the use of a canonical form in the construction of locally optimal designs for non linear problems optimal experimental designs for non linear problems depend on the values of the underlying undknown parameters in the model for various reasons there is interest in providing explicit formulae for the optimal designs as a function of the unknown parameters this paper shows that for a certain class of generalized linear models the problem can be reduced to a canonical form this simplifies the underlying problem and designs are constructed for several contexts with a single variable using geometric and other arguments

a kam theorem for hamiltonian partial differential equations in higher dimensional spaces in this paper we give a kam theorem for a class of infinite dimensional nearly integrable hamiltonian systems the theorem can be applied to some hamiltonian partial differential equations in higher dimensional spaces with periodic boundary conditions to construct linearly stable quasi periodic solutions and its local birkhoff normal form the applications to the higher dimensional beam equations and the higher dimensional schrodinger equations with nonlocal smooth nonlinearity are also given in this paper

an optimal design problem in rhythmometry a trigonometric regression model is assumed for a problem involving circadian rhythm exhibited by peak expiratory flow experimental designs are sought with a view to estimating a particular nonlinear function of the parameters both optimal and nonoptimal but more practicable designs are derived and their relative efficiencies are established

integrals for monoidal hom hopf algebras and their applications integrals of monoidal hom hopf algebras are introduced and the existence and uniqueness of integrals for finite dimensional monoidal hom hopf algebras are investigated first then integrals are applied to the maschke type theorem for monoidal hom hopf algebras controlling the semisimplicity and separability of monoidal hom hopf algebras further monoidal hom algebras are characterized with additional frobenius property and the question when finite dimensional monoidal hom hopf algebras are frobenius is studied as applications of integrals the maschke type theorem for hom smash product is given and the morita context in the hom category h mk is constructed

kam tori of hamiltonian perturbations of 1d linear beam equations abstract in this paper one dimensional 1d nonlinear beam equations u tt u xxxx mu f u with hinged boundary conditions are considered the nonlinearity f is an analytic odd function and f u o u3 it is proved that for all real parameters m 0 but a set of small lebesgue measure the above equation admits small amplitude quasi periodic solutions corresponding to finite dimensional invariant tori of an associated infinite dimensional dynamical system the proof is based on infinite dimensional kam theory developed by kuksin lecture notes in mathematics vol 1556 springer berlin 1993 wayne commun math phys 127 1990 479 528 poschel ann sc norm sup pisa cl sci 23 1996 119 148

yetter drinfeld modules for hom bialgebras the aim of this paper is to define and study yetter drinfeld modules over hom bialgebras a generalized version of bialgebras obtained by modifying the algebra and coalgebra structures by a homomorphism yetter drinfeld modules over a hom bialgebra with bijective structure map provide solutions of the hom yang baxter equation the category yhhd of yetter drinfeld modules with bijective structure maps over a hom bialgebra h with bijective structure map can be organized in two different ways as a quasi braided pre tensor category if h is quasitriangular respectively coquasitriangular the first respectively second quasi braided pre tensor category yhhd contains as a quasi braided pre tensor subcategory the category of modules respectively comodules with bijective structure maps over h

radford s biproducts and yetter drinfeld modules for monoidal hom hopf algebras let h be a monoidal hom bialgebra and b be a left h hom module algebra and also a left h hom comodule coalgebra then in this paper we first introduce the notion of a hom smash coproduct which is a monoidal hom coalgebra second we find sufficient and necessary conditions for the hom smash product algebra structure and the hom smash coproduct coalgebra structure on b h to afford b h a monoidal hom bialgebra structure generalizing the well known radford s biproduct where the conditions are equivalent to that b is a bialgebra in the category of hom yetter drinfeld modules hydhh finally we illustrate the category of hom yetter drinfeld modules hydhh and prove that the category hydhh is a braided monoidal category

hom l r smash products hom diagonal crossed products and the drinfeld double of a hom hopf algebra abstract we introduce the hom analogue of the l r smash product and use it to define the hom analogue of the diagonal crossed product when h is a finite dimensional hom hopf algebra with bijective antipode and bijective structure map we define the drinfeld double of h its algebra structure is a hom diagonal crossed product and it has all expected properties namely it is quasitriangular and modules over it coincide with left right yetter drinfeld modules over h

