on the descending central sequence of absolute galois groups let p be an odd prime number and f a field containing a primitive p th root of unity we prove a new restriction on the group theoretic structure of the absolute galois group g f of f namely the third subgroup g f 3 in the descending p central sequence of g f is the intersection of all open normal subgroups n such that g f n is 1 bbb z p 2 or the extra special group m p 3 of order p 3 and exponent p 2

on the positive almost periodic type solutions for some nonlinear delay integral equations in this paper we discuss the existence of positive almost periodic type solutions for some nonlinear delay integral equations by constructing a new fixed point theorem in the cone some known results are extended

on the number of quintic fields we show that the number of quintic number fields whose discriminant does not exceed x in absolute value is bounded by a constant times x1 e for any e 0 this may be compared with the conjecture that the number of such fields is asymptotic to a constant times x as x tends to infinity

positive almost periodic solutions of some delay integral equations the delay integral equation x t tt f s x s ds which arises in models for the spread of epidemics is studied with the aim of establishing the existence of positive almost periodic solutions for large values of when f t x is uniformly almost periodic in t for x in compact subsets of r under reasonable assumptions on f it is shown that there exist two positive numbers 0 they do exist a priori bounds on the set of positive solutions and uniqueness results are also obtained

on the super fixed point property in product spaces abstract we prove that if f is a finite dimensional banach space and x has the super fixed point property for nonexpansive mappings then f x has the super fixed point property with respect to a large class of norms including all l p norms 1 p this provides a solution to the super version of the problem of khamsi 1989

banach lattices which are order uniformly noncreasy the class of order uniformly noncreasy banach lattices is introduced and studied a fixed point theorem for those lattices is proved

fixed point property of direct sums abstract for a uniformly convex space z we show that z direct sums x 1 x n z of banach spaces x 1 x n with r a x i 1 a for some a 0 1 have the fixed point property for nonexpansive mappings as a direct consequence the result holds for all direct sums with being strictly convex the same result is extended to all direct sums x y of spaces x and y with property m whenever 1 the permanence of properties that are sufficient for the fixed point property are obtained for z direct sums and then for direct sums such properties include the properties r x 2 wnus c nj a x 2 ukk and nuc

one sided fuzzy numbers and applications to integral equations from epidemiology in this paper we present the algebraic and topological structure of one sided fuzzy numbers and introduce the notion of side preserving fuzzy number valued function we define the dual decomposition of a commutative monoid and prove that the sets of left sided fuzzy numbers and right sided fuzzy numbers realize a dual decomposition of the additive monoid of all fuzzy numbers we prove the usefulness of right sided fuzzy numbers in epidemiology presenting an application of these fuzzy numbers to a mathematical model for the spread of infectious diseases with a rate of contact that varies seasonally

a stable numerical method for volterra integral equations with discontinuous kernel numerical methods for volterra integral equations with discontinuous kernel need to be tuned to their peculiar form here we propose a version of the trapezoidal direct quadrature method adapted to such a type of equations in order to delineate its stability properties we first investigate about the behavior of the solution of a suitable basic test equation and then we find out under which hypotheses the trapezoidal direct quadrature method provides numerical solutions which inherit the properties of the continuous problem

iterated collocation methods for volterra integral equations with delay arguments in this paper we give a complete analysis of the global convergence and local superconvergence properties of piecewise polynomial collocation for volterra integral equations with constant delay this analysis includes continuous collocation based volterra runge kutta methods as well as iterated collocation methods and their discretizations

cohomology of nilpotent groups of class 2 abstract we compute the cohomology rings of a number of nilpotent groups of class 2 for appropriate coefficients and we do some more sample calculations of various cohomology groups the basic tool is a suitable small free resolution for an arbitrary nilpotent group of class 2 constructed in a previous paper

