on multiple solutions of a semilinear schrodinger equation with periodic potential abstract this paper is concerned with the semilinear schrodinger equation s u v x u f x u u h 1 r n where v and f are periodic in the x variables f is a superlinear and subcritical nonlinearity and 0 lies in a spectral gap of u v it is shown that if f is odd in u then s has infinitely many large energy solutions the proof relies on a generalized variant fountain theorem for strongly indefinite functionals established in this paper

heat flow for the equation of surfaces with prescribed mean curvature let d z x y e r2 x 2 y2 1 and h be a function from r 3 to r if u d r a is the parametrization of a surface whose mean curvature at the point u z is h u z then u solves in d the equation au 2h u uxa 1 1 we are interested here in the behavior of the heat flow corresponding to this equation that is we look for f 0 oo x d r 3 which satisfies ft a f 2h f f x a fy 1 2 more precisely boundary data z o d r a and initial data b d r a with the compatibility condition 10d x being given we consider the problem

representations of the quantum group suq 2 and the little q jacobi polynomials abstract in this paper we study the finite dimensional unitary representations of the quantum group suq 2 then we obtain the peter weyl theorem for suq 2 and the matrix elements of these unitary representations are explicitly expressed in terms of the little q jacobi polynomials which are known as q analogues of orthogonal polynomials using these expressions the orthogonality relations of these polynomials are obtained in terms of the haar measure on the quantum group suq 2

conservation laws for conformally invariant variational problems we succeed in writing 2 dimensional conformally invariant non linear elliptic pde harmonic map equation prescribed mean curvature equations etc in divergence form these divergence free quantities generalize to target manifolds without symmetries the well known conservation laws for weakly harmonic maps into homogeneous spaces from this form we can recover without the use of moving frame all the classical regularity results known for 2 dimensional conformally invariant non linear elliptic pde see hel it enables us also to establish new results in particular we solve a conjecture by e heinz asserting that the solutions to the prescribed bounded mean curvature equation in arbitrary manifolds are continuous and we solve a conjecture by s hildebrandt hil1 claiming that critical points of continuously differentiable elliptic conformally invariant lagrangian in two dimensions are continuous

generalized boson algebra and its entangled bipartite coherent states starting with a given generalized boson algebra known as the bosonized version of the quantum super hopf algebra we employ the hopf duality arguments to provide the dually conjugate function algebra with both the hopf algebras being finitely generated we produce a closed form expression of the universal matrix that caps the duality and generalizes the familiar exponential map relating a lie algebra with its corresponding group subsequently using an inverse mellin transform approach the coherent states of single node systems subject to the symmetry are found to be complete with a positive definite integration measure the nonclassical coalgebraic structure of the algebra is found to generate naturally entangled coherent states in bipartite composite systems

su 3 chern simons vortex theory and toda systems motivated by the study of the asymptotic properties of non topological condensates in the non abelian chern simons vortex theory see 26 we analyze the su 3 toda system p 1 2 zj j e 2i 1kijzi me i 12kijzi 1 on m mzj 0j 1 2 where m r2 z2 k kij 2 1 12 is the su 3 cartan matrix and j are positive parameters we study the variational problem associated with the system p 1 2 in a range of parameters where the trivial solution is a strict local minimum and the corresponding sobolev type inequality fails to apply in this situation a lack of compactness may occur due to concentration phenomena nonetheless we are able to establish the existence of a non trivial solution for p 1 2 which is not a minimizer

on a free boundary problem for minimal surfaces forc 4 embedded manifoldss 3 which are differmorphic to the standard sphere in 3 the existence of non constant minimal surfaces bounded bys and intersectings orthogonally along their boundaries is deduced

creation operators and bethe vectors of the osp 1 2 gaudin model a gaudin model based on the orthosymplectic lie superalgebra osp 1 2 is studied the eigenvectors of the osp 1 2 invariant gaudin hamiltonians are constructed by algebraic bethe ansatz corresponding creation operators are defined by a recurrence relation furthermore explicit solution to this recurrence relation is found the action of the creation operators on the lowest spin vector yields bethe vectors of the model the relation between the bethe vectors and solutions to the knizhnik zamolodchikov equation of the corresponding super conformal field theory is established

