existence of positive solutions of superlinear second order neumann boundary value problem abstract in this paper we consider the neumann boundary value problem p t u t q t u t f t u t t 0 1 u 0 u 1 0 where p c 1 0 1 p t 0 q c 0 1 q t 0 f c 0 1 by using topological degree theory we investigate the existence of nontrivial solutions in particular we prove the existence of positive solutions provided that q t 0

conflict and coincidence of interest in job matching some new results and open questions the game theoretic solution to certain job assignment problems allows the interests of agents on the same side of the market e g firms or workers to be simultaneously maximized this is shown to follow from the lattice structure of the set of stable outcomes however it is shown that in a more general class of problems the optimality results persist but the lattice structures do not thus this paper raises as many questions as it answers

exact multiplicity and stability of solutions of second order neumann boundary value problem abstract the purpose of this paper is to establish the exact multiplicity and stability of solutions of the equation u g x u f x with the neumann boundary value conditions u 0 u 1 0 exactly three ordered solutions are obtained by taking advantage of the anti maximum principle combined with the methods of upper and lower solutions moreover we obtain that one of three solutions is negative while the other two are positive the middle solution is unstable and the remaining two are stable

a model of neural control of the heart rate a simple model of heart rate regulation is proposed using the assumption that the nervous system regulates the generation of pulses of the pacemaker previous values of intervals between heart beats rr intervals are used for this regulation which is described by a nonlinear feedback loop with time delay the conductance of the excitation in the heart is phenomenologically described by one nonlinear function recovery curve the model reproduces time series of rr intervals different known patterns of heart rate variability are observed depending on the type of control and the parameter values

entropy pattern entropy and related methods for the analysis of data on the time intervals between heartbeats from 24 h electrocardiograms sequences of the time intervals between heartbeats char22 medically termed rr intervals char22 extracted from 24 h electrocardiogram recordings are examined as three dimensional return map images the recordings were made in humans by means of the medically widely used portable electrocardiograph holter system a time window measured in the number of heartbeats is used and different types of behavior are classified bifurcations between the types of dynamics of the heart are noted and a form of intermittency is found an alternative quantitative measure char22 a form pattern entropy of the return map image char22 is defined that characterizes the dynamics of the rr interval sequence it is shown that this is a measure of the degree of ordering of the rr interval sequence and as such it is a good novel medical diagnostic tool for analyzing heart rate variability which distinguishes between illness and health where other diagnostics fail

on houseswapping the strict core segmentation and linear programming we consider then player houseswapping game of shapley and scarf 1974 with indifferences in preferences allowed it is well known that the strict core of such a game may be empty single valued or multi valued we define a condition on such games called segmentability which means that the set of players can be partitioned into a top trading segmentation it generalizes gale s well known idea of the partition of players into top trading cycles which is used to find the unique strict core allocation in the model with no indifference we prove that a game has a nonempty strict core if and only if it is segmentable we then use this result to devise ano n3 algorithm which takes as input any houseswapping game and returns either a strict core allocation or a report that the strict core is empty finally we are also able to construct a linear inequality system whose feasible region s extreme points precisely correspond to the allocations of the strict core this last result parallels the results of vande vate 1989 and rothblum 1992 for the marriage game of gale and shapley 1962

polyhedral aspects of stable marriage in the setting of the stable matching sm problem it has been observed that some of the man woman pairs cannot be removed although they participate in no stable matching since such a removal would alter the set of solutions these pairs are yet to be identified likewise and despite the sizeable literature some of the fundamental characteristics of the sm polytope e g its dimension its facets etc have not been established in the current work we show that these two seemingly distant open issues are closely related more specifically we identify the pairs with the above mentioned property and present a polynomial algorithm for producing a set of minimal preference lists we utilize this result in the context of two different representations of the sm structure rotation poset graph and algebraic formulation and derive the dimension of the sm polytope to obtain all alternative minimal linear descriptions

