On decay estimates

We show here that decay estimates can be derived simply by integral inequalities. This result allows us to prove these kind of estimates, with an unified proof, for different nonlinear problems, thus obtaining both well known results (for example for the p-Laplacian equation and the porous medium equation) and new decay estimates.     

Monoids and decay

We propose some formalization of the concept of critical decay number and describe the class of models with this number at most 4 (i.e., every object is decomposable which consists of four or more elements).     

Subexponential decay of correlations

We describe a method for proving subexponential lower bounds for correlations functions, and apply it to study decay of correlations for maps with countable Markov partitions. One result is that LS Young’s upper estimates [Y2] are optimal in many situations. Our method is based on a general result concerning the asymptotics of renewal sequences of bounded operators acting on Banach spaces, which we apply to the iterates of the transfer operator. Oblatum 14-VII-2001 & 5-VI-2002?Published online: 6 August 2002 Dedicated to B. Weiss on the occasion of his 60th birthday RID="*" ID="*"This research was supported by the Nuffield Foundation, NUF-NAL 00.     

Domination with exponential decay

Let G be a graph and S⊆V(G). For each vertex u∈S and for each v∈V(G)−S, we define to be the length of a shortest path in 〈V(G)−(S−{u})〉 if such a path exists, and ∞ otherwise. Let v∈V(G). We define if v⁄∈S, and w_S(v)=2 if v∈S. If, for each v∈V(G), we have w_S(v)≥1, then S is an exponential dominating set. The smallest cardinality of an exponential dominating set is the exponential domination number, γ_e(G). In this paper, we prove: (i) that if G is a connected graph of diameter d, then γ_e(G)≥(d+2)/4, and, (ii) that if G is a connected graph of order n, then .     

Magnetohydrodynamic shock wave decay

Summary A modified hodograph transformation is used to obtain an exact solution of the equations governing the one-dimensional unsteady flow of an ideal, inviscid, perfectly conducting compressible fluid, subjected to a transverse magnetic field. This solution is used to obtain an approximate representation of the path of an initially uniform shock wave which intersects a centered simple wave. In the limit of vanishing magnetic field, the solution reduces exactly to the solution of the corresponding problem for conventional gas dynamics.

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Résumé Une transformation hodographe modifiée est employée pour obtenir une solution exacte des équations relatives aux écoulements unidimensionnels non-stationnaires et non-isentropiques d'un fluide non visqueux idéal, parfaitement conducteur d'électricité et compressible, soumis à l'action d'un champ magnétique transversal. On utilise cette solution pour obtenir une représentation approximative de la trajectoire d'une onde de choc magnétohydrodynamique initialement uniforme, rencontrant une onde simple centrée.Dans le cas limite d'un champ magnétique nul, la solution se réduit exactement à celle du problème correspondant de la dynamique classique des gaz. C'est là une confirmation de la validité de la théorie.

     

A Generalized Double Crossproduct and Drinfeld Double

In this paper we construct a new and more complicated algebra construction of two algebras B and H, a generalized double crossproduct B H. The left generalized smash product, the right generalized smash product, Majids double crossproduct, especially, the smash product, the Drinfeld Double D(H) and Doi-Takeuchi algebra B H are all special cases as our algebra structure. Next, we analyze conditions under which this new algebra B H is a Hopf algebra termed a generalized double crossproduct of Hopf algebra, and describe a coquasitriangular structure over the generalized double crossproduct Hopf algebra B H. Finally, what we do is to construct a new braided monoidal category ^J_JMod^Q_Q obtained from the structure of the generalized double crossproduct, and establish a kind of new quantum Yang-Baxter operators.AMS Subject Classification (1991): 16W20, 16D90, 16S40, 16W30     

Energy decay in piezoelectric systems

We establish that when a dissipation term is introduced in the equilibrium equations of a piezoelectric body, the energy decays exponentially and we give an estimate of the decay rate.     

Radioactive decay of Eu154

The radioactive decay of Eu¹⁵⁴ (t _1/2=16y), obtained from thermal neutron irradiations of 95% enriched Eu¹⁵³, has been studied by using the Seigbahn-Slätis intermediate image spectrometer, a thin lens magnetic spectrometer and a coincidence scintillation spectrometer. The following gamma-rays (energy in kev.) have been identified as belonging to this isotope: 123, 248, 585, 717, 759, 875, 998, 1007, 1285, 1600. Beta end points of Eu¹⁵⁴ were measured at 275 (20%), 590 (45%), 890 (23%) and 1860 (12%). The K-conversion coefficient of 123 kev. gamma-ray has been experimentally determined to be ～0·5. On the basis of gamma-gamma and beta-gamma coincidences, the decay scheme of Eu¹⁵⁴ has been deduced: the resulting level-structure of Gd¹⁵⁴ conforms well with the predictions of the unified nuclear model.     

