q deformed chern characters for quantum groups suq n in this paper we introduce an n n matrix eab in the quantum groups suq n to transform the conjugate representation into the standard form so that we are able to compute the explicit forms of the important quantities in the bicovariant differential calculus on suq n such as the q deformed structure constant ckij and the q deformed transposition operator from the q gauge covariant condition we study the generalized q deformed killing form and construct the mth q deformed chern class pm for the quantum groups suq n in terms of the q deformed homotopy operator we are able to compute the q deformed chern simons q2m 1 by the condition dq2m 1 pm furthermore the q deformed cocycle hierarchy the q deformed gauge covariant lagrangian and the q deformed yang mills equation are derived

rotationally symmetric p harmonic maps from d2 to s2 we consider rotationally symmetric p harmonic maps from the unit disk d2 r2 to the unit sphere s2 r3 subject to dirichlet boundary conditions and with 1 p we show that the associated energy functional admits a unique minimizer which is of class c in the interior and c1 up to the boundary we also show that there exist infinitely many global solutions to the associated euler lagrange equation and we completely characterize them

logarithmically improved regularity criterion for the harmonic heat flow and related equations abstract we use an interpolation inequality on besov spaces to show a logarithmically improved regularity criterion for the harmonic heat flow the landau lifshitz equations and the landau lifshitz maxwell system

on the formation of singularities in the critical o 3 sigma model we study the phenomena of energy concentration for the critical o 3 sigma model also known as the wave map flow from 2 1 minkowski space into the sphere s 2 we establish rigorously and constructively existence of a set of smooth initial data resulting in a dynamic finite time formation of singularities the construction and analysis are done in the context of the k equivariant symmetry reduction and we restrict to maps with homotopy class k 4 the concentration mechanism we uncover is essentially due to a resonant self focusing shrinking of a corresponding harmonic map we show that the phenomenon is generic e g in certain sobolev spaces in that it persists under small perturbations of initial data while the resulting blowup is bounded by a log modified self similar asymptotic

elliptic equations strongly degenerate at a point abstract in this paper we will mainly propose some problems for a class of degenerate elliptic equations either linear or nonlinear we will study some special cases of these problems and reveal some phenomena which may not have been noticed previously our problems originated from the self similar solutions of the heat flow of harmonic maps we will prove that the self similar solutions or the so called quasi harmonic spheres are discontinuous at infinity for the equivariant case in other words the equivariant quasi harmonic spheres are not continuous images of topological spheres

nonuniqueness for the heat flow of harmonic maps on the disk we prove that for suitable initial data the heat flow of harmonic maps from the disk to the sphere admits infinitely many solutions characterised by backward bubbling at some arbitrarily large time all having uniformly bounded energy

finite element approximations of harmonic map heat flows and wave maps into spheres of nonconstant radii we prove the existence of weak solutions to the harmonic map heat flow and wave maps into spheres of nonconstant radii weak solutions are constructed as proper limits of iterates from a fully practical scheme based on lowest order conforming finite elements where discrete lagrange multipliers are employed to exactly meet the sphere constraint at mesh points computational studies are included to motivate interesting dynamics in two and three spatial dimensions

integrability of rotationally symmetric n harmonic maps abstract a rotationally symmetric n harmonic map is a rotationally symmetric p harmonic map between two n dimensional model spaces such that p n we show that rotationally symmetric n harmonic maps can be integrated and are n harmonic diffeomorphism and apply such results to investigate the asymptotic behaviors of these maps we also derive this integrability using lie theory

homotopy classes of harmonic maps of the stratified 2 spheres and applications to geometric flows abstract we show that the set of harmonic maps from the 2 dimensional stratified spheres with uniformly bounded energies contains only finitely many homotopy classes we apply this result to construct infinitely many harmonic map flows and mean curvature flows of 2 sphere in the connected sum of two closed 3 dimensional manifolds m 1 s 3 and m 2 s 3 r p 3 which must develop finite time singularity

