decomposing modular tensor products and periodicity of jordan partitions let jr denote an r r matrix with minimal and characteristic polynomials t 1 r suppose r 6 s it is not hard to show that the jordan canonical form of jr js is similar to j 1 jr where 1 r 0 and p r 1 i rs the partition r s p 1 r of rs which depends only on r s and the characteristic p char f has many applications including to the study of algebraic groups we prove new periodicity and duality results for r s p that depend on the smallest p power exceeding r this generalizes results of j a green b srinivasan and others which depend on the smallest p power exceeding the potentially large integer s we show that for fixed r we can construct a finite table allowing the computation of r s p for all s r and all primes p this generalizes work of k i iima and r iwamatsu

soft groups and normalistic soft groups soft set theory proposed by molodtsov has been regarded as an effective mathematical tool to deal with uncertainties in this paper first we correct some of the problematic cases in a previous paper by aktas and email protected man h aktas n email protected man soft sets and soft groups inf sci 177 2007 2726 2735 moreover we introduce the concepts of normalistic soft group and normalistic soft group homomorphism study their several related properties and investigate some structures that are preserved under normalistic soft group homomorphisms

on the grassmann modules for the symplectic groups abstract let v be a 2n dimensional vector space n 1 over a field k equipped with a nondegenerate alternating bilinear form f and let g sp 2 n k denote the group of isometries of v f for every k 1 n there exists a natural representation of g on the subspace w k of k v generated by all vectors v 1 v k such that v 1 v k is totally isotropic with respect to f with the aid of linear algebra we prove some properties of this representation in particular we determine a necessary and sufficient condition for the representation to be irreducible and characterize the largest proper g submodule these facts allow us to determine when the grassmann embedding of the symplectic dual polar space dw 2 n 1 k is isomorphic to its minimal full polarized embedding

application of fuzzy soft set in decision making problems based on grey theory there are many uncertain problems in practical production and life which need decisions made with soft sets and fuzzy soft sets however the basis of evaluation of the decision method is single and simple the same decision problem can obtain different results from using a different evaluation basis in this paper in order to obtain the right result we discuss fuzzy soft set decision problems a new algorithm based on grey relational analysis is presented the evaluation bases of the new algorithm are multiple there is more information in a decision result based on multiple evaluation bases which is more easily accepted and logical to one s thinking for the two cases examined the results show that the new algorithm is efficient for solving decision problems

soft nexuses in this paper we define soft nexuses over a nexus n after that we define the notions cyclic soft nexus prime and maximal soft subnexuses and we obtain some results about the above definitions finally we define the integer number induced by soft nexus a a and denoted by a a and show that for any n there exists soft nexus a a such that a a n

outer unipotent classes in automorphism groups of simple algebraic groups we study the unipotent elements of disconnected algebraic groups of the formg whereg is a simple algebraic group in characterisctic p possessing a graph automorphism of order p we classify the unipotent classes in the coset g and determine the corresponding centralizers showing that these bear a close relation to classes in a certain natural connected overgroup of g we also obtain a formula for the total number of outer unipotent elements in the finite group g where is a frobenius morphism analogous to the well known steinberg formula for the number of inner unipotent elements

fuzzy filters of mtl algebras characterizations of fuzzy filters in mtl algebras are given the fuzzy filter generated by a fuzzy set is considered the notion of boolean fuzzy filters and mv fuzzy filters are introduced and related properties are investigated a condition for a fuzzy filter to be boolean is provided a characterization of a boolean fuzzy filter is given a congruence relation on a mtl algebra induced by a fuzzy filter is established and we show that the set of all congruence relations induced by a fuzzy filter is a completely distributive lattice

applications of soft sets in ideal theory of bck bci algebras the notion of soft ideals and idealistic soft bck bci algebras is introduced and several examples are given relations between soft bck bci algebras and idealistic soft bck bci algebras are provided the intersection union and operation and or operation of soft ideals and idealistic soft bck bci algebras are established