existence and uniqueness of weak solutions for a non uniformly parabolic equation in this paper we develop a unifying method to prove the existence and uniqueness of weak solutions for the initial boundary value problem of a non uniformly parabolic equation some well known parabolic equations are the special cases of this equation

large solutions for harmonic maps in two dimensions we seek critical points of the functionale u mathop smallint limits omega u 2 where is the unit disk in 2 andu s2 satisfies the boundary conditionu on we prove that if is not a constant thene has a local minimum which is different from the absolute minimum we discuss in more details the case where x y rx ry sqrt 1 r 2 andr 1

model based analyses of bioequivalence crossover trials using the stochastic approximation expectation maximisation algorithm in this work we develop a bioequivalence analysis using nonlinear mixed effects models nlmem that mimics the standard noncompartmental analysis nca we estimate nlmem parameters including between subject and within subject variability and treatment period and sequence effects we explain how to perform a wald test on a secondary parameter and we propose an extension of the likelihood ratio test for bioequivalence we compare these nlmem based bioequivalence tests with standard nca based tests we evaluate by simulation the nca and nlmem estimates and the type i error of the bioequivalence tests for nlmem we use the stochastic approximation expectation maximisation saem algorithm implemented in monolix we simulate crossover trials under h 0 using different numbers of subjects and of samples per subject we simulate with different settings for between subject and within subject variability and for the residual error variance the simulation study illustrates the accuracy of nlmem based geometric means estimated with the saem algorithm whereas the nca estimates are biased for sparse design nca based bioequivalence tests show good type i error except for high variability for a rich design type i errors of nlmem based bioequivalence tests wald test and likelihood ratio test do not differ from the nominal level of 5 type i errors are inflated for sparse design we apply the bioequivalence wald test based on nca and nlmem estimates to a three way crossover trial showing that omnitrope sandoz gmbh kundl austria powder and solution are bioequivalent to genotropin pfizer pharma gmbh karlsruhe germany nlmem based bioequivalence tests are an alternative to standard nca based tests however caution is needed for small sample size and highly variable drug

a direct method for minimizing the yang mills functional over 4 manifolds a direct method is employed to minimize the yang mills functional over a 4 dimensional manifold the limiting connection is shown to be yang mills but in a possibly new bundle we show that a topological invariant of the bundle is preserved by the minimizing process this implies the existence of an absolute minimum of the yang mills functional in a wide class of bundles

universal t matrix representations of ospq 1 2 and little q jacobi polynomials we obtain a closed form expression of the universal t matrix encapsulating the duality between the quantum superalgebra uq osp 1 2 and the corresponding supergroup ospq 1 2 the classical q 1 limit of this universal t matrix yields the group element of the undeformed ospq 1 2 supergroup the finite dimensional representations of the quantum supergroup ospq 1 2 are readily constructed employing the above mentioned universal t matrix and the known finite dimensional representations of the dually related deformed uq osp 1 2 superalgebra proceeding further we derive the product law the recurrence relations and the orthogonality of the representations of the quantum supergroup ospq 1 2 it is shown that the entries of these representation matrices are expressed in terms of the little q jacobi polynomials with q q two mutually complementary singular maps of the universal t matrix on the universal r matrix are also presented

multiple solutions of h systems and rellich s conjecture soit x y r 2 x 2 y 2 1 on considere une fonction u r 3 satisfaisant le systeme h u 2hu x u y sur avec l une des conditions suivantes soit dirichlet u sur soit plateau u x 2 u y 2 u x u y 0 sur u et u non decroissante sur

constant q curvature metrics in arbitrary dimension working in a given conformal class we prove existence of constant q curvature metrics on compact manifolds of arbitrary dimension under generic assumptions the problem is equivalent to solving a nth order non linear elliptic differential or integral equation with variational structure where n is the dimension of the manifold since the corresponding euler functional is in general unbounded from above and below we use critical point theory jointly with a compactness result for the above equation

duality for the matrix quantum group glp q 2 c it is shown that the algebra up q dual to glp q 2 c is isomorphic to u pq 1 2 sl 2 c z as a commutation algebra where z is a subalgebra central in up q the subalgebra z is a hopf subalgebra of up q while the commutation subalgebra u pq 1 2 sl 2 c is not a hopf subalgebra

