are grades of membership probabilities abstract a small sample is given of the difficulties with present day fuzzy set theory with respect to the requirements of a scientific theory and a summary of some probabilistic interpretations of grades of membership to be found in the literature the tee model for grades of membership is then suggested instead of starting out from mathematical postulates such as the assumed max and min operations for or and and the tee model uses a semantic physio logical psycho logical starting point by investigating the possibilities which a person has for assigning linguistic labels and partial grades of membership in a meaningful way the assignment of partial grades of membership is explained by the assumption that humans have the ability to take errors of observation and intersubject differences into consideration a membership value uex is identified with the subject s estimate of the probability that the label e g tall would be assigned to an object of exact attribute value uex in a natural language situation this situation being a labeling or a yes no one in which at least one of three possible sources of uncertainty is present almost all the accepted formulas of fuzzy set theory as well as the shapes of the grade of membership curves are then derived instead of having to be postulated however the derived formulas for or and and reduce to the max and min operations only in a number of special cases in another special case they reduce to the summation and the zero operation respectively the generally valid formulas are presented

a probabilistic fuzzy logic system for modeling and control in this paper a probabilistic fuzzy logic system pfls is proposed for the modeling and control problems similar to the ordinary fuzzy logic system fls the pfls consists of the fuzzification inference engine and defuzzification operation to process the fuzzy information different to the fls it uses the probabilistic modeling method to improve the stochastic modeling capability by using a three dimensional membership function mf the pfls is able to handle the effect of random noise and stochastic uncertainties existing in the process a unique defuzzification method is proposed to simplify the complex operation finally the proposed pfls is applied to a function approximation problem and a robotic system it shows a better performance than an ordinary fls in stochastic circumstance

noether theorem for nonholonomic nonconservative mechanical systems in phase space on time scales the paper focuses on studying the noether theorem for nonholonomic nonconservative mechanical systems in phase space on time scales first the hamilton equations of nonholonomic nonconservative systems on time scales are established which is based on the lagrange equations for nonholonomic systems on time scales then based upon the quasi invariance of hamilton action of systems under the infinitesimal transformations with respect to the time and generalized coordinate on time scale the noether identity and the conserved quantity of nonholonomic nonconservative systems on time scales are obtained finally an example is presented to illustrate the application of the results

multiple results of p laplacian dynamic equations on time scales in this paper a new fixed point theorem introduced by avery and peterson and another fixed point theorem are applied to boundary value problems for p laplacian dynamic equations on time scales by imposing some growth conditions on the nonlinearity f we establish the existence results of at least three positive solutions as an application some examples are included to illustrate the main results

a philos type theorem for third order nonlinear retarded dynamic equations a new philos type theorem for a class of third order nonlinear dynamic equations is presented among others the restrictive condition in terms of the commutativity of the jump and delay operators is removed here

frequency measures on time scales with applications the concept of frequency measures of subsets of a time scale is introduced and the relevant properties are discussed then frequent oscillation is defined to strengthen the classical concept of oscillation applications are shown by deriving oscillation criteria for first order dynamic equations on time scales

eigenvalue problems for nonlinear differential equations on a measure chain abstract values of are determined for which there exist positive solutions of the second order differential equation on a measure chain u t a t f u t 0 t 0 1 satisfying either the conjugate boundary conditions u 0 u 1 0 or the right focal boundary conditions u 0 u 1 0 where a and f are positive valued and both lim x 0 f x x and lim x f x x exist

existence and exponential stability of piecewise mean square almost periodic solutions for impulsive stochastic nicholson s blowflies model on time scales the concept of piecewise mean square almost periodic stochastic process is introduced a new impulsive stochastic nicholsons blowflies model is introduced and studied on time scales the first results of the piecewise mean square almost periodic solutions for the model are obtained in this paper a class of impulsive stochastic nicholson s blowflies model with patch structure and nonlinear harvesting terms is introduced and studied on time scales by using contraction mapping principal and gronwall bellman inequality technique some sufficient conditions for the existence and exponential stability of piecewise mean square almost periodic solutions for the model with infinite delays are established on time scales finally an example is given to demonstrate the validity of the conditions of the main theorem

