existence of bounded positive solutions of semilinear elliptic equations abstract in this paper by using fixed point theory under quite general conditions on the nonlinear term we obtain an existence result on bounded positive solutions of certain semilinear elliptic equations in r n n 3

existence of unbounded positive solutions of quasilinear elliptic equations in two dimensional exterior domains in this paper by using the fixed point theory we obtain a new existence result for bounded positive solutions of the quasilinear elliptic equations in two dimensional exterior domains

inverse gaussian and its inverse process as the subordinators of fractional brownian motion in this paper we study the fractional brownian motion fbm time changed by the inverse gaussian ig process and its inverse called the inverse to the inverse gaussian iig process some properties of the time changed processes are similar to those of the classical fbm such as long range dependence however one can also observe different characteristics that are not satisfied by the fbm we study the distributional properties of both subordinators namely ig and iig processes and also that of the fbm time changed by these subordinators we establish also the connections between the subordinated processes considered and the continuous time random walk model for the application part we introduce the simulation procedures for both processes and discuss the estimation schemes for their parameters the effectiveness of these methods is checked for simulated trajectories

connes moscovici characteristic map is a lie algebra morphism let h be a hopf algebra with a modular pair in involution character 1 let a be a module algebra over h equipped with a non degenerated character invariant 1 trace tau we show that connes moscovici characteristic map varphi tau hc character 1 h rightarrow hc lambda a is a morphism of graded lie algebras we also have a morphism phi of batalin vilkovisky algebras from the cotorsion product of h text cotor h bbbk bbbk to the hochschild cohomology of a hh a a let k be both a hopf algebra and a symmetric frobenius algebra suppose that the square of its antipode is an inner automorphism by a group like element then this morphism of batalin vilkovisky algebras phi text cotor k vee mathbb f mathbb f cong text ext k mathbb f mathbb f hookrightarrow hh k k is injective

universal deformation formulas and braided module algebras abstract we study formal deformations of a crossed product s v f g of a polynomial algebra with a group induced from a universal deformation formula introduced by witherspoon these deformations arise from braided actions of hopf algebras generated by automorphisms and skew derivations we show that they are non trivial in the characteristic free context even if g is infinite by showing that their infinitesimals are not coboundaries for this we construct a new complex which computes the hochschild cohomology of s v f g

hopf algebras of dimension pq ii abstract let h be a hopf algebra of dimension pq over an algebraically closed field of characteristic zero where p q are odd primes with p q 4 p 11 we prove that h is semisimple and thus isomorphic to a group algebra or the dual of a group algebra

on the theory of frobenius extensions and its application to lie superalgebras by using an approach to the theory of frobenius extensions that emphasizes notions related to associative forms we obtain results concerning the trace and corestriction mappings and transitivity these are employed to show that the extension of enveloping algebras determined by a subalgebra of a lie superalgebra is a frobenius extension and to study certain questions in representation theory

the continuation of solutions for certain nonlinear differential equations and its applications we give some sufficient conditions for the continuation of solutions for some nonlinear differential equations as an application we obtain a new criterion for the oscillation of solutions of the lienard equation

ergodicity breaking and localization we study the joint action of the non poisson renewal events npr yielding continuous time random walk ctrw with index ensuremath alpha l1 and two different generators of hurst coefficient h ensuremath ne 0 5 one generating fractional brownian motion fbm and another scaled brownian motion sbm we discuss the ergodicity breaking emerging from these joint actions and we find that in both cases the adoption of time averages leads to localization in the case of the joint action of npr and sbm localization occurs when sbm would produce subdiffusion the joint action of npr and fbm on the contrary may lead to localization when fbm is a source of superdiffusion the joint action of npr and fbm is equivalent to extending the ctrw to the case where the jumps of the runner are correlated and we argue that the the memory induced localization requires a refinement of the theoretical perspective about determinism and randomness

subordinated stochastic processes with aged operational time in this paper subordinated stochastic processes are considered where the renewal process acting as the operational time it is assumed that the observation of the process begins at a certain time after the start of the renewal process a recurrence formula was derived for calculating the multipoint probability density functions of the aged renewal process two point correlation functions for certain subordinated stochastic processes particularly for the generalized ornstein uhlenbeck process were calculated a model of relaxation in a disordered medium with traps and obstacles is proposed

an approach to quasi hopf algebras via frobenius coordinates abstract we study quasi hopf algebras and their subobjects over certain commutative rings from the point of view of frobenius algebras we introduce a type of radford formula involving an anti automorphism and the nakayama automorphism of a frobenius algebra then view several results in quantum algebras from this vantage point in addition separability and strong separability of quasi hopf algebras are studied as frobenius algebras