fixed sign solutions of second order difference equations with neumann boundary conditions in this paper we study the existence of solution of the nonlinear second order difference problem with neumann boundary conditions assuming the existence of a pair of ordered lower and upper solutions and we obtain optimal existence results for the case and even for to this end we do an exhaustive study of the values of the real parameters and for which the associated green s function to the linear operator l u u 2 2 u 1 u with neumann boundary conditions has fixed sign

many to one stable matching geometry and fairness baiou and balinski characterized the stable admissions polytope using a system of linear inequalities the structure of feasible solutions to this system of inequalities fractional stable matchings is the focus of this paper the main result associates a geometric structure with each fractional stable matching this insight appears to be interesting in its own right and can be viewed as a generalization of the lattice structure for integral stable matchings to fractional stable matchings in addition to obtaining simple proofs of many known results the geometric structure is used to prove the following two results first it is shown that assigning each agent their median choice among all stable partners results in a stable matching which can be viewed as a fair compromise second sufficient conditions are identified under which stable matchings exist in a problem with externalities in particular in the stable matching problem with couples

stable matchings optimal assignments and linear programming vande vate 1989 described the polytope whose extreme points are the stable core matchings in the marriage problem rothblum 1989 simplified and extended this result this paper explores a corresponding linear program its dual and consequences of the fact that the dual solutions have an unusually direct relation to the primal solutions this close relationship allows us to provide simple proofs both of vande vate and rothblum s results and of other important results about the core of marriage markets these proofs help explain the structure shared by the marriage problem without sidepayments and the assignment game with sidepayments the paper further explores fractional matchings which may be interpreted as lotteries over possible matches or as time sharing arrangements we show that those fractional matchings in the stable marriage polytope form a lattice with respect to a partial ordering that involves stochastic dominance thus all expected utility functions corresponding to the same ordinal preferences will agree on the relevant comparisons finally we provide linear programming proofs of slightly stronger versions of known incentive compatibility results

existence and uniqueness of positive solutions for singular nonlinear elliptic boundary value problems abstract in this paper we establish the existence and the uniqueness of positive solutions for dirichlet boundary value problems of nonlinear elliptic equations with singularity we obtain the existence and the uniqueness by using the mixed monotone method in the cone theory moreover we give an iterative method of constructing the solution the rate of convergence of the iterative sequence is analyzed

how random is your heart beat we measure the content of random uncorrelated noise in heart rate variability using a general method of noise level estimation using a coarse grained entropy we show that usually except for atrial fibrillation the level of such noise is within 5 15 of the variance of the data and that the variability due to the linearly correlated processes is dominant in all cases analyzed but atrial fibrillation the nonlinear deterministic content of heart rate variability remains significant and may not be ignored

multiplicity of solutions for integral boundary value problems of fractional differential equations with upper and lower solutions abstract in this paper we study the existence of multiple solutions for the integral boundary value problems of fractional differential equations by the method of upper and lower solutions and leray schauder degree theory the sufficient conditions about the existence of at least three solutions are obtained moreover it is proved that the integral boundary value problem has at least three positive solutions under the conditions of m 0 and f is nonnegative by given two upper and lower solutions which can be easily obtained through our methods we can present the existence theorem of at least three solutions two examples are also included to illustrate the effectiveness of the proposed results

existence of positive solution to a singular second order initial value problem with impulses this paper deals with the existence of positive solutions to singular initial value problem with impulse effects the right hand side of the differential equation can be singular in its dependent variable

stochastic heart rate model can reveal pathologic cardiac dynamics a simple one dimensional langevin type stochastic difference equation can simulate the heart rate fluctuations in a time scale from minutes to hours the model consists of a deterministic nonlinear part and a stochastic part typical of gaussian noise and both parts can be directly determined from measured heart rate data data from healthy subjects typically exhibit the deterministic part with two or more stable fixed points studies of 15 congestive heart failure subjects reveal that the deterministic part of pathologic heart dynamics has no clear stable fixed points direct simulations of the stochastic model for normal and pathologic cases can produce statistical parameters similar to those of real subjects results directly indicate that pathologic situations simplify the heart rate control system