multiple solutions for 2mth order sturm liouville boundary value problems growth conditions are imposed on f such that the following boundary value problem 1 my 2m f t y i 1y 2i 0 i 1y 2i 1 0 i 1y 2i 1 i 1y 2i 1 1 0 0 i m 1 has an arbitrary number of positive solutions

comparison of eigenvalues for sturm liouville boundary value problems on a measure chain under consideration is a class of even ordered linear differential equations 1 m 2m t i 0m 1pi t 2i t with sturm liouville boundary conditions i 2i 0 i 2i 0 yi 1 2i 1 i 1 2i 1 0 for 0 i m 1 the derivative in this dynamic equation is the generalized delta derivative defined on a measure chain for a pair of eigenvalue problems for this dynamic equation we first verify the existence of smallest positive eigenvalues and then establish a comparison between the smallest eigenvalues of each eigenvalue problem

higher order boundary value problems on time scales in this paper we study the existence of solutions for lidstone boundary value problems on time scale firstly by using schauder fixed point theorem in a cone we obtain the existence of solutions to a lidstone boundary value problem lbvp secondly existence result for this problem is also given by the monotone method finally by using krasnosel skii fixed point theorem it is proved that the lbvp has a positive solution

oscillation criteria for two dimensional dynamic systems on time scales we establish some oscillation criteria for the two dimensional dynamic system x d t b t g y s t y d t a t f x t on a time scale t our results not only unify the oscillation of two dimensional differential systems and difference systems but include the oscillation results for differential systems and provide new oscillation criteria for difference systems several examples are considered to illustrate the main results

pressure boundary condition for the lattice boltzmann method we propose a lattice boltzmann realization for the hydrodynamic pressure drop condition introduced in j heywood r rannacher s turek artificial boundaries and flux and pressure conditions for the incompressible navier stokes equations int j numer methods fluids 22 1996 325 352 this condition has the advantage that only the average pressure needs to be prescribed at the boundary in general a second order accurate velocity and a first order accurate pressure are recovered with the proposed lattice boltzmann implementation the analytical investigation is supported by numerical simulations of a poiseuille flow and a less symmetric flow with nontrivial pressure field

triple positive solutions and dependence on higher order derivatives abstract in this paper we consider the lidstone boundary value problem y 2 m t f y t y 2 j t y 2 m 1 t 0 t 1 y 2 i 0 0 y 2 i 1 0 i m 1 where 1 m f 0 growth conditions are imposed on f and inequalities involving an associated green s function are employed which enable us to apply the leggett williams fixed point theorem to cones in ordered banach spaces this in turn yields the existence of at least three positive symmetric concave solutions the emphasis here is that f depends on higher order derivatives

eigenvalue comparisons for a class of boundary value problems of second order difference equations abstract we consider the boundary value problem for second order difference equation r i 1 y i 1 b i y i a i y i 0 1 i n y 0 y 1 y n 1 y n 0 in this study we do not require the positiveness of a k k 1 n we focus on the structure of eigenvalues of this problem and comparisons of all eigenvalues as the coefficients a i i 1 n b i i 1 n r i i 0 n and the parameters change

existence of triple positive solutions of two point right focal boundary value problems on time scales we consider the following boundary value problem 1 n 1y d n t 1 p 1f t y s n 1 t email protected a b t y d n a 0 email protected email protected p 1 y d n s b 0 email protected email protected n 1 where n 2 1 p n 1 is fixed and t is a time scale by applying fixed point theorems for operators on a cone existence criteria are developed for triple positive solutions of the boundary value problem we also include examples to illustrate the usefulness of the results obtained

monotone flows and fixed points for dynamic systems on time scales abstract utilizing dynamic systems on time scales the theory of monotone flows and fixed points is considered which unifies the theory of continuous and discrete dynamic systems

spectral theory of second order vector difference equations abstract this paper is concerned with spectral problems of second order vector difference equations with two point boundary value conditions where the matrix valued coefficient of the leading term may be singular a concept of self adjointness of the boundary value conditions is introduced the self adjointness of the corresponding difference operator is discussed on a suitable admissible function space and fundamental spectral results are obtained the dual orthogonality of eigenfunctions is shown in a special case rayleigh s principles and the minimax theorems in two linear spaces are given as an application a comparison theorem for eigenvalues of two sturm liouville problems is presented