optimal designs for estimating individual coefficients in fourier regression models in the common trigonometric regression model we investigate the optimal design problem for the estimation of the individual coefficients where the explanatory variable varies in the interval a a 0 a le pi it is demonstrated that the structure of the optimal design depends sensitively on the size of the design space for many important cases optimal designs can be found explicitly where the complexity of the solution depends on the value of the parameter a and the order of the term for which the corresponding coefficient has to be estimated the main tool of our approach is the reduction of the problem for the trigonometric regression model to a design problem for a polynomial regression in particular we determine the optimal designs for estimating the parameters corresponding to the cosine terms explicitly if the design space is sufficiently small and prove that under this condition all optimal designs for estimating the parameters corresponding to the sine terms are supported at the same points

optimal weights for experimental designs on linearly independent support points an explicit formula is derived to compute the a optimal design weights on linearly independent regression vectors for the mean parameters in a linear model with homoscedastic variances the formula emerges as a special case of a general result which holds for a wide class of optimality criteria there are close links to iterative algorithms for computing optimal weights

on hom algebras with surjective twisting abstract a hom associative structure is a set a together with a binary operation and a self map such that an twisted version of associativity is fulfilled in this paper we assume that is surjective we show that in this case under surprisingly weak additional conditions on the multiplication the binary operation is a twisted version of an associative operation as an application an earlier result fregier and gohr 1 on weakly unital hom algebras is recovered with a different proof in the second section consequences for the deformation theory of hom algebras with surjective twisting map are discussed

constructing new braided t categories over monoidal hom hopf algebras let autmhh h denote the set of all automorphisms of a monoidal hopf algebra h with bijective antipode in the sense of caenepeel and goyvaerts monoidal hom hopf algebras commun algebra 39 2216 2240 2011 and let g be a crossed product group autmhh h autmhh h the main aim of this paper is to provide new examples of braided t category in the sense of turaev crossed group categories arabian j sci eng sect c 33 2c 483 503 2008 for this purpose we first introduce a class of new categories mhydhh a b of a b yetter drinfeld hom modules with a b autmhh h then we construct a category mhyd h mhydhh a b a b g and show that such category forms a new braided t category generalizing the main constructions by panaite and staic generalized anti yetter drinfel d modules as components of a braided t category isr j math 158 349 366 2007 finally we compute an explicit new example of such braided t categories

symmetries and the u condition in hom yetter drinfeld categories let h s be a monoidal hom hopf algebra and hydhh the hom yetter drinfeld category over h then in this paper we first find sufficient and necessary conditions for hydhh to be symmetric and pseudosymmetric respectively second we study the u condition in hydhh and show that the hom yetter drinfeld module h adjoint resp h m coadjoint satisfies the u condition if and only if s2 id finally we prove that hydhh over a triangular resp cotriangular hom hopf algebra contains a rich symmetric subcategory

quasi periodic solutions of hamiltonian perturbations of 2d linear schrodinger equations the general problem discussed here is the persistency of quasi periodic solutions of linear or integrable equations after hamiltonian perturbation this subject is closely related to the well known kam theory of invariant tori in smooth dynamical systems the main source of new difficulties is the fact that one considers here finite dimensional tori in an infinite dimensional phase space for instance already in the study of time periodic solutions the fact that the phase space is infinite dimensional leads to small divisor problems now the standard kam technology may be reworked in a form applicable to treat persistency problems in space dimension 1d in the case of dirichlet boundary conditions say where in particular the normal frequencies of the problem are well separated results along this line were obtained by s kuksin ki and c e wayne w among other works we mentioned ki as the main expository reference for the kam approach considering pde s in id with periodic boundary conditions and especially in space dimension 1 a significant new problem arises due to the presence of clusters of normal frequencies

weak hopf algebras with projection and weak smash bialgebra structures abstract in this paper we study weak hopf algebras with projection if f h b g b h are morphisms of weak hopf algebras such that g f idh we prove that it is possible to find an object bh in the new category of weak yetter drinfeld modules that verifies similar conditions to the ones include in the definition of weak hopf algebra finally we define weak smash bialgebra structures and prove that under central and cocentral conditions bh and h determine an example of them

the usefulness of optimum experimental designs optimum experimental designs were originally developed by kiefer mainly for response surface models this survey of recent developments emphasizes potential or actual usefulness for linear models the construction of exact designs particularly over irregular design regions is stressed as is the blocking of response surface designs other important areas include systematic designs that are robust against trend and designs for mixtures with irregular design regions several industrial examples are mentioned both d and c optimum designs are found for a non linear model of the economic response of cereal production to fertilizer level the c optimum design being for the conditions of maximum economic return locally optimum and bayesian designs are both described similar results for generalized linear models lead to designs for the ld 95 in a logistic model in which male and female subjects respond differently designs with structure in the variance suggest alternatives to the potentially wasteful product designs of taguchi designs for sequential clinical trials to include random balance are presented the last section outlines some applications including life testing and models in which time is a factor

