DIFFEOMORPHISMS WITH VARIOUS C1 STABLE PROPERTIES

Let M be a smooth compact manifold and Λ be a compact invariant set.In this article,we prove that,for every robustly transitive set Λ,f|Λ satisfies a C1-genericstable shadowable property (resp.,C1-gene...     

On the hyperbolicity of flows

Let X be a C~1 vector field on a compact boundaryless Riemannian manifold M(dim M≥2),and A a compact invariant set of X.Suppose that A has a hyperbolic splitting,i.e.,T∧M = E~sX E~u with E~s uniformly contracting and E~u uniformly expanding.We prove that if,in addition,A is chain transitive,then the hyperbolic splitting is continuous,i.e.,A is a hyperbolic set.In general,when A is not necessarily chain transitive,the chain recurrent part is a hyperbolic set.Furthermore,we show that if the whole manifold M admits a hyperbolic splitting,then X has no singularity,and the flow is Anosov.     

Norming sets and integration with respect to vector measures

Let v be a countably additive measure defined on a measurable space (Ω, Σ) and taking values in a Banach space X. Let f : Ω → ? be a measurable function. In order to check the integrability (respectively, weak integrability) of f with respect to v it is sometimes enough to test on a norming set Λ ⊂ X^*. In this paper we show that this is the case when A is a James boundary for BX^* (respectively, Λ is weak^*-thick). Some examples and applications are given as well.     

Inductive limits of spaces of vector- valued integrable functions

For an order-continuous Banach function space Λ and a separated inductive limit E:= ind_n E _n, we prove that ind_n A {E_n} is a topological subspace of Λ {E}; moreover, both spaces coincide if the inductive limit is hyperstrict. As a consequence, we deduce that if E is an LF-space, then L ^p {E} is barrelled for 1 ≤ p ≤ ∞.     

Außenraumaufgaben in der linearen Elastizitätstheorie

The paper starts with a short survey of the treatment of initial-boundary-value problems in temperature-free linear elasticity with unisotropic media. The main part of the paper is concerned with exterior initial-boundary-value problems in thermoelasticity. In this case the underlying differential operator A is no longer selfadjoint. Thus the spectrum of A has to be discussed. In 2.1 it is shown that all λ with Re λ < 0 belong to the resolvent set. In 2.2 the case G = R³ with homogeneous isotropic media is considered. Let Λ be the essential spectrum in this case. In 2.3 Λ depending on the thermic coupling parameter is discussed. 2.4 treats the spectrum of A assuming the medium to be homogeneous and isotrop outside a large ball. In this case Λ is the essential spectrum for A too. Radiation conditions are formulated. Finally 2.5 presents a short treatment of the time dependent case with Laplace-transformation.     

POLYNOMIALS RELATED TO HALL NUMBERS

Let Λ be a finite dimensional algebra of finite representation type over a finite field k. For any modules A, B and Pin mod Λ with P projective, we prove that there exists a polynomial ? ^B _(P)Λ over Z whose evaluation at |E| for any conservative finite field extension E of Λ is the sum of Hall numbers F ^{B E} _{C ^E A ^E} where C ^E runs through isoclasses in mod Λ ^E and P ^E is the projective cover of C ^E . As a consequence of this result and its dual version, Hall polynomials ? ^E _CA exist when C or A is semisimple. As applications of the main result, we obtain the existence of Hall polynomials for Nakayama algebras and some selfinjective algebras.

     

Binding energy andπ + decay of light hyperfragments

Binding energy values of hyperfragments from a sample of 541 uniquely identified mesic decays with mass numbers A=3 to 14 are presented. There does not seem to be any detectable difference in the binding energy value of Λ in_AH⁴ obtained from its two-body and three-body decay modes. Within statistical error, the binding energy values of Λ in_AH⁴ and_AH⁴ are also the same. From a sample of 2π ⁺ decay events of hyperfragments the branching ratio of_AH⁴ decaying byπ ⁺ toπ ^? mode is found to be (1·5±1·0)%.     

Probability and Fourier Duality for Affine Iterated Function Systems

Let d be a positive integer, and let μ be a finite measure on ? ^d . In this paper we ask when it is possible to find a subset Λ in ? ^d such that the corresponding complex exponential functions e _λ indexed by Λ are orthogonal and total in L ²(μ). If this happens, we say that (μ,Λ) is a spectral pair. This is a Fourier duality, and the x-variable for the L ²(μ)-functions is one side in the duality, while the points in Λ is the other. Stated this way, the framework is too wide, and we shall restrict attention to measures μ which come with an intrinsic scaling symmetry built in and specified by a finite and prescribed system of contractive affine mappings in ? ^d ; an affine iterated function system (IFS). This setting allows us to generate candidates for spectral pairs in such a way that the sets on both sides of the Fourier duality are generated by suitably chosen affine IFSs. For a given affine setup, we spell out the appropriate duality conditions that the two dual IFS-systems must have. Our condition is stated in terms of certain complex Hadamard matrices. Our main results give two ways of building higher dimensional spectral pairs from combinatorial algebra and spectral theory applied to lower dimensional systems.     