on collapse of wave maps abstract we derive the universal collapse law of degree 1 equivariant wave maps solutions of the sigma model from the 2 1 minkowski space time to the 2 sphere to this end we introduce a nonlinear transformation from original variables to blowup ones our formal derivations are confirmed by numerical simulations

optimal design for elisa and other forms of immunoassay in enzyme linked immunosorbent assay elisa as well as in many other kinds of immunoassay a log logistic or similar shaped calibration curve is fit using standards at a series of known levels and then used to transform the measured values for the unknowns into estimated concentrations the choice of the number of standards the concentration of the standards and the number of replicates of the standards and of the unknowns all affect the precision of the measurement this article develops an optima1 design paradigm for this type of problem and shows how optimal choices can be calculated so that the system achieves the maximum precision of which it is capable although exact calculation of optimal designs requires use of a computer program close approximations to the optimum can be derived from simple rules for hand calculation

finite time blow up for the yang mills heat flow in higher dimensions we consider the l 2 gradient flow associated with the yang mills functional the so called yang mills heat flow in the setting of a trivial principal so n bundle over mathbb r n in dimension n greater than 4 we show blow up in finite time for a class of so n equivariant initial connections

le langage des espaces et des groupes quantiques we study the foundations of the differential calculus in quantum geometry the notions of differential quantum space and cone are introduced generalizing a construction of manin to a quantum cone we associate the quantum group of its linear automorphisms preserving the differentials and deduce a de rham complex on this group we give examples of differential calculi on quantum hyperplanes and quantum linear groups

singularity formation for the two dimensional harmonic map flow into s 2 we construct finite time blow up solutions to the 2 dimensional harmonic map flow into the sphere s 2 begin aligned u t delta u nabla u 2 u quad text in omega times 0 t u varphi quad text on partial omega times 0 t u cdot 0 u 0 quad text in omega end aligned where omega is a bounded smooth domain in mathbb r 2 u omega times 0 t rightarrow s 2 u 0 bar omega rightarrow s 2 is smooth and varphi u 0 big partial omega given any k points q 1 ldots q k in the domain we find initial and boundary data so that the solution blows up precisely at those points the profile around each point is close to an asymptotically singular scaling of a 1 corotational harmonic map we build a continuation after blow up as a h 1 weak solution with a finite number of discontinuities in space time by reverse bubbling which preserves the homotopy class of the solution after blow up furthermore we prove the codimension one stability of the one point blow up phenomenon

robust optimum designs for transformation of the responses in a multivariate chemical kinetic model transformation of both sides of a nonlinear model is often necessary to obtain tractable error distributions but can have a dramatic effect on optimum designs for the parameters of the model this article develops methods for the design of experiments when the value of the power transformation parameter is not precisely known optimum designs for particular transformations together with the efficiency of these designs as the transformation varies are studied for a multivariate model it is shown that by a suitable choice of prior bayesian designs can be found that are robust to the correct transformation a typical equispaced design is evaluated and the properties of designs are studied under various departures from the assumptions

convergence of an implicit constraint preserving finite element discretization of p harmonic heat flow into spheres we propose an implicit discretization of the p harmonic map heat flow into the sphere s 2 that enjoys a discrete energy inequality and converges under only a mild mesh constraint to a weak solution a fully practical iterative scheme that approximates the solution of the nonlinear system of equations in each time step is proposed and analyzed computational studies to motivate possible finite time blow up behavior of solutions for p 2 are included

regularity and existence of global solutions to the ericksen leslie system in mathbb r 2 in this paper we first establish the regularity theorem for suitable weak solutions to the ericksen leslie system in mathbb r 2 building on such a regularity we then establish the existence of a global weak solution to the ericksen leslie system in mathbb r 2 for any initial data in the energy space under the physical constraints on the leslie coefficients ensuring the dissipation of energy of the system which is smooth away from at most finitely many times this extends earlier works by lin et al arch ration mech anal 197 297 336 2010 on a simplified nematic liquid crystal flow to the general ericksen leslie system

differential calculus on compact matrix pseudogroups quantum groups the paper deals with non commutative differential geometry the general theory of differential calculus on quantum groups is developed bicovariant bimodules as objects analogous to tensor bundles over lie groups are studied tensor algebra and external algebra constructions are described it is shown that any bicovariant first order differential calculus admits a natural lifting to the external algebra so the external derivative of higher order differential forms is well defined and obeys the usual properties the proper form of the cartan maurer formula is found the vector space dual to the space of left invariant differential forms is endowed with a bilinear operation playing the role of the lie bracket commutator generalized antisymmetry relation and jacobi identity are proved

