permanence and extinction in nonlinear single and multiple species system with diffusion in this paper we consider the effect of diffusion on the permanence and extinction of single and multiple endangered species that live in changing patch environments average conditions are obtained for the permanence and extinction of the systems considered the results obtained in this paper generalize the main results of cui and chen the effect of diffusion on the time varying logistic population growth comput math appl 36 3 1998 1 9 permanence and extinction in logistic and lotka volterra systems with diffusion j math anal appl 258 2 2001 512 535

some special su 3 r 3 wigner coefficients and their application bargmann space expansions of oscillator functions are used to derive analytic expressions for su 3 r 3 wigner coefficients for the couplings 10 0 2 3 3 l3 0 and 10 20 3 3 l3 0 with arbitrary 3 3 these lead to expansions useful in nuclear cluster problems and are used to give a simple form for the su 3 irreducible tensor expansion of a scalar two body interaction an application which motivated this investigation

coherent families of weight modules of lie superalgebras and an explicit description of the simple admissible sl n 1 1 modules abstract let g be a classical lie superalgebra of type i we introduce coherent families of weight g modules with bounded weight multiplicities and establish a correspondence between cuspidal and highest weight submodules of these families by extending mathieu s work ann inst fourier 50 2000 537 this enables us to reduce the description of the g 0 module structure of arbitrary simple weight g modules with bounded weight multiplicities to the g 0 module structure of highest weight modules with bounded weight multiplicities we then construct tensor coherent families for g sl n 1 1 which yield an explicit description of the g 0 structure of an arbitrary simple weight module with bounded weight multiplicities in particular we show that for g sl n 1 1 the maximal length of an indecomposable g 0 submodule of a simple weight module with bounded multiplicities equals 5

a note on persistence and extinction of a randomized food limited logistic population model this paper addresses the issue of the asymptotic behavior for a non autonomous randomized food limited logistic population model several sufficient conditions are formulated and proved for p moment persistence and extinction of the population as well as in sense of almost sure results show that food limited assumption has an influence on the convergence rate of the solution to the equilibria for the deterministic and stochastic model some previously known results are improved numerical simulations are provided to support the results

positive periodic solutions for impulsive predator prey model with dispersion and time delays abstract in this paper we study the existence and global attractivity of positive periodic solutions for impulsive predator prey systems with dispersion and time delays by using coincidence degree theorem a set of easily verifiable sufficient conditions are obtained for the existence of at least one strictly positive periodic solutions and by means of a suitable lyapunov functional the uniqueness and global attractivity of positive periodic solution is presented some known results subject to the underlying systems without impulses are improved and generalized

dual bases and some coupling coefficients for su4 su2 su2 sun son and sp4 u2 general analytical expressions for isoscalar factors reduced wigner coefficients for the couplings p0 0q to 0 and p10 p20 to 0 in the chains su4 su2 su2 and sun son n 3 are derived by using the algebra of complementary groups and methods of analytical continuation a review of alternative approaches to the problem grounded on the concept of biorthogonal systems of non canonical bases is given it is demonstrated that the construction of dual bases polynomial and stretched or related ones is associated with the use of certain bilinear combinations of isoscalar factors and solutions of the boundary value problem for isoscalar factors overlaps are given for different non canonical basis states of the two parametric irreducible representations for the chains su4 su2 su2 sun son and sp4 u2 as well as the expansions of the projected basis states for sp4 u2 in terms of canonical basis states a new expression for some special su2 clebsch gordan coefficients is also given

finite dimensional representations of periplectic lie superalgebras abstract we study categories of finite dimensional modules over the periplectic lie superalgebras and obtain a bgg type reciprocity in particular we prove that these categories have only finitely many blocks we also compute the characters for irreducible modules over periplectic lie superalgebras of ranks 2 and 3 and obtain explicit description of the blocks for ranks 2 3 and 4

the center of a simple p type lie superalgebra we describe the center of a simple lie superalgebra of type p n the description is based on the notion of anticenter