soft p ideals of soft bci algebras molodtsov d molodtsov soft set theory first results comput math appl 37 1999 19 31 introduced the concept of soft set as a new mathematical tool for dealing with uncertainties that is free from the difficulties that have troubled the usual theoretical approaches jun y b jun soft bck bci algebras comput math appl 56 2008 1408 1413 applied first the notion of soft sets by molodtsov to the theory of bck bci algebras in this paper we introduce the notion of soft p ideals and p idealistic soft bci algebras and then investigate their basic properties using soft sets we give characterizations of fuzzy p ideals in bci algebras we provide relations between fuzzy p ideals and p idealistic soft bci algebras

existence stability and bifurcation of random complete and periodic solutions of stochastic parabolic equations abstract in this paper we study the existence stability and bifurcation of random complete and periodic solutions for stochastic parabolic equations with multiplicative noise we first prove the existence and uniqueness of tempered random attractors for the stochastic equations and characterize the structures of the attractors by random complete solutions we then examine the existence and stability of random complete quasi solutions and establish the relations of these solutions and the structures of tempered attractors when the stochastic equations are incorporated with periodic forcing we obtain the existence and stability of random periodic solutions for the stochastic chafee infante equation we further establish the multiplicity and stochastic bifurcation of complete and periodic solutions

notes on interval valued intuitionistic fuzzy soft sets and their properties comput math appl 60 2010 906 918 in this paper we point out two definitions definition 18 and definition 19 in a previous paper by jiang et al y jiang y tang q chen h liu j tang interval valued intuitionistic fuzzy soft sets and their properties comput math appl 60 2010 906 918 are not appropriate accordingly the proofs of some relevant theorems are also not right we redefine the two definitions and reprove these theorems by using the new definitions

periodic solutions in an inhibitory two neuron network in this paper we consider a delayed network of two neurons with self feedback and interaction described by an all or none threshold function the discontinuity of signal function makes it difficult to apply directly dynamical system we show that the dynamics of the network can be understood in terms of the iterations of a one dimensional map and we obtain the existence and attractivity of periodic solutions moreover because the network is a limiting case of the corresponding smooth system as the parameter tends to infinity the above results can act as the guide to the rich dynamics of the smooth system therefore our results have important significance in both theory and applications

monotone dynamical systems with dense periodic points abstract in this paper we prove a recent conjecture by m hirsch which says that if f is a discrete time monotone dynamical system with f a homeomorphism on an open connected subset of a finite dimensional vector space and the periodic points of f are dense in then f is periodic

on soft equality molodtsov introduced the concept of soft sets which can be seen as a new mathematical tool for dealing with uncertainty in this paper we deal with the algebraic structure of soft sets the lattice structures of soft sets are constructed the concept of soft equality is introduced and some related properties are derived it is proved that soft equality is a congruence relation with respect to some operations and the soft quotient algebra is established

generalizations of fuzzy subalgebras in bck bci algebras more general form of the notion of quasi coincidence of a fuzzy point with a fuzzy set is considered and generalizations of results in the papers y b jun on a b fuzzy subalgebras of bck bci algebras bull korean math soc 42 4 2005 703 711 y b jun fuzzy subalgebras of type a b in bck bci algebras kyungpook math j 47 2007 403 410 are discussed the notions of q k fuzzy subalgebras and email protected q k fuzzy subalgebras in a bck bci algebra x are introduced and several properties are investigated characterizations of email protected q k fuzzy subalgebra in a bck bci algebra x are discussed

fuzzy subinclines ideals of incline algebras the fuzzification of subinclines ideals in inclines are considered and some related properties are investigated we also state the product of fuzzy subinclines ideals and the projections of fuzzy subinclines ideals we discuss fuzzy relations fuzzy characteristic subinclines ideals

involutory and invertible fuzzy bck algebras the concept of a fuzzy annihilator in a commutative bck algebra will be introduced and then we investigate some basic properties using this notion we define an involutory resp invertible fuzzy ideal we prove that i every bounded implicative bck algebra is an involutory fuzzy bck algebra and ii every categorical commutative bck algebra is an invertible fuzzy bck algebra let x be an involutory and invertible fuzzy bck algebra and let fi x denote the set of all fuzzy ideals of x we show that iii fi x is a distributive lattice and iv fi x is a quasi boolean algebra