substructures of bi frobenius algebras abstract bi frobenius algebras or bf algebras were recently introduced by the author and takeuchi these are both frobenius algebras and frobenius coalgebras and satisfy some compatibility conditions the concept generalizes finite dimensional hopf algebras in section 1 we give conditions for finite dimensional algebras and coalgebras to be bf algebras in section 2 we discuss substructures quotient structures of bf algebras section 3 is devoted a study of morphisms and we deduce some results in koppinen s theory

weak hopf algebras i integral theory and c structure we give an introduction to the theory of weak hopf algebras proposed as a coassociative alternative of weak quasi hopf algebras we follow an axiomatic approach keeping as close as possible to the classical theory of hopf algebras the emphasis is put on the new structure related to the presence of canonical subalgebras al and ar in any weak hopf algebra a that play the role of non commutative numbers in many respects a theory of integrals is developed in which we show how the algebraic properties of a such as the frobenius property or semisimplicity or innerness of the square of the antipode are related to the existence of non degenerate normalized or haar integrals in case of c weak hopf algebras we prove the existence of a unique haar measure h a and of a canonical grouplike element g a implementing the square of the antipode and factorizing into left and right elements g glg 1r gl al gr ar further discussion of the c case will be presented in part ii

on antipodes and integrals in hopf algebras over rings and the quantum yang baxter equation abstract the authors showed previously 2 that every frobenius algebra over a commutative ring defines a solution of the quantum yang baxter equation applying this result to hopf algebras over commutative rings which are finitely generated and projective as modules we obtain an explicit formula for this solution it turns out that this solution can be expressed in terms of the integral and antipode we use this solution to characterize separable hopf algebras over rings some results on the order of the antipode are also obtained

on integrals and cointegrals for quasi hopf algebras abstract using the theory of frobenius algebras we study how the antipode of a quasi hopf algebra h acts on the space of left and right integrals and cointegrals we obtain formulas that allow us to find out the explicit form of the integrals and cointegrals for the drinfeld double d h in terms of the integrals and cointegrals of h this leads to an answer to a conjecture made by hausser and nill at the end of the nineties

the jones polynomial and certain separable frobenius extensions 1 introductionthe jones knot polynomial was a significant advance in the mid 1980 sfor the theory of knot invariants as well as an intriguing object ofcross disciplinary research within days of a jones seminar talk at pennstate the homfly polynomial in two variables was discovered it combinedthe power of discrimination among knots and indeed oriented links ofboth the jones polynomial and the much older alexander conway polyno mial the homfly polynomial was derived by ocneanu as the trace oncertain hecke algebras this was succeeded by the kaufmann polynomialand other link invariants from partition functions in statistical mechanics then came the exhaustive works by drinfeld 10 turaev 36 vassilievwx wxwx37 and others which produced the so called quantum group hopf algebra invariants and vassiliev invariants that include all the previous knot polynomials and enough new ones to possibly classify knots theinterested reader should first consult 21 and 3 wx wxjones originally discovered his knot polynomials through his work ontype

relative hopf modules for dual quasi hopf algebras univ bucharest fac math ro 70109 bucharest 1 romania limburgs univ ctr dept math b 3590 diepenbeek belgium bulacu d univ bucharest fac math str acad 14 ro 70109 bucharest 1 romania

ribbon transformations integrals and triangular decompositions abstract we study the theory of integrals in yetter drinfel d hopf algebras and use the results to determine the integrals of hopf algebras with triangular decomposition

radford s s 4 formula for co frobenius hopf algebras abstract this note extends radford s formula for the fourth power of the antipode of a finite dimensional hopf algebra to co frobenius hopf algebras and studies equivalent conditions to a hopf algebra being involutory for finite dimensional and co frobenius hopf algebras

weak ergodicity breaking in an anomalous diffusion process of mixed origins the ergodicity breaking parameter is a measure for the heterogeneity among different trajectories of one ensemble in this report this parameter is calculated for fractional brownian motion with a random change of time scale often called subordination we show that this quantity is the same as the known continuous time random walks case

the structure of hopf algebras with a projection the smash product algebra and the smash coproduct coalgebra are well known in the context of hopf algebras 1 5 and these notions can be viewed as being motivated by the semidirect product construction in the theory of groups and in the theory of afiine group schemes respectively let

on hopf algebras of dimension 4p abstract in this paper we prove that a non semisimple hopf algebra h of dimension 4 p with p an odd prime over an algebraically closed field of characteristic zero is pointed provided h contains more than two group like elements in particular we prove that non semisimple hopf algebras of dimensions 20 28 and 44 are pointed or their duals are pointed and this completes the classification of hopf algebras in these dimensions