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

multiplicity of positive solutions to second order neumann boundary value problems with impulse actions abstract this paper deals with existence theorems for single and multiple positive solutions to a kind of neumann boundary value problems with impulse actions the proof of the main results relies on a nonlinear alternative principle of leray schauder type and a well known fixed point theorem in cones the impulses are not restricted to be monotonous in the results obtained by us

universality and self similarity in the bifurcations of circle maps abstract the bifurcation structure in a two parameter family of circle maps is considered these maps have a topological degree that may be different from one a generalization of the rotation number is given and symmetries of the bifurcations in parameter space are described continuity arguments are used to establish the existence of periodic orbits by plotting the locus of parameter values associated with superstable cycles self similar bifurcations are found these bifurcations are a generalization of the familiar period doubling cascade in maps with one extrema to two parameter maps with two extrema finally a scheme for the global organization of bifurcation in these maps is proposed

characterization of stable matchings as extreme points of a polytope the purpose of this paper is to extend a modified version of a recent result of vande vate 1989 which characterizes stable matchings as the extreme points of a certain polytope our proofs are simpler and more transparent than those of vande vate

on a cutting plane heuristic for the stable roommates problem and its applications abstract we propose a new cutting plane heuristic for the classical stable roommates problem our approach utilises a new linear programming formulation for the problem and the underlying geometric properties of the fractional solution to construct the violated inequality we test the approach on moderate size problems with encouraging computational performance to further illustrate the versatility of this approach we also show how it can be suitably extended to handle variants of the basic stable roommates model

long range anticorrelations and non gaussian behavior of the heartbeat we find that the successive increments in the cardiac beat to beat interals of healthy subjects display scale invariant long range anticorrelations up to 10 4 heart beats furthermore we find that the histogram for the heartbeat intervals increments is well described by a l evy stable distribution for a group of subjects with severe heart disease we find that the distribution is unchanged but the long range correlations vanish therefore the different scaling behavior in health and disease must relate to the underlying dynamics of the heartbeat

blockers and antiblockers of stable matchings an implicit linear description of the stable matching polytope is provided in terms of the blocker and antiblocker sets of constraints of the matroid kernel polytope the explicit identification of both these sets is based on a partition of the stable pairs in which each agent participates here we expose the relation of such a partition to rotations we provide a time optimal algorithm for obtaining such a partition and establish some new related results most importantly that this partition is unique

linearized domain decomposition approaches for nonlinear boundary value problems abstract linearized schwarz domain decomposition approaches for nonlinear boundary value problems of the form u f x u u subject to dirichlet boundary conditions are proposed and analyzed in the presence of subsolutions and supersolutions we construct a globally convergent linear monotone iteration suitable for implementation in a distributed computing environment these iterations provide an alternative to the typical locally convergent approach of discretizing and solving the resulting non linear algebraic equations using a newton iteration the work also extends previous results obtained in the case where f has no dependence on the derivative of the solution the schwarz iteration is first proposed and studied in detail on two subdomains the result is then generalized to an arbitrary number of subdomains both alternating and parallel schwarz iterations are analyzed numerical results are provided to demonstrate the theory and the utility of the proposed iterations

multiple positive solutions of some boundary value problems abstract we study the existence of multiple positive solutions of the equations u t u subject to linear boundary conditions we show that there are at least two positive solutions if t u is superlinear at one end point zero or infinity and sublinear at the other applications of these results are provided to yield multiple positive solutions of some elliptic boundary value problems on an annulus

a constructive monotone iterative method for second order bvp in the presence of lower and upper solutions this paper concerns the monotone approximations of solutions of boundary value problems such as u f t u u 0 u 0 u 1 0 we consider linear iterative scheme in case f is lipschitz in u and satisfies a one sided lipschitz condition in u the initial approximations are lower and upper solutions which can be ordered one way a email protected we also consider the periodic and the dirichlet problems

boundary value problems involving upper and lower solutions in reverse order in this paper we discuss the existence of extreme solutions of the boundary value problem for a class of first order functional equations with a nonlinear boundary condition in the presence of a lower solution a and an upper solution b with email protected email protected we establish existence results of extreme solutions by using the method of upper and lower solutions and a monotone iterative technique