vague soft hemirings abstract xu et al introduced the concept of vague soft sets which is an extension to the soft set and the vague set in this paper we apply the concept of vague soft sets to hemiring theory the notion of q vague soft left h ideals of a hemiring is introduced and some related properties are investigated

soft matrix theory and its decision making in this work we define soft matrices and their operations which are more functional to make theoretical studies in the soft set theory we then define products of soft matrices and their properties we finally construct a soft max min decision making method which can be successfully applied to the problems that contain uncertainties

kernels and closures of soft set relations and soft set relation mappings in this paper the notions of anti reflexive kernel symmetric kernel reflexive closure and symmetric closure of a soft set relation are first introduced respectively then their accurate calculation formulae and some properties are obtained finally soft set relation mappings and inverse soft set relation mappings are proposed and some related properties are discussed

asymptotic behavior of strongly monotone time periodic dynamical processes with symmetry given a strongly monotone discrete time dynamical system tn x x n z in an open and order convex subset x of a separable strongly ordered banach space v and a compact connected metrizable group g whose action on x is monotone and commutes with t we prove under some reasonable additional hypotheses that the limit set x of every stable point x x consists of symmetric points only i e g w w for all w x and g g moreover the set of all unstable points is contained in a union of at most countably many lipschitz manifolds of codimension one in v where each manifold is invariant under t and the action of g this result is applied to the time periodic spatially independent irreducible cooperative system of n reaction diffusion equations u t d t u f t u for t x r1 rn with spatially periodic boundary conditions in rn and with an initial distribution u0 which is continuous and satisfies the boundary conditions if u0 is stable then u0 contains spatially constant functions only and the dynamics on u0 is given by the irreducible cooperative system of n odes dudt f t u for t r1 here t is the poincare map if n 1 then u0 is a single fixed point of t if n 2 then v0 is a single fixed point of t for each v0 u0

on fuzzy h ideals in hemirings the fuzzy setting of a left h ideal in a hemiring is constructed and basic properties are investigated using a collection of left h ideals of a hemiring s fuzzy left h ideals of s are established the notion of a finite valued fuzzy left h ideal is introduced and its characterization is given fuzzy relations on a hemiring s are discussed

hesselink normal forms of unipotent elements in some representations of classical groups in characteristic two abstract let g be a simple linear algebraic group over an algebraically closed field k of characteristic two any non trivial self dual irreducible k g module w admits a non degenerate g invariant alternating bilinear form thus giving a representation f g sp w in the case where g sl n k and w has highest weight 1 n 1 and in the case where g sp 2 n k and w has highest weight 2 we determine for every unipotent element u g the conjugacy class of f u in sp w as a part of this result we describe the conjugacy classes of unipotent elements of sp v 1 sp v 2 in sp v 1 v 2

fuzzy strong implicative hyper bck ideals of hyper bck algebras the fuzzy setting of strong implicative hyper bck ideals in hyper bck algebras is considered some of their properties are investigated relations among fuzzy strong hyper bck ideals fuzzy implicative hyper bck ideals and fuzzy strong implicative hyper bck ideals are given a characterization of a fuzzy strong implicative hyper bck ideal is provided the hyper homomorphic preimage of a fuzzy strong implicative hyper bck ideal is discussed

soft bck bci algebras molodtsov d molodtsov soft set theory first results comput math appl 37 1999 19 31 introduced the concept of soft set as a new mathematical tool for dealing with uncertainties that is free from the difficulties that have troubled the usual theoretical approaches in this paper we apply the notion of soft sets by molodtsov to the theory of bck bci algebras the notion of soft bck bci algebras and soft subalgebras are introduced and their basic properties are derived