nonstationary markovian replication process causing diverse diffusions we introduce a single generative mechanism that can be used to describe diverse nonstationary diffusions a nonstationary markovian replication process for steps is considered for which we derive analytically the time evolution of the probability distribution of the walker s displacement and the generalized telegrapher equation with time varying coefficients and we find that diffusivity can be determined by temporal changes of replication of an immediate step by controlling the replications we realize diverse diffusions such as alternating diffusion superdiffusion subdiffusion and marginal diffusion which originate from oscillating increasing decreasing and slowly increasing or decreasing replications with time respectively

explicit conditions for asymptotic stability of stochastic lienard type equations with markovian switching this paper deals with the boundedness in probability and convergence for solutions of stochastic lienard type equations some explicit conditions to ensure that all solution is bounded in probability and convergent to some fixed sets are obtained we also show that white noise can affect the boundedness of corresponding deterministic lienard equations

frobenius extensions of subalgebras of hopf algebras we consider when extensions s r of subalgebras of a hopf algebra are frobenius that is frobenius of the second kind given a hopf algebra h we show that when s r are hopf algebras in the yetter drinfeld category for h the extension is frobenius provided r is finite over s and the extension of biproducts s h r h is cleft more generally we give conditions for an extension to be frobenius in particular we study extensions of integral type and consider when the frobenius property is inherited by the subalgebras of coinvariants we apply our results to extensions of enveloping algebras of lie coloralgebras thus extending a result of bell and farnsteiner for lie superalgebras 0 introduction in this paper we consider when various extensions s r of subalgebras of a hopf algebra are frobenius such extensions generalize the usual notion of frobenius extensions by having the module action on one side twisted by an automorphism of s it was already known that any extension of finite dimensional hopf algebras is frobenius a result of the third author sch 92 as is any finite extension u k u l of enveloping algebras of lie superalgebras a result of bell and farnsteiner bf note that u l is not an ordinary hopf algebra but rather a hopf algebra in the category of z2 graded modules these results were an important motivation for this paper and raised the question as to when an extension of hopf algebras in a category was frobenius one of the main results of this paper is that an extension s r of hopf algebras of finite index in the yetter drinfeld category hyd for a given hopf algebra h is frobenius provided that the associated extension of hopf algebras s h r h the biproducts of s and r with h has a normal basis theorem 5 6 this will happen whenever r and h are finite dimensional or when r h is pointed as an application we are able to generalize the bf result to lie coloralgebras if u k u l is a finite extension of enveloping algebras of lie coloralgebras then it is frobenius moreover we give an explicit description of the automorphism of u k and of the frobenius homomorphism f u l u k corollary 6 3 along the way we prove a number of other results about frobenius extensions and conditions that ensure that an extension is frobenius in section 1 we give a short direct proof of the fact that an extension b a of finite dimensional hopf algebras is always frobenius moreover we give explicit received by the editors december 10 1995 1991 mathematics subject classification primary 16w30 secondary 17b35 17b37 c 1997 american mathematical society

on nakayama automorphisms of double frobenius algebras abstract double frobenius algebras or df algebras were recently introduced by the author the concept generalizes finite dimensional hopf algebras adjacency algebras of non commutative association schemes and c algebras or character algebras this paper studies basic properties of various nakayama automorphisms in a df algebra as an application the theorem of d e radford stating that the antipode s of a finite dimensional hopf algebra is of finite order is generalized to df algebras and so is his formula for s 4 n in terms of certain group like elements

integrals for dual quasi hopf algebras applications abstract a classical result in the theory of hopf algebras concerns the uniqueness and existence of integrals for an arbitrary hopf algebra the integral space has dimension 1 and for a finite dimensional hopf algebra this dimension is exactly one we generalize these results to quasi hopf algebras and dual quasi hopf algebras in particular it will follow that the bijectivity of the antipode follows from the other axioms of a finite dimensional quasi hopf algebra we give a new version of the fundamental theorem for quasi hopf algebras we show that a dual quasi hopf algebra is co frobenius if and only if it has a non zero integral in this case the space of left or right integrals has dimension one

on frobenius algebras and the quantum yang baxter equation it is shown that every frobenius algebra over a commutative ring determines a class of solutions of the quantum yang baxter equation which forms a subbimodule of its tensor square moreover this subbimodule is free of rank one as a left right submodule an explicit form of a generator is given in terms of the frobenius homomorphism it turns out that the generator is invertible in the tensor square if and only if the algebra is azumaya