explicit canonical tensor operators and orthonormal coupling coefficients of su 3 the canonical unit su 3 tensor operators are constructed by means of the stretched coupling of the auxiliary maximal and minimal null space tensor operators with the renormalization factors expressed in terms of the denominator functions of biedenharn gustafson lohe louck and milne the matrix elements of the maximal null space tensor operators are expressed with the help of the modified projection operators of asherova and smirnov the self conjugate minimal null space tensor operators are expressed in terms of the group generators with the help of the weight lowering operator technique the corresponding extreme isoscalar factors of the clebsch gordan wigner coefficients are used as constructive elements of the explicit recursive expression for the general orthonormal isoscalar factors of su 3 with its considerable simplication for the boundary values of parameters the general isofactors are also expanded in the different ways in terms of their boundary values the new classes of the generaliz

biorthogonal systems for su4 su2 su2 sun son and sp4 u2 and analytical inversion symmetry analytical inversion symmetry of the biorthogonal systems of su4 contains implies su2 su2 sun contains implies son and sp4 contains implies u2 bases for two parametric covariant and mixed tensor irreducible representation is discovered this symmetry relates the dual isoscalar factors or resubducing coefficients it allowed us to invert by means of a special analytical continuation procedure the non orthogonal isofactors of sun contains implies son for couplings p0 0q to 0 and p10 p20 to 0 as well as the resubducing coefficients transformation brackets for expansion of the su3 contains implies so3 elliott basis states and sp4 contains implies u2 smirnov and tolstoy basis states in terms of the corresponding canonical basis states new expressions for bilinear combinations of sun contains implies son special isofactors are obtained expansion of su3 canonical basis states in terms of su3 contains implies so3 elliott states is found isofactors for coupling of two elliott states are given

the general linear supergroup and its hopf superalgebra of regular functions abstract the structure of the hopf superalgebra b of regular functions on the general linear supergroup is developed and applied to study the representation theory of the supergroup it is shown that the general linear supergroup can be reconstructed from b in a way reminiscent of the tannaka krein theory a borel weil type realization is also obtained for the irreducible integrable representations as a side result on the structure of b schur superalgebras are introduced and are shown to be semi simple over the complex field with the simple ideals determined explicitly

stability analysis of a fractional order diffused prey predator model with prey refuges abstract in this paper a fractional order diffused prey predator model with prey refuges is considered the existence uniqueness non negativity and boundedness of the solutions for the model are proved moreover some sufficient conditions are given to ensure the existence and uniform asymptotic stability of the equilibrium point of the studied system finally numerical simulations are presented in order to support the theoretical results

positive periodic solution of two species ratio dependent predator prey system with time delay in two patch environment in this paper we are concerned with the existence of positive periodic solution to a class of two species ratio dependent predator prey diffusion model with time delay by using the continuation theorem of coincidence degree theory we transform this problem into a problem of calculating the topological degree of a continuous mapping and then some sufficient conditions of the existence of positive periodic solution is established for the system

permanence and global attractivity of an impulsive ratio dependent predator prey system in a patchy environment this paper studies an impulsive nonautonomous two species predator prey lotka volterra type dispersal system in a patchy environment in which the prey species can disperse among n different patches but the predator species is confined to one patch and cannot disperse on the basis of inequality estimation techniques and the comparison theory of impulsive differential equations sufficient conditions of integrable form for the permanence and extinction are obtained by constructing appropriate lyapunov function conditions for the global attractivity of the system are established

on the structure of weight modules given any simple lie superalgebra g we investigate the structure of an arbitrary simple weight 0 module we introduce two invariants of simple weight modules the shadow and the small weyl group generalizing results of fernando and futorny we show that any simple module is obtained by parabolic induction from a cuspidal module of a levi subsuperalgebra then we classify the cuspidal levi subsuperalgebras of all simple classical lie superalgebras and of the lie superalgebra w n most of them are simply levi subalgebras of go in which case the classification of all finite cuspidal representations has recently been carried out by one of us mathieu our results reduce the classification of the finite simple weight modules over all classical simple lie superalgebras to classifying the finite cuspidal modules over certain lie superalgebras which we list explicitly

canonical solution of the state labelling problem for su n so n and littlewood s branching rule i general formulation the internal state labelling problem for the d row irreducible representations of su n where 2d or n when reduced with respect to so n is shown to amount to the external state labelling problem for u d the canonical solution of the latter due to biedenharn et al 1967 provides a canonical solution of the former which reflects the operation of littlewood s branching rule for u n contains implies o n in a very simple way

