The lifetimes of positrons in oxides of arsenic and antimony

The lifetimes of positrons in crystalline powders of dimeric oxides of arsenic and antimony, and in trioxymethylene and polyoxymethylene are reported. In As₄O₆ and polyoxymethylene a longer componentτ ₄ is observed in addition to the usually observedτ ₂ component. The variation ofτ ₄ with temperature and pressure is studied in As₄O₆. On the basis of these results and the X-ray diffraction pictures, it is suggested that ortho-positronium atoms quenched in intercrystallite regions in As₄O₆ gives rise toτ ₄.     

Recognition of finite groups by a set of orders of their elements

For G a finite group, ω(G) denotes the set of orders of elements in G. If ω is a subset of the set of natural numbers, h(ω) stands for the number of nonisomorphic groups G such that ω(G)=ω. We say that G is recognizable (by ω(G)) if h(ω(G))=1. G is almost recognizable (resp., nonrecognizable) if h(ω(G)) is finite (resp., infinite). It is shown that almost simple groups PGL_n(q) are nonrecognizable for infinitely many pairs (n, q). It is also proved that a simple group S₄(7) is recognizable, whereas A₁₀, U₃(5), U₃(7), U₄(2), and U₅(2) are not. From this, the following theorem is derived. Let G be a finite simple group such that every prime divisor of its order is at most 11. Then one of the following holds: (i) G is isomorphic to A₅, A₇, A₈, A₉, A₁₁, A₁₂, L₂(q), q=7, 8, 11, 49, L₃(4), S₄(7), U₄(3), U₆(2), M₁₁, M₁₂, M₂₂, HS, or M^cL, and G is recognizable by the set ω(G); (ii) G is isomorphic to A₆, A₁₀, U₃(3), U₄(2), U₅(2), U₃(5), or J₂, and G is nonrecognizable; (iii) G is isomorphic to S₆(2) or O ₈ ⁺ (2), and h(ω(G))=2. Supported by RFFR grant No. 96-01-01893. Translated fromAlgebra i Logika, Vol. 37, No. 6, pp. 651–666, November–December, 1998.     

Stability of the solutions of one-sided variational problems with applications to the theory of plasticity

In the paper one investigates the one-sided variational problem of the form $$/u - u_0 / = min, u \in M,$$ where ¦·¦ is the norm in some Hilbert space H₀, ? is a nonempty convex set, closed in the metric of H₀, and u₀ is a given element of this space. The fundamental results are: 1) The solution of the problem (1) is stable relative to small perturbations of the data of this problem: the element u₀, the norm ¦·¦, and the set ? the concept of small perturbation is precisely formulated. 2) Assume that the set ? is defined by the formula where g is an element of some Hilbert space containing the space H₀, ||| · ||| is some seminorm, and a is a positive constant. Let H⁽ⁿ⁾ be a subspace of the space H₀ on all of whose elements the seminorm ||| · ||| is finite. If u_n is the approximate solution of the problem (1), obtained as the solution of the problem ¦u?u₀¦=min, u_n ∈ M ∩ H⁽ⁿ⁾, then ¦u_*?u_n¦=0 (e_n(u_*)), where u_* is the exact solution of the problem (1), while e_n(u_*) is the best approximation of u_* by the elements of the subspace H⁽ⁿ⁾. The given results are used in a series of problems regarding the elastoplastic state according to the Saint-Venant-Mises theory; one assume that for these problems the Haar-Karman variational principle holds.     

On an analogue of a conjecture of Gross

The paper is concerned with a problem in the theory of congruence function fields which is analogous to a conjecture of Gross in Iwasawa Theory. Z_p-extensions K_∞/K₀ of congruence function fields K₀ of characteristic p≠2 involving no new constants are considered such that the set S of ramified primes is finite and these primes are fully ramified. Is the set of S-classes invariant under Gal(K_∞/K₀) finite ? Gross' conjecture asserts that a similar question has an affirmative answer for the class of cyclotomic Z_p- extensions of CM-type if S is the set of p-primes and the classes considered are minus S-classes. Using a formula of Witt for the norm residue symbol in cyclic p-extensions of local fields of characteristic p, a necessary and sufficient condition for the validity of the analogue of Gross' conjecture is given for a class of extensions K_∞/K₀. It is shown by examples that the analogue of Gross' conjecture is not always true.     

