initial value problems for systems of integrodifferential equations in banach spaces in this paper by the use of new comparison results and mixed monotone iterative techniques the existence of solutions of initial value problems for systems of integrodifferential equations in banach spaces is discussed the results obtained in this paper generalize and improve the results corresponding to those obtained by others our result is new even in finite dimensional spaces

fixed points and approximate solutions for nonlinear operator equations we study a nonlinear operator equation and obtain a sequence of approximate solutions by extending the monotone iterative technique to new situations some examples and applications are presented

riemann roch and abel jacobi theory on a finite graph abstract it is well known that a finite graph can be viewed in many respects as a discrete analogue of a riemann surface in this paper we pursue this analogy further in the context of linear equivalence of divisors in particular we formulate and prove a graph theoretic analogue of the classical riemann roch theorem we also prove several results analogous to classical facts about riemann surfaces concerning the abel jacobi map from a graph to its jacobian as an application of our results we characterize the existence or non existence of a winning strategy for a certain chip firing game played on the vertices of a graph

integral boundary value problems for first order integro differential equations with deviating arguments this paper deals with first order integro differential equations of mixed type with deviating arguments we investigate the existence of solutions of such problems with integral boundary conditions by establishing a comparison result and applying the monotone iterative technique to obtain corresponding results we also discuss first order differential inequalities with deviating arguments two examples demonstrate the application of our results

trees parking functions syzygies and deformations of monomial ideals for a graph g we construct two algebras whose dimensions are both equal to the number of spanning trees of g one of these algebras is the quotient of the polynomial ring modulo certain monomial ideal while the other is the quotient of the polynomial ring modulo certain powers of linear forms we describe the set of monomials that forms a linear basis in each of these two algebras the basis elements correspond to g parking functions that naturally came up in the abelian sandpile model these ideals are instances of the general class of monotone monomial ideals and their deformations we show that the hilbert series of a monotone monomial ideal is always bounded by the hilbert series of its deformation then we define an even more general class of monomial ideals associated with posets and construct free resolutions for these ideals in some cases these resolutions coincide with scarf resolutions we prove several formulas for hilbert series of monotone monomial ideals and investigate when they are equal to hilbert series of deformations in the appendix we discuss the abelian sandpile model

initial value problems for nonlinear second order impulsive integro differential equations in banach spaces in this paper the fixed point theory is used to investigate the existence and uniqueness of solutions of initial value problems for nonlinear second order impulsive integro differential equations in banach spaces

self organized critical state of sandpile automaton models we study a general bak tang wiesenfeld type automaton model of self organized criticality in which the toppling conditions depend on local height but not on its gradient we characterize the critical state and determine its entropy for an arbitrary finite lattice in any dimension the two point correlation function is shown to satisfy a linear equation the spectrum of relaxation times describing the approach to the critical state is also determined exactly

extremal solutions of periodic boundary value problems for first order integro differential equations of mixed type this paper investigates the maximal and minimal solutions of periodic boundary value problems for first order nonlinear integro differential equations of mixed type by establishing a comparison result and using the monotone iterative technique

polynomial ideals for sandpiles and their grobner bases a polynomial ideal encoding topplings in the abelian sandpile model on a graph is introduced a grbner basis of this ideal is interpreted combinatorially in terms of well connected subgraphs this gives rise to algorithms to determine the identity and the operation in the group of recurrent configurations

a class of second order impulsive integro differential equations on unbounded domain in a banach space in this paper by using the cone theory and monotone iterative technique we investigate the existence of extremal solutions and unique solution of the initial value problem ivp for a class of second order impulsive integro differential equations on unbounded domain in a banach space our results improve and extend many recent results

monotone and numerical analytic methods for differential equations abstract the method of lower and upper solutions combined with monotone iterative techniques is used for ordinary differential equations with integral boundary conditions showing the existence of extremal solutions some existence results are also formulated using the numerical analytic method sufficient conditions for existence are given

linear series on metrized complexes of algebraic curves a metrized complex of algebraic curves over an algebraically closed field kappa is roughly speaking a finite metric graph gamma together with a collection of marked complete nonsingular algebraic curves c v over kappa one for each vertex v of gamma the marked points on c v are in bijection with the edges of gamma incident to v we define linear equivalence of divisors and establish a riemann roch theorem for metrized complexes of curves which combines the classical riemann roch theorem over kappa with its graph theoretic and tropical analogues from amini and caporaso adv math 240 1 23 2013 baker and norine adv math 215 2 766 788 2007 gathmann and kerber math z 259 1 217 230 2008 and mikhalkin and zharkov tropical curves their jacobians and theta functions contemporary mathematics 203 231 2007 providing a common generalization of all of these results for a complete nonsingular curve x defined over a non archimedean field mathbb k together with a strongly semistable model mathfrak x for x over the valuation ring r of mathbb k we define a corresponding metrized complex mathfrak c mathfrak x of curves over the residue field kappa of mathbb k and a canonical specialization map tau mathfrak c mathfrak x from divisors on x to divisors on mathfrak c mathfrak x which preserves degrees and linear equivalence we then establish generalizations of the specialization lemma from baker algebra number theory 2 6 613 653 2008 and its weighted graph analogue from amini and caporaso adv math 240 1 23 2013 showing that the rank of a divisor cannot go down under specialization from x to mathfrak c mathfrak x as an application we establish a concrete link between specialization of divisors from curves to metrized complexes and the theory of limit linear series due to eisenbud and harris invent math 85 337 371 1986 using this link we formulate a generalization of the notion of limit linear series to curves which are not necessarily of compact type and prove among other things that any degeneration of a mathfrak g r d in a regular family of semistable curves is a limit mathfrak g r d on the special fiber