dynamics integrability and topology for some classes of kolmogorov hamiltonian systems in r 4 abstract in this paper we first give the sufficient and necessary conditions in order that two classes of polynomial kolmogorov systems in r 4 are hamiltonian systems then we study the integrability of these hamiltonian systems in the liouville sense finally we investigate the global dynamics of the completely integrable lotka volterra hamiltonian systems in r 4 as an application of the invariant subsets of these systems we obtain topological classifications of the 3 submanifolds in r 4 defined by the hypersurfaces a x y b z w c x 2 y d x y 2 e z 2 w f z w 2 h where a b c d e f w and h are real constants

algebraic structures of soft sets associated with new operations recently new operations have been defined for soft sets in this paper we study some important properties associated with these new operations a collection of all soft sets with respect to new operations give rise to four idempotent monoids then with the help of these monoids we can study semiring hemiring structures of soft sets some of these semirings hemirings are actually lattices finally we show that soft sets with a fixed set of parameters are mv algebras and bck algebras

soft semirings molodtsov introduced the concept of soft sets which can be seen as a new mathematical tool for dealing with uncertainty in this paper we initiate the study of soft semirings by using the soft set theory the notions of soft semirings soft subsemirings soft ideals idealistic soft semirings and soft semiring homomorphisms are introduced and several related properties are investigated

symmetric bilinear forms and vertices in characteristic 2 let g be a finite group and let k be an algebraically closed field of characteristic 2 suppose that m is an indecomposable kg module which affords a non degenerate g invariant symmetric bilinear form we assign to m a collection of 2 subgroups of g called its symmetric vertices each of which contains a green vertex of m with index at most 2 if m is irreducible then its symmetric vertices are uniquely determined up to g conjugacy if b is the real 2 block of g containing m we show that each symmetric vertex of m is contained in an extended defect group of b moreover we characterise the extended defect groups in terms of symmetric vertices in order to prove these results we develop the theory of involutary g algebras this allows us to translate questions about symmetric kg modules into questions about projective modules of quadratic type

combination of interval valued fuzzy set and soft set the soft set theory proposed by molodtsov can be used as a general mathematical tool for dealing with uncertainty by combining the interval valued fuzzy set and soft set models the purpose of this paper is to introduce the concept of the interval valued fuzzy soft set the complement and and or operations are defined on the interval valued fuzzy soft sets the demorgan s associative and distribution laws of the interval valued fuzzy soft sets are then proved finally a decision problem is analyzed by the interval valued fuzzy soft set some numerical examples are employed to substantiate the conceptual arguments

fuzzy prime ideals and invertible fuzzy ideals in bck algebras we state the relation between fuzzy prime ideals and invertible fuzzy ideals in commutative bck algebras

unipotent classes in maximal subgroups of exceptional algebraic groups abstract let g be a simple algebraic group of exceptional type over an algebraically closed field and m be a maximal closed connected reductive subgroup of g for each unipotent m class we determine the g class in which it lies

soft bl algebras based on fuzzy sets by means of soft sets and q soft sets some characterizations of implicative positive implicative and fantastic filteristic soft bl algebras are investigated finally we prove that a soft set is an implicative filteristic soft bl algebra if and only if it is both a positive implicative filteristic soft bl algebra and a fantastic filteristic soft bl algebra

soft hyperstructure in this paper we study soft hypergroupoids firstly we introduce the notion of soft hypergroupoids and some examples are given also we show that soft hypergroupoids are closely related to l subhypergroupoid secondly using the notion of soft hypergroupoid some new properties of soft hypergroupoids are obtained lastly we investigate some properties of soft subhypergroupoids

the indecomposable symplectic and quadratic modules of the klein four group abstract we determine all indecomposable symplectic modules for the klein four group k 4 over a perfect field of characteristic 2 and classify the symplectic forms up to isometry we also determine all k 4 invariant quadratic forms which polarize to a given symplectic form and classify such quadratic forms up to isometry

soft polygroups soft set theory introduced by molodtsov has been considered as an effective mathematical tool for modeling uncertainties in this paper we initiate the study of algebraic hyperstructures of soft sets the concepts of soft polygroups normal soft polygroups soft subpolygroups and normal soft subpolygroups are introduced and some related properties are investigated furthermore we propose the homomorphism and isomorphism of soft polygroups and establish three isomorphism theorems for soft polygroups