comparison of eigenvalues for lidstone boundary value problems on a measure chain preprint the theory of u0 positive operators with respect to a cone in a banach space is applied to the class of even order differential equation on measure chains x 2m t 0m 1 pi t x 2i t t 0 1 satisfying the lidstone boundary conditions x 2i 0 0 0 i m 1 x 2j 2 1 0 0 j m 1 the existence of a smallest positive eigenvalue is obtained and then a theorem is established comparing the smallest positive eigenvalues for two problems of this type

asymptotic behavior of higher order nonlinear equations on time scales abstract utilizing the theory of dynamic systems on time scales which unifies the theory of continuous and discrete dynamic systems a necessary and sufficient condition is given for the asymptotic behavior of solutions of higher order nonlinear equations

hamiltonian systems on time scales linear and nonlinear hamiltonian systems are studied on time scales t we unify symplectic flow properties of discrete and continuous hamiltonian systems a chain rule which unifies discrete and continuous settings is presented for our so called alpha derivatives on generalized time scales this chain rule allows transformation of linear hamiltonian systems on time scales under simultaneous change of independent and dependent variables thus extending the change of dependent variables recently obtained by dosl and hilscher we also give the legendre transformation for nonlinear euler lagrange equations on time scales to hamiltonian systems on time scales

smoothness of invariant manifolds in this paper we present some functional analytic tools that allow us to prove a theorem on ck smoothness of general discrete and continuous invariant manifolds for ck systems a crucial role in this proof will be played by a theorem on ck parameter dependence of a fixed point of a contraction defined on a scale of banach spaces this fixed point principle is stated independently and may be of interest in itself further functional analytic considerations concerning smoothness properties of the nemytski operator are presented in a rather general form throughout the paper we treat the two cases of continuous and discrete dynamical systems in a unified manner thereby we use some concepts and results from the so called calculus on measure chains which was developed by the author in res in math 18 1990 18 56 knowledge of this calculus is not necessary for understanding the paper

some current cfd issues relevant to the incompressible navier stokes equations abstract the goals of this paper are to carefully define a particular class of well set incompressible navier stokes problems in the continuum partial differential equation pde setting and to discuss some relevant and sometimes poorly understood issues related to these well posed pde problems both in the continuum world and in its computer counterpart emphasized are three common formulations used to generate computer codes the primitive variable velocity pressure formulation and two derived variable formulations pressure poisson equation and vorticity transport equation

inequalities and asymptotics for riccati matrix difference operators in the first part inequalities for solutions of riccati matrix difference equations are obtained which correspond to the linear hamiltonian difference system formula whereak bk ck xk ukaren n matrices with symmetricbkandck if the matricesxkare invertible then the matricesqk ukx 1ksolve the riccati matrix difference equation formula in contrast to some recent papers dealing with these equations we do not assume that the matricesbkare invertible the second part of the paper deals with the asymptotic behaviour of solutionsqk as of the special riccati matrix difference equation which corresponds to the sturm liouville equation formula of even order 2nwith constant coefficientsr0 rn

oscillation criteria for second order matrix dynamic equations on a time scale we obtain oscillation criteria for a second order self adjoint matrix differential equation on a measure chain in terms of the eigenvalues of the coefficient matrices and the graininess function we illustrate our results with some nontrivial examples

monotone iterative technique and positive solutions of lidstone boundary value problems the purpose of this paper is to investigate the existence and iteration of n symmetric positive solutions for lidstone boundary value problem 1 nw 2 n t f t w t 0

time scale boundary value problems on infinite intervals two new existence results are presented for time scale boundary value problems on infinite intervals the first is based on a growth argument and the second on an upper and lower solution idea

positive solutions for boundary value problems of second order difference equations and their computation abstract we consider the following two classes of second order boundary value problems for difference equation r i 1 y i 1 b i y i a i y i 0 1 i n y 0 y 1 y n 1 y n 0 with 0 1 and r i 1 y i 1 b i y i a i y i 0 1 i n y 0 y n y n 1 y 1 with 0 1 we establish the existence of positive solutions to both problems a solver with linear computational complexity for almost tridiagonal linear systems is developed by exploring the special structure of linear system of equations based on fast solvers for linear systems effective algorithms for the computation of positive solutions will be proposed

