sequences of willmore surfaces in this paper we develop the theory of willmore sequences for willmore surfaces in the 4 sphere we show that under appropriate conditions this sequence has to terminate in this case the willmore surface either is the twistor projection of a holomorphic curve into mathbb c mathbb p 3 or the inversion of a minimal surface with planar ends in mathbb r 4 these results give a unified explanation of previous work on the characterization of willmore spheres and willmore tori with non trivial normal bundles by various authors

harmonic maps into the orthogonal group and null curves we find algebraic parametrizations of extended solutions of harmonic maps of finite uniton number from a surface to the orthogonal group mathrm o n in terms of free holomorphic data which lead to formulae for all such harmonic maps our work reveals an interesting correspondence between certain harmonic maps and the free weierstrass representation of null curves and minimal surfaces in 3 and 4 space

on the decay of solutions for porous elastic systems with history in this paper we study the asymptotic behavior to an one dimensional porous elasticity problem with history we show the lack of exponential stability when the porous dissipation or the elastic dissipation is absent and we show the lack of analyticity and exponential stability when the porous viscosity and the elastic dissipation are present

analyticity in porous thermoelasticity with microtemperatures abstract in this note we study the analyticity of the solutions to the one dimensional porous elasticity problem with temperatures and microtemperatures when viscoelasticity and porous viscosity effects are also present we show the lack of analyticity when the porous dissipation is weak and the analyticity when it is strong

exponential decay of solutions in type ii porous thermo elasticity with quasi static microvoids abstract in this note we study the problem proposed by the one dimensional thermo porous elasticity of type ii with quasi static microvoids or in mathematical terms when the second time derivative of the volume fraction is so small that it can be negligible it is known that the isothermal deformations decay in a slow way here we prove that the introduction of a conservative mechanism as it is the type ii heat conduction makes the deformations damp generically in an exponential way which is a striking fact

on the time polynomial decay in elastic solids with voids in this paper we investigate the temporal decay behavior of the solutions of the one dimensional problem in various theories of continua with voids it has been proved that the coupling of the elastic structure with porous microstructure is weak in the sense that in many situations the temporal decay of solutions is slow we have considered some theories of porous continua when the deformation rate tensor or time rate or porosity function or thermal effects is present we have proved that the decay cannot be controlled by a negative exponential the natural question now is whether there exist or not a polynomial rate of decay of the solution in some appropriate norms in this paper we consider some cases where the decay is slow and we obtain polynomial decay estimates in concrete we consider the case when only the viscoelastic effect is present the case when the motion of voids is assumed to be quasi static and the porous viscosity is present and we finish with the case of the porous elasticity when thermal effect is coupled

the construction of harmonic maps into complex grassmannians on developpe une technique d analyse des applications harmoniques d une surface de riemann dans un grassmannien complexe en utilisant des diagrammes qui etablissent plusieurs resultats

rigidity of pseudo holomorphic curves of constant curvature in grassmann manifolds rigidity of minimal immersions of constant curvature in harmonic sequences generated by holomorphic curves in grassmann manifolds is studied in this paper by lifting them to holomorphic curves in certain projective spaces we prove that for such curves the curvature must be positive and that all such simply connected curves in cp are generated by veronese curves thus generalizing calabi s counterpart for holomorphic curves in cp we also classify all holomorphic curves from the riemann sphere into g 2 4 whose curvature is equal to 2 into two families which illustrates pseudo holomorphic curves of positive constant curvature in g m n are in general not unitarily equivalent constracting to the fact that generic isometric complex submanifolds in a kaehler manifold are congruent where f x dfi for j 0 1 2 and f m c7 w n are harmonic maps one defines mj x 0 if f is anti holomorphic we call fr a pseudo holomorphic curve of position r generated by when is holomorphic where is called the directrix of fr such curves with the induced metrics from the associated grassmannians form a class of minimal immersions when special ized to g l n i cp a pseudo holomorphic curve of position r is just the r th position vector of a frenet frame of a holomorphic curve projected into cp the importance of such maps comes from the fact that any har monic map from the riemann sphere or any harmonic map of nonzero degree from a torus into cp is pseudo holomorphic 7 furthermore in 6 these curves play a central role when m s defined in the sequence 0 1 are all equal and f s are orthogonal called frenet harmonic sequences for the study of

exponential decay in one dimensional type ii thermoviscoelasticity with voids abstract in this paper we consider the one dimensional type ii thermoviscoelastic theory with voids we prove that generically we have exponential stability of the solutions this is a striking fact if one compares it with the behavior in the case of the classical thermoviscoelastic theory based on the classical fourier law for which the decay is generically slower