monotone method for the neumann problem with lower and upper solutions in the reverse order this work is devoted to the study of the existence and approximation of solutions of the problem u f t u u u a u b 0 in the presence of lower and upper solutions in the reverse order to this end we prove anti maximum principles for the nonlinear operator u 2k u email protected

the dimension of chaotic attractors dimension is perhaps the most basic property of an attractor in this paper we discuss a variety of different definitions of dimension compute their values for a typical example and review previous work on the dimension of chaotic attractors the relevant definitions of dimension are of two general types those that depend only on metric properties and those that depend on the frequency with which a typical trajectory visits different regions of the attractor both our example and the previous work that we review support the conclusion that all of the frequency dependent dimensions take on the same value which we call the dimension of the natural measure and all of the metric dimensions take on a common value which we call the fractal dimension furthermore the dimension of the natural measure is typically equal to the lyapunov dimension which is defined in terms of lyapunov numbers and thus is usually far easier to calculate than any other definition because it is computable and more physically relevant we feel that the dimension of the natural measure is more important than the fractal dimension

the monotone method for periodic differential equations with the non well ordered upper and lower solutions in this paper we consider the following periodic problem x t g t x t x t a e t a b x a x b x a x b the unique solution is obtained by constructing an auxiliary periodic system with bounded solutions and proving these bounds to be equal in which case they are the expected unique solution

a positive operator approach to the neumann problem for a second order ordinary differential equation abstract in this paper the solvability of the second order neumann problem u t cu t f t u t 0 qquad u 0 a u r b is studied we suppose that there is a lower solution and an upper solution in the reversed order and we obtain optimal conditions infto assure the existence of a solution lying between and

nonlinear triple point problems with change of sign in this paper we study the existence of at least one or two positive solutions to the second order triple point nonlinear boundary value problem y x h x f y x 0 x a b y a ay h y b by h where 0 a b 1 and h a b here h changes sign in h as an application we also give some examples to demonstrate our results

some observations on the questions is ventricular fibrillation chaos abstract ventricular fibrillation has been modeled as cardiac chaos occuring after a series of subharmonic bifurcations however previous experimental studies have suggested that fibrillatory oscillations have a relatively narrow band frequency spectrum inconsistent with a turbulent process similarly during the first minute of canine fibrillation we observed only a few localized frequency peaks from the epicardial and body surface electrocardiogram rather than a broadband type of spectrum as would be predicted for chaotic dynamics further narrowing of the frequency spectrum occured during the second minute of fibrillation the frequency spectrum of ventricular fibrillation contrasts with scaled broadband spectra observed in normal cardiac function we suggest that ventricular fibrillation may serve as a general model for transitions from broadband stability to certain types of pathological periodicities in other physiological perturbations

on the existence of positive radial solutions for nonlinear elliptic equations in annular domains abstract we study the existence of positive radially symmetric solutions of u g x f u 0 in annulus with dirichlet dirichlet neumann boundary conditions we show that the equation has a positive radial solution on any annulus if f and f are positive and f is superlinear at 0 and

multiplicity of positive solutions for second order three point boundary value problems we study the multiplicity of positive solutions for the second order three point boundary value problem u h t f u 0 t 0 1 u 0 0 u u 1 where 0 1 0 1 the methods employed are fixed point index theorems and leray schauder degree and upper and lower solutions

stable fractional matchings abstract we study a generalization of the classical stable matching problem that allows for cardinal preferences as opposed to ordinal and fractional matchings as opposed to integral in this cardinal setting stable fractional matchings can have much larger social welfare than stable integral ones our goal is to understand the computational complexity of finding an optimal i e welfare maximizing stable fractional matching we consider both exact and approximate stability notions and provide simple approximation algorithms with weak welfare guarantees our main result is that somewhat surprisingly achieving better approximations is computationally hard to the best of our knowledge these are the first computational complexity results for stable fractional matchings in the cardinal model en route to these results we provide a number of structural observations that could be of independent interest