soft sets and soft rings molodtsov 1999 introduced the concept of soft sets in 1 then maji et al 2003 defined some operations on soft sets in 2 aktas and ca man 2007 defined the notion of soft groups in 3 finally soft semirings are defined by feng et al 2008 in 5 in this paper we have introduced initial concepts of soft rings

application of level soft sets in decision making based on interval valued fuzzy soft sets molodtsov s soft set theory was originally proposed as a general mathematical tool for dealing with uncertainty research on fuzzy soft set based decision making has received much attention in recent years this paper aims to give deeper insights into decision making involving interval valued fuzzy soft sets a hybrid model combining soft sets with interval valued fuzzy sets the concept called reduct fuzzy soft sets of interval valued fuzzy soft sets is introduced using reduct fuzzy soft sets and level soft sets flexible schemes for decision making based on weighted interval valued fuzzy soft sets are proposed and some illustrative examples are employed to show that the proposals presented here are not only more reasonable but more efficient in practical applications

new generic quasi convergence principles with applications in this paper essentially strongly order preserving and conditionally set condensing semiflows are considered obtained is a new type of generic quasi convergence principles implying the existence of an open and dense set of stable quasi convergent points when the state space is order bounded the generic quasi convergence principles are then applied to essentially cooperative and irreducible systems in the forms of ordinary differential equations and delay differential equations giving some results of theoretical and practical significance

stability and convergence in strongly monotone dynamical systems soit x un systeme dynamique x est un espace topologique et le flot t t r est une famille d applications continues de sous ensembles ouverts de x dans x on decrit qualitativement le comportement asymptotique quand t des trajectoires t t x pour les etats initiaux x dans le cas de systemes ayant un principe de comparaison fort

fuzzy positive implicative and fuzzy associative filters of lattice implication algebras we fuzzify the concept of positive implicative filters and associative filters in lattice implication algebras we prove that i every fuzzy positive implicative filter is a fuzzy implicative filter and ii every fuzzy associative filter is a fuzzy filter we provide equivalent conditions for both fuzzy positive implicative filter and fuzzy associative filter

attractors in strongly monotone flows where f is a c vector field in r and all the off diagonal terms of its jacobian matrix are nonnegative the well known kamke theorem implies that the flow 4 i ir0 generated by 1 has the property it preserves the partial ordering 0 another system which has this property is the semilinear parabolic equation on a compact n dimensional submanifold solutions of its dirichlet or neumann problem determine a monotone flow in appropriate function space see 11 or 51 in general a flow which preserves a partial ordering on the state space is called monotone m w hirsch has studied this flow in a series of papers 14 io he 2 31 has studied the limiting behavior and convergence of solutions of system 1 he 1 4 lo has investigated this flow in the considerably abstract state space in chapter iii of cl he has used two sections to discuss the properties of attractors for monotone flows and obtained some very important results he has shown that a monotone flow cannot have an attracting cycle see l corollary 2 41 and that every attractor must contain an equilibrium see cl theorem 3 11 in particular if the flow is strongly monotone he has shown that every attractor k contains an order stable equilibrium see 1 theorem 4 11 meanwhile if we suppose z is attracted to k but is not quasiconvergent then k contains two order stable equilibria p q such that p o z 4 q see cl theorem 4 31 the purpose of this paper is further to discuss the properties of attractors for strongly monotone flows we shall study when an o limit set can be an 210 0022 247x 91 3 00

soft rough fuzzy sets and soft fuzzy rough sets fuzzy set theory soft set theory and rough set theory are mathematical tools for dealing with uncertainties and are closely related feng et al introduced the notions of rough soft set soft rough set and soft rough fuzzy set by combining fuzzy set rough set and soft set all together this paper is devoted to the further discussion of the combinations of fuzzy set rough set and soft set a new soft rough set model is proposed and its properties are derived furthermore fuzzy soft set is employed to granulate the universe of discourse and a more general model called soft fuzzy rough set is established the lower and upper approximation operators are presented and their related properties are surveyed