quasi periodic solutions of nonlinear beam equation with prescribed frequencies consider the one dimensional nonlinear beam equation utt uxxxx mu u3 0 under dirichlet boundary conditions we show that for any m 0 but a set of small lebesgue measure the above equation admits a family of small amplitude quasi periodic solutions with n dimensional diophantine frequencies these diophantine frequencies are the small dilation of a prescribed diophantine vector the proofs are based on an infinite dimensional kolmogorov arnold moser iteration procedure and a partial birkhoff normal form

on the classification of finite dimensional pointed hopf algebras we classify finite dimensional complex hopf algebras a which are pointed that is all of whose irreducible comodules are one dimensional and whose group of group like elementsg a is abelian such that all prime divisors of the order of g a are 7 since these hopf algebras turn out to be deformations of a natural class of generalized small quantum groups our result can be read as an axiomatic description of generalized small quantum groups

optimal designs for a class of nonlinear regression models for a broad class of nonlinear regression models we investigate the local e and c optimal design problem it is demonstrated that in many cases the optimal designs with respect to these optimality criteria are supported at the chebyshev points which are the local extrema of the equi oscillating best approximation of the function f 0 0 by a normalized linear combination of the regression functions in the corresponding linearized model the class of models includes rational logistic and exponential models and for the rational regression models the e and c optimal design problem is solved explicitly in many cases

optimum experimental designs for properties of a compartmental model summary three properties of interest in bioavailability studies using compartmental models are the area under the concentration curve the maximum concentration and the time to maximum concentration methods are described for finding designs that minimize the variance of the estimates of these quantities in such a model these methods use prior information both prior estimates and prior distributions are used the designs for an open one compartment model are compared with the corresponding d optimum design for all parameters and also with designs that minimize the sum of the scaled variances of the individual properties

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 the existence of sobolev quasi periodic solutions of multidimensional nonlinear beam equation in this paper we prove the existence of quasi periodic solutions of the multidimensional nonlinear beam equation with finitely differentiable nonlinearities and quasi periodic forcing in time

quasi periodic solutions for d dimensional beam equation with derivative nonlinear perturbation in this paper we consider the d dimensional beam equation with convolution potential under periodic boundary conditions we will apply the kolmogorov arnold moser theorem in eliasson and kuksin ann math 172 371 435 2010 into this system and obtain that for sufficiently small e there is a large subset s of s such that for all s s the solution u of the unperturbed system persists as a time quasi periodic solution which has all lyapunov exponents equal to zero and whose linearized equation is reducible to constant coefficients

kam for the nonlinear schrodinger equation we consider the d dimensional nonlinear schrodinger equation under periodic boundary conditions i dot u delta u v x u ep frac p f p bar u x u bar u quad u u t x x in t d where v x sum hat v a e i sc a x is an analytic function with hat v real and f is a real analytic function in re u im u and x this equation is a popular model for the real nls equation where instead of the convolution term v u we have the potential term vu for ep 0 the equation is linear and has time quasi periodic solutions u u t x sum a in a hat u a e i a 2 hat v a t e i sc a x quad hat u a 0 where a is any finite subset of z d we shall treat omega a a 2 hat v a a ina as free parameters in some domain u subset r a this is a hamiltonian system in infinite degrees of freedom degenerate but with external parameters and we shall describe a kam theory which under general conditions will have the following consequence if ep is sufficiently small then there is a large subset u of u such that for all omega in u the solution u persists as a time quasi periodic solution which has all lyapounov exponents equal to zero and whose linearized equation is reducible to constant coefficients

logarithmic sobolev inequalities for information measures for alpha ges 1 the new vajda type information measure j alpha x is a quantity generalizing fisher s information fi to which it is reduced for alpha 2 in this paper a corresponding generalized entropy power n alpha x is introduced and the inequality n alpha x j alpha x ges n is proved which is reduced to the well known inequality of stam for alpha 2 the cases of equality are also determined furthermore the blachman stam inequality for the fi of convolutions is generalized for the vajda information j alpha x and both families of results in the context of measure of information are discussed that is logarithmic sobolev inequalities lsis are written in terms of new more general entropy type information measure and therefore new information inequalities are arisen this generalization for special cases yields to the well known information measures and relative bounds