new fixed point theorems for mixed monotone operators and local existence uniqueness of positive solutions for nonlinear boundary value problems abstract in this article we present a new fixed point theorem for a class of general mixed monotone operators which extends the existing corresponding results moreover we establish some pleasant properties of nonlinear eigenvalue problems for mixed monotone operators based on them the local existence uniqueness of positive solutions for nonlinear boundary value problems which include neumann boundary value problems three point boundary value problems and elliptic boundary value problems for lane emden fowler equations is proved the theorems for nonlinear boundary value problems obtained here are very general

the revealed preference theory of stable and extremal stable matchings we investigate the testable implications of the theory of stable matchings we provide a characterization of the matchings that are rationalizable as stable matchings when agents preferences are unobserved the characterization is a simple nonparametric test for stability in the tradition of revealed preference tests we also characterize the observed stable matchings when monetary transfers are allowed and the stable matchings that are best for one side of the market extremal stable matchings we find that the theory of extremal stable matchings is observationally equivalent to requiring that there be a unique stable matching or that the matching be consistent with unrestricted monetary transfers

the lattice structure of the set of stable matchings with multiple partners we continue recent work on the matching problem for firms and workers and show that for a suitable ordering the set of stable matchings is a lattice

bifurcation and chaos in a periodically stimulated cardiac oscillator abstract periodic stimulation of an aggregate of spontaneously beating cultured cardiac cells displays phase locking period doubling bifurcations and aperiodic chaotic dynamics at different values of the stimulation parameters this behavior is analyzed by considering an experimentally determined one dimensional poincare or first return map a simplified version of the experimentally determined poincare map is proposed and several features of the bifurcations of this map are described

existence and localization of solution for second order elliptic bvp in presence of lower and upper solutions without any order abstract we prove an existence and localization result for a solution of a second order elliptic equations with dirichlet and regular oblique derivative boundary conditions the main result is obtained assuming the existence of a lower and an upper solution without particular order and a positively homogeneous asymptotic behaviour of the right hand member of the equation

transition to topological chaos for circle maps abstract many biperiodic flows can be modelled by maps of a circle to itself for such maps the transition from zero to positive topological entropy can be achieved in several ways we describe all the possible routes for smooth circle maps and discuss the relevance of our results to the transition to chaos for two frequency systems

classical and weak solutions of a singular semilinear elliptic problem the singular semilinear elliptic equation u p x f u 0 is shown to have a unique positive classical solution inrnthat decays to zero at ifp x is simply a nontrivial nonnegative continuous function satisfying 0 t max x t p x dt providedfis a non increasing continuously differentiable function on 0 it is also shown that the equation has a unique weakh10 solution on a bounded domain provided e0 f s ds andp x l2

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

nonlinear dynamics chaos and complex cardiac arrhythmias periodic stimulation of a nonlinear cardiac oscillator in vitro gives rise to complex dynamics that is well described by one dimensional finite difference equations as stimulation parameters are varied a large number of different phase locked and chaotic rhythms is observed similar rhythms can be observed in the intact human heart when there is interaction between two pacemaker sites simplified models are analysed which show some correspondence to clinical observations the normal adult human heart at rest usually beats at a rate of between 50 and 100 times per minute in many circumstances some of which are lifethreatening but most of which are not the normal rhythmicity is altered resulting in abnormal rhythms called cardiac arrhythmias the point of this paper is to show that a branch of mathematics called nonlinear dynamics may be useful in the analysis of physiological processes believed to underlie normal heart rate regulation and some cardiac arrhythmias the idea that mathematical analysis can play a role in understanding cardiac arrhythmias is not novel indeed in the 1920s it was demonstrated that as parameters in mathematical models for the heart were varied several different rhythms that resembled clinically observed arrhythmias could be generated mobitz 1924 van de pol van der mark 1928 in nonlinear mathematics these changes in the qualitative features of the rhythms that are observed as parameters vary are called bifurcations thus the problem of understanding cardiac arrhythmias in the human heart is identified with understanding the bifurcations and complex dynamics in mathematical models of the human heart one type of dynamic behaviour that is the object of intensive analysis in mathematics is chaos loosely chaos is defined as aperiodic dynamics in deterministic systems in which there is sensitive dependence to the initial conditions this means that although in principle one could determine precisely the future evolution of the system starting from some initial condition for chaotic dynamics any difference in the initial condition no matter how small will eventually lead to marked differences in the future evolution of the system although the existence of chaos was known to poincare and others since the end of the last century in the