graded tensor calculus we develop a graded tensor calculus corresponding to arbitrary abelian groups of degrees and arbitrary commutation factors the standard basic constructions and definitions like tensor products spaces of multilinear mappings contractions symmetrization symmetric algebra as well as the transpose adjoint and trace of a linear mapping are generalized to the graded case and a multitude of canonical isomorphisms is presented moreover the graded versions of the classical lie algebras are introduced and some of their basic properties are described

periodic solution for a two species nonautonomous competition lotka volterra patch system with time delay abstract by using the continuation theorem of coincidence degree theory the existence of a positive periodic solution for a two species nonautonomous competition lotka volterra patch system with time delay x 1 t x 1 t r 1 t a 1 t x 1 t b 1 t y t d 1 t x 2 t x 1 t x 2 t x 2 t r 2 t a 2 t x 2 t d 2 t x 1 t x 2 t y t y t r 3 t a 3 t x 1 t b 3 t y t t 0 k s y t s ds is established where ri t ai t i 1 2 3 di t i 1 2 bi t i 1 3 and t are all positive periodic continuous functions with period w 0 is a nonnegative constant and k s is a continuous nonnegative function on 0

coefficients of fractional parentage for u m p n q u m n u p q and u m n u m u n the outer product reduction coefficients orc which reduce the representation rep induced from the irreps of the permutation groups s f1 and s f2 into the irreps of s f1 f2 are shown to be the indirect coupling coefficients for the u m p n q u m n u p q irreducible basis the non standard orc for reducing the rep induced from the non standard irreps of s f13 s f1 s f3 and s f24 s f2 s f4 into that of s f s f12 s f34 with fij fi fj f f12 f34 are identified with the u f u f12 u f34 clebsch gordan coefficient for the special gel fand bases of u f12 and u f34 the u m p n q u m n u p q cfp as well as its special case the u m p u m u p cfp are identified with the s f s f12 s f34 outer product isoscalar factor the u m n u m u n cfp are obtained from the u m n u m u n cfp by simply changing all the partition labels for u n into their conjugates interchanging rows with columns and taking into account a phase change the cfp can be calculated from the orc numerical values of the one body cfp for systems with up to six particles are tabulated

symmetric and unitary group representations i duality theory an extension of the schur weyl duality connecting the representations of the symmetric and unitary groups is given the schur weyl basis is constructed using annihilation and creation operators three factorisation lemmas are derived their importance lies in the fact that they relate the phase freedoms within the racah wigner algebra of the symmetric groups and the unitary groups extensions of the regge symmetries are also given these are expressed in five duality relations

construction of coupling coefficients of su 4 in a supermultiplet basis matrix elements of the unit tensor operators of ranks 1 2 and 1 1 in the non orthonormal draayer basis of su 4 are found the evaluation algorithms for the su 4 coupling coefficients are proposed for coupling one arbitrary and one four six or ten dimensional irreducible representation of su 4 in the su 2 su 2 chain as well as in the case of the semistretched coupling the construction of the overlaps of the draayer basis states is considered

casimir elements of e lie algebras the classical framework for investigating the casimir elements of a lie algebra is generalized to the case of an e lie algebra l we construct the standard l module isomorphism of the e symmetric algebra of l onto its enveloping algebra and we introduce the harish chandra homomorphism in case the generators of l can be written in a canonical two index form we construct the associated standard sequence of casimir elements and derive a formula for their eigenvalues in an arbitrary highest weight module

parisi s mean field solution for spin glasses as an analytic continuation in the replica number parisi s replica symmetry breaking solution for spin glasses is extended to finite replica number n the free energy fp n obtained this way as well as its first two derivatives with respect to n are shown to join the corresponding values in the sherrington kirkpatrick sk solution at a characteristic value ns t where stability breaks down in the latter the continuation composed of the sk branch fsk n for n or ns t and the parisi branch fp n for 0 or n or ns t fulfils the requirements of convexity monotonicity and stability for all n