Oblique magnetohydrodynamic shock wave decay

Summary A modified hodograph transformation is used to obtain an exact solution of the equations governing the one-dimensional unsteady flow of an ideal, inviscid, perfectly conducting compressible fluid, subjected to an oblique magnetic field. This solution is used to obtain an approximate representation of the path of an initially uniform shock wave which intersects a centered simple wave. The solutions for the corresponding problems in the conventional, non-magnetic case and for a transverse orientation of the applied magnetic field are contained as special limiting cases of the solutions of the present paper. This provides a valuable check on the theory.

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Résumé Une transformation hodographe modifiée est employée pour obtenir une solution exacte des équations relatives aux écoulements unidimensionnels non-stationnaires et non-isentropiques d'un fluide non visqueux idéal, parfaitement conducteur d'électricité et compressible, soumis à l'action d'un champ magnétique oblique avec deux composantes différentes de zero. On utilise cette solution pour obtenir une représentation approximative de la trajectoire d'une onde de choc magnétohydrodynamique initialement uniforme, rencontrant une onde simple centrée. Les solutions pour le cas non magnétique et pour un champ transversal apparaissent comme des cas limites particuliers de la solution présentée ici, c'est là une confirmation de la validité de la theorie.

     

Partial decay on simple manifolds

Existence, uniqueness and weighted regularity of solutions of linear and nonlinear second-order uniformly elliptic differential equations on complete punctured compact N-manifolds, N > 2. Application to prescribed curvature problems: scalar curvature in a quasi-isometry class (including a contribution to the Lichnérowicz-York equation of General Relativity); Ricci curvature in a weighted Kähler class (with a related result in equiaffine geometry). A new asymptonic behaviour is allowed throughout, called partial decay, which requires its own maximum principle.Current support: CNRS; partial support; CEE contract GADGET # SC1-0105-C.     

Vacuum decay of non-Abelian vortices

This note is a case study of a general SU(2) gauge vortex model where the two Higgs multiplets are in the adjoint representation of the gauge group and the Higgs potential energy density contains cross interaction terms The vacuum decay of finite-energy solutions is proved and the existence of a non-trivial solution is established. Moreover, for a special choice of the parameter region, the occurrence of a non-linear desingularization phenomenon is observed.     

A study of alpha decay

The process of alpha decay in nuclei has traditionally been assumed to be governed by the many characteristic properties (Coulomb barrier, spin, parity, etc.) of the parent isotope and the alpha particle. This implies that each pair of parent–daughter transition is only marginally related to other pairs of the same element. In this paper, the author shows that the experimental data suggests there is a strong scale-independent relationship between the isotopes of an alpha emitting element. In most cases, the relationship between the energy and half-life values for the isotopes of an element can be represented by a single power law with mathematical precision. The presence of this relationship can be used to deduce information on the nuclear structure of some nuclei. Also it suggests that alpha decay properties may play a less restrictive role in the process than traditional models have previously assumed. The exponent of the power law is negative and slightly decreases in value linearly with increasing mass number. There is also a large negative peak in the vicinity of mass 82.     

Rate of decay of s-numbers

For an operator $T\in B(X,Y)$, we denote by $a_m\left(T\right)$, $c_m\left(T\right)$, $d_m\left(T\right)$, and $t_m\left(T\right)$ its approximation, Gelfand, Kolmogorov, and absolute numbers, respectively. We show that, for any infinite-dimensional Banach spaces $X$ and $Y$, and any sequence ${\alpha }_m\searrow 0$, there exists $T\in B(X,Y)$ for which the inequality $3{\alpha }_{?m/6?}?a_m\left(T\right)?max\{c_m\left(t\right),d_m\left(T\right)\}?min\{c_m\left(t\right),d_m\left(T\right)\}?t_m\left(T\right)?{\alpha }_m/9$ holds for every $m\in \mathbb{N}$. Similar results are obtained for other $s$-scales.     

Exponential decay of expansive constants

A map f on a compact metric space is expansive if and only if fn is expansive.We study the exponential rate of decay of the expansive constant of fn and find some of its relations with other quantities about the dynamics,such as box dimension and topological entropy.     

Verblunsky coefficients with Coulomb-type decay

We show that probability measures on the unit circle associated with Verblunsky coefficients obeying a Coulomb-type decay estimate have no singular continuous component.