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

quantum group gauge theory on quantum spaces we construct quantum group valued canonical connections on quantum homogeneous spaces including aq deformed dirac monopole on the quantum sphere of podles with quantum differential structure coming from the 3d calculus of woronowicz onsu q 2 the construction is presented within the setting of a general theory of quantum principal bundles with quantum group hopf algebra fibre associated quantum vector bundles and connection one forms both the base space spacetime and the total space are non commutative algebras quantum spaces

convergent discretization of heat and wave map flows to spheres using approximate discrete lagrange multipliers we propose fully discrete schemes to approximate the harmonic map heat flow and wave maps into spheres the finite element based schemes preserve a unit length constraint at the nodes by means of approximate discrete lagrange multipliers satisfy a discrete energy law and iterates are shown to converge to weak solutions of the continuous problem comparative computational studies are included to motivate finite time blow up behavior in both cases

quantum group covariant noncommutative geometry an algebraic formulation of the quantum group covariant noncommutative geometry in the framework of the r matrix approach to the theory of quantum groups is given structure groups are considered taking values in the quantum groups the notion of noncommutative connections and curvatures is introduced transforming as comodules under the local coaction of the structure group that is an exterior extension of glq n these noncommutative connections and curvatures generate glq n covariant quantum algebras for these algebras combinations of generators are found which are coinvariants under the local coaction of the exterior extension of the quantum group and one can formally consider these coinvariants as noncommutative images of the lagrangians for the topological chern simons models non abelian gauge theories and the einstein gravity also an explicit realization of such covariant quantum algebras is presented via the investigation of the coset construction glq n 1 glq n glq 1

global solutions to the 3d incompressible nematic liquid crystal system abstract in this paper we consider the global well posedness of the cauchy problem of the 3d incompressible nematic liquid crystal system with initial data in the critical besov space b 2 1 1 2 r 3 b 2 1 3 2 r 3 in particular we prove that there exists a positive constant c 0 such that the nematic liquid crystal system has a unique global solution with initial data u 0 d 0 u 0 h u 0 3 d 0 which satisfies 1 1 d 0 d 0 b 2 1 3 2 1 u 0 h b 2 1 1 2 exp c 0 2 u 0 3 b 2 1 1 2 1 2 c 0 for some c 0 sufficiently small where d 0 is a constant vector with d 0 1 here and are two positive viscosity constants

global solution to the 3 d density dependent incompressible flow of liquid crystals abstract in this paper we consider the global wellposedness of the 3 d density dependent incompressible flow of liquid crystals in the critical besov spaces we first get the local solution for this system without assumptions of small density variation and then extend this local solution to be global under the smallness assumptions on initial density initial orientation field and the horizontal components of the initial velocity field this result implies the global well posedness of this system with large initial vertical velocity component

on a hyperbolic parabolic system arising in magnetoelasticity the evolution of a magnetoelastic material is described by a nonlinear hyperbolic parabolic system we introduce a simplified but nontrivial model and prove the existence of a unique solution to the corresponding initial boundary value problem

on the nonexistence of finite time bubble trees in symmetric harmonic map heat flows from the disk to the 2 sphere abstract let b 2 r 2 and s 2 r 3 be the unit disk and the unit sphere and let v b 2 r s 2 be a radially symmetric harmonic map heat flow whose singularities coincide with downward energy jumps then its finite time singularities are simple in the sense that precisely one harmonic sphere separates at a time