periodic second order superlinear hamiltonian systems abstract we consider periodic solutions for superlinear second order non autonomous dynamical systems including both kinetic and potential terms we study the existence of nontrivial and ground state solutions

a general existence result for the toda system on compact surfaces in this paper we consider the following toda system of equations on a compact surface u1 2 1 h1eu1 h1eu1dvg 1 2 h2eu2 h2eu2dvg 1 u1 4 j 1m 1 j pj 1 u2 2 2 h2eu2 h2eu2dvg 1 1 h1eu1 h1eu1dvg 1 u2 4 j 1m 2 j pj 1 which is motivated by the study of models in non abelian chern simons theory here h1 h2h1 h2 are smooth positive functions 1 2 1 2 two positive parameters pipi points of the surface and 1 i 2 j 1 i 2 j non negative numbers we prove a general existence result using variational methods the same analysis applies to the following mean field equation u 1 heu heudvg 1 2 he u he udvg 1 which arises in fluid dynamics

superlinear schrodinger operators abstract we find nontrivial and ground state solutions for the nonlinear schrodinger equation under conditions weaker than those previously assumed

a note on the use of laplace s approximation for nonlinear mixed effects models the asymptotic properties of estimates obtained using laplace s approximation for nonlinear mixed effects models are investigated unlike the restricted maximum likelihood approach e g wolfinger 1993 here the laplace approximation is applied only to the random effects of the integrated likelihood this results in approximate maximum likelihood estimation the resulting estimates are shown to be consistent with the rate of convergence depending on both the number of individuals and the number of observations per individual conditions under which the leading term laplace approximation should be avoided are discussed

compact matrix pseudogroups the compact matrix pseudogroup is a non commutative compact space endowed with a group structure the precise definition is given and a number of examples is presented among them we have compact group of matrices duals of discrete groups and twisted deformed su n groups the representation theory is developed it turns out that the tensor product of representations depends essentially on their order the existence and the uniqueness of the haar measure is proved and the orthonormality relations for matrix elements of irreducible representations are derived the form of these relations differs from that in the group case this is due to the fact that the haar measure on pseudogroups is not central in general the corresponding modular properties are discussed the haar measures on the twistedsu 2 group and on the finite matrix pseudogroup are found

design evaluation and optimisation in crossover pharmacokinetic studies analysed by nonlinear mixed effects models bioequivalence or interaction trials are commonly studied in crossover design and can be analysed by nonlinear mixed effects models as an alternative to noncompartmental approach we propose an extension of the population fisher information matrix in nonlinear mixed effects models to design crossover pharmacokinetic trials using a linearisation of the model around the random effect expectation including within subject variability and discrete covariates fixed or changing between periods we use the expected standard errors of treatment effect to compute the power for the wald test of comparison or equivalence and the number of subjects needed for a given power we perform various simulations mimicking crossover two period trials to show the relevance of these developments we then apply these developments to design a crossover pharmacokinetic study of amoxicillin in piglets and implement them in the new version 3 2 of the r function pfim

absence of self similar blow up and local well posedness for the constant mean curvature wave equation abstract in this note we consider the constant mean curvature wave equation in 1 2 dimensions we show that it does not admit any self similar blow up we also remark that the equation is locally well posed for initial data in h 3 2

on clebsch gordan coefficients and matrix elements of representations of the quantum algebra uq su2 clebsch gordan coefficients and matrix elements of irreducible representations of the quantum algebra uq su2 were considered in several papers in particular a few expressions for them were derived an approach to clebsch gordan coefficients and to matrix elements of representations of uq su2 on the base of the theory of basic hypergeometric functions is given this approach allows one to obtain q analogs of all well known classical expressions for clebsch gordan coefficients most of them were absent new symmetry relations generating functions and recurrence formulas for clebsch gordan coefficients of uq su2 are obtained unlike other papers clebsch gordan coefficients and matrix elements are considered on the base of minimal theoretical constructions in fact without using the notion of a c algebra and of a hopf algebra

new connection formulae for the q orthogonal polynomials via a series expansion of the q exponential using a realization of the q exponential function as an infinite multiplicative series of the ordinary exponential functions we obtain new nonlinear connection formulae of the q orthogonal polynomials such as q hermite q laguerre and q gegenbauer polynomials in terms of their respective classical analogues