On analytic microlocal hypoellipticity of linear partial differential operators of principal type

It is shown that if P is a linear partial differential uperator with analytic coefficients defined near a point xo in Rⁿ and if P in Rⁿ - 0 is such that: the principal symbol p_m,(x, ξ) vanishes at (x₀. ξ⁰). the differential of p_m, with respect to ξ is different from zero at (x₀, ξ⁰). the Poisson bracket {P_m, P_m} is zero at (x₀. ξ⁰) and the Poisson bracket {p_m, {p_m.p_m }} is different from zero at (x₀, ξ⁰), then P is analytic hypoelliptic at (x₀, ξ⁰). It is also proved that P is analytic hypoelliptic under the assumption that the first non-vanishing repeated Poisson bracket of p_m, and p_m, is of odd length and under some additional hypothesis on the commutators of the Hamilton fields of Re p_m, and Im p_m,     

The Enumeration of Fully Commutative Elements of Coxeter Groups

A Coxeter group element w is fully commutative if any reduced expression for w can be obtained from any other via the interchange of commuting generators. For example, in the symmetric group of degree n, the number of fully commutative elements is the nth Catalan number. The Coxeter groups with finitely many fully commutative elements can be arranged into seven infinite families A_n, B_n, D_n, E_n,F_n, H_n and I₂(m). For each family, we provide explicit generating functions for the number of fully commutative elements and the number of fully commutative involutions; in each case, the generating function is algebraic.     

数域中tame 核的p-秩

Let E/F be a Galois extension of number fields with Galois group G=Gal(E/F), and let p be a prime not dividing #G. In this paper, using character theory of finite groups, we obtain the upper bound of #K₂O_E if the group K₂O_E is cyclic, and prove some results on the divisibility of the p-rank of the tame kernel K₂O_E, where E/F is not necessarily abelian. In particular, in the case of G=C_n, D_n, A₄, we easily get some results on the divisibility of the p-rank of the tame kernel K₂O_E by the character table. Let E/Q be a normal extension with Galois group D_l, where l is an odd prime, and F/Q a non-normal subextension with degree l. As an application, we show that f|p-rank K₂O_F, where f is the smallest positive integer such that p^f≡±1(mod l).     

Stability of travelling wave solutions of the active Josephson junction transmission line

The behavior of the Josephson line, which is a type of active pulse transmission line, is governed by a partial differential equation which is similar to the sine-Gordon equation. This equation has two solitary travelling wave solutions with different propagation speeds c₁ and c₂, 0 < c₁ < c₂, and a one-parameter family of spatially periodic travelling wave solutions whose propagation speeds range over the intervals (0, c₁) and (c₂, + ∞). First we prove the existence of these solutions. Second we consider the stability of these solutions by linearized stability analysis. It is shown that the slow solitary solution is stable in the sense of linearized stability and that the fast solitary solution is unstable. It is shown also that the periodic solution with the speed c, 0 < c < c₁, is stable in the sense of linearized stability and that the periodic solution with the speed c, c₂ < c < c₄, is unstable, where c₄ is a certain point in (c₂, + ∞).     

On Dilatations and Substantial Boundary Points of Homeomorphisms of Jordan Curves

We study the relation between the dilatations K_h and K_h* of a homeomorphism h of Jordan curves. We show that if K_h= K_h*, then either h is induced by an affine map or there is a substantial boundary point for h. In particular, we prove that if h is symmetric (in the sense of Gardiner and Sullivan), then K_h* > K_h. This is quite contrary to a previously conjectured relation between K_h and K_h*.     

Minima of initial segments of infinite sequences of reals

Suppose that 〈x_k〉_k∈? is a countable sequence of real numbers. Working in the usual subsystems for reverse mathematics, RCA₀ suffices to prove the existence of a sequence of reals 〈u_k〉_k∈? such that for each k, u_k is the minimum of {x₀, x₁, …, x_k}. However, if we wish to prove the existence of a sequence of integer indices of minima of initial segments of 〈x_k〉_k∈?, the stronger subsystem WKL₀ is required. Following the presentation of these reverse mathematics results, we will derive computability theoretic corollaries and use them to illustrate a distinction between computable analysis and constructive analysis. (© 2003 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Products of threads

A topological semigroup S is a thread if S is a metric arc in which one endpoint is the identity of S and the other endpoint is the zero of S. Let [x0, x₁] and [y₀, y₁] be subsets of threads in a semigroup S. Then define A(x₀, x₁) = x [x₀, x₁] | xy₁ = x₁y for some y [y₀, y[in1}]). The main result of this paper states that if X and Y are threads in a topological semigroup S, then XY is an arc or a point, or contains a two-cell.This paper is part of the author's doctoral dissertation written under the direction of Professor D. R. Brown at the University of Houston. This work was supported in part by an NSF Science Faculty Fellowship.     

Am×n矩阵的加边矩阵的奇异性问题

给定m×n阶矩阵A,我们给出了它的加边矩阵M=[A B C O] (1)为非奇的充分必要条件。其中O为r₁×r₂阶零矩阵。把M的逆矩阵记为分块形式M^-1=[A₁ B₂ C₃ O₄]其中C₁为n×m、C₂为n×r₁、C₃为r₂×m、C₄为r₂×r₁阶矩阵。在一定条件下,我们证明了其中的C₁为A的广义逆矩阵A⁺。     

Specialization of a generic hyperplane section through a rational point of an algebraic variety

Summary Let V/k be an irreducible algebraic variety of dimension ≥3, defined over a field k of characteristic O, passing through the origin (O) of the ambient affine n-space. Let p be the prime ideal of V in the polynomial ring k[X₁, ..., X_n]. If V/k is k-normal at (O), then for almost all hyperplanes H_a: a₁X₁+...+a_nX_n=0 with a₁, ..., a_n ε k the ideal (p, a₁X₁+...+a_nX_n) is a prime ideal. If the generic hyperplane section of V through (O) is normal over the ground field of the generic section of V, then the section V ∩ H_a is k-normal at (O) for almost all H_a. Entrata in Redazione il 1 ottobre 1971.     