eigenvalue comparisons for boundary value problems for second order difference equations abstract we consider the eigenvalue problems for boundary value problems of second order difference equations 1 r i 1 y i 1 a i y i 0 1 i n y 0 y n 1 y n 0 and 2 r i 1 y i 1 b i y i 0 1 i n y 0 y n 1 y n 0 comparison results for the eigenvalues of the problem 1 and the problem 2 are established

existence multiplicity and nonexistence of positive solutions to a differential equation on a measure chain abstract we are concerned with proving existence of one or more than one positive solution of a general two point boundary value problem for the nonlinear equation lx t p t x t q t x t a t f t x t we shall also obtain criteria which leads to nonexistence of positive solutions here the independent variable t is in a measure chain we will use fixed point theorems for operators on a banach space

asymptotic analysis of lattice boltzmann boundary conditions in this article we use a general method for the analysis of finite difference schemes to investigate lattice boltzmann algorithms for navier stokes problems with dirichlet boundary conditions several link based boundary conditions for commonly used lattice boltzmann bgk models are considered with our method the accuracy of the algorithms can be exactly predicted moreover the analytical results can be used to construct new algorithms which is demonstrated with a corrected bounce back rule that requires only local evaluations but still yields second order accuracy for the velocity the analysis is applicable to general geometries and instationary flows

discrete linear hamiltonian eigenvalue problems abstract this paper introduces general discrete linear hamiltonian eigenvalue problems and characterizes the eigenvalues assumptions are given among them the new notion of strict controllability of a discrete system that imply isolatedness and lower boundedness of the eigenvalues due to the quite general assumptions discrete sturm liouville eigenvalue problems of higher order are included in the presented theory

spectral theory of higher order discrete vector sturm liouville problems abstract this paper is concerned with spectral problems of higher order vector difference equations with self adjoint boundary conditions where the coefficient of the leading term may be singular a suitable admissible function space is constructed so that the corresponding difference operator is self adjoint in it and the fundamental spectral results are obtained rayleigh s principles and minimax theorems in two special linear spaces are given as an application comparison theorems for eigenvalues of two sturm liouville problems are presented especially the dual orthogonality and multiplicity of eigenvalues are discussed

systems control with generalized probabilistic fuzzy reinforcement learning reinforcement learning rl is a valuable learning method when the systems require a selection of control actions whose consequences emerge over long periods for which input output data are not available in most combinations of fuzzy systems and rl the environment is considered to be deterministic in many problems however the consequence of an action may be uncertain or stochastic in nature in this paper we propose a novel rl approach to combine the universal function approximation capability of fuzzy systems with consideration of probability distributions over possible consequences of an action the proposed generalized probabilistic fuzzy rl gpfrl method is a modified version of the actor critic ac learning architecture the learning is enhanced by the introduction of a probability measure into the learning structure where an incremental gradient descent weight updating algorithm provides convergence our results show that the proposed approach is robust under probabilistic uncertainty while also having an enhanced learning speed and good overall performance

eigenvalues of discrete linear second order periodic and antiperiodic eigenvalue problems with sign changing weight abstract by virtue of the eigenvalues of discrete linear second order neumann eigenvalue problems we study the eigenvalues of discrete linear second order periodic and antiperiodic eigenvalue problems with sign changing weight we find that these two problems have t real eigenvalues including the multiplicity respectively furthermore the numbers of positive eigenvalues are equal to the numbers of positive elements in the weight function and the numbers of negative eigenvalues are equal to the numbers of negative elements in the weight function furthermore these eigenvalues including the eigenvalues of neumann problem satisfy the order relation

a comparison of fuzzy forecasting and markov modeling abstract fuzzy time series models were introduced by song and chissom fuzzy sets and systems 54 1993 269 277 54 1993 1 9 62 1994 1 8 to model and forecast processes whose values are described by linguistic variables song and chissom used as an application the forecasting of educational enrollments this paper reviews the two methods set forth by song and chissom a first order time invariant fuzzy time series model and a first order time variant model these models are compared with each other and with a time invariant markov model using linguistic labels with probability distributions the results of these methods for the enrollment data are compared with three traditional time series models a first order autoregressive ar 1 model and two second order auto regressive ar 2 models all of which are time invariant