persistence and periodicity of a delayed ratio dependent predator prey model with stage structure and prey dispersal a delayed periodic ratio dependent predator prey model with prey dispersal and stage structure for predator is investigated it is assumed that immature individuals and mature individuals of the predator species are divided by a fixed age and that immature predators don t have the ability to attack prey and that predator species is confined to one of the patches while the prey species can disperse between two patches we first discuss the uniform persistence and impermanence of the model by using gaines and mawhin s continuation theorem of coincidence degree theory a set of easily verifiable sufficient conditions are derived for the existence of positive periodic solutions of the proposed model numerical simulations are presented to illustrate the feasibility of our main results

affine periplectic brauer algebras we formulate nazarov wenzl type algebras p over cap d for the representation theory of the periplectic lie superalgebras p n we establish an arakawa suzuki type functor to provide a connec

the clebsch gordan coefficients and isoscalar factors of the graded unitary group su m n it is pointed out that the clebsch gordan coefficients cgc of the permutation group are the coefficients which couple irreducible bases irb of su m n and su p q to the irb of su mp nq mp np and the outer product reduction coefficients orc of the permutation group are the coefficients which couple the irb of su m n and su p q into the irb of su m p n q the orc of permutation groups with due modification in signs are the cgc for the special gel fand basis of su m n the isoscalar factor isf for the permutation group chain s f contains implies s f1 s f2 is the isf for the graded unitary group chain su mp nq mq np contains implies su m n su p q and the outer product isf for the group chain s f contains implies s f1 s f2 is the isf for su mp nq mq np contains implies su m n x su p q all these coefficients can be calculated easily and some are already available

some coupling and recoupling coefficients for symmetric representations of son a new expression of son contains implies son 1 isoscalar factors reduced wigner coefficients for coupling l1 l2 to l1l2 is obtained special classes of these factors including those used together with special isofactors of sun contains implies son in on scalar basis functions depending on the microscopic collective variables of a nucleus are shown as being proportional to the 6j coefficients of su2 with standard or quartervalued parameters group chain reflection symmetry of isofactors is discovered which allows the author to interchange certain reflected parameters of irreducible representations of the group and its subgroup recoupling coefficients 6l coefficients for symmetric representations of son n or 5 are expanded in terms of 6j coefficients of su2 with standard or quartervalued parameters new expressions for special clebsch gordan and 6j coefficients of su2 so3 are presented

the z2 graded schouten nijenhuis bracket and generalized super poisson structures the super or z2 graded schouten nijenhuis bracket is introduced using it new generalized super poisson structures are found which are given in terms of certain graded skew symmetric contravariant tensors of even order the corresponding super jacobi identities are expressed by stating that these tensors have a zero super schouten nijenhuis bracket with themselves 0 as a particular case we provide the linear generalized super poisson structures which can be constructed on the dual spaces of simple superalgebras with a non degenerate killing metric the su 3 1 superalgebra is given as a representative example

su mn su m su n isoscalar factors and s f1 f2 s f1 s f2 isoscalar factors a simple relation is found between the isoscalar factor isf of the unitary group and those of the permutation group i e the su mn su m su n isf is equal to the s f1 f2 s f1 s f2 isf since the values of s f1 f2 s f1 s f2 isf are independent of m and n one arrives at an important conclusion that the values of su mn su m su n isf are also independent of m and n therefore they can be calculated for all m and n by a single stroke instead of one m and one n at a time an eigenfunction metho for evaluating the su mn su m su n isf is given which can be easily translated into a computer program

classification selection rules and symmetry properties of the clebsch gordan coefficients of symmetric group new analytical expressions for clebsch gordan coefficients cgcs of symmetric group are formulated based on the racah factorization lemma as examples cgcs for the coupling f 1 1 f 1 1 and f 1 1 f 2 2 are tabulated we have introduced a new technique called the clebsch gordan sequences cgss cgss provide a partial understanding of vanishing of cgcs and an explanation of new symmetry properties of multiplicity free cgcs

cohomology of lie superalgebras and their generalizations the cohomology groups of lie superalgebras and more generally of e lie algebras are introduced and investigated the main emphasis is on the case where the module of coefficients is nontrivial two general propositions are proved which help to calculate the cohomology groups several examples are included to show the peculiarities of the super case for l sl 1 2 the cohomology groups h1 l v and h2 l v with v a finite dimensional simple graded l module are determined and the result is used to show that h2 l u l with u l the enveloping algebra of l is trivial this implies that the superalgebra u l does not admit any nontrivial formal deformations in the sense of gerstenhaber garland s theory of universal central extensions of lie algebras is generalized to the case of e lie algebras