constraint preserving implicit finite element discretization of harmonic map flow into spheres discretization of the harmonic map flow into spheres often uses a penalization or projection strategy where the first suffers from the proper choice of an additional parameter and the latter from the lack of a discrete energy law and restrictive mesh constraints we propose an implicit scheme that preserves the sphere constraint at every node enjoys a discrete energy law and unconditionally converges to weak solutions of the harmonic map heat flow

a convergent and constraint preserving finite element method for the p harmonic flow into spheres an explicit fully discrete finite element method which satisfies the nonconvex side constraint at every node is developed for approximating the p harmonic flow for p in 1 infty convergence of the method is established under certain conditions on the domain and mesh computational examples are presented to demonstrate finite time blow ups and qualitative geometric changes of weak solutions of the p harmonic flow

on the blow up of heat flow for conformal 3 harmonic maps using a comparison theorem chang ding and ye 1992 proved a finite time derivative blow up for the heat flow of harmonic maps from d 2 a unit ball in r 2 to s 2 a unit sphere in r 3 under certain initial and boundary conditions we generalize this result to the case of 3 harmonic map heat flow from d 3 to s 3 in contrast to the previous case our governing parabolic equation is quasilinear and degenerate technical issues such as the development of a new comparison theorem have to be resolved

t g t a toy model for conformal field theory we study a chiral operator algebra of conformal field theory and quantum deformation of the finite dimensional lie group to obtain the definition of t g t and its representation the closeness of the kac moody algebras constituting the chiral operator algebra of a typical and generic conformal field theory model namely the wznw model and quantum deformation of corresponding finite dimensional lie groupg has become more and more evident in recent years 1 5 this in particular prompts further investigation of the differential geometry of such deformations the notion of tangent and cotangent bundles is basic in classical differential geometry it is only natural that the quantum deformations oftg andt g are to be introduced alongside those forg itself physical ideas could be useful for this goal indeed thet g can be interpreted as a phase space for a kind of a top generalizing the usual top associated withg so 3 the classical mechanics is a natural language to describe differential geometry whereas the usual quantization is nothing but the representation theory in this paper we put corresponding formulas in such a fashion that their deformation becomes almost evident given the experience in this domain as a result we get the definition of t g t and its representation t is the deformation parameter to make the exposition most simple and formulas transparent we shall work on an example ofg sl 2 and present results in such a way that the generalizations become evident we shall stick to generic complex versions real and especially compact forms requiring some additional consideration not all of which are self evident

brownian motion and the formation of singularities in the heat flow for harmonic maps we develop a general framework for a stochastic interpretation of certain nonlinear pdes on manifolds the linear operation of takin expectations is replaced by the concept of martingale means namely the notion of deterministic starting points of martingales with respect to the levi civita connection ending up at a prescribed state we formulate a monotonicity condition for the riemannian quadratic variation of such martingales that allows us to turn smallness of the quadratic variation into a priori gradient bounds for solutions of the nonlinear heat equation such estimates lead to simple criteria for blow ups in the nonlinear heat flow for harmonic maps with small initial energy

a weak energy identity and the length of necks for a sequence of sacks uhlenbeck α harmonic maps abstract in this paper we discuss the convergence behavior of a sequence of harmonic maps u with e u c from a compact surface m g into a compact riemannian manifold n h without boundary generally such a sequence converges weakly to a harmonic map in w 1 2 m n and strongly in c away from a finite set of points in m if energy concentration phenomena appears we show a generalized energy identity and discover a direct convergence relation between the blow up radius and the parameter which ensures the energy identity and no neck property we show that the necks converge to some geodesics moreover in the case there is only one bubble a length formula for the neck is given in addition we also give an example which shows that the necks contain at least a geodesic of infinite length

finite time singularity of the nematic liquid crystal flow in dimension three in this paper we consider the initial and boundary value problem of a simplified nematic liquid crystal flow in dimension three and construct two examples of finite time singularity the first example is constructed within the class of axisymmetric solutions while the second example is constructed for any generic initial data u 0 d 0 that has sufficiently small energy and d 0 has a nontrivial topology