combinatorics of compactified universal jacobians abstract we show that the combinatorial structure of the compactified universal jacobians over m g in degrees g 1 and g is governed by orientations on stable graphs in particular for a stable curve we exhibit graded stratifications of the compactified jacobians in terms of totally cyclic respectively rooted orientations on its dual graph we prove functoriality under edge contraction of the posets of totally cyclic and rooted orientations on stable graphs

iterative method for solutions and coupled quasi solutions of nonlinear integro differential equations of mixed type in banach spaces we consider in this paper the existence of solutions coupled minimal and maximal quasi solutions and iterative approximation of the unique solution for the following initial value problems ivp of the nonlinear integro di erential equations of mixed type in ordered banach spaces e u f t u u tu su t i u t0 x0 1 where i t0 t0 a a 0 x0 e f c i e e e e e and

existence of solutions of boundary value problems for differential equations with delayed arguments we study the existence and approximation of solution of boundary value problems for differential equations with delayed arguments sufficient conditions are established for the existence of a unique solution or extremal ones of the given problem a monotone iterative technique is applied

boundary value problems for first order differential equations of mixed type abstract we apply the monotone iterative method to formulate existence results for integro differential equations with nonlinear boundary conditions some results for integro differential inequalities are also given examples illustrate obtained results

non gaussian ornstein uhlenbeck based models and some of their uses in financial economics non gaussian processes of ornstein uhlenbeck ou type offer the possibility of capturing important distributional deviations from gaussianity and for flexible modelling of dependence structures this paper develops this potential drawing on and extending powerful results from probability theory for applications in statistical analysis their power is illustrated by a sustained application of ou processes within the context of finance and econometrics we construct continuous time stochastic volatility models for financial assets where the volatility processes are superpositions of positive ou processes and we study these models in relation to financial data and theory

advanced differential equations with nonlinear boundary conditions we investigate the existence of solutions for advanced differential equations with nonlinear boundary conditions sufficient conditions when the problem has extremal solutions or a unique solution are formulated linear advanced differential inequalities are also discussed

monotone iterative technique for differential equations in a banach space iffis continuous steps i and iii are standard and straightforward it is step ii that deserves attention this in turn leads to three possibilities namely to show that the sequence of approximate solutions is a a cauchy sequence b relatively compact so that one can appeal to ascoli s theorem and c a monotone sequence in a cone the first two possibilities are well known and are discussed in 2 31 this paper is devoted to the investigation of c which leads to the development of a monotone iterative technique in an arbitrary cone

riemann roch theory for graph orientations abstract we develop a new framework for investigating linear equivalence of divisors on graphs using a generalization of gioan s cycle cocycle reversal system for partial orientations an oriented version of dhar s burning algorithm is introduced and employed in the study of acyclicity for partial orientations we then show that the baker norine rank of a partially orientable divisor is one less than the minimum number of directed paths which need to be reversed in the generalized cycle cocycle reversal system to produce an acyclic partial orientation these results are applied in providing new proofs of the riemann roch theorem for graphs as well as luo s topological characterization of rank determining sets we prove that the max flow min cut theorem is equivalent to the euler characteristic description of orientable divisors and extend this characterization to the setting of partial orientations furthermore we demonstrate that p i c g 1 g is canonically isomorphic as a p i c 0 g torsor to the equivalence classes of full orientations in the cycle cocycle reversal system acted on by directed path reversals efficient algorithms for computing break divisors and constructing partial orientations are presented

extremal solutions for the first order impulsive functional differential equations with upper and lower solutions in reversed order this paper studies the existence of solutions of first order impulsive functional differential equations with lower and upper solutions in the reversed order obtains the sufficient conditions for the existence of solutions by establishing a new comparison principle and using the monotone iterative technique a concrete example is presented and solved to illustrate the obtained results

a riemann roch theorem in tropical geometry recently baker and norine have proven a riemann roch theorem for finite graphs we extend their results to metric graphs and thus establish a riemann roch theorem for divisors on abstract tropical curves

boundary value problems for systems of nonlinear integro differential equations with deviating arguments by establishing a comparison result and using the method of upper and lower solutions and the monotone iterative technique we investigate the systems of nonlinear mixed integro differential equations with deviating arguments and mixed boundary value conditions sufficient conditions are established for the existence of extremal system of solutions of the given problem

ehrenfest model with large jumps in finance changes returns in stock index prices and exchange rates for currencies are argued based on empirical data to obey a stable distribution with characteristic exponent 2 for short sampling intervals and a gaussian distribution for long sampling intervals in order to explain this phenomenon an ehrenfest model with large jumps elj is introduced to explain the empirical density function of price changes for both short and long sampling intervals

differential equations with integral boundary conditions the method of lower and upper solutions combined with monotone iterative technique is used for ordinary differential equations with integral boundary conditions problems of existence of extremal and unique solutions are discussed some comparison results are formulated too