size distribution of clusters in irreversible kinetic aggregation the size distribution of clusters is derived analytically at a given time in a process of irreversible kinetic aggregation of diffusive clusters which starts from a collection of a great number of individual particles a general reduced shape is given in the scaling regime where gelation does not occur the time evolution is derived by use of smoluchowski s equation then a scaling reasoning allows one to find the exponents in real cases and a quantitative comparison is made with numerical simulations

monte carlo series analysis of irreversible self avoiding walks i the indefinitely growing self avoiding walk igsaw high precision monte carlo data are used to estimate the exponents which govern the asymptotic behaviour of the recently introduced indefinitely growing self avoiding walk in two dimensions for this walk the exponent gamma is by definition equal to one applying the same methods which are used to extract the exponents from exact series enumeration the authors give an estimate for the exponent nu of 0 567 or 0 003 the leading corrections to this asymptotic behaviour are also calculated

existence and nonexistence of nontrivial solutions of some nonlinear degenerate elliptic equations in connection with the maximizing problem for the functional r u u lq u lp in w01 p 0 we consider the equation div u p 2 u x u q 2 u x x 1 p resp q p e has no nontrivial resp nonnegative nontrivial solution belonging to the class p u w01 p lq xi u q 2u lp p 1 i 1 2 n w01 p provided that is star shaped the crucial point of the proof of our result is to obtain an l estimate of weak solutions and to verify a certain pohozaev type inequality for weak solutions belonging to p

static and dynamic scaling for free reptation limited chain chain aggregation in two dimensions chain chain aggregation is studied by monte carlo simulations on the triangular lattice n conserving local deformations lead to snake like motion or free reptation of the aggregating chains the scaling of the chain size distribution function is carefully examined and estimates of the static and dynamic exponents are obtained

comment on reflecting and absorbing boundary conditions on the tail of the laplacian random walk in a recent letter lyklema and evertsz see ibid vol 19 p 895 900 1986 found a value of nu for the eta 1 laplacian random walk which differs from the value the authors obtained for the diffusion limited self avoiding walk dlsaw they show that this results from different boundary conditions at the ends of these chains and not from a failing in our monte carlo studies of the dlsaw

the nehari manifold for systems of nonlinear elliptic equations abstract this paper deals with the existence and multiplicity results of nonlocal positive solutions to the following system p u u p 1 2 u 1 u u 1 v 1 q v v q 2 v 1 u 1 v 1 v together with dirichlet or mixed boundary conditions under some hypotheses on the parameters p p 1 and q more precisely the system considered corresponds to a perturbed eigenvalue equation combined with a second equation having concave and convex nonlinearities the study is based on the extraction of palais smale sequences in the nehari manifold the behaviour of the energy corresponding to these positive solutions with respect to the real parameters and is established

finiteness conditions co frobenius hopf algebras and quantum groups abstract some finiteness conditions for infinite dimensional coalgebras particularly right or left semiperfect coalgebras or co frobenius hopf algebras are studied as well examples of co frobenius hopf algebras are constructed via a hopf algebra structure on an ore extension of a group algebra and it is shown that bicrossproducts of co frobenius hopf algebras are themselves co frobenius

bicrossproducts of multiplier hopf algebras abstract in this paper we generalize majid s bicrossproduct construction we start with a pair a b of two regular multiplier hopf algebras we assume that b is a right a module algebra and that a is a left b comodule coalgebra the right action of a on b gives rise to the smash product a b the left coaction of b on a gives a possible coproduct on a b we discuss in detail the necessary compatibility conditions between the action and the coaction for to be a proper coproduct on a b the result is again a regular multiplier hopf algebra majid s construction is obtained when we have hopf algebras we also look at the dual case constructed from a pair c d of regular multiplier hopf algebras where now c is a left d module algebra while d is a right c comodule coalgebra we show that indeed these two constructions are dual to each other in the sense that a natural pairing of a with c and of b with d yields a duality between a b and the smash product c d we show that the bicrossproduct of an algebraic quantum group is again an algebraic quantum group i e a regular multiplier hopf algebra with integrals the algebra case is also considered some special cases are treated and they are related with other constructions available in the literature the basic example coming from a not necessarily finite group g with two subgroups h and k such that g k h and h k e where e is the identity of g is used to illustrate our theory more examples will be considered in forthcoming papers on the subject

