asymptotic behavior of nonlinear difference systems in this paper we consider two dimensional nonlinear difference systems of the email protected n a nf y n dy n 1 b ng x n we classify their solutions according to asymptotic behavior and give some necessary and sufficient conditions for the existence of solutions of such classes

pinning of a rough interface by an external potential abstract an analysis is given of the behavior of an interface between two phases in the presence of an external pinning potential in the solid on solid limit of the two dimensional ising model it is found that the potential turns a rough interface into a smooth one except in the case of a boundary potential where a minimum potential strength is required the connection with the roughening transition found by abraham is discussed the interface width is calculated as a function of the potential parameters in the limit of a weak pining potential

reflection sieve obstructions in finite groups of type dn abstract in 4 we constructed certain homology representations of a finite group g of type an bn or cn and showed that these representations can be used to sift out the reflection compound characters of g in the present note we show that for a group g of type dn each reflection compound character k 2 k n 2 determines a unique obstruction character k which occurs with positive multiplicity in every homology representation containing k

oscillation and nonoscillation of two dimensional difference systems this paper is concerned with the oscillation and nonoscillation behavior of solution of the nonlinear two dimensional difference system xn ang yn yn 1 f n xn n n n0 n0 n0 1 some necessary and sufficient conditions are given for the system to admit the existence of oscillatory and nonoscillatory solutions with special asymptotic properties some important results in the literatures are generalized examples to illustrate the result are included

correlation functions in the two dimensional gaussian column model of the interface in a weak external field calculations of the correlation functions c and ccond for the two dimensional gaussian column model of the interface in a weak gravitational field g to 0 indicate the universality of the parametrisation of the direct correlation function c found for the sos model by stecki ciach and dudowicz 1986 the representations of the conditional correlation function ccond are slightly different in these two models

short distance expansion for the local susceptibility and pair correlation function at continuous wetting transitions a scaling ansatz is proposed for the density profile rho z with z the distance normal from the substrate for a fluid undergoing a continuous wetting transition at a wall the ansatz predicts that in the fluctuation dominated regime the local susceptibility delta rho z delta mu t with mu the chemical potential has a simple power law position dependence for short distances z zeta perpendicular to the perpendicular correlation length the power law is determined by the wetting critical exponents which is different for complete and critical wetting the scaling predictions are confirmed in dimension d 2 by explicit analysis for an interfacial hamiltonian model of the wetting transition for critical wetting a scaling ansatz for the form of the transverse moments of the two point correlation function g is postulated which now yields the z1 z2 dependence of g in terms of critical exponents calculations again confirm the scaling theory for d 2 the analysis highlights the different qualitative and quantitative features of the response functions for critical and complete wetting for fluids with short ranged forces

invariant and attracting sets of impulsive delay difference equations with continuous variables the aim of this paper is to study the invariant and attracting sets of impulsive delay difference equations with continuous variables some criteria for the invariant and attracting sets are obtained by using the decomposition approach and delay difference inequalities with impulsive initial conditions

an existence theorem for a nonlinear difference equation where p 1 and s p is a real sequence we establish conditions under which 1 1 has a positive nondecreasing solution here a solution of 1 1 is a real sequence y y which satisfies 1 1 since 1 1 is a recurrence relation given real initial values y and y it is clear that we can inductively obtain y y since p is a real number greater than 1 the sequence yk may not be real that is not a solution note however that any constant multiple of a solution is again a solution the existence question originated in l where it was shown that hardy s inequality for a series 2 can be viewed as a necessary condition for the existence of a positive nondecreasing solution of 1 1 our existence theorem reduces to a nonoscillation criterion in the case p 2 since then 1 1 changes to a second order linear difference equation see e g 3 a brief outline of the paper is as follows section 2 introduces a riccati type transformation and then develops various necessary conditions for the existence of a positive nondecreasing solution section 3 discusses some of the functional analytic background which is needed in order to apply schauder s theorem section 4 contains the proof of our existence theorem and section 5 describes a comparison theorem which allows us to drop the assumption that the coefficients sk in 1 1 are nonnegative