oscillation criteria of second order half linear dynamic equations on time scales in this paper by using the riccati transformation technique chain rule and inequalitya l lab l 1 l 1 b l 0 l 1 where a and b are positive constants we will establish some oscillation criteria for the second order half linear dynamic equation p t x d t c d q t x c t 0 t a b on time scales where c 1 is an odd positive integer our results not only unify the oscillation of half linear differential and half linear difference equations but can be applied on different types of time scales and improve some well known results in the difference equation case some examples are considered here to illustrate our main results

fuzzy pair wise dominance and fuzzy indices an evaluation of productive performance abstract usually efficiency measurement and evaluation are based on the definition of a frontier that envelops the observed production plans measurement and evaluation of productive performance is also achieved with the concept of pair wise dominance that does not require the existence of a frontier along with the required technological assumptions needed for its definition in situations where measurement inaccuracies occur the traditional assumption of crisp production plans can be substituted with the alternative assumption of fuzzy production plans as proposed by fuzzy set theory this research presents indices that capture the degree to which pair wise dominance occurs between two fuzzy production plans the proposed approach is based on the various comparison indices known from the literature that are used to compare fuzzy intervals and is compared with an earlier fuzzy pair wise classification scheme finally the approach is used to evaluate the productive performance of suspect production plans from the preprint insertion manufacturing process

on the number of positive solutions of systems of nonlinear dynamic equations on time scales in this paper we consider the following n dimensional second order nonlinear system on time scalesu d d t email protected t f u s t 0 email protected a b twith the sturm liouville boundary email protected a email protected d a 0 cu s b email protected d s b 0 where u u 1 u n a diag a 1 a n b diag b 1 b n c diag c 1 c n d diag d 1 d n let f email protected i 1 nlim u 0f i u email protected and f email protected i 1 email protected email protected f i u email protected define i 0 number of zeros in the set f 0 f and i number of infinities in the set f 0 f by using fixed point index theory we show that i if i 0 1 or 2 then there exist l 0 0 such that the system has i 0 positive solution s for l l 0 ii if i 1 or 2 then there exist l 0 0 such that the system has i 0 positive solution s for 0 0 respectively

mimetic methods on measure chains we introduce the divergence and the gradient for functions defined on a measure chain and this includes as special cases both continuous derivatives and discrete forward differences it is shown that in one dimension subject to dirichlet boundary conditions the divergence and the gradient are negative adjoints of each other and that the divergence of the gradient is negative semidefinite these are well known results in tile continuous theory and hence mimic those properties also for the case of a general measure chain 2001 elsevier science ltd all rights reserved

lyapunov inequality for linear hamiltonian systems on time scales the principal aim of this paper is to state and prove some lyapunov inequalities for linear hamiltonian system on an arbitrary time scale t so that the well known case of differential linear hamiltonian systems t r and the recently developed case of discrete hamiltonian systems t z are unified applying these inequalities a disconjugacy criterion for hamiltonian systems on time scales is obtained

linear hamiltonian difference systems disconjugacy and jacobi type conditions abstract we consider a linear hamiltonian difference system for the so called singular case so that discrete sturm liouville equations of higher order are included in our theory we introduce the concepts of focal points for matrix valued and generalized zeros for vector valued solutions of the system and define disconjugacy for linear hamiltonian difference systems we prove a reid roundabout theorem which gives conditions equivalent to positive definiteness of a certain discrete quadratic functional among them the strengthened jacobi s condition and a condition on a certain riccati difference equation the key to this theorem is a discrete version of picone s identity furthermore for the sake of generalization of our theorem we introduce controllability for linear hamiltonian difference systems and prove a reid roundabout theorem for a more general functional and more general boundary conditions

asymptotic analysis of the lattice boltzmann equation in this article we analyze the lattice boltzmann equation lbe by using the asymptotic expansion technique we first relate the lbe to the finite discrete velocity model fdvm of the boltzmann equation with the diffusive scaling the analysis of this model directly leads to the incompressible navier stokes equations as opposed to the compressible navier stokes equations obtained by the chapman enskog analysis with convective scaling we also apply the asymptotic analysis directly to the fully discrete lbe as opposed to the usual practice of analyzing a continuous equation obtained through the taylor expansion of the lbe this leads to a consistency analysis which provides order by order information about the numerical solution of the lbe the asymptotic technique enables us to analyze the structure of the leading order errors and the accuracy of numerically derived quantities such as vorticity it also justifies the use of richardson s extrapolation method as an example a two dimensional taylor vortex flow is used to validate our analysis the numerical results agree very well with our analytic predictions