diffusion of general data on non flat manifolds viaharmonic maps theory the direction diffusion case in a number of disciplines directional data provides a fundamental source of information a novel framework for isotropic and anisotropic diffusion of directions is presented in this paper the framework can be applied both to denoise directional data and to obtain multiscale representations of it the basic idea is to apply and extend results from the theory of harmonic maps and in particular harmonic maps in liquid crystals this theory deals with the regularization of vectorial data while satisfying the intrinsic unit norm constraint of directional data we show the corresponding variational and partial differential equations formulations for isotropic diffusion obtained from an l 2 norm and edge preserving diffusion obtained from an l norm in general and an l 1 norm in particular in contrast with previous approaches the framework is valid for directions in any dimensions supports non smooth data and gives both isotropic and anisotropic formulations in addition the framework of harmonic maps here described can be used to diffuse and analyze general image data defined on general non flat manifolds that is functions between two general manifolds we present a number of theoretical results open questions and examples for gradient vectors optical flow and color images

a further note on the regularity criterion for the 3d nematic liquid crystal flows we give a further investigation on the regularity criteria for the 3d nematic liquid crystal flows it is show that the obtained anisotropic integrability regularity criterion to the 3d nematic liquid crystal flows involving i u j i j 1 2 3 is an improvement of qian 2016 besides we also prove the solution is regular if some components of the velocity field and the vectorial field modeling the orientation of the crystal molecules satisfy the prodi serrin type conditions

energy non collapsing and refined blowup for a semilinear heat equation abstract refined structures of blowup for non collapsing maximal solution to a semilinear parabolic equation u t u u p 1 u with p 1 are studied we will prove that the blowup set is empty for non collapsing blowing up in subcritical case and all finite time non collapsing blowing up must be refined type ii in critical case when p p s n 2 n 2 for n 3 the hausdorff dimension of the blowup set for maximal solution whose energy is non collapsing is shown to be no greater than n 2 4 p 1 which answers a question proposed in 7 positively at the end of this paper we also present some new examples of collapsing and non collapsing blowups

asymptotic stability of harmonic maps under the schrodinger flow for schr odinger maps from r 2 r to the 2 sphere s 2 it is not known if finite energy solutions can form singularities blow up in finite time we consider equivariant solutions with energy near the energy of the two parameter family of equivariant harmonic maps we prove that if the topological degree of the map is at least four blowup does not occur and global solutions converge in a dispersive sense i e scatter to a fixed harmonic map as time tends to infinity the proof uses among other things a time dependent splitting of the solution the generalized hasimoto transform and strichartz dispersive estimates for a certain two space dimensional linear schr odinger equation whose potential has critical power spatial singularity and decay along the way we establish an energy space local well posedness result for which the existence time is determined by the length scale of a nearby harmonic map

global existence of the equivariant yang mills heat flow in four space dimensions we show that the yang mills heat flow of so 4 equivariant connections on an su 2 bundle over a ball in inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 01i admits a smooth solution for all time for any initial and boundary data of finite energy

liquid crystal flows in two dimensions this paper is concerned with a simplified hydrodynamic equation proposed by ericksen and leslie modeling the flow of nematic liquid crystals in dimension two we establish both interior and boundary regularity theorems for such a flow under smallness conditions as a consequence we establish the existence of global in time weak solutions on a bounded smooth domain in mathbb r 2 which are smooth everywhere with possible exceptions of finitely many singular times

a two component model for measurement error in analytical chemistry in this article we propose and test a new model for measurement error in analytical chemistry often the standard deviation of analytical errors is assumed to increase proportionally to the concentration of the analyte a model that cannot be used for very low concentrations for near zero amounts the standard deviation is often assumed constant which does not apply to larger quantities neither model applies across the full range of concentrations of an analyte by positing two error components one additive and one multiplicative we obtain a model that exhibits sensible behavior at both low and high concentration levels we use maximum likelihood estimation and apply the technique to toluene by gas chromatography mass spectrometry and cadmium by atomic absorption spectroscopy