oscillation of second order nonlinear difference equation with continuous variable in this paper we are mainly concerned with the second order nonlinear difference equation with continuous variable here by using the iterated integral transformations generalized riccati transformations and integrating factors we give some oscillatory criteria for this equation

bounded solutions and wavefronts for discrete dynamics this paper deals with the second order nonlinear difference equation dd r k dd u k q kg u k 1 0 where r k and q k are positive real sequences defined on n cup 0 and the nonlinearity g r to r is nonnegative and nontrivial sufficient and necessary conditions are given for the existence of bounded solutions starting from a fixed initial condition u 0 the same dynamic with f instead of g such that uf u 0 for u not 0 was recently extensively investigated on the contrary our nonlinearity g is of a small appearance in the discrete case its introduction is motivated by the analysis of wavefront profiles in biological and chemical models the paper emphasizes the many different dynamical behaviors caused by such a g with respect to the equation involving function f some applications in the study of wavefronts complete this work

oscillation for linear non autonomous systems of difference equations with continuous arguments abstract in this paper we establish sufficient conditions for the oscillation of the linear non autonomous systems of difference equations with continuous arguments n x t p x t j 1 n q j t x t j 0 where x t x t x t n 1 p r m m q j c r r m m j 1 2 n and j j 1 2 n are non negative constants furthermore assume q j t q j l k t where q j l k t l k 1 2 m j 1 2 n are continuous bounded and do not change signs on r

oscillatory and asymptotic behavior of second order nonlinear difference equations in this paper we are dealing with the oscillatory and asymptotic behaviour of solutions of second order nonlinear difference equations of the form rn xn f n xn 0 n n n0 1 we obtain the following results a if k n0 l rk any nonoscillatory solution of 1 must belong to one of the following four types k k k 0 k 0 b if k n0 l rk any nonoscillatory solution of 1 must belong to one of the following three types k0 k k0 c necessary and sufficient conditions for 1 to have a nonoscillatory solution which belongs to k k k 0 k0 or k are given depending on whether f is a superlinear or sublinear function all these results include and improve b szmanda s results in bull polish acad sci math 34 nos 3 4 1986 133 141

on decomposition of modular representations from cohen macaulay geometries abstract chain spaces for a cohen macaulay complex split into subspaces corresponding to cycles for truncations of the complex precisely when the cycles are non degenerate in the natural bilinear form application to the tits building provides a simple geometric approach to the well known splitting of ind g b 1 for a lie type group g in natural characteristic an application to a sporadic geometry is also indicated

the dependence on external field of the correlation functions and susceptibilities of the one dimensional sos interface a numerical study of the sos interface in two dimensions extends the asymptotic analysis of van leeuwen and hilhorst 1981 global properties one point functions and two point correlations computed earlier including the direct correlation function and the susceptibilities are parameterised and their dependence on the external field is analyzed in detail intrinsic properties of the interface including the new longitudinal correlation length are discussed

oscillation criteria for nonlinear partial difference equations with delays abstract we offer sufficient conditions for the oscillation of all solutions of the partial difference equations y m 1 n m n y m n 1 m n y m n p m n y m k n l q m n y m k n l and y m 1 n m n y m n 1 m n y m n i 1 p i m n y m k i n l i i 1 q i m n y m k i n l i several examples which dwell upon the importance of our results are also included

oscillation and nonoscillation criteria for linear dynamic systems on time scales in this paper we establish oscillation and nonoscillation criteria for the linear dynamic system u d pv v d qu s here we assume that p and q are nonnegative rd continuous functions on a time scale t such that supt indeed we extend some known oscillation results for differential systems and difference systems to the so called dynamic systems

oscillation of the emden fowler difference systems abstract in this paper we are concerned with some new criteria for the oscillation of the discrete emden fowler system

nonoscillatory solutions for the one dimensional p laplacian abstract in this paper we study the existence of nonoscillatory solutions of the equation xk 1 f k xk 0 k 1 2 where r r is defined by s s p 2 s with p 1 and xk 1 is a nonnegative sequence with infinitely many positive terms

oscillation criteria for two dimensional difference systems of first order linear difference equations sufficient conditions are established for the oscillation of the linear two dimensional difference system dx n p ny n dy n 1 q nx n n n n 0 n 0 n 0 1 where p n q n are nonnegative real sequences our results extend the results in the literature