uniform convexity of ψ direct sums of banach spaces abstract let x and y be banach spaces and a continuous convex function on the unit interval 0 1 satisfying certain conditions let x y be the direct sum of x and y equipped with the associated norm with we show that x y is uniformly convex if and only if x y are uniformly convex and is strictly convex as a corollary we obtain that the l p q direct sum x p q y 1 q p not p q 1 nor is uniformly convex if and only if x y are where l p q is the lorentz sequence space these results extend the well known fact for the l p sum x p y 1 some other examples are also presented

noncreasy and uniformly noncreasy orlicz function spaces we show that in orlicz function spaces with orlicz luxemburg norm the criteria for being noncreasy and uniformly noncreasy are interesting combinations of conditions

a note on geometrical properties of banach spaces using ψ direct sums abstract let x be a banach space and a continuous convex function on 0 1 satisfying certain conditions let x x be the direct sum of x in this note we characterize the strict convexity uniform convexity and uniformly non squareness of banach spaces using direct sums which extends the well known characterization of these spaces

absolute norms on cn abstract in this paper we study the absolute normalized norms on c n we show that the set of all absolute normalized norms on c n is in one to one correspondence with the set n of all continuous convex functions on n with some suitable conditions where n s1 sn 1 r n 1 s1 s2 sn 1 1 si 0 1 i n 1 as some applications we show that an absolute norm on c n is strictly convex if and only if the corresponding function on n is strictly convex further we consider the von neumann jordan constant of c n with an absolute normalized norm

a characterization of c fields via galois groups abstract it is known that those fields f which are of class c in the sense of r ware can be characterized by their witt ring structure as well as by the behavior of their binary quadratic forms and the structure of their galois 2 extensions in this paper we show that c fields which have at least 8 square classes are characterized by the absence of a certain group dc of order 16 as a galois group over them moreover we show that the level of such a field is determined by the presence or absence of the cyclic group of order 4 and the dihedral group of order 8 as galois groups over it these results provide an interesting continuation of the work of ware in the appendix we give an explicit construction of field extensions with galois group dc

r k formulae applied to volterra equations with delay abstract we consider convergence and stability of a class of runge kutta formulae applied to a class of volterra integral equations with fixed delay although derived from standard runge kutta tableau the formulae differ from those applied to classical volterra integral equations consideration of the formulae is prompted by the search for highly stable formulae which have acceptable orders of convergence the theory and numerical results presented establish the existence of acceptable runge kutta formulae

complex strict convexity of absolute norms on cn and direct sums of banach spaces abstract we show that an absolute normalized norm on c 2 is complex strictly convex if and only if the associated convex function on 0 1 satisfies t max 1 t t for all 0 t 1 using this result we characterize when the direct sum x y of the complex banach spaces x and y is complex strictly convex and complex uniformly convex a characterization of complex strict convexity of c n for n 2 equipped with an absolute normalized norm is also given

on the stability of runge kutta methods for delay integral equations we present a class of runge kutta methods for the numerical solution of a class of delay integral equations dies described by two different kernels and with a fixed delay the stability properties of these methods are investigated with respect to a test equation with linear kernels depending on complex parameters the results are then applied to collocation methods in particular we obtain that any collocation method for dies resulting from ana stable collocation method for odes with a stepsize which is submultiple of the delay preserves the asymptotic stability properties of the analytic solutions

extreme points smooth points and noncreasiness of ψ direct sum of banach spaces abstract characterizations for noncreasiness and uniform noncreasiness of the direct sum of banach spaces are given as a consequence the geometry of the infinite l p direct sum l p x n and the lebesgue bochner space l p x with respect to these notions is investigated where 1 p

the existence of positive almost periodic type solutions for some neutral nonlinear integral equation abstract this paper presents the conditions of existence of positive almost periodic type solutions for some neutral nonlinear integral equation by using a fixed point theorem in the cone some known results are extended

non squareness and uniform non squareness of z direct sums abstract we give a characterization of uniform non squareness of the direct sum of three banach spaces thereby partially answering a question of kato saito and tamura