yang baxter matrices and differential calculi on quantum hyperplanes it is shown that any invertible matrix r that solves the yang baxter equations generates a set of quantum hyperplanes where differential calculi can be defined the number of such quantum hyperplanes is given by the number of different eigenvalues of the matrix r several examples of two dimensional quantum hyperplanes and differential calculi are presented the relations of quantum hyperplanes and differential calculi are covariant wrt the quantum groups defined by the matrix r in the generic cases the exterior differential satisfies the condition d2 0

weighted random effects regression models with application to interlaboratory calibration in this article we present a general random effects regression model for the case of heteroscedastic measurement errors the model is both motivated by and illustrated with a problem from analytical chemistry in which measurement errors are constant for near zero concentrations and increase proportionally with higher concentrations the parameters of the calibration curve that relate instrument responses to true concentration are allowed to vary over laboratories the estimation of model parameters is accomplished by iteratively reweighted maximum marginal likelihood estimation properties of the method are examined in a limited simulation study and are applied to a typical interlaboratory calibration example for copper in distilled water we illustrate a few applications of the model that include 1 determining if an analyte is present in a new sample 2 approximate confidence bounds for true concentration given a new measurement and 3 determination of the minimum concentration that supports quant

numerical methods for the landau lifshitz equation we discuss numerical schemes for various forms of the landau lifshitz equation a new simple projection method is introduced and is shown to be unconditionally stable the advantages over other schemes are also demonstrated numerically

heat flow of yang mills higgs functionals in dimension two abstract we consider the heat flow of yang mills higgs functional where the base manifold is a riemannian surface and the fiber is a compact symplectic manifold we show that the corresponding cauchy problem admits a global weak solution for any h 1 initial data moreover the solution is smooth except for finitely many singularities we prove an energy identity at finite time singularities and give a description of the asymptotic behavior at time infinity

schrodinger flow near harmonic maps for the schrodinger flow from r 2 r to the 2 sphere s 2 it is not known if finite energy solutions can blow up in finite time we study equivariant solutions whose energy is near the energy of the family of equivariant harmonic maps we prove that such solutions remain close to the harmonic maps until the blowup time if any and that they blow up if and only if the length scale of the nearest harmonic map goes to 0 c 2006 wiley periodicals inc

long time existence for yang mills flow we establish that finite time singularities do not occur in four dimensional yang mills flow confirming the conjecture of schlatter et al am j math 120 117 128 1998 the proof relies on a weighted energy identity and sharp decay estimates in the neck region

stable blowup dynamics for the 1 corotational energy critical harmonic heat flow we exhibit a stable finite time blowup regime for the 1 corotational energy critical harmonic heat flow from 2 into a smooth compact revolution surface of 3 that reduces to the semilinear parabolic problem for a suitable class of functions f the corresponding initial data can be chosen smooth well localized and arbitrarily close to the ground state harmonic map in the energy critical topology we give sharp asymptotics on the corresponding singularity formation that occurs through the concentration of a universal bubble of energy at the speed predicted by van den berg hulshof and king our approach lies in the continuation of the study of the 1 equivariant energy critical wave map and schrodinger map with 2 target by merle raphael and rodnianski 2012 wiley periodicals inc

well posedness for the heat flow of harmonic maps and the liquid crystal flow with rough initial data we investigate the well posedness of 1 the heat flow of harmonic maps from mathbb r n to a compact riemannian manifold n without boundary for initial data in bmo and 2 the hydrodynamic flow u d of nematic liquid crystals on mathbb r n for initial data in bmo 1 bmo

remarks on the regularity criterion for the nematic liquid crystal flows in r 3 in this paper we investigate the regularity criteria for the 3d nematic liquid crystal flows in terms of the components of the velocity u or the gradient of the velocity field u more precisely the anisotropic integrability regularity criterion to the 3d nematic liquid crystal flows involving i u i 1 2 3 is obtained firstly and then it is proved that the solution is regular if u3 3 or 3u3 3 satisfies the prodi serrin type conditions

