existence of nonoscillatory solutions of first order linear neutral delay differential equations in this paper the existence of nonoscillatory solutions of the first order neutral delay differential equations with variable coefficients and delays are studied some new sufficient conditions are given in particular conditions given in this paper are weaker than those known so the results in this paper have wider application than the existing ones

the total coordinate ring of a wonderful variety abstract we study the cone of effective divisors and the total coordinate ring of wonderful varieties with applications to their automorphism group we show that the total coordinate ring of any spherical variety is obtained from that of the associated wonderful variety by a base change of invariant subrings

tian s alpha _ m k hat k invariants on group compactifications in this paper we compute tian s alpha m k k times k invariant on a polarized g group compactification where k denotes a maximal compact subgroup of a connected complex reductive group g we prove that tian s conjecture see conjecture 1 1 below is true for alpha m k k times k invariant on such manifolds when k 1 but it fails in general by producing counter examples when k ge 2

numerical oscillation of neutral logistic delay differential equation the equation is transformed by an invariant oscillation transformation some conditions under which the numerical solution oscillates are obtained we consider the asymptotic property of non oscillatory numerical solution this paper mainly deals with the oscillation of numerical solution for the neutral logistic delay differential equation applying the methods to the simplified type of the original equation which is got through an invariant oscillation transformation it is proven that every non oscillatory numerical solution tends to the steady state of the model moreover some conditions under which the numerical solution oscillates are obtained finally to demonstrate our theoretical results some numerical examples are adopted

oscillation analysis of numerical solutions for delay differential equations with real coefficients abstract the paper is mainly concerned with the oscillations of numerical solutions by the linear methods for a kind of linear delay differential equations with positive and negative coefficients some conditions under which the numerical solutions are oscillatory are obtained and it is proved that oscillations of the analytical solutions are preserved by the numerical solutions under mild conditions numerical experiments are given to demonstrate our results

upper bounds on coarsening rates we consider two standard models of surface energy driven coarsening a constant mobility cahn hilliard equation whose large time behavior corresponds to mullins sekerka dynamics and a degenerate mobility cahn hilliard equation whose large time behavior corresponds to motion by surface diffusion arguments based on scaling suggest that the typical length scale should behave as in the first case and in the second we prove a weak one sided version of this assertion showing roughly speaking that no solution can coarsen faster than the expected rate our result constrains the behavior in a time averaged sense rather than pointwise in time and it constrains not the physical length scale but rather the perimeter per unit volume the argument is simple and robust combining the basic dissipation relations with an interpolation inequality and an ode argument

the distribution of zeros of all solutions of first order neutral differential equations this paper is concerned with the distribution of zeros of all solutions of the first order neutral differential equation x t p t x t q t x t 0 t t 0 where p c t 0 0 q c t 0 0 and r new estimations for the distance between adjacent zeros of this neutral equation are obtained via comparison with a corresponding differential inequality these results extend some known results from the non neutral to the neutral case and improve other published results as well

nonoscillation of a class of neutral differential equations for the neutral differential equation x t x t n p t x t 0 where n is an odd number 0 r we give a complete classification of nonoscillatory solutions and obtain conditions for the existence of each type of nonoscillatory solutions

interpolation inequalities in pattern formation abstract we prove some interpolation inequalities which arise in the analysis of pattern formation in physics they are the strong version of some already known estimates in weak form that are used to give a lower bound of the energy in many contexts coarsening and branching in micromagnetics and superconductors the main ingredient in the proof of our inequalities is a geometric construction which was first used by choksi conti kohn and one of the authors in 4 in the study of branching in superconductors

k energy on polarized compactifications of lie groups abstract in this paper we study mabuchi s k energy on a compactification m of a reductive lie group g which is a complexification of its maximal compact subgroup k we give a criterion for the properness of k energy on the space of k k invariant kahler potentials in particular it turns to give an alternative proof of delcroix s theorem for the existence of kahler einstein metrics in case of fano manifolds m we also study the existence of minimizers of k energy for general kahler classes of m

oscillation criteria for second order neutral equations with distributed deviating argument abstract we present new oscillation criteria for the second order neutral delay differential equations with distributed deviating argument r t x t z t a b p t f x g t d 0 t t 0 where z t x t q t x t new oscillation criteria are established which are based on a class of new functions t s l defined in the sequel our results are sharper than some previous results which can be seen by the example at the end of this paper

some new oscillation criteria for second order quasi linear neutral delay differential equations in this paper we will establish some new oscillation criteria for second order quasi linear neutral delay differential equations of the form r t x t p t x email protected a 1 x t p t x email protected q t f x s t 0 the results obtained essentially improve and extend those of dzurina and stavroulakis j dzurina i p stavroulakis oscillation criteria for second order delay differential equations appl math comput 140 2003 445 453 sun and meng y g sun f w meng note on the paper of dzurina and stavroulakis appl math comput 174 2006 1634 1641