dynamical scaling in self associating polymer aggregates the authors present a simple model that simulates the dynamics of the long flexible self associating polymer chains immersed in water and develop a dynamical scaling description for the cluster size distribution function for irreversible aggregation each chain may have one or several functional groups at each end that can associate with one another they find that the chain length is a new scaling variable that appears explicitly in the scaling function the validity of their scaling predictions is confirmed by extensive computer simulations

the drinfel d double of multiplier hopf algebras abstract let a b be a pairing of two regular multiplier hopf algebras a and b the drinfel d double associated to this pairing is constructed by using appropriate representations of a and b on the same vector space b a we realize the drinfel d double denoted by d as an algebra of operators on the vector space b a in the case that a b is a multiplier hopf algebra pairing we prove that d is again a multiplier hopf algebra if a and b carry positive integrals we prove that d also has a positive integral this proof is not given before

existence result for quasilinear elliptic problem on unbounded domains abstract in this paper we obtain the existence of a nontrivial solution for inhomogeneous quasilinear elliptic systems on arbitrary domains with lack of compactness the method used here is essentially based on preliminary results on the convergence almost everywhere of the gradients of palais smale sequences

twisted tensor product of multiplier hopf algebras abstract we combine two not necessarily commutative or co commutative multiplier hopf algebras to a new multiplier hopf algebra we use the construction of a twisted tensor product for algebras as introduced by a van daele we then proceed to find sufficient conditions on the twist map for this twisted tensor product to be a multiplier hopf algebra with the natural comultiplication for usual hopf algebras we find that majid s double crossed product by a matched pair of hopf algebras is exactly the twisted tensor product hopf algebra according to an appropriate twist map starting from two dually paired multiplier hopf algebras we construct the drinfel d double multiplier hopf algebra in the framework of twisted tensor products

existence of entire positive solutions for a critical system of nonlinear elliptic equations abstract in this paper using the fibering method introduced by pohozaev we establish an existence of multiple nontrivial positive solutions for a system of nonlinear elliptic equations in r n with lack of compactness studying the properties of palais smale sequence of the energy functional associated with the system

fingered growth in channel geometry a loewner equation approach a simple model of laplacian growth is considered in which the growth takes place only at the tips of long thin fingers following carleson and makarov l carleson and n makarov j anal math 87 103 2002 the evolution of the fingers is studied with use of the deterministic loewner equation the method is then extended to study the growth in a linear channel with reflecting sidewalls one and two finger solutions are found and analyzed it turns out that the presence of the walls has a significant influence on the shapes of the fingers and the dynamics of the screening process in which longer fingers suppress the growth of the shorter ones

static and dynamic scaling for chain chain aggregation in two dimensions chain chain aggregation is studied on the square lattice by monte carlo simulations the fractal dimension of the aggregates is found to be d 1 32 or 0 04 the results support the dynamic scaling relation ns t approximately s 2f s tz with z 0 72 or 0 02

existence results for some nonlinear elliptic system with lack of compactness abstract we are interested in existence of solutions for some typical elliptic systems governed by two pseudo laplacian operators with critical sobolev exponents we show this result by a local minimization for an adapted variational problem a concentration compactness principle allows us to obtain some convergence results

twisted tensor coproduct of multiplier hopf algebras we put a non trivial comultiplication on the natural tensor product algebra of two multiplier hopf algebras by means of a cotwisting map as a special case we characterize the dual of the drinfel d double of an algebraic quantum group because any finite dimensional hopf algebra is an algebraic quantum group our characterization applies to the dual of the drinfel d double of a finite dimensional hopf algebra then it coincides with a result of lu

self directed walk a monte carlo study in two dimensions the self directed walk is studied in three dimensions monte carlo simulations on the simple cubic lattice provide an estimate of the radius of gyration exponent nu 0 67 or 0 01 in agreement with the authors recent flory like theory leading to nu 2 d when 2 or d or 4

the analytic structure of algebraic quantum groups abstract in adv math 140 1998 323 366 van daele introduced the notion of an algebraic quantum group we proved in internat j math 8 8 1997 1067 1139 that such algebraic quantum groups give rise to reduced c algebraic quantum groups in the sense of j kustermans s vaes ann sci ecole norm sup 4 33 2000 837 934 after introducing the universal c algebraic quantum group associated to an algebraic one we will pull down the analytic structure of this c algebraic quantum group to the algebraic quantum group the multiplier algebra of the dual quantum group will be realized as a space of linear functionals on the original algebra we also identify the analytic structure of the dual quantum group in terms of the analytic structure of the original algebraic quantum group