asymptotic stability concentration and oscillation in harmonic map heat flow landau lifshitz and schrodinger maps on mathbb r 2 we consider the landau lifshitz equations of ferromagnetism including the harmonic map heat flow and schrodinger flow as special cases for degree m equivariant maps from mathbb r 2 to mathbb s 2 if m 3 we prove that near minimal energy solutions converge to a harmonic map as t asymptotic stability extending previous work gustafson et al duke math j 145 3 537 583 2008 down to degree m 3 due to slow spatial decay of the harmonic map components a new approach is needed for m 3 involving among other tools a normal form for the parameter dynamics and the 2d radial double endpoint strichartz estimate for schrodinger operators with sufficiently repulsive potentials which may be of some independent interest when m 2 this asymptotic stability may fail in the case of heat flow with a further symmetry restriction we show that more exotic asymptotics are possible including infinite time concentration blow up and even eternal oscillation

strong solutions to the density dependent incompressible nematic liquid crystal flows abstract in this paper we investigate the density dependent incompressible nematic liquid crystal flows in n dimensional n 2 or 3 bounded domain the local existence and uniqueness of strong solutions are obtained when the viscosity coefficient of fluid depends on density furthermore one establishes blowup criterions for the regularity of the strong solutions in dimensions two and three respectively in particular we build a blowup criterion just in terms of the gradient of density if the initial direction field satisfies some geometric configuration for these results the initial density need not be strictly positive

change point models to estimate the limit of detection in many biological and environmental studies measured data is subject to a limit of detection the limit of detection is generally defined as the lowest concentration of analyte that can be differentiated from a blank sample with some certainty data falling below the limit of detection is left censored falling below a level that is easily quantified by a measuring device a great deal of interest lies in estimating the limit of detection for a particular measurement device in this paper we propose a change point model to estimate the limit of detection using data from an experiment with known analyte concentrations estimation of the limit of detection proceeds by a two stage maximum likelihood method extensions are considered that allow for censored measurements and data from multiple experiments a simulation study is conducted demonstrating that in some settings the change point model provides less biased estimates of the limit of detection than conventional methods the proposed method is then applied to data from an hiv pilot study

winding behaviour of finite time singularities of the harmonic map heat flow we settle a number of questions about the possible behaviour of the harmonic map heat flow at finite time singularities in particular we show that a type of nonuniqueness of bubbles can occur at finite time we show that the weak limit of the flow at the singular time can be discontinuous we determine exactly the polynomial rate of blow up in one particular example and we show that winding behaviour of the flow can lead to an unexpected failure of convergence when the flow is locally lifted to the universal cover of the target manifold

numerical analysis of an explicit approximation scheme for the landau lifshitz gilbert equation the landau lifshitz gilbert equation describes magnetic behavior in ferromagnetic materials construction of numerical strategies to approximate weak solutions for this equation is made difficult by its top order nonlinearity and nonconvex constraint in this paper we discuss necessary scaling of numerical parameters and provide a refined convergence result for the scheme first proposed by alouges and jaisson 2006 as an application we numerically study discrete finite time blowup in two dimensions

global existence and blow up for harmonic map heat flow abstract for degree one equivariant maps on bounded domains the question of finite time blow up vs global existence of solutions to the harmonic map heat flow has been well studied in this paper we study the cauchy problem for degree m equivariant harmonic map heat flow from 2 1 dimensional space time into the 2 sphere with initial energy close to the energy of harmonic maps it is proved that solutions are globally smooth for m 4 whereas for m 1 we show that finite time singularities can form for this class of data

q deformed poincare algebra theq differential calculus for theq minkowski space is developed the algebra of theq derivatives with theq lorentz generators is found giving theq deformation of the poincare algebra the reality structure of theq poincare algebra is given the reality structure of theq differentials is also found the real laplacian is constructed finally the comultiplication counit and antipode for theq poincare algebra are obtained making it a hopf algebra

heat flow of harmonic maps whose gradients belong to l n _ x l infty _ t for any compact n dimensional riemannian manifold m g without boundary a compact riemannian manifold n subset mathbb r k without boundary and 0 t we prove that for n 4 if u m 0 t n is a weak solution to the heat flow of harmonic maps such that nabla u in l n x l infty t m times 0 t then u c m 0 t n as a consequence we show that for n 3 if 0 t is the maximal time interval for the unique smooth solution u c m 0 t n of 1 1 then nabla u t l n m blows up as t t

on the evolution of harmonic maps in higher dimensions on etablit des resultats de regularite partielle et l existence de solutions regulieres globales pour le probleme d evolution pour des applications harmoniques avec des donnees petites