existence and uniqueness of solutions for singular fourth order boundary value problems by mixed monotone method the existence and uniqueness are established for singular fourth order boundary value problems the theorems obtained are very general and complement previous known results

the stable admissions polytope the stable admissions polytope the convex hull of the stable assignments of the university admissions problem is described by a set of linear inequalities it depends on a new characterization of stability and arguments that exploit and extend a graphical approach that has been fruitful in the analysis of the stable marriage problem

the geometry of fractional stable matchings and its applications we study the classical stable marriage and stable roommates problems using a polyhedral approach we propose a new lp formulation for the stable roommates problem which has a feasible solution if and only if the underlying roommates problem has a stable matching furthermore for certain special weight functions on the edges we construct a 2 approximation algorithm for the optimal stable roommates problem our technique exploits features of the geometry of fractional solutions of this formulation for the stable marriage problem we show that a related geometry allows us to express any fractional solution in the stable marriage polytope as a convex combination of stable marriage solutions this also leads to a genuinely simple proof of the integrality of the stable marriage polytope

nonstationary langevin equation statistical properties and application to explain effects observed in cardiological time series using the langevin equation we develop the model of a stochastic process subject to a given time dependent regulatory mechanism the effects of this nonstationarity on the statistical properties of the time series i e on global and conditional probability densities and on the moments of the distribution are derived application of these results on simple model trends allows one to approximate cardiological data and thus to explain effects recently observed in the reconstruction of the deterministic part of the langevin equation for time series of heart rate

the economics of matching stability and incentives this paper considers some game theoretic aspects of matching problems and procedures of the sort which involve matching the members of one group of agents with one or more members of a second disjoint group of agents ail of whom have preferences over the possible resulting matches the main focus of this paper is on determining the extent to which matching procedures can be designed which give agents the incentive to honestly reveal their preferences and which produce stable matches two principal results are demonstrated the first is that no matching procedure exists which always yields a stable outcome and gives players the incentive to reveal their true preferences even though procedures exist which accomplish either of these goals separately the second result is that matching procedures do exist however which always yield a stable outcome and which always give all the agents in one of the two disjoint sets of agents the incentive to reveal their true preferences

stochastic aspects of cardiac arrhythmias abnormal cardiac rhythms cardiac arrhythmias often display complex changes over time that can have a random or haphazard appearance mathematically these changes can on occasion be identified with bifurcations in difference or differential equation models of the arrhythmias one source for the variability of these rhythms is the fluctuating environment however in the neighborhood of bifurcation points the fluctuations induced by the stochastic opening and closing of individual ion channels in the cell membrane which results in membrane noise may lead to randomness in the observed dynamics to illustrate this we consider the effects of stochastic properties of ion channels on the resetting of pacemaker oscillations and on the generation of early afterdepolarizations the comparison of the statistical properties of long records showing arrhythmias with the predictions from theoretical models should help in the identification of different mechanisms underlying cardiac arrhythmias

the monotone method for neumann functional differential equations with upper and lower solutions in the reverse order abstract in this paper we show that the monotone technique produces two monotone sequences that converge uniformly to extremal solutions of second order functional differential equations and laplacian equations with neumann boundary value conditions moreover we obtain existence results assuming upper and lower solutions in the reverse order