oscillation of certain two dimensional nonlinear difference systems abstract several new oscillation criteria for two dimensional nonlinear difference systems are established examples which dwell upon the importance of our results are also included

the direct correlation function for an interface of a two dimensional model in a weak gravitational field the direct correlation function for a fluctuating interface in a two dimensional solid on solid lattice model is studied they obtain for a weak gravitational field an asymptotic expression for the direct correlation function that agrees well with previous numerical results in particular two different vertical length scales appear

monotone properties of certain classes of solutions of second order difference equations the authors consider the difference equations an xn qnxn 1 and an xn qnf xn 1 where an 0 qn 0 and f r r is continuous with uf u 0 for u 0 they obtain necessary and sufficient conditions for the asymptotic behavior of certain types of nonoscillatory solutions of and sufficient conditions for the asymptotic behavior of certain types of nonoscillatory solutions of sufficient conditions for the existence of these types of nonoscillatory solutions are also presented some examples illustrating the results and suggestions for further research are included

classification schemes for positive solutions of a second order nonlinear difference equation classification schemes for eventually positive solutions of a class of second order nonlinear difference equations are given in terms of their asymptotic magnitudes and necessary as well as sufficient conditions for the existence of these solutions are also provided

comparison theorems for second order nonlinear difference equations abstract new oscillation results are obtained for the second order nonlinear difference equation r n f x n 1 g n x n 0 and its functional form r n f x n 1 g n x n 0 the role played by the argument n on the oscillation of the functional equation is explored in particular we characterize a class of sequences n which have a harmless effect on the oscillation of this type of equations some of our results generalize improve or unify known fundamental oscillation results for several particular cases of the above equations

on oscillation of difference equations with bounded phi laplacian oscillation of second order difference equations with bounded phi laplacian is studied by comparing it with the discrete emden fowler difference equation analogues and discrepancies in behavior of solutions of these equations are also presented and a comparison with the continuous case is given

existence of bounded positive solutions for a system of difference equations abstract this paper deals with the second order nonlinear neutral delay system of difference equations a n x n b n x n f n x h 1 n x h kn y w 1 n y w kn c n n n 0 p n y n q n y n g n x s 1 n x s kn y t 1 n y t kn r n n n 0 by virtue of the banach fixed point theorem and some natural modifications of the techniques in the literature we prove the existence results of uncountably many bounded positive solutions for the system of difference equations seven examples are constructed to explain the main results presented in this paper

necessary and sufficient conditions for the oscillation of systems of difference equations with continuous arguments abstract in this paper the oscillation of all solutions of system of the form y t i 1 n p i y t i 0 where p i r m m i r i 1 2 n is studied necessary and sufficient conditions in terms of the characteristic equation and explicit conditions in terms of the eigenvalues or the logarithmic norms of the coefficient matrices are established

classification schemes for nonoscillatory solutions of two dimensional nonlinear difference systems abstract classification schemes for nonoscillatory solutions of a class of nonlinear two dimensional nonlinear difference systems are given in terms of their asymptotic magnitudes and necessary as well as sufficient conditions for the existence of these solutions are also provided

existence for nonoscillatory solutions of higher order nonlinear neutral difference equations abstract in this paper we consider the following forced higher order nonlinear neutral difference equation m x n c n x n k s 1 u p s n f s x n r s q n n n 0 where m u 1 k 0 and rs 0 are integers cn p s n s 1 2 u and qn are sequence of real numbers and f s c r r s 1 2 u by using krasnoselskii s fixed point theorem and some new techniques we obtain sufficient conditions for the existence of nonoscillatory solutions for general p s n s 1 2 u and qn which means that we allow oscillatory p s n s 1 2 u and qn

monotone solutions of a class of nonlinear difference equations abstract comparison theorems and existence criteria are summarized and new ones are derived for the monotone solutions of a class of nonlinear difference equations which arises from hardy s inequality