weak solutions to the heat flow for surfaces of prescribed mean curvature in this talk we establish the existence of global weak solutions to the heat flow for surfaces of prescribed mean curvature i e the existence for the cauchy dirichlet problem to parabolic systems of the type tu u 2 h u d1u d2u in b 0 u uo on par b 0 where h r3 r is a bounded continuous function satisfying an isoperimetric condition b the unit ball in r2 and u b 0 r3 as one of the possible applications we show that the problem has a solution with values inbr r3 whenever uo b br and furthermore there holds br h 3 2r h d 9 2 h a 1 r for a br the results that will be presented in the talk are joint work with verena bogelein und chrsitoph scheven from erlangen frank duzaar department of mathematics university erlangen nurnberg cauerstr 11 91056 erlangen germany e mail address frank duzaar zuv uni erlangen de date december 29 2011 1

cantor families of periodic solutions for wave equations via a variational principle abstract we prove existence of small amplitude periodic solutions of completely resonant wave equations with frequencies in a cantor set of asymptotically full measure via a variational principle a lyapunov schmidt decomposition reduces the problem to a finite dimensional bifurcation equation variational in nature defined on a cantor set of non resonant parameters the cantor gaps are due to small divisors phenomena to solve the bifurcation equation we develop a suitable variational method in particular we do not require the typical arnold non degeneracy condition of the known theory on the nonlinear terms as a consequence our existence results hold for new generic sets of nonlinearities

the qualitative behavior at the free boundary for approximate harmonic maps from surfaces let u n be a sequence of maps from a compact riemann surface m with smooth boundary to a general compact riemannian manifold n with free boundary on a smooth submanifold k subset n satisfying begin aligned sup n left vert nabla u n vert l 2 m vert tau u n vert l 2 m right le lambda end aligned where tau u n is the tension field of the map u n we show that the energy identity and the no neck property hold during a blow up process the assumptions are such that this result also applies to the harmonic map heat flow with free boundary to prove the energy identity at finite singular time as well as at infinity time also the no neck property holds at infinity time

an elementary partial regularity proof for vector valued obstacle problems soit r n et m r n des ensembles ouverts bornes on suppose n 3 n 2 et on requiert que la frontiere de m est une hyper surface lisse de classe c 2 l espace de fonction h 1 2 m des fonctions de comparaison consiste en toutes les fonctions de sobolev v h 1 2 r n avec la propriete v x m pour presque tous les points x dans si u h 1 2 m minimise localement l energie alors il y a un sous ensemble ouvert 0 de tel que u c 1 0 r n pour tout 0 1 h n 2 0 0 et x 0 si et seulement si lim 1 0 r 2 n br x du 2 dz 0

twist deformation of the rank one lie superalgebra the drinfeld twist is applied to deform the rank one orthosymplectic lie superalgebra the twist element is the same as for the sl 2 lie algebra due to the embedding of the sl 2 into the superalgebra the r matrix has the direct sum structure in the irreducible representations of the dual quantum group is defined using the frt formalism it includes the jordanian quantum group as subalgebra and grassmann generators as well

on the kirchhoff type choquard problem with hardy littlewood sobolev critical exponent abstract in this paper we study the following kirchhoff type choquard problem 0 1 a b r n u 2 d x u u r n f u y u y 2 x y d y f u 2 u 2 2 u in r n where n 3 a b 0 are constants 0 is a parameter when 0 4 under suitable conditions on b and f we prove that 0 1 has a ground state solution when 4 we also obtain some related existence results

properties of clebsch gordan coefficients and 3 j symbols for the quantum superalgebra uq osp 1 mod 2 this paper is a continuation of the study begun in an earlier paper of the structure of grade star representations of the quantum superalgebra uq osp 1 mod 2 the general case of the tensor product of two grade star representations acting in representation spaces with arbitrary not necessarily positive definite hermitian forms is considered an explicit analytical formula for clebsch gordan coefficients for this general case is derived using the projection operator method pseudo orthogonality relations are given and symmetry properties including regge symmetry are discussed the quantum analogues of super 3 j symbols are defined and their symmetry properties are analysed