3jm and 6j tables for some bases of su6 and su3 tables of 6j symbols for su6 and su3 and tables of 3jm factors for su6 contains implies su2 su3 su3 contains implies u1 su2 and su3 contains implies so3 are presented the tables are computer produced using a program that implements the building up principle in a general form these tables are useful for calculations in high energy nuclear and solid state physics some other tabulations contain errors and none uses all the symmetries available the n independence of sun results is discussed by using the various symmetric group unitary group duality relations

new expressions for the eigenvalues of the invariant operators of the general linear and the orthosymplectic lie superalgebras we obtain expansions for the eigenvalues cp of the invariant operators casimir operators of the general linear and the orthosymplectic lie superalgebras in terms of products of suitably defined graded power sums pk the resulting expressions are closed and provide unified formulas for computing the cp s for those superalgebras as well as their corresponding lie algebras the formulas are remarkably simple to suggest that the power sums used in this text could play a more basic role in the understanding of the pattern of the expansion coefficients explicit illustrations are given for the various series for p 8

matrix elements of the labelling operators for su 4 su 2 su 2 a matrix representation of the labelling operators of moshinsky and nagel 1963 and of partensky and maguin 1978 in the non orthogonal draayer basis of su 4 is derived this allows one to solve explicitly the missing label problem for the spin isospin multiplets in the arbitrary su 4 supermultiplets the simplification and degeneration of these representations are considered for two parametric irreducible representations of su 4 as well as for some special cases of irreps typical of nuclear theory the expansion of the linearly dependent states of the draayer basis is discussed

periodic solution of a lotka volterra predator prey model with dispersion and time delays a periodic lotka volterra predator prey model with dispersion and time delays is investigated by using gaines and mawhin s continuation theorem of coincidence degree theory and by means of a suitable lyapunov functional a set of easily verifiable sufficient conditions are derived for the existence uniqueness and global stability of positive periodic solutions of the system sufficient conditions are also established for the uniform persistence of the system numerical simulations are presented to illustrate our main results

existence and global attractivity of positive periodic solutions of functional differential equations with impulses abstract sufficient and realistic conditions are obtained for the existence and global attractivity of positive periodic solutions of the delay differential system with impulses d y t d t y t f t y t 1 t y t n t a e t 0 t t k y t k y t k b k y t k k 1 2 the method involves the application of the gaines and mawhin s coincidence degree theory the constructing suitable lyapunov functionals and estimations of uniform upper bounds on solutions when these results are applied to some special delay population models some new results are obtained and some known results are generalized in particular our results indicate that under the appropriate linear periodic impulsive perturbations the above impulsive delay differential equation preserves the original periodicity and global attractivity of the nonimpulsive delay differential equation d y t d t y t f t y t 1 t y t n t

laplace operators of infinite dimensional lie algebras and theta functions abstract until recently the generalized casimir operator constructed by kac kac v g 1974 funct anal appl 8 68 70 has been the only known element of the center of a completion of the enveloping algebra of a kac moody algebra it has been conjectured deodhar v v gabber o kac v g 1982 adv math 45 92 116 however that the image of the harish chandra homomorphism contains all theta functions defined on the interior of the complexified tits cone and hence separates the orbits of the weyl group developing the ideas of feigin and fuchs feigin b l fuchs d b 1983 dokl akad nauk sssr 269 1057 1060 i prove this conjecture another application of this method is the chevalley type restriction theorem for simple finite dimensional lie superalgebras

eigenvalues of casimir operators for the general linear the special linear and the orthosymplectic lie superalgebras the generators of the algebras under consideration can be written in a canonical two index form and hence the associated standard sequence of casimir elements can be constructed following the classical approach by perelomov and popov we obtain the eigenvalues of these casimir elements in an arbitrary highest weight module by calculating the corresponding generating functions