Upper bound for the product of nonhomogeneous linear forms

It is proved that for any unimodular lattice Λ with homogeneous minimum L>0 and any set of real numbers α₁, α₂,..., α_n there exists a point (y₁, y₂,..., y_n) of Λ such that $$\Pi _{1 \leqslant i \leqslant n} |y_i + \alpha _i | \leqslant 2^{ - n/2_\gamma n} (1 + 3L^{8/(3n)/(\gamma ^{2/3} - 2L^{8/(3n)} )} )^{ - n/2} ,$$ where γⁿ= n^n/(n?1).     

On the maximum cocliques of the rank 3 graph of 211 : M24

In this article, we consider the maximum cocliques of the 2¹¹: M₂₄ ‐graph Λ. We show that the maximum cocliques of size 24 of Λ can be obtained from two Hadamard matrices of size 24, and that there are exactly two maximum cocliques up to equivalence. We verify that the two nonisomorphic designs with parameters 5‐(24,9,6) can be constructed from the maximum cocliques of Λ, and that these designs are isomorphic to the support designs of minimum weights of the ternary extended quadratic residue and Pless symmetry [24,12,9] codes. Further, we give a new construction of Λ from these 5‐(24,9,6) designs. © 2009 Wiley Periodicals, Inc. J Combin Designs 17: 323–332, 2009     

The Chen-Type of the Spiral Surfaces

We show that a spiral surface M in E³ is of finite type if and only if M is minimal Also, the plane is the only spiral surface in E³ whose the Gauss map G is of finite type, or satisfies the condition ΔG = ΛG, where Λ ∈ R^3×3.     

Sur les automorphismes de l'espace topologique ordonné 2Λ

Let Λ be a non-empty set, and suppose that the space 0,1^Λ is endowed with the product topology and the product order. We show that every automorphism of this ordered topological space is a permutation of the coordinates.     

The spin dependence of an weak interaction in the decay of hypernuclei

From an analysis of 468 hypernuclei (HFs) with ranges > 120 μm, the non-mesic to π^?-mesic ratio (Q^?) for_ΛHe and_ΛHe⁵ HFs was found to be 1.37 ±0.17 and 1.58± 0.20 respectively. This data, together with results on_ΛHe⁴ and heavy hypernuclei, has been used to deduce spin dependences for Λⁿ and ΛP weak interactions in decay of hypernuclei. It is found that the rates for triplet and singlet interactions between Λ and neutron are 22 Γ_Λ and 11 Γ_Λ and for Λ and proton are 8.2 Γ_Λ and 5.5 Γ_Λ respectively, where Γ_Λ is the decay rate of Λ. The total decay rates for ΛHe⁴ and_ΛHe⁵ are 1.28 Γ_Λ and 0.99 Γ_Λ and the non-mesic decay rates are 0.17 Γ_Λ and 0.51 Γ_Λ respectively.     

A couple of triples

The standard contravariant adjunction between TOP (the category of topological spaces) and LAT (the category of distributive lattices) induces a triple Λ on LAT and a triple Σ on TOP. We show that the category LAT^Λ of Λ-algebras is just the category of frames, and describe the category TOP^Σ of Σ-algebras as a subcategory of TOP.     

Commutative Algebras with Radical Cube Zero

Abstract

We present “canonical forms” of finite dimensional (quasi-Frobenius) commutative algebras Λ over a field k such that the radical cubed is zero and Λ modulo the radical is a product of copies of k. We also determine the isomorphism classes of the algebras Λ over some typical fields.     

Ball-covering property of Banach spaces

We consider the following question: For a Banach spaceX, how many closed balls not containing the origin can cover the sphere of the unit ball? This paper shows that: (1) IfX is smooth and with dimX=n<∞, in particular,X=R ⁿ,then the sphere can be covered byn+1 balls andn+1 is the smallest number of balls forming such a covering. (2) Let Λ be the set of all numbersr>0 satisfying: the unit sphere of every Banach spaceX admitting a ball-covering consisting of countably many balls not containing the origin with radii at mostr impliesX is separable. Then the exact upper bound of Λ is 1 and it cannot be attained. (3) IfX is a Gateaux differentiability space or a locally uniformly convex space, then the unit sphere admits such a countable ball-covering if and only ifX ^* isw ^*-separable.     

Optimal control of nonlinear hereditary systems

A function space Λ is introduced for the study of nonlinear hereditary differential equations. The properties of Λ include: it is a Banach space under the supremum norm, the continuous functions constitute a closed proper subspace, and the unit ball is sequentially compact in the weak-¹ topology. Existence, uniqueness, and continuous dependence results are obtained for solutions of a broad class of initial value problems. An optimization problem is formulated for systems which are affine in the control, and solutions are approximated by means of a sequence of problems which are finite-dimensional in the control.     

Properties of the false vacuum as a quantum unstable state

We analyze properties of unstable vacuum states from the standpoint of quantum theory. Some suggestions can be found in the literature that some false (unstable) vacuum states can survive up to times when their survival probability takes a nonexponential form. At asymptotically large times, the survival probability as a function of the time t has an inverse power-law form. We show that in this time region, the energy of false vacuum states tends to the energy of the true vacuum state as 1/t ² as t→∞. This means that the energy density in the unstable vacuum state and hence also the cosmological constant Λ = Λ(t) should have analogous properties. The conclusion is that Λ in a universe with an unstable vacuum should have the form of a sum of the “bare” cosmological constant and a term of the type 1/t ²: Λ(t) ≡ Λ_bare + d/t ² (where Λ_bare is the cosmological constant for a universe with the true vacuum).