a short note on the true self avoiding walk the scaling laws for the true self avoiding walk and a fokker planck equation for the end to end probability distribution are combined in order to calculate the scaling functions and the end to end distance in one dimension explicitly

a novel growing self avoiding walk in three dimensions the authors introduce a growing self avoiding walk in three dimensions 3d that can terminate only by returning to its point of origin this symmetric tricolour walk stw is a direct generalization of the smart kinetic walk to 3d and yet is readily simulated their monte carlo simulations strongly suggest that the fractal dimension of the stw is exactly 2 this conclusion is supported by a mapping of the stw onto a self attracting self avoiding walk at its collapse transition

hierarchical model for irreversible kinetic cluster formation a model is proposed to describe the growth of clusters by a mechanism of irreversible clustering of clusters the fractal exponent is extracted by means of numerical simulations on small systems both directly and in the form of a renormalisation group analysis the results are in excellent agreement with previous monte carlo simulations the numerical precision is better due to the simpler hierarchical formulation of the model in the present form the model looks like the diffusion limited aggregation model which for the sake of comparison is treated by the same renormalisation group method

monte carlo study of linear diffusion limited aggregation linear diffusion limited aggregation is studied on the square lattice the radius of gyration exponent nu 0 79 or 0 01 is estimated using the monte carlo method and a scaling analysis

convergence and extrapolation in finite size scaling renormalization abstract finite size renormalization technique is studied by examining a test model which is exactly solvable and the problem of lattice animals and self avoiding walks bulk estimates of the leading irrelevant rg eigenvalue are found and compared with independent estimates from finite size data we introduce an extrapolation technique which is applicable to non monotonic sequences of exponent approximants

reflecting and absorbing boundary conditions on the tail of the laplacian random walk the authors introduce a new version of the laplacian random walk lrw for which the tail of the trajectory acts like a hard wall for incoming diffusing particles they show how to implement these reflecting boundary conditions through the use of a modified discrete laplace equation from an exact enumeration on the square lattice they find that reflecting boundary conditions on the tail of the trajectory give rise to a denser fractal compared with the recently studied laplacian random walk with absorbing boundary conditions

the growing self avoiding trail the author introduces a new random walk which can be used as a model for the theta polymer the walk belongs to a different universality class from the usual saw extensive monte carlo calculations have been performed to calculate the exponents gamma and nu the author finds in two dimensions nu 0 535 and gamma 1 025 and in three dimensions nu 0 50 and gamma 1 0 this result strongly suggests that the upper critical dimension is equal to three

an algebraic framework for group duality abstract a hopf algebra is a pair a whereais an associative algebra with identity and a homomorphism formatoa asatisfying certain conditions if we drop the assumption thatahas an identity and if we allow to have values in the so called multiplier algebram a a we get a natural extension of the notion of a hopf algebra we call this a multiplier hopf algebra the motivating example is the algebra of complex functions with finite support on a group with the comultiplication defined as dual to the product in the group also for these multiplier hopf algebras there is a natural notion of left and right invariance for linear functionals called integrals in hopf algebra theory we show that if such invariant functionals exist they are unique up to a scalar and faithful for a regular multiplier hopf algebra a i e with invertible antipode with invariant functionals we construct in a canonical way the dual it is again a regular multiplier hopf algebra with invariant functionals it is also shown that the dual of is canonically isomorphic with the original multiplier hopf algebra a it is possible to generalize many aspects of abstract harmonic analysis here one can define the fourier transform one can prove plancherel s formula because any finite dimensional hopf algebra is a regular multiplier hopf algebra and has invariant functionals our duality theorem applies to all finite dimensional hopf algebras then it coincides with the usual duality for such hopf algebras but our category of multiplier hopf algebras also includes in a certain way the discrete quantum groups and the compact quantum groups our duality includes the duality between discrete quantum groups and compact quantum groups in particular it includes the duality between compact abelian groups and discrete abelian groups one of the nice features of our theory is that we have an extension of this duality to the non abelian case but within one category this is shown in the last section of our paper where we introduce the algebras of compact type and the algebras of discrete type we prove that also these are dual to each other we treat an example that is sufficiently general to illustrate most of the different features of our theory it is also possible to construct the quantum double of drinfel d within this category this provides a still wider class of examples so we obtain many more than just the compact and discrete quantum within this setting