invariant supersymmetric multilinear forms and the casimir elements of p type lie superalgebras the casimir elements of the p type lie superalgebras are investigated depending on the class of algebras under consideration either there do not exist any nontrivial casimir elements at all or else the casimir elements are highly degenerate basic to the investigation is a lemma about invariant supersymmetric multilinear forms on a finite dimensional module over a lie superalgebra some comments on the cartan subalgebras of a lie superalgebra are also included an appendix provides some information on multilinear algebra with e commuting scalars

analysis of a stochastic non autonomous food limited lotka volterra cooperative model in this paper a stochastic non autonomous food limited lotka volterra cooperative model is proposed and investigated sufficient conditions are formulated and verified for p moment persistence and extinction of the system results demonstrate that cooperative coefficients have important effects on the convergence rate of the solution to the equilibria of the stochastic model some numerical simulations are introduced to support the analytical results

existence of positive periodic solution for nonautonomous predator prey system with diffusion and time delay a two species nonautonomous predator prey system with time delay and diffusion is investigated a sufficient condition of the existence of positive periodic solution is established for the system by using the continuation theorem of coincidence degree theory

existence and global attractivity of positive periodic solutions for delay lotka volterra competition patch systems with stocking abstract by means of mawhin s continuation theorem of coincidence degree and lyapunov functional a set of easily verifiable criteria are established for the existence and global attractivity of positive periodic solutions for delay lotka volterra competition patch system with stocking x 1 t h 1 t x 1 t a 1 t b 1 t x 1 t c 1 t y t d 1 t x 2 t 1 x 1 t s 1 t x 2 t h 2 t x 2 t a 2 t b 2 t x 2 t d 2 t x 1 t 2 x 2 t s 2 t y t h 3 t y t a 3 t b 3 t y t t 0 k s y t s ds c 3 t x 1 t s 3 t some known results are generalized and improved

casimir invariants characteristic identities and tensor operators for strange superalgebras we define a class of super subalgebras of gl m n realized as the set of fixed points of a graded endomorphism of gl m n this class includes the superalgebras gp m and gq m related to the so called strange simple superalgebras p m and q m as well as osp m n general covariant contravariant and mixed tensor operators are defined for this class in terms of appropriate module homomorphisms traces of certain tensors give the usual sequence of casimir invariants for gp m these are shown to vanish identically while for gq m eigenvalues of the quadratic and cubic casimir invariants are derived in terms of highest weights and a polynomial characteristic identity is exhibited

some isoscalar factors for son son 1 and state expansion coefficients for son son 1 in terms of sun sun 1 son 1 general analytical expressions of state expansion coefficients for son son 1 in terms of sun sun 1 son 1 are derived analytical expressions of isoscalar factors for son son 1 for coupling w1w2 w30 to w 1w2 for the son n 4 irrep and v1v2 v30 to v 1v2 for the son 1 irrep with w1 w2 w3 w 1 w2 and v1 v2 v3 v 1 v2 are obtained by using these coefficients and isoscalar factors for sun sun 1

overlaps of the biorthogonal 3 coupling coefficients and related basic hypergeometric and other q factorial series the intermediate expansion technique is developed for the overlap coefficients of different biorthogonal coupled states and coupling coefficients of the quantum algebra and group su 3 with repeating irreducible representations and the role of separate basic and classical hypergeometric functions is demonstrated some expansion coefficients such as new prime overlap functions equivalent to the bilinear combinations of the different boundary isofactors are expressed in terms of the balanced saalschutzian basic or classical hypergeometric series these new overlap functions their analytical inversion some known triangular expansion matrices transition matrices related to definite racah coefficients the well poised or series and compositions of q factorial series resembling the well poised and series or equivalent to and series provide themselves as generators for mutual expansion of different non orthonormal systems of and su 3 isofactors which may be orthonormalized to the paracanonical or with a definite caution canonical version