asymptotic behavior of nonoscillatory solutions to n th order nonlinear neutral differential equations abstract for a class of n th order nonlinear neutral differential equations sufficient conditions for all nonoscillatory solutions to satisfy lim t t 1 n x t a are established for another class of equations necessary and sufficient conditions for nonoscillatory solutions to satisfy the above condition are obtained our theorems complement and extend recent results reported in the literature

new oscillatory criteria for higher order nonlinear neutral delay differential equation abstract in this paper we consider the higher order nonlinear neutral delay differential equation 1 1 x t p t x t n f t x t 0 where n is an odd number and n 3 0 p c t 0 r t t lim t t f c t 0 r r f t u is nondecreasing in u

forced oscillation of nth order functional differential equations abstract in this paper we investigate the oscillation of forced functional differential equations x n t a t f x q t e t when the forcing term e t is not required to be the nth derivative of an oscillatory function some new oscillatory criteria are given we also apply our technique to the forced neutral differential equation of the form x t cx t n a t x t b t x t e t c t f 1 x t d t f 2 x t where xf1 x 0 and xf2 x 0 for x 0 n 1 are nonnegative constants a t 0 b t 0 c t 0 d t 0 which includes the special case f1 x x sgn x f2 x x sgn x 1 and 1

controllability for a class of fractional neutral integro differential equations with unbounded delay abstract in this paper we consider a class of fractional neutral integro differential equations with unbounded delay in banach spaces this paper deals with the exact controllability for fractional integro differential neutral control systems first we establish a new set of sufficient conditions for the exact controllability of nonlinear fractional systems by using a fixed point analysis approach further we extend the result to study the exact controllability concept with nonlocal conditions examples are provided to illustrate our main results

oscillation criteria for certain nth order differential equations with deviating arguments abstract oscillation criteria for nth order differential equations with deviating arguments of the form x n 1 t 1 x n 1 t f t x g t 0 n even are established where g c t0 r f c t0 r r and 0 is a constant

on categories of equivariant d modules abstract let x be a variety with an action by an algebraic group g in this paper we discuss various properties of g equivariant d modules on x such as the decompositions of their global sections as representations of g when g is reductive and descriptions of the categories that they form when g acts on x with finitely many orbits the category of equivariant d modules is equivalent to the category of finite dimensional representations of a finite quiver with relations we describe explicitly these categories for irreducible g modules x that are spherical varieties and show that in such cases the quivers are almost always representation finite i e with finitely many indecomposable representations

oscillation of even order half linear functional differential equations with damping in this paper a class of even order half linear functional differential equations with damping are studied by using the generalized riccati transformation and the integral averaging technique the new oscillation criteria which generalize and improve some known results are obtained for all solutions of the equations

on the distribution of zeros of solutions of first order delay differential equations abstract this paper contains new estimates for the distance between adjacent zeros of solutions of the first order delay differential equation x t p t x t 0 where p is a nonnegative continuous function our results are new and improve some known criteria illustrative examples are given to show the strength of some obtained results over the known ones

stability of θ methods for advanced differential equations with piecewise continuous arguments abstract this paper deals with the stability analysis of numerical methods for the solution of advanced differential equations with piecewise continuous arguments we focus on the behaviour of the one leg method and the linear method in the solution of the equation x t ax t a 0 x t a 1 x t 1 with real a a 0 a 1 and designates the greatest integer function the stability regions of two methods are determined the conditions under which the analytic stability region is contained in the numerical stability region are obtained and some numerical experiments are given

on oscillation of second order neutral type delay differential equations oscillation criteria are obtained by using the so called h method for the second order neutral type delay differential equations of the form r t j x t z t q t f x s t 0 t t 0 where z t x t p t x t t r p q t s c t 0 r and f email protected c r r the results of the paper contains several results obtained previously as special cases furthermore we are also able to fix an error in a recent paper related to the oscillation of second order nonneutral delay differential equations

stability of a critical nonlinear neutral delay differential equation abstract this work deals with a scalar nonlinear neutral delay differential equation issued from the study of wave propagation a critical value of the coefficients is considered where only few results are known the difficulty follows from the fact that the spectrum of the linear operator is asymptotically closed to the imaginary axis an analysis based on the energy method provides new results about the asymptotic stability of constant and periodic solutions a complete analysis of the stability diagram is given in the linear homogeneous case under periodic forcing existence of periodic solutions is discussed involving a diophantine condition on the period of the source

collocation methods for impulsive differential equations by choosing a suitable piecewise continuous collocation space the convergence global superconvergence and local superconvergence of the collocation solution for linear impulsive differential equations are derived the conditions that the collocation solution is asymptotical stable are obtained and some numerical experiments are given

split subvarieties of group embeddings let g be a connected reductive group and x an equivariant com pactifiction of g in x we study generalised and opposite generalised schu bert varieties their intersections called generalised richardson varieties and projected generalised richardson varieties any complete g embedding has a canonical frobenius splitting and we prove that the compatibly split subvari eties are the generalised projected richardson varieties extending a result of knutson lam and speyer to the situation