classification and existence of positive solutions of systems of volterra nonlinear difference equations a classification scheme for the eventually positive solutions of a class of two dimensional volterra nonlinear difference equations is given in terms of their asymptotic magnitudes and necessary as well as sufficient conditions for the existence of such solutions are provided

correlations at a liquid gas interface asymptotic analysis for weak gravity density density correlation functions at the phase separating layer in a two dimensional solid on solid lattice model are studied the authors perform for weak gravitational fields an exact asymptotic analysis and obtain explicit expressions a recent numerical analysis by stecki and dudowicz 1986 is shown to be in good agreement with their exact expansion

existence of uncountably many bounded positive solutions for second order nonlinear neutral delay difference equations this paper deals with the second order nonlinear neutral delay difference equation d a n d x n b n x n t c n f n x f 1 n x f 2 n x f k n d n n n 0 by using krasnoselskii s fix

nonexistence of unbounded nonoscillatory solutions of partial difference equations abstract we develop criteria for the nonexistence of eventually positive negative and nondecreasing nonincreasing solutions of the partial difference equation m n y m n p m n y m k n l q m n y m k n l and m n y m n i 1 p i m n y m k i n l i i 1 q i m n y m k i n l i several examples which dwell upon the importance of our results are also included

unbounded solutions of quasi linear difference equations we study positive increasing solutions of the nonlinear difference equation an p n bnf n 1 p u u p 2u p 1 where an bn are positive real sequences for n 1 fr r is continuous with uf u 0 for u 0 a full characterization of limit behavior of all these solutions in terms of an bn is established examples showing the essential role of used hypotheses are also included the tools used are the schauder fixed point theorem and a comparison method based on the reciprocity principle

unbounded positive solutions of higher order difference equations with singular nonlinear term in this paper several necessary and or sufficient conditions are given for the existence of unbounded positive solutions of nonlinear difference equations of the form mxn 1 f n xn 0 nen0 where m 2 1 or 1 and f n0 r r is a real valued continuous function such that f n x 0 for all n x n0 0 where n0 0 1

some combinatorial and algebraic properties of coxeter complexes and tits buildings a des groupes de coxeter et des groupes a bn paire sont associes certaines structures combinatoires les complexes de coxeter et les constructions de tits on etudie ces structures du point de vue des complexes de cohen macaulay et des complexes decorticables

scaling of confined membranes and interfaces we have carried out monte carlo studies of the probability distribution functions pdfs for models of two and three dimensional membranes and interfaces confined between two parallel repulsive walls separated by a distance d for two dimensional interfaces it is known that the position pdf p z for conformally mapped binding potentials scales and is characterized by a universal scaling function p z approximately sin pi z dtheta 1 where theta is the short distance expansion critical exponent for strong weak and intermediate fluctuation regimes our simulation studies show that for a variety of membrane models the pdf has the expected scaling p z u z d d and we find that the same parametrization of the membrane pdfs gives an excellent fit to the numerical data

oscillation for system of delay difference equations abstract consider the system of delay difference equations x i t x i t k 1 l j 1 n p ijk x j t k 0 where p ijk and k 0 i j 1 2 n k 1 2 l sufficient conditions are obtained for all solutions of the system to be oscillatory

oscillation and asymptotic behavior of two dimensional difference systems this paper is concerned with the oscillation behavior of solutions of the nonlinear two dimesional difference system dx n b ng y n dy n 1 a nf x n n n n 0 n 0 n 0 1 some necessary and sufficient conditions are given for the oscillation of all solution of the system our result improve and generalize some results in the literature examples to illustrate the result are included

oscillation criteria for a class of neutral difference equations with continuous variable in this paper we are mainly concerned with oscillatory behaviour of solutions for a class of second order nonlinear neutral difference equations with continuous variable using an integral transformation the riccati transformation and iteration some oscillation criteria are obtained

bounded and zero convergent solutions of second order difference equations abstract in this paper we study boundedness and monotonicity properties of a homogeneous second order linear difference equation under certain conditions it is shown that every solution must eventually be monotonic the question of when such monotonic solutions diverge to infinity or converge to zero and the corresponding impact this behavior has on recessive and dominant solutions is investigated a necessary and sufficient condition for all solutions to be bounded is presented comparison theorems are also discussed