initial and boundary conditions for the lattice boltzmann method an alternative approach of implementing initial and boundary conditions for the lattice boltzmann method is presented the basic idea is to calculate the lattice boltzmann populations at a boundary node from the fluid variables that are specified at this node using the gradients of the fluid velocity the numerical performance of the lattice boltzmann method is tested on several problems with exact solutions and is also compared to an explicit finite difference projection method the discretization error of the lattice boltzmann method decreases quadratically with finer resolution both in space and in time the roundoff error of the lattice boltzmann method creates problems unless double precision arithmetic is used

lattice boltzmann modeling of microchannel flow in slip flow regime we present the lattice boltzmann equation lbe with multiple relaxation times mrt to simulate pressure driven gaseous flow in a long microchannel we obtain analytic solutions of the mrt lbe with various boundary conditions for the incompressible poiseuille flow with its walls aligned with a lattice axis the analytical solutions are used to realize the dirichlet boundary conditions in the lbe we use the first order slip boundary conditions at the walls and consistent pressure boundary conditions at both ends of the long microchannel we validate the lbe results using the compressible navier stokes ns equations with a first order slip velocity the information preservation direct simulation monte carlo ip dsmc and dsmc methods as expected the lbe results agree very well with ip dsmc and dsmc results in the slip velocity regime but deviate significantly from ip dsmc and dsmc results in the transition flow regime in part due to the inadequacy of the slip velocity model while still agreeing very well with the slip ns results possible extensions of the lbe for transition flows are discussed

new definitions of exponential hyperbolic and trigonometric functions on time scales abstract we propose two new definitions of the exponential function on time scales the first definition is based on the cayley transformation while the second one is a natural extension of exact discretizations our exponential functions map the imaginary axis into the unit circle therefore it is possible to define hyperbolic and trigonometric functions on time scales in a standard way the resulting functions preserve most of the qualitative properties of the corresponding continuous functions in particular pythagorean trigonometric identities hold exactly on any time scale dynamic equations satisfied by cayley motivated functions have a natural similarity to the corresponding differential equations the exact discretization is less convenient as far as dynamic equations and differentiation are concerned

existence of weak solutions of two point boundary value problems for second order dynamic equations on time scales abstract in this paper by using critical point theory we establish the existence of weak solutions of the two point boundary value problem for a second order dynamic equation on an arbitrary time scale t so that the well known case of differential dynamic systems t r and the recently developed case of discrete dynamic systems t z are unified to the best of our knowledge this is the first time that boundary value problems of dynamic equations on time scales have been dealt with by using critical point theory

higher order three point boundary value problem on time scales in this paper we consider a higher order three point boundary value problem on time scales we study the existence of solutions of a non eigenvalue problem and of at least one positive solution of an eigenvalue problem later we establish the criteria for the existence of at least two positive solutions of a non eigenvalue problem examples are also included to illustrate our results

unity and diversity of fuzziness spl minus from a probability viewpoint like the fields of probability and statistics fuzzy set theory is characterized by a variety of viewpoints adherents of fuzzy methods however consistently maintain that probability is not necessarily the optimal representation of uncertainty we rebut this view

upper and lower solution method for a fourth order four point boundary value problem on time scales in this work we consider a fourth order four point boundary value problem on time scales we establish criteria for the existence of a solution by developing the upper and lower solution method and the monotone iterative technique

oscillation of nonlinear dynamic equations on time scales by means of riccati transformation techniques we establish some new oscillation criteria for the second order nonlinear dynamic equation p t x d t d q t f x s t 0 email protected a b on time scales in terms of the coefficients and the graininess function we illustrate our results with a nontrivial example

existence of multiple positive solutions for sturm liouville like four point boundary value problem with p laplacian abstract in this paper we consider the sturm liouville like four point boundary value problem with p laplacian p u t f t u t 0 t 0 1 u 0 u 0 u 1 u 0 where p s s p 2 s p 1 by means of a fixed point theorem for operators on a cone the existence of multiple at least three positive solutions to the above boundary value problem is obtained