noncommutative geometry of super jordanian osph 2 1 covariant quantum space extending a recently proposed procedure of construction of various elements of differential geometry on noncommutative algebras we obtain these structures on noncommutative superalgebras as an example a quantum superspace covariant under the action of super jordanian osph 2 1 is studied it is shown that there exist a two parameter family of torsionless connections and the curvature computed from this family of connections is bilinear it is also shown that the connections are not compatible with the metric

quantum super spheres and their transformation groups representations and little t jacobi polynomials abstract quantum super 2 spheres and the corresponding quantum super transformation group are introduced in analogy to the well known quantum 2 spheres and quantum sl 2 connection between little t jacobi polynomials and the finite dimensional representations of the quantum super group is formulated and the peter weyl theorem is obtained

evaluation by simulation of tests based on non linear mixed effects models in pharmacokinetic interaction and bioequivalence cross over trials we propose tests based on non linear mixed effects models nlmem in pharmacokinetic interaction and bioequivalence cross over trials comparing two treatments or two formulations to compare the logarithm of the area under the curve auc using these models two approaches are studied in the first one concentration data are analysed globally with and without the estimation of a treatment effect and in the second one they are analysed separately in each treatment group with the estimation of the individual parameters four tests for comparison of the logarithm auc between two treatment arms are studied a likelihood ratio test lrt a wald test and two tests parametric and non parametric comparing the individual empirical bayes eb estimates these tests are adapted to the case of equivalence except the lrt which does not have any simple extension we evaluate by simulation of the type i error and the power for both comparison and equivalence tests they are compared to the standard tests recommended by the fda and the emea based on non compartmental nc auc trials for a usual pk model are simulated under h0 and several h1 using s plus software and analysed with the nlme function different configurations of the number of subjects n 12 24 and 40 and of the number of samples per subject j 10 5 and 3 are studied the type i error of lrt and wald comparison test in the 5000 replications of interaction cross over trials is found to be 20 9 per cent and 21 7 per cent respectively in the original design n 12 j 10 which is far superior to 5 per cent and decreases when n increases when n is fixed is found to increase with j power is satisfactory for both tests after correction of the significance threshold results of eb and nc tests are similar with satisfactory powers and a type i error close to 5 per cent except when j 3 for eb tests similar results are obtained for equivalence tests except for eb and nc student tests which are not of a great interest nc tests keep their place when the number of samples per subject j is large but nlmem seem useful for cross over studies performed in special populations where j limited the evaluation by monte carlo simulations of empirical threshold seems however necessary because of the inflation of the type i error copyright 2005 john wiley sons ltd

multiple solutions to the plateau problem for nonconstant mean curvature we prove the existence of at least two solutions to the plateau problem for any curvature function h close enough in l norm to a nonzero constant h 0 such that h 0 1 where denotes the l norm of the boundary condition

new approach to assess bioequivalence parameters using generalized gamma mixed effect model model based asymptotic bioequivalence test in the pharmacokinetic pk study under a 2x2 crossover design that involves both the test and reference drugs we propose a mixed effects model for the drug concentration time profiles obtained from subjects who receive different drugs at different periods in the proposed model the drug concentrations repeatedly measured from the same subject at different time points are distributed according to a multivariate generalized gamma distribution and the drug concentration time profiles are described by a compartmental pk model with between subject and within subject variations we then suggest a bioequivalence test based on the estimated bioavailability parameters in the proposed mixed effects model the results of a monte carlo study further show that the proposed model based bioequivalence test is not only better on maintaining its level but also more powerful for detecting the bioequivalence of the two drugs than the conventional bioequivalence test based on a non compartmental analysis or the one based on a mixed effects model with a normal error variable the application of the proposed model and test is finally illustrated by using data sets in two pk studies copyright 2013 john wiley sons ltd

representation functions for jordanian quantum group slh 2 and jacobi polynomials the explicit expressions of the representation functions d functions for jordanian quantum group slh 2 are obtained by combination of tensor operator technique and drinfeld twist it is shown that the d functions can be expressed in terms of jacobi polynomials as the undeformed d functions can some of the important properties of the d functions for slh 2 such as wigner s product law recurrence relations and rtt type relations are also presented

