical theory of absolute stability considers some very special problems of this kind the problems treated arise when a general problem is linearized it is hoped that the behavior in the case of the special problem provide guidelines as to the behavior in the case of a general problem a synthesis is proposed here which responds to this unsatisfactory state of affairs in the classical theory

internal error propagation in explicit runge kutta methods in practical computation with runge kutta methods the stage equations are not satisfied exactly due to roundoff errors algebraic solver errors and so forth we show by example that propagation of such errors within a single step can have catastrophic effects for otherwise practical and well known methods we perform a general analysis of internal error propagation emphasizing that it depends significantly on how the method is implemented we show that for a fixed method essentially any set of internal stability polynomials can be obtained by modifying the implementation details we provide bounds on the internal error amplification constants for some classes of methods with many stages including strong stability preserving methods and extrapolation methods these results are used to prove error bounds in the presence of roundoff or other internal errors

fuzzy h v groups in this paper we introduce the concept of fuzzy subhypergroup of a hypergroup as well as the fuzzy hv group we prove some results in this respect we also consider the fundamental relation defined on an hv group h and for a fuzzy subset of h we define the fuzzy subset of h and prove a fundamental theorem concerning the group h

generalized fuzzy rough sets this paper presents a general framework for the study of fuzzy rough sets in which both constructive and axiomatic approaches are used in constructive approach a pair of lower and upper generalized approximation operators is defined the connections between fuzzy relations and fuzzy rough approximation operators are examined in axiomatic approach various classes of fuzzy rough approximation operators are characterized by different sets of axioms axioms of fuzzy approximation operators guarantee the existence of certain types of fuzzy relations producing the same operators

a hybrid discontinuous in space and time galerkin method for wave propagation problems summary medium frequency regime and multi scale wave propagation problems have been a subject of active research in computational acoustics recently new techniques have attempted to overcome the limitations of existing discretization methods that tend to suffer from dispersion one such technique the discontinuous enrichment method incorporates features of the governing partial differential equation in the approximation in particular the solutions of the homogeneous form of the equation here based on this concept and by extension of a conventional space time finite element method a hybrid discontinuous galerkin method dgm for the numerical solution of transient problems governed by the wave equation in two and three spatial dimensions is described the discontinuous formulation in both space and time enables the use of solutions to the homogeneous wave equation in the approximation in this contribution within each finite element the solutions in the form of polynomial waves are employed the continuity of these polynomial waves is weakly enforced through suitably chosen lagrange multipliers results for two dimensional and three dimensional problems in both low frequency and medium frequency regimes show that the proposed dgm outperforms the conventional space time finite element method copyright 2014 john wiley sons ltd

an improved surrogate method for detecting the presence of chaos in gait it has been suggested that the intercycle variability present in the time series of biomechanical gait data is of chaotic nature however the proper methodology for the correct determination of whether intercycle fluctuations in the data are deterministic chaos or random noise has not been identified our goal was to evaluate the pseudoperiodic surrogation pps small et al 2001 surrogate test for pseudoperiodic time series data physical review letters 87 18 188 101 188 104 and the surrogation algorithms of theiler et al 1992 testing for nonlinearity in time series the method of surrogate data physica d 58 1 4 77 94 and of theiler and rapp 1996 re examination of the evidence for low dimensional nonlinear structure in the human electroencephalogram electroencephalography and clinical neurophysiology 98 213 222 to determine which is the more robust procedure for the verification of the presence of chaos in gait time series the knee angle kinematic time series from six healthy subjects generated from a 2 min walk were processed with both algorithms the lyapunov exponent lye and the approximate entropy apen were calculated from the original data and both surrogates paired t tests that compared the lye and the apen values revealed significant differences between both surrogated time series and the original data indicating the presence of deterministic chaos in the original data however the theiler algorithm affected the intracycle dynamics of the gait time series by changing their overall shape this resulted in significantly higher lye and apen values for the theiler surrogated data when compared with both the original and the pps generated data thus the discovery of significant differences was a false positive because it was not based on differences in the intercycle dynamics but rather on the fact that the time series was of a completely different shape the pps algorithm on the other hand preserved the intracycle dynamics of the original time series making it more suitable for the investigation of the intercycle dynamics and the identification of the presence of chaos in the gait time series

soft bck bci algebras molodtsov d molodtsov soft set theory first results comput math appl 37 1999 19 31 introduced the concept of soft set as a new mathematical tool for dealing with uncertainties that is free from the difficulties that have troubled the usual theoretical approaches in this paper we apply the notion of soft sets by molodtsov to the theory of bck bci algebras the notion of soft bck bci algebras and soft subalgebras are introduced and their basic properties are derived

soft semirings molodtsov introduced the concept of soft sets which can be seen as a new mathematical tool for dealing with uncertainty in this paper we initiate the study of soft semirings by using the soft set theory the notions of soft semirings soft subsemirings soft ideals idealistic soft semirings and soft semiring homomorphisms are introduced and several related properties are investigated