periodic solutions of a class of impulsive neutral delay differential equation abstract a class of impulsive neutral delay differential equation is studied by using fixed point theorem in cone some sufficient conditions of the existence for multiple periodic solutions are obtained some known results are generalized two examples are also given to support our main results

domain branching in uniaxial ferromagnets a scaling law for the minimum energy we address the branching of magnetic domains in a uniaxial ferromagnet our thesis is that branching is required by energy minimization to show this we consider the nonlocal nonconvex variational problem of micromagnetics we identify the scaling law of the minimum energy by proving a rigorous lower bound which matches the already known upper bound we further show that any domain pattern achieving this scaling law must have average width of order l 2 3 where l is the length of the magnet in the easy direction finally we argue that branching is required by considering the constrained variational problem in which branching is prohibited and the domain structure is invariant in the easy direction its scaling law is different

kahler geometry of horosymmetric varieties and application to mabuchi s k energy functional we introduce a class of almost homogeneous varieties contained in the class of spherical varieties and containing horospherical varieties as well as complete symmetric varieties we develop kahler geometry on these varieties with applications to canonical metrics in mind as a generalization of the guillemin abreu donaldson geometry of toric varieties namely we associate convex functions with hermitian metrics on line bundles and express the curvature form in terms of this function as well as the corresponding monge ampere volume form and scalar curvature we then provide an expression for the mabuchi functional and derive as an application a combinatorial sufficient condition of properness similar obtained by li zhou and zhu on group compactifications

forced oscillation of a class of neutral hyperbolic differential equations in this paper we study the following boundary value problem for a class of neutral hyperbolic differential equations 2 t2 u c t u x t a0 t u a1 t u x t ab q x t f u x g t d g x t x t r g u n v x t u 0 x t r a number of theorems for oscillatory solutions of the problem under two different cases are developed

oscillation behavior of even order nonlinear neutral differential equations with variable coefficients in this paper some sufficient conditions are obtained for the oscillation of all solutions of even order nonlinear neutral differential equations with variable coefficients our results improve and generalize known results in particular the results are new even when n 2

complete moduli in the presence of semiabelian group action i prove the existence and describe the structure of moduli space of pairs p consisting of a projective variety p with semiabelian group action and an ample cartier divisor on it satisfying a few simple conditions every connected component of this moduli space is proper a component containing a projective toric variety is described by a configuration of several polytopes the main one of which is the secondary polytope on the other hand the component containing a principally polarized abelian variety provides a moduli compactification of a g the main irreducible component of this compactification is described by an infinite periodic analog of the secondary polytope and coincides with the toroidal compactification of a g for the second voronoi decomposition

distribution of zeros of solutions of functional differential equations abstract by improving the bracketing techniques for a functional differential inequality in a previous paper h w wu y t xu the distribution of zeros of solutions of neutral differential equations appl math comput 156 3 2004 665 677 we are able to derive sharper upper bounds on the distance between zeros of solutions of a class of neutral functional differential equations with delays and hence improve many known bounds in the literature

oscillation theory of delay differential equations i gyori and g ladas oscillation theory for neutral differential equations with delay d d bainov and d p mishev

the distribution of zeros of solutions of neutral differential equations in this paper the distribution of zeros of solutions of the first order neutral differential equation with two variable delays x t p t x g t q t x h t 0is studied the estimate for the distance between adjacent zeros of oscillatory solutions of the above equation is obtained

global attractivity of solutions of nonlinear delay differential equations with a forcing term abstract in this paper we give sufficient conditions for every solution of the delay differential equation x t p t f x t r t to converge to zero our results extend and improve several known results in the literature an application of our main results to an equation derived from mathematical biology is also given

stable reductive varieties ii projective case abstract we construct a moduli space of stable projective pairs with a nontrivial action of a connected reductive group these stable reductive pairs are higher dimensional analogs of stable n pointed curves and generalize to the non commutative case a functorial compactification of moduli of abelian varieties and of toric pairs we prove that confirming a prediction of log minimal program stable reductive pairs have semi log canonical singularities

stability analysis of runge kutta methods for systems u t lu t mu t this paper deals with the stability of runge kutta methods applied to the complex linear system u t lu t mu t the condition under which the numerical solution is asymptotically stable is presented which is stronger than a stability and weaker than a f stability furthermore in the case of 2 norm and l being a real symmetric matrix by using email protected approximation and order star theory it is proved that for a stable runge kutta methods suppose whose stability function is given by the r s email protected approximation to e x the numerical solution is asymptotically stable if and only if r is even

oscillation properties for even order neutral equations with distributed deviating arguments in this paper we establish several oscillatory criteria for even order neutral differential equations with distributed deviating arguments which generalize and improve some known results