on green s functions and positive solutions for boundary value problems on time scales in this paper we offer a form of self adjoint differential equations on time scales so that the associated green s function is found symmetric in the usual sense for this purpose together with the delta derivative we employ the nabla derivative as well we introduce the concepts of lebesgue delta and nabla integrals on time scales next sign properties of the green s function are investigated and existence results for positive solutions of nonlinear boundary value problems are established upper and lower bounds for these positive solutions also are given

positive solutions of semipositone higher order differential equations on time scales abstract in this paper we are concerned with the following 2 n th order differential equations on time scales 1 n y 2 n t g t f t y t t a b y 2 i a i 1 y 2 i 1 a i 1 y 2 i i 1 y 2 i y 2 i b 0 i n 1 where a b n 1 i 0 1 i b a i a i 0 i b i i 1 a i b i 1 2 n the functions g a b 0 and f a b 0 are continuous or g is singular at t a and or t b we obtain some properties and sharp estimates of the corresponding green s function and investigate the existence of positive solutions of the semipositone problems for 2 n order differential equations by the use of the property of green s function variable transformation and the fixed point index theorem

dynamic equations on time scales a survey the study of dynamic equations on time scales which goes back to its founder stefan hilger 1988 is an area of mathematics that has recently received a lot of attention it has been created in order to unify the study of differential and difference equations in this paper we give an introduction to the time scales calculus we also present various properties of the exponential function on an arbitrary time scale and use it to solve linear dynamic equations of first order several examples and applications among them an insect population model are considered we then use the exponential function to define hyperbolic and trigonometric functions and use those to solve linear dynamic equations of second order with constant coefficients finally we consider self adjoint equations and more generally so called symplectic systems and present several results on the positivity of quadratic functionals

pressure condition for lattice boltzmann methods on domains with curved boundaries we propose a lattice boltzmann algorithm for an average pressure boundary condition at outlets in pipe flow systems the advantage of this boundary condition is that only the average pressure is used to recover the non trivial flow fields the asymptotic analysis shows that this algorithm works for general curved boundaries and renders a second order accurate velocity and a first order accurate pressure approximation of the incompressible navier stokes solution here we verify the accuracy by numerical simulations of a poiseuille flow and a less symmetric flow with non trivial pressure field in channels inclined with arbitrary angle and flows in a pipe with three outlets

eigenvalues of lidstone boundary value problems we consider the following boundary value problem 1 ny 2 n lf t y n 1 t 0 1 y 2 i 0 y 2 i 1 0 0 0 the values of l are characterized so that the boundary value problem has a positive solution in addition we derive explicit intervals of l such that for any l in the interval existence of a positive solution of the boundary value problem is guaranteed several examples are also included to dwell upon the importance of the results obtained

instability results for slowly time varying linear dynamic systems on time scales abstract we develop eigenvalue criteria under which the solutions of a slowly time varying linear dynamic system of the form x t a t x t are unstable

regular article an accurate curved boundary treatment in the lattice boltzmann method the lattice boltzmann equation lbe is an alternative kinetic method capable of solving hydrodynamics for various systems major advantages of the method are due to the fact that the solution for the particle distribution functions is explicit easy to implement and natural to parallelize because the method often uses uniform regular cartesian lattices in space curved boundaries are often approximated by a series of stairs that leads to reduction in computational accuracy in this work a second order accurate treatment of the boundary condition in the lbe method is developed for a curved boundary the proposed treatment of the curved boundaries is an improvement of a scheme due to o filippova and d hanel 1998 j comput phys 147 219 the proposed treatment for curved boundaries is tested against several flow problems 2 d channel flows with constant and oscillating pressure gradients for which analytic solutions are known flow due to an impulsively started wall lid driven square cavity flow and uniform flow over a column of circular cylinders the second order accuracy is observed with a solid boundary arbitrarily placed between lattice nodes the proposed boundary condition has well behaved stability characteristics when the relaxation time is close to 1 2 the zero limit of viscosity the improvement can make a substantial contribution toward simulating practical fluid flow problems using the lattice boltzmann method

on the existence of positive solutions for 2 n order singular boundary value problems by applying upper and lower solutions method the existence of c2n 2 0 1 and c2n 1 0 1 positive solution for a class of 2n order singular differential equations boundary value problems is obtained