on some new operations in soft set theory molodtsov introduced the theory of soft sets which can be seen as a new mathematical approach to vagueness in this paper we first point out that several assertions proposition 2 3 iv vi proposition 2 4 and proposition 2 6 iii iv in a previous paper by maji et al p k maji r biswas a r roy soft set theory comput math appl 45 2003 555 562 are not true in general by counterexamples furthermore based on the analysis of several operations on soft sets introduced in the same paper we give some new notions such as the restricted intersection the restricted union the restricted difference and the extended intersection of two soft sets moreover we improve the notion of complement of a soft set and prove that certain de morgan s laws hold in soft set theory with respect to these new definitions

a practical method for calculating largest lyapunov exponents from small data sets detecting the presence of chaos in a dynamical system is an important problem that is solved by measuring the largest lyapunov exponent lyapunov exponents quantify the exponential divergence of initially close state space trajectories and estimate the amount of chaos in a system we present a new method for calculating the largest lyapunov exponent from an experimental time series the method follows directly from the definition of the largest lyapunov exponent and is accurate because it takes advantage of all the available data we show that the algorithm is fast easy to implement and robust to changes in the following quantities embedding dimension size of data set reconstruction delay and noise level furthermore one may use the algorithm to calculate simultaneously the correlation dimension thus one sequence of computations will yield an estimate of both the level of chaos and the system complexity

soft hyperstructure in this paper we study soft hypergroupoids firstly we introduce the notion of soft hypergroupoids and some examples are given also we show that soft hypergroupoids are closely related to l subhypergroupoid secondly using the notion of soft hypergroupoid some new properties of soft hypergroupoids are obtained lastly we investigate some properties of soft subhypergroupoids

testing for nonlinearity in time series the method of surrogate data we describe a statistical approach for identifying nonlinearity in time series the method first specifies some linear process as a null hypothesis then generates surrogate data sets which are consistent with this null hypothesis and finally computes a discriminating statistic for the original and for each of the surrogate data sets if the value computed for the original data is significantly different than the ensemble of values computed for the surrogate data then the null hypothesis is rejected and nonlinearity is detected we discuss various null hypotheses and discriminating statistics the method is demonstrated for numerical data generated by known chaotic systems and applied to a number of experimental time series which arise in the measurement of superfluids brain waves and sunspots we evaluate the statistical significance of the evidence for nonlinear structure in each case and illustrate aspects of the data which this approach identifies

kinematic variability and local dynamic stability of upper body motions when walking at different speeds a ubiquitous characteristic of elderly and patients with gait disabilities is that they walk slower than healthy controls many clinicians assume these patients walk slower to improve their stability just as healthy people slow down when walking across ice however walking slower also leads to greater variability which is often assumed to imply deteriorated stability if this were true then slowing down would be completely antithetical to the goal of maintaining stability this study sought to resolve this paradox by directly quantifying the sensitivity of the locomotor system to local perturbations that are manifested as natural kinematic variability eleven young healthy subjects walked on a motorized treadmill at five different speeds three dimensional movements of a single marker placed over the first thoracic vertebra were recorded during continuous walking mean stride to stride standard deviations and maximum finite time lyapunov exponents were computed for each time series to quantify the variability and local dynamic stability respectively of these movements quadratic regression analyses of the dependent measures vs walking speed revealed highly significant u shaped trends for all three mean standard deviations but highly significant linear trends with significant or nearly significant quadratic terms for five of the six finite time lyapunov exponents subjects exhibited consistently better local dynamic stability at slower speeds for these five measures these results support the clinically based intuition that people who are at increased risk of falling walk slower to improve their stability even at the cost of increased variability

control of local error stabilizes integrations codes for the solution of the initial value problem for a system of ordinary differential equations adjust their step sizes so as to keep the estimated local errors smaller than a given tolerance and at the same time solve the problem as efficiently as possible step sizes providing the desired accuracy may be too large for stability yet this does not cause the popular codes to become unstable the theory explaining why this is so holds only in very restricted circumstances this paper broadens and deepens the theory for explicit runge kutta methods

characterization of strange attractors a new measure of strange attractors is introduced which offers a practical algorithm to determine their character from the time series of a single observable the relation of this new measure to fractal dimension and information theoretic entropy is discussed

determining lyapunov exponents from a time series we present the first algorithms that allow the estimation of non negative lyapunov exponents from an experimental time series lyapunov exponents which provide a qualitative and quantitative characterization of dynamical behavior are related to the exponentially fast divergence or convergence of nearby orbits in phase space a system with one or more positive lyapunov exponents is defined to be chaotic our method is rooted conceptually in a previously developed technique that could only be applied to analytically defined model systems we monitor the long term growth rate of small volume elements in an attractor the method is tested on model systems with known lyapunov spectra and applied to data for the belousov zhabotinskii reaction and couette taylor flow

fuzzy soft semigroups and fuzzy soft ideals in this paper the notions of fuzzy soft semigroup and fuzzy soft left right ideal are given and the a level set union and intersection of them were studied for each a 0 1 finally fuzzy soft image and fuzzy soft inverse image of fuzzy soft semigroup ideal are discussed