on the time decay of solutions in porous elasticity with quasi static microvoids in this paper we investigate the temporal asymptotic behavior of the solutions of the one dimensional porous elasticity problem with porous dissipation when the motion of microvoids is assumed to be quasi static this question has been recently studied in the general dynamical case thus the natural question is to know if the assumption of quasi static motion for the microvoids implies significant differences in the behavior of the solutions from the results obtained in the general dynamical case it is worth noting that this assumption involves a qualitative change in the system of equations to be analyzed because it arises from the combination of a parabolic equation with an hyperbolic one rather different from the well known system of the thermo elastic problem first we study the coupling of elasticity with porosity and we show that if only porous dissipation is present the decay of solutions is slow but if viscoelasticity is added then the solutions decay exponentially after that we introduce thermal effects in the system and we show that while temperature brings exponential stability to the solutions microtemperature does not

studies in the history of probability and statistics xlviii the bayesian contributions of ernest lhoste summary the contributions of ernest lhoste are largely unknown outside france and even within that country are not well known his important contributions were in the two areas of the development of prior distributions that represent little or no information and a sophisticated posterior analysis for normal and binomial populations his results are similar to those of haldane 1948 and jeffreys 1961 but they appeared much earlier in 1923 he gave a great deal of thought to how to represent vague prior knowledge and his results represent a significant and unique contribution to bayesian ideas in the early part of the 20th century

an a priori error analysis of poro thermoviscoelastic problems abstract in this paper we study from the numerical point of view a dynamic one dimensional problem arising in thermoelasticity and thermoviscoelasticity of types ii and iii porosity is also included into the models the generic variational formulation leads to a coupled system written in terms of the velocity the volume fraction speed and the temperature fully discrete approximations are then introduced by using the finite element method and the implicit euler scheme a discrete stability property and a priori error estimates are proved finally some numerical examples are presented to demonstrate the numerical convergence of the algorithm the exponential decay of the discrete energy and the behavior of the solution

optimal decay for a porous elasticity system with memory abstract in this paper we consider a one dimensional linear porous system with finite memory effective on the equilibrated stress vector by assuming minimal conditions on the relaxation function we establish an optimal explicit and energy decay rate for which exponential and polynomial rates are special cases this result is new and substantially improves earlier results in the literature

tournaments flags and harmonic maps twistor space constructions have shown that under quite general hypotheses harmonic maps of riemann surfaces into riemannian manifolds can be represented by holomorphic curves with respect to almost complex structures which are often non integrable see for example 19 17 5 for maps into complex grassmannians the almost complex structures are invariant ones on flag manifolds and can be identified with tournaments i e digraphs in which any two nodes are joined by exactly one oriented edge elementary properties of tournaments are summarised in sect i the basic references are moon 14 and reid and beineke 18 emphasis is given to certain types of tournament which are interpreted in sect 2 in terms of the homogeneous structure of complex flag manifolds holomorphic curves in such flag manifolds are described in sect 3 by collections of subbundles of a trivial bundle over a riemann surface whose second fundamental forms define a tournament this approach relies on techniques of burstall and wood 6 and gives rise naturally to harmonic maps into grassmannians when the riemann surface has genus zero a result from algebraic geometry namely the birkhoff grothendieck decomposition theorem for holomorphic vector bundles fits into the scheme and allows one to reconstruct a tournament from a harmonic map into a grassmannian in sect 4 we use such techniques to show that harmonic maps of tl2p 1 into a complex grassmannian can be built up successively from holomorphic data this last result extends results of burstall and wood 6 and is closely related to recent work of uhlenbeck 21 and wolfson 23

student t tests for potentially abnormal data when the one sample or two sample t test is either taught in the class room or applied in practice to small samples there is considerable divergence of opinion as to whether or not the inferences drawn are valid many point to the robustness of the t test to violations of assumptions while others use rank or other robust methods because they believe that the t test is not robust against violations of such assumptions it is quite likely despite the apparent divergence of these two opinions that both arguments have considerable merit if we agree that this question cannot possibly be resolved in general the issue becomes one of determining before any actual data have been collected whether the t test will or will not be robust in a specific application this paper describes statistical analysis system software covering a large collection of potential input probability distributions to investigate both the null and power properties of various one and two sample t tests and their normal approximations as well as the wilcoxon two sample and sign rank one sample tests allowing potential practitioners to determine at the study design stage whether the t test will be robust in their specific application sample size projections based on these actual distributions are also included this paper is not intended as a tool to assess robustness after the data have been collected

studies in the history of probability and statistics xliv a forerunner of the t distribution summary the t distribution first occurred in a paper by ltiroth 1876 on the classical theory of errors in connection with a bayesian result