a new bernoulli wavelet method for accurate solutions of nonlinear fuzzy hammerstein volterra delay integral equations in this article bernoulli wavelet method has been developed to solve nonlinear fuzzy hammerstein volterra integral equations with constant delay this type of integral equation has a particular case the fuzzy variant of a mathematical model from epidemiology bernoulli wavelets have been generated by dilation and translation of bernoulli polynomials the properties of bernoulli wavelets and bernoulli polynomials are first presented the present wavelet method reduces these integral equations to a system of nonlinear algebraic equations and again these algebraic systems have been solved numerically by newton s method convergence analysis of the present method has been discussed in this article also the results obtained by present wavelet method have been compared with that of by b spline wavelet method some illustrative examples have been demonstrated to show the applicability and accuracy of the present method

collocation and continuous implicit runge kutta methods for a class of delay volterra integral equations abstract in this paper we present an analysis of the global convergence properties of certain piecewise polynomial collocation methods for a class of volterra integral equations with constant delay this analysis also encompasses continuous implicit m stage volterra runge kutta methods based on collocation techniques

existence of positive almost automorphic solutions to nonlinear delay integral equations abstract this paper is concerned with the existence of positive almost automorphic solutions to some nonlinear delay integral equations we first establish a new fixed point theorem for mixed monotone operator in a cone and then with its help we obtain existence theorems of positive almost automorphic solutions some examples are given to illustrate our results as one will see even in the case of almost periodicity our theorems extend some earlier results and moreover the approach dealing with the integral equation arising in an epidemic problem in this paper is also new

step method for a system of integral equations from biomathematics using the step method we study the following system of integral equations from biomathematics x t g t x t x t t t f s x s ds t a b 0 and we prove the existence uniqueness and the convergence of the successive approximation sequence using the perov contraction principle and step method with a weaker lipschitz condition also we propose a new algorithm of successive approximation sequence generated by the step method and we give an example to illustrate the applications of the abstract results

on positive solutions of some pairs of differential equations ii on etudie l existence de solutions strictement positives de systemes predateur proie on demontre l unicite de la solution strictement positive dans le systeme de conway smoller

banach spaces which are somewhat uniformly noncreasy we consider a family of spaces wider than r unc spaces and we give some fixed point results in the setting of these spaces

extremal structure of absolute normalized norms on r2 and the james constant abstract we denote by an2 the set of all absolute normalized norms on r 2 the set an2 has a convex structure with respect to the usual operation in this paper we calculate the james constant of r 2 when is an extreme point of an2

cohomology of metacyclic groups group n by a finite cyclic group k using homological perturbation theory we introduce the beginning of a free resolution of the integers z over the group ring zg of g in such a way that the resolution reflects the structure of g as an extension of n by k and we use this resolution to compute the additive structure of the integral cohomology of g in many cases we proceed by first establishing a number of special cases thereafter constructing suitable cohomology classes thereby obtaining a lower bound then computing characteristic classes introduced in an earlier paper and finally exploiting these classes obtaining upper bounds for the cohomology via the integral cohomology spectral sequence of the extension e the calculation is then completed by comparing the two bounds

noncreasy and uniformly noncreasy orlicz bochner function spaces abstract we point out that uniform noncreasiness is a super property in banach spaces moreover we prove that orlicz bochner function spaces are noncreasy if and only if they are rotund or smooth finally we obtain that orlicz bochner function spaces are uniformly noncreasy if and only if they are uniformly rotund or uniformly smooth

extremal structure of the unit ball of direct sums of banach spaces abstract we characterize the extreme points and smooth points of the unit ball of certain direct sums of banach spaces we use these results to characterize noncreasiness and uniform noncreasiness of direct sums thereby extending results of the second author s saejung extreme points smooth points and noncreasiness of direct sum of banach spaces nonlinear anal 67 2007 1649 1653

positive almost periodic solutions of some neutral integral equation abstract in this paper we investigate the existence of positive almost periodic solutions for some neutral integral equation by constructing a new fixed point theorem in the cone some new results are obtained