a new physical basis for the irreducible representations of the orthogonal group so 5 in the quasi spin formalism new physical state vectors for the irs of the group so 5 are constructed in an analytical form the state vectors are labelled by the quantum numbers of the isospin its third component by the number of particles and by a fourth properly defined quantum number the previously constructed bases have been compared with the new construction from the same point of view two examples illustrate the new construction

phase conventions consistent with duality between sun and sl the schur weyl construction of irreducible tensors by symmetrized lth rank exterior products of a defining n dimensional vector space establishes a duality between the coupling algebra of the unitary group un and the symmetric group sl the coupling coefficients shared by these two groups are real and possess symmetries due to complex conjugation in un and association in sl the unitary group is factored by its unitary unimodular subgroup sun un u1 so it is usual to identify the coupling algebras of un and sun by choosing the trivial phaseless coupling for u1 this establishes a set of equivalence relations since all pseudoscalar irreducible representations irreps of un subduce onto the scalar irrep of sun the question remains can this trivial identification with the coupling algebra of sun be made consistent with the symmetries which follow from duality specifically the symmetries which follow from duality must be consistent with the equivalence relations we argue such consistency may be obtaine

orthogonalization of the projected states and isofactors the explicit direct and inverse orthogonalization coefficients ocs are derived for the projected basis states of the two parametric covariant irreducible representations of including elliott s n 3 case and draayer with the alternative choices of the gram schmidt processes began respectively from the lowest vergados or highest absolute value of the intrinsic parameter k the different direct and inverse ocs the latter equivalent to the definite boundary isofactors or the boundary resubducing coefficients are found to be connected by the definite analytical continuation contraction procedures with mutually related ocs of the biorthogonal states and the boundary orthonormal pseudocanonical and paracanonical isofactors of the orthogonalization coefficients considered are presented as definite algebraic polynomial structures under the square root with the linear factors and numerator denominator polynomials in terms of the partition dependent functions of biedenharn and louck

lie groups and lie algebras with generalized supersymmetric parameters matrices with symmetric parameters the most general extension of supersymmetric parameters are investigated the superdeterminants of such matrices are defined lie groups consisting of these matrices and their lie algebras are studied

existence of positive periodic solutions for an impulsive semi ratio dependent predator prey model with dispersion and time delays in this paper we propose an impulsive semi ratio dependent predator prey model with dispersion and time delays by applying the continuation theorem of coincidence degree theory we establish a set of sufficient conditions on the existence of at least one positive periodic solution the result not only improves but also generalizes that for the case without pulses

coupling coefficients of sun son for on scalar microscopic theory of collective states boson realisations of all on scalar states which span a subspace of the hilbert space for the collective degrees of freedom of the nucleus and are labelled by irreducible representations of the chain of subgroups u3 contains implies u2 contains implies u1 of the complementary group sp 6 r are given two general expressions for isoscalar factors reduced wigner coefficients of sun contains implies son needed for constructing on scalar basis functions depending on the microscopic collective variables in the oscillator basis are derived these isoscalar factors couple three symmetric representations of sun un p10 p20 p30 to the representation h1h2h3 of sun subduced to the son on scalar representation and more generally to the son irreducible representation fff which appears in the case of the closed shells

asymptotic behavior of solutions in nonautonomous predator prey patchy system with beddington type functional response abstract in this paper we study the asymptotic behavior of solutions in nonautonomous predator prey patchy system with beddington type functional response it is proved that the system is permanent under some appropriate conditions furthermore if the system is a n almost periodic one a set of easily verifiable sufficient conditions which guarantee the existence uniqueness and global asymptotic stability of a positive almost periodic solutions of system are obtained

eigenvalues of casimir operators for the general linear and orthosymplectic lie superalgebras a racah basis is introduced for the generators of these matrix superalgebras and explicit formulas are derived for eigenvalues of casimir operators in terms of the components of the highest weight the result contains as special cases the corresponding expressions for the general linear orthogonal and symplectic lie algebras

automorphisms of toroidal lie superalgebras abstract we give a description of the algebraic group aut g of automorphisms of a simple finite dimensional lie superalgebra g over an algebraically closed field k of characteristic 0 which is obtained by viewing g as a module over a levi subalgebra of its even part as an application we give a detailed description of the group of automorphism of the k lie superalgebra g k r for a large class of commutative rings r