3d geometric scale variability in range images features and descriptors despite their ubiquitous presence little has been investigated about the scale variability the relative variations in the spatial extents of local structures of 3d geometric data in this paper we present a comprehensive framework for exploiting this 3d geometric scale variability in range images that provides rich information for characterizing the overall geometry we derive a sound scale space representation which we refer to as the geometric scale space that faithfully encodes the scale variability of the surface geometry and derive novel detectors to extract prominent features and identify their natural scales the result is a hierarchical set of features of different scales which we refer to as scale dependent geometric features we then derive novel local shape descriptors that represent the surface structures that give rise to those features by carving out and encoding the local surface that fall within the support regions of the features this leads to scale dependent or scale invariant local shape descriptors that convey significant discriminative information of the object geometry we demonstrate the effectiveness of geometric scale analysis on range images and show that it enables novel applications in particular fully automatic registration of multiple objects from a mixed set of range images and 3d object recognition in highly cluttered range image scenes

quantum and braided linear algebra quantum matrices a r are known for every r matrix obeying the quantum yang baxter equations it is also known that these act on vectors given by the corresponding zamalodchikov algebra this interpretation is developed in detail distinguishing between two forms of this algebra v r vectors and v r covectors a r v r21 v r is an algebra homomorphism i e quantum matrices are realized by the tensor product of a quantum vector with a quantum covector while the inner product of a quantum covector with a quantum vector transforms as a scaler it is shown that if v r and v r are endowed with the necessary braid statistics then their braided tensor product v r v r is a realization of the braided matrices b r introduced previously while their inner product leads to an invariant quantum trace introducing braid statistics in this way leads to a fully covariant quantum braided linear algebra the braided groups obtained from b r act on themselves by conjugation in a way impossible

a regularity criterion for the solution of nematic liquid crystal flows in terms of the b 1 norm abstract in this paper we investigate the regularity criterion for the solution of nematic liquid crystal flows in three dimensions n 3 and in two dimensions n 2 we prove that the solution u d is smooth up to time t provided that there exists a positive constant e 0 0 such that i for n 3 u d l 0 t b 1 e 0 and ii for n 2 d l 0 t b 1 e 0

singularities of first kind in the harmonic map and yang mills heat flows by constructing examples which are explicit up to solving an ode we prove that singularities of first kind exist for the harmonic map and yang mills heat flows as a by product we also get a simplified proof of ratto s ding s theorem about the existence of harmonic hopf constructions

confidence regions for random effects calibration curves with heteroscedastic errors we construct confidence bounds for a random effects calibration curve model an example application is analysis of analytical chemistry data in which the calibration curve contains measurements y for several values of known concentration x in each of q laboratories laboratory is considered a random effect in this design and the intercept and slope of the calibration curve are allowed to have laboratory specific values here we a develop an appropriate interlaboratory calibration curve for heteroscedastic data of the type commonly observed in analytical chemistry b compute a point estimate for an unknown true concentration x when corresponding measured concentrations y1 y2 yq are provided from q laboratories i e a subset of the original q laboratories used to calibrate the model where 1 q q c compute the asymptotic mean and variance of the estimate and d construct a confidence region for x we then illustrate the methods are using both simulated and typical interlaboratory calib

covariant differential complexes on quantum linear groups we consider the possible covariant external algebra structures for cartan s 1 forms omega on glq n and slq n our starting point is that the omega realize an adjoint representation of quantum group and all monomials of the omega possess the unique ordering for the external algebras obtained define the differential mapping d possessing the usual nilpotence condition and the generally deformed version of the leibnitz rules the status of the known examples of glq n differential calculi in the proposed classification scheme and the problems of slq n reduction are discussed