numerical solutions of volterra integral equations with a solution dependent delay on demontre l existence et l unicite des solutions pour l equation ainsi qu une limitation a priori de la solution on definit une solution numerique et on demontre que la solution numerique converge vers la solution de l equation integrale

von neumann jordan constant of absolute normalized norms on c2 abstract we determine and estimate the von neumann jordan constant of absolute normalized norms on c 2 by means of their corresponding continuous convex functions on 0 1 this provides many new interesting examples including those of non lp type as well as some previous ones it is also shown that all such norms are uniformly non square except l1 and l norms

application of simpson quadrature rule and iterative method for solving nonlinear fuzzy delay integral equations abstract in this study firstly we present an iterative method by using simpson quadrature formula for solving nonlinear fuzzy delay integral equations in addition the convergence analysis of the proposed method is investigated also we prove numerical stability analysis of the method by means of choosing the perturbation in the first iteration finally numerical examples to illustrate applicability of this method are presented

remarks on sufficient conditions for fixed points of multivalued nonexpansive mappings abstract in recent papers s dhompongsa t dominguez benavides a kaewcharoen a kaewkhao b panyanak the jordan von neumann constants and fixed points for multivalued nonexpansive mappings j math anal appl 320 2006 916 927 s dhompongsa a kaewcharoen a kaewkhao the dominguez lorenzo condition and multivalued nonexpansive mappings nonlinear anal 64 2006 958 970 two sufficient conditions namely the dominguez lorenzo condition and property d for fixed points of multivalued nonexpansive mappings are introduced the authors also give some sufficient conditions for the dominguez lorenzo condition and property d in their proofs it seems reasonable to use the james and von neumann jordan constants with slight modifications significant improvements are obtained some new estimates are tight in hilbert spaces

numerical solutions of the nonlinear fuzzy hammerstein volterra delay integral equations in this paper an iterative numerical method that solves nonlinear fuzzy hammerstein volterra integral equations with constant delay is developed by using the error estimates a practical stopping criterion of the algorithm is obtained the convergence and the numerical stability of the method is proved and its accuracy is illustrated on three numerical examples the study of this integral equation is important because it has as a particular case the fuzzy variant of a mathematical model from epidemiology

banach spaces which are r uniformly noncreasy abstract we consider a family of spaces wider than unc spaces introduced by prus and we give some fixed point results in the setting of these spaces

dissipative approximations to neutral ddes abstract we approximate the solution of a neutral dde with the solution of a retarded dde to exploit the fact that retarded ddes are much easier to solve numerically after demonstrating the validity of the approach we develop a m atlab program ddensd that solves ddes of neutral type the new approach and a simple user interface make it easy to solve a wide range of test problems from the literature to moderate accuracy

multi derivation maurer cartan algebras and sh lie rinehart algebras abstract we extend the classical characterization of a finite dimensional lie algebra g in terms of its maurer cartan algebra the familiar differential graded algebra of alternating forms on g with values in the ground field endowed with the standard lie algebra cohomology operator to sh lie rinehart algebras to this end we first develop a characterization of sh lie rinehart algebras in terms of differential graded cocommutative coalgebras and lie algebra twisting cochains that extends the nowadays standard characterization of an ordinary sh lie algebra equivalently l algebra in terms of its associated generalized cartan chevalley eilenberg coalgebra our approach avoids any higher brackets but reproduces these brackets in a conceptual manner the new technical tool we develop is a notion of filtered multi derivation chain algebra somewhat more general than the standard concept of a multicomplex endowed with a compatible algebra structure the crucial observation just as for ordinary lie rinehart algebras is this for a general sh lie rinehart algebra the generalized cartan chevalley eilenberg operator on the corresponding graded algebra involves two operators one coming from the sh lie algebra structure and the other one from the generalized action on the corresponding algebra the sum of the two operators is defined on the algebra while the operators are individually defined only on a larger ambient algebra we illustrate the structure with quasi lie rinehart algebras