on nonlinear schrodinger poisson equations with general potentials abstract we study the existence of infinitely many finite energy radial solutions to the nonlinear schrodinger poisson equations u u x u f u 0 in r 3 u 2 0 lim x x 0 in r 3 nspe for short under some structure conditions on the nonlinearity function f as consequences of the main result we can provide examples of f which guarantee the existence of infinitely many finite energy solutions but i f t grows faster than t 2 and slower than t p for all p 2 or ii f t is the same as t t when t t 0 for arbitrarily given t 0 0 if f t t p 1 t it is known that nspe admits no finite energy nontrivial solutions when p 1 2 and admits infinitely many finite energy solutions when p 2 5 so examples i and ii show some interesting features of nspe

basic hypergeometric functions and covariant spaces for even dimensional representations of uq osp 1 2 representations of the quantum superalgebra uq osp 1 2 and their relations to the basic hypergeometric functions are investigated we first establish clebsch gordan decomposition for the superalgebra uq osp 1 2 in which the representations having no classical counterparts are incorporated formulae for these clebsch gordan coefficients are derived and is observed that they may be expressed in terms of the q hahn polynomials we next investigate representations of the quantum supergroup ospq 1 2 which are not well defined in the classical limit employing the universal matrix the representation matrices are obtained explicitly and found to be related to the little q jacobi polynomials characteristically the relation q q is satisfied in all cases using the clebsch gordan coefficients derived here we construct new noncommutative spaces that are covariant under the coaction of the even dimensional representations of the quantum supergroup ospq 1 2

finite dimensional representations of the quantum group glp q 2 using the exponential map from up q gl 2 using the fronsdal galindo formula for the exponential mapping from the quantum algebra up q gl 2 to the quantum group glp q 2 we show how the 2j 1 dimensional representations of glp q 2 can be obtained by exponentiating the well known 2j 1 dimensional representations of up q gl 2 for j 1 3 2 j 1 2 corresponds to the defining two dimensional t matrix the earlier results on the finite dimensional representations of glq 2 and slq 2 or suq 2 are obtained when p q representations of uq q 2 q in c mod r and uq 2 q in r mod 0 are also considered the structure of the clebsch gordan matrix for up q gl 2 is studied the same clebsch gordan coefficients are applicable in the reduction of the direct product representations of the quantum group glp q 2

stationary partitioning of convex bodies on considere une version particuliere du probleme de partage soit 7b b un corps convexe dans r 3 de volume m 3 7b b une surface de type disque s est a l interieur de 7b b divisant cet interieur en deux cellules simplement connexes 7b b et 7b b de volumes m 3 7b b m 3 7b b m 3 7b b 1 m 3 7b b 0 1 on considere comme fixee et on etudie les cas ou s a l aire la plus petite possible

droplet footprint control controlling droplet shape via surface tension has numerous technological applications such as droplet lenses and lab on a chip this motivates a partial differential equation constrained shape optimization approach for controlling the shape of droplets on flat substrates by controlling the surface tension of the substrate we use shape differential calculus to derive an l 2 gradient flow approach to compute equilibrium shapes for sessile droplets on substrates we then develop a gradient based optimization method to find the substrate surface tension coefficient yielding an equilibrium droplet shape with a desired footprint i e the liquid solid interface has a desired shape moreover we prove a sensitivity result with respect to the substrate surface tensions for the free boundary problem associated with the footprint numerical results are also presented to showcase the method

nonlinear mixed effects models for repeated measures data we propose a general nonlinear mixed effects model for repeated measures data and define estimators for its parameters the proposed estimators are a natural combination of least squares estimators for nonlinear fixed effects models and maximum likelihood or restricted maximum likelihood estimators for linear mixed effects models we implement newton raphson estimation using previously developed computational methods for nonlinear fixed effects models and for linear mixed effects models two examples are presented and the connections between this work and recent work on generalized linear mixed effects models are discussed

an application of gauge theory to four dimensional topology soit x une u variete compacte reguliere simplement connexe orientee avec la propriete que la forme associee q est definie positive alors cette forme est equivalente sur les entiers a la forme diagonale standard soit dans une base q u 1 u 2 u 2 u 2 1 u 2 2 u 2 2