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

surrogate time series before we apply nonlinear techniques e g those inspired by chaos theory to dynamical phenomena occurring in nature it is necessary to first ask if the use of such advanced techniques is justified by the data while many processes in nature seem very unlikely a priori to be linear the possible nonlinear nature might not be evident in specific aspects of their dynamics the method of surrogate data has become a very popular tool to address such a question however while it was meant to provide a statistically rigorous foolproof framework some limitations and caveats have shown up in its practical use in this paper recent efforts to understand the caveats avoid the pitfalls and to overcome some of the limitations are reviewed and augmented by new material in particular we will discuss specific as well as more general approaches to constrained randomisation providing a full range of examples new algorithms will be introduced for unevenly sampled and multivariate data and for surrogate spike trains the main limitation which lies in the interpretability of the test results will be illustrated through instructive case studies we will also discuss some implementational aspects of the realisation of these methods in the tisean software package

the asymptotic behaviour of the unique solution for the singular lane emden fowler equation abstract by karamata regular variation theory and constructing comparison functions we show the exact asymptotic behaviour of the unique classical solution u c 2 c near the boundary to a singular dirichlet problem u k x g u u 0 x u 0 where is a bounded domain with smooth boundary in r n g c 1 0 0 lim t 0 g t g t for each 0 for some 0 and k c loc for some 0 1 is nonnegative on which is also singular near the boundary

randomness and degrees of irregularity the fundamental question are sequential data random arises in myriad contexts often with severe data length constraints furthermore there is frequently a critical need to delineate nonrandom sequences in terms of closeness to randomness e g to evaluate the efficacy of therapy in medicine we address both these issues from a computable framework via a quantification of regularity apen approximate entropy defining maximal randomness for sequences of arbitrary length indicating the applicability to sequences as short as n 5 points an infinite sequence formulation of randomness is introduced that retains the operational and computable features of the finite case in the infinite sequence setting we indicate how the foundational definition of independence in probability theory and the definition of normality in number theory reduce to limit theorems without rates of convergence from which we utilize apen to address rates of convergence of a deficit from maximal randomness refining the aforementioned concepts in a computationally essential manner representative applications among many are indicated to assess i random number generation output ii well shuffled arrangements and iii the quality of bootstrap replicates

theory of reentrant excitation in a ring of cardiac tissue a cardiac pathology reentrant tachycardia is caused by the sustained circulation of activation along a reentrant path in cardiac tissue a new theoretical model for wave propagation in discrete excitable media employing coupled maps with continuous time is used to derive analytical stability criteria for the uni directional circulation of the excitation pulse on the ring of cardiac tissue numerical simulations of the model that incorporate experimentally measurable characteristics of the cardiac tissue reproduce the experimental data quantitatively the complex oscillations in the cycle length of unstable tachycardia observed experimentally are quasiperiodic oscillations that arise via the multiple hopf bifurcation in high dimensional maps

maximum and anti maximum principles for the general operator of second order with variable coefficients this paper is devoted to the study of existence of solutions of the nonlinear second order differential equation u t p t u t f t u t 0 together with different types of linear boundary conditions to this end we assume the existence of a pair of ordered lower and upper solutions and deduce comparison results for the general linear operator l p q u t u t p t u t q t u t together with the condisered boundary conditions

stochastic model for heart rate fluctuations a normal human heart rate shows complex fluctuations in time which is natural because the heart rate is controlled by a large number of different feedback control loops these unpredictable fluctuations have been shown to display fractal dynamics long term correlations and 1 f noise these characterizations are statistical and they have been widely studied and used but much less is known about the detailed time evolution dynamics of the heart rate control mechanism here we show that a simple one dimensional langevin type stochastic difference equation can accurately model the heart rate fluctuations in a time scale from minutes to hours the model consists of a deterministic nonlinear part and a stochastic part typical to gaussian noise and both parts can be directly determined from the measured heart rate data studies of 27 healthy subjects reveal that in most cases the deterministic part has a form typically seen in bistable systems there are two stable fixed points and one unstable one

analysis of time series from stochastic processes analysis of time series from stochastic processes governed by a langevin equation is discussed several applications for the analysis are proposed based on estimates of drift and diffusion coefficients of the fokker planck equation the coefficients are estimated directly from a time series the applications are illustrated by examples employing various synthetic time series and experimental time series from metal cutting