uniform convexity and the splitting problem for selections abstract we continue to investigate cases when the repovs semenov splitting problem for selections has an affirmative solution for continuous set valued mappings we consider the situation in infinite dimensional uniformly convex banach spaces we use the notion of polyak of uniform convexity and modulus of uniform convexity for arbitrary convex sets not necessary balls we study general geometric properties of uniformly convex sets we also obtain an affirmative solution of the splitting problem for selections of certain set valued mappings with uniformly convex images

on the numerical stability of volterra integral equations with delay argument abstract stability properties of numerical methods for volterra integral equations with delay arguments are considered some suitable definitions for the stability of the numerical methods are included and also plots of the stability regions for particular cases are included

positive solutions of nonlinear integral equations arising in infectious diseases on considere l equation integrale non lineaire x t t t f s x s ds on utilise la theorie d indice du point fixe et la technique monotone pour etablir trois theoremes sur les solutions le premier affirme l existence de deux solutions non negatives non triviales de periode les deux autres concernent l existence et l unicite des solutions positives non triviales sous certaines conditions

an extension of matlab to continuous functions and operators an object oriented matlab system is described for performing numerical linear algebra on continuous functions and operators rather than the usual discrete vectors and matrices about eighty matlab functions from plot and sum to svd and cond have been overloaded so that one can work with our chebfun objects using almost exactly the usual matlab syntax all functions live on 1 1 and are represented by values at sufficiently many chebyshev points for the polynomial interpolant to be accurate to close to machine precision each of our overloaded operations raises questions about the proper generalization of familiar notions to the continuous context and about appropriate methods of interpolation differentiation integration zerofinding or transforms applications in approximation theory and numerical analysis are explored and possible extensions for more substantial problems of scientific computing are mentioned

perturbation theory and free resolutions for nilpotent groups of class 2 abstract using homological perturbation theory we construct a small free resolution for any nilpotent group g of class 2 which reflects the structure of g as a central extension of an abelian group by an abelian group

positive almost periodic solutions of a nonlinear integral equation from the theory of epidemics abstract a generalization of a nonlinear integral equation governing the spread of certain infectious diseases with almost periodic contact rate is shown to have almost periodic positive solutions

existence of positive solutions for elliptic systems degenerate and nondegenerate ecological models with homogeneous dirichlet conditions w o on dd the function s satisfies the conditions rl e c o oo q o and s o for s o problems of this nature are of interest in reaction diffusion processes in biology and chemistry for example the case for u urn m 1 or m e 0 1 for single parabolic equations i e u du f x u has been studied recently for porous medium analysis and population dynamics cf 2 7 15 18 191 as t cc these solutions tend to a solution of the corresponding elliptic scalar equation studies have also been carried out in these and other papers e g 3 4 16 171 with urn replaced by u satisfying the conditions described above in this article however the hypotheses on f are quite different from those in the papers mentioned above for example f is not necessarily lipschitz in u and may depend discontinuously on x thus even for the scalar case the results here are not covered by the other papers although there are some overlaps moreover our emphasis here is on degenerate systems section 3 and their applications section 4 these results are quite different and generalize the papers mentioned above to practical interesting cases other relevant results for the nondegenerate cases can be found in s 9 111 in section 2 we discuss some existence and uniqueness theorems for

nearly uniformly noncreasy banach spaces we introduce and study the class of nearly uniformly noncreasy banach spaces it is proved that they have the weak fixed point property a stability result for this property is obtained

on convexity properties of ψ direct sums of banach spaces the direct sum of banach spaces is strictly convex respectively uniformly convex locally uniformly convex uniformly convex in every direction if each of the banach spaces are strictly convex respectively uniformly convex locally uniformly convex uniformly convex in every direction and the corresponding norm is strictly convex

neocompact sets and the fixed point property abstract we use a newly introduced concept of neocompactness to study problems from metric fixed point theory in particular we give a sufficient condition for a superreflexive banach space x to have the fixed point property and obtain shorter proofs of some well known results in that theory