the dynamical systems approach to differential equations bulletin new series of the american mathematical society volume 11 number 1 july 1984 the dynamical systems approach to differential equations by morris w hirsch 1 this harmony that human intelligence believes it discovers in nature does it exist apart from that intelligence no without doubt a reality completely independent of the spirit which conceives it sees it or feels it is an impossibility a world so exterior as that even if it existed would be forever inaccessible to us but what we call objective reality is in the last analysis that which is common to several thinking beings and could be common to all this common part we will see can be nothing but the harmony expressed by mathematical laws h poincare la valeur de la science p 9 ignorance of the roots of the subject has its price no one denies that modern formulations are clear elegant and precise it s just that it s impossible to comprehend how any one ever thought of them m spivak a comprehensive introduction to differential geometry introduction the mathematical subject we call dynamical systems was fathered by poin care developed sturdily under birkhoff and has enjoyed a vigorous new growth for the last twenty years as i try to show in chapter i it is interesting to look at this mathematical development as the natural outcome of a much broader theme which is as old as science itself the universe is a sytem which changes in time every mathematician has a particular way of thinking about mathematics but rarely makes it explicit yet such perspectives in any particular field can be of great value to nonexperts who must apply the results of the field or who want to learn them in some fields the points of view of its practitioners cluster around several comparatively clearly defined concepts and insights dynamical systems theory is one of them the basic concepts go back to poincare the main thrust of chapters i and ii is to explain rather discursively some of received by the editors december 14 1983 1980 mathematics subject classification primary 00a25 00a99 01a45 01a55 01a60 34a40 34c35 34d10 34d30 35b05 35b35 35b40 35b50 35b30 35k55 54h20 58f25 58f40 58f12 58f10 58d25 58d07 46a40 46e10 47h07 47h20 92a15 92a17 secondary 06f30 35b65 58f13 35j60 46e05 92 03 90 03 90a16 supported in part by national science foundation and institute for advanced study 1984 american mathematical society 0273 0979 84 1 00 25 per page

fuzzy soft set theory applied to bck bci algebras abstract in the paper p k maji r biswas a r roy fuzzy soft sets j fuzzy math 9 3 2001 589 602 maji et al introduced the concept of fuzzy soft sets as a generalization of the standard soft sets and presented an application of fuzzy soft sets in a decision making problem the aim of this manuscript is to apply fuzzy soft set for dealing with several kinds of theories in bck bci algebras the notions of fuzzy soft bck bci algebras closed fuzzy soft ideals and fuzzy soft p ideals are introduced and related properties are investigated

on operations of soft sets soft set theory proposed by molodtsov has been regarded as an effective mathematical tool to deal with uncertainties in this paper first we prove that certain de morgan s law hold in soft set theory with respect to different operations on soft sets then we discuss the basic properties of operations on soft sets such as intersection extended intersection restricted union and restricted difference moreover we illustrate their interconnections between each other also we define the notion of restricted symmetric difference of soft sets and investigate its properties the main purpose of this paper is to extend the theoretical aspect of operations on soft sets

soft set theory applied to ideals in d algebras the notions of transitive soft d algebras soft edge d algebras soft d algebras soft d ideals soft d ideals soft d ideals and d idealistic d idealistic or d idealistic soft d algebras are introduced also their related properties are surveyed

quotient structures of some implicative algebras via fuzzy implicative filters in this paper we discuss quotient implicative algebras induced by fuzzy implicative filters and establish the fuzzy fundamental homomorphism theorem for some implicative algebras

on fuzzy ideals in bcc algebras the purpose of this paper is description of properties of fuzzy bcc ideals in bcc algebras and its images we describe also an extension of a fuzzy bcc ideal of a given bcc subalgebra s of x to a fuzzy bcc ideal of x such that and have the same image

soft set relations and functions the traditional soft set is a mapping from a parameter to the crisp subset of universe molodtsov introduced the theory of soft sets as a generalized tool for modeling complex systems involving uncertain or not clearly defined objects in this paper the concepts of soft set relations are introduced as a sub soft set of the cartesian product of the soft sets and many related concepts such as equivalent soft set relation partition composition function etc are discussed