some oscillation results for second order nonlinear dynamic equations of neutral type abstract in this paper some oscillation results for the second order nonlinear neutral delay dynamic equation r t y t p t y t q t y t sgn y t 0 are obtained on a time scale t under the assumption t 0 1 r t 1 t where 0 is a quotient of odd positive integers

oscillatory behavior of third order nonlinear delay dynamic equations on time scales in this paper a class of third order nonlinear delay dynamic equations on time scales is studied by using the generalized riccati transformation and the integral averaging technique three new sufficient conditions which ensure that every solution is oscillatory or converges to zero are established the results obtained essentially generalize and improve earlier ones

on the positive solutions of lidstone boundary value problems the existence nonexistence and multiplicity of positive solutions are considered for lidstone boundary value problem 1 email protected 2 n email protected t w t 0 0 by making use of krasnosel skii fixed point theorem some new results are obtained particularly it is proved that the lidstone boundary value problem has n positive solutions under suitable conditions where n is an arbitrary natural number

symmetric positive solutions of nonlinear boundary value problems abstract we study the nonlinear boundary value problem u 2 m f t u u u 2 m 2 t 0 1 u 2 i 0 u 2 i 1 0 i 0 m 1 the existence of symmetric positive solutions of the above problem is discussed sufficient conditions are obtained for the problem to have one any finite number and a countably infinite number of such solutions our results extend some recent work in the literature on boundary value problems of ordinary differential equations we illustrate our results by two examples none of which can be handled using the existing results

even order nonlinear eigenvalue problems on a measure chain we consider the even order nonlinear eigenvalue problem 1 mu 2m t f t u t u 2i 0 u 2i 1 0 0 i m 1 on a measure chain t results on existence and nonexistence of positive solutions are obtained for evaluated in different intervals under certain assumptions the complete scenario for all 0 is established our work develops and improves many known results in the literature even for the case that t is the real number line we also interpret our general results on measure chains to the discrete case which yields a new set of conditions for the existence and nonexistence of positive solutions of eigenvalue problems for difference equations

higher order dynamic equations on measure chains wronskians disconjugacy and interpolating families of functions this paper introduces generalized zeros and hence disconjugacy of nth order linear dynamic equations which cover simultaneously as special cases among others both differential equations and difference equations we also define markov fekete and descartes interpolating systems of functions the main result of this paper states that disconjugacy is equivalent to the existence of any of the above interpolating systems of solutions and that it is also equivalent to a certain factorization representation of the operator the results in this paper unify the corresponding theories of disconjugacy for nth order linear ordinary differential equations and for nth order linear difference equations

sturm liouville eigenvalue problems on time scales for sturm liouville eigenvalue problems on time scales with separated boundary conditions we give an oscillation theorem and establish rayleigh s principle our results not only unifly the corresponding theories for differential and difference equations but are also new in the discrete case

trigonometric transformations of symplectic difference systems abstract in this paper we show that any symplectic difference system can be transformed into a trigonometric system using a transformation that preserves oscillatory properties necessary and sufficient conditions for nonoscillation of a certain class of trigonometric systems are given and this result is applied to oscillation theory of hamiltonian difference systems

eigenvalue comparisons for second order difference equations with neumann boundary conditions abstract the boundary value problem for second order difference equation r i 1 y i 1 b i y i a i y i 0 1 i n y 0 y 1 y n 1 y n 0 with 0 1 and 2 was recently discussed in ji and yang 2007 j ji b yang eigenvalue comparisons for a class of boundary value problems of second order difference equations linear algebra appl 420 1 2007 218 227 in this paper we extend our earlier results to the second order difference equations with neumann boundary conditions the case of 1 as in ji and yang 2007 mentioned above we will also focus on the structure of its eigenvalues and comparisons of all eigenvalues as the coefficients a i b i and r i change

function series theory of time scales in this paper we extend the concept of function series to time scales and then we present two necessary and sufficient conditions and several criteria for uniform convergence moreover we demonstrate several analytical properties of function series on general time scales furthermore we illustrate our conclusions through examples respectively

some new dynamic inequalities on time scales in this paper based on some known dynamic inequalities we investigate certain new dynamic inequalities on time scales which provide explicit bounds on unknown functions our results unify and extend some continuous inequalities and their corresponding discrete analogues