Stein extensions of Riemannian symmetric spaces and dualities of orbits on flag manifolds

It is known [M4] that K_ℂ-orbits S and G_ℝ-orbits S' on a complex flag manifold are in one-to-one correspondence by the condition that S ∩ S' is nonempty and compact. It is possible to replace K_ℂ by some conjugate xK_ℂx⁻¹ so that the correspondence is preserved. We investigate the sets C(S) of such x for various orbits S and their relations with each other. We prove that for classical groups the intersection C = ∩_S C(S) equals D₀Z where D₀ = D₀/K_ℂ is the universal domain in G_ℂ/K_ℂ introduced in [AG] and Z is the center of G. As a corollary we prove that D₀ is Stein for classical groups. Moreover we conjecture that C(S)₀ = D₀ for generic S where C(S)₀ is the connected component of C(S) containing the identity.     

Effect of Mg and C contents in MgCNi3, and structure and superconductivity of MgCNi3-x -Co x

The effect of Mg and C contents on T_C in MgCN₃, and structure and superconductivity of MgCNi_3-x Co _x were studied. It is found that the excess of Mg and C in initial material mixture is favorable to improvement inT _c and helps to obtain single-phase samples. For preparing MgCNi₃ superconductor, the optimum composition of starting materials is MgC_1.45Ni₃ with excess of Mg (20 wt.%) of the stoichiometric composition. In gCNi_3-x Co _x system, a continuous solid solution is formed, lattice parameter decreases slightly andT _c decreases obviously with increasingx. A suppression of superconductivity is observed due to the substitution of Co (Mn) for Ni. The suppression effect is smaller for the substitution of Co than that of Mn     

Matrices of bisimple regular semigroups

A semigroup S is a matrix of subsemigroups S_iμ, i ε I, μ ε M if the S_iμ form a partition of S and S_iμS_jν≤S_iν for all i, j in I, μ, ν in M. If all the S_iμ are bisimple regular semigroups, then S is a bisimple regular semigroup. Properties of S are considered when the S_iμ are bisimple and regular; for example, if S is orthodox then each element of S has an inverse in every component S_iμ.     

On the Hopf Algebraic Structure of Lie Group Integrators

A commutative but not cocommutative graded Hopf algebra H_N, based on ordered (planar) rooted trees, is studied. This Hopf algebra is a generalization of the Hopf algebraic structure of unordered rooted trees H_C, developed by Butcher in his study of Runge-Kutta methods and later rediscovered by Connes and Moscovici in the context of noncommutative geometry and by Kreimer where it is used to describe renormalization in quantum field theory. It is shown that H_N is naturally obtained from a universal object in a category of noncommutative derivations and, in particular, it forms a foundation for the study of numerical integrators based on noncommutative Lie group actions on a manifold. Recursive and nonrecursive definitions of the coproduct and the antipode are derived. The relationship between H_N and four other Hopf algebras is discussed. The dual of H_N is a Hopf algebra of Grossman and Larson based on ordered rooted trees. The Hopf algebra H_C of Butcher, Connes, and Kreimer is identified as a proper Hopf subalgebra of H_N using the image of a tree symmetrization operator. The Hopf algebraic structure of the shuffle algebra H_Sh is obtained from H_N by a quotient construction. The Hopf algebra H_P of ordered trees by Foissy differs from H_N in the definition of the product (noncommutative concatenation for H_P and shuffle for H_N) and the definitions of the coproduct and the antipode, however, these are related through the tree symmetrization operator.     

Sets of values for two systems of functionals on a class of functions associated with the caratheodory class

Let P_k, k 2, be the class of functions g(z)=1+C₁Z + ... that is regular in the disk ¦ z ¦ < 1 and such that is the class of functions of P_k that have real coefficients. In this paper we find the sets of values of the systems in the class P_k,R and the set of values for g(z₁) (0 < | z₁| < 1) in the class P_k(c₁) of functions of P_k with fixed c₁ (| c₁ | < k). The proof is based on representing the functions in the classes under discussion in terms of C-functions.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova Akademii Nauk SSSR, Vol. 185, pp. 29–36, 1990.     

On the infinite divisibility of the product of two г-distributed stochastical variables

The authors give a positive answer to the question “if X_α is г-distributed of order α, and X_β of order β, with X_α and X_β independent, is X_αX_β infinitely divisible?”. This question, posed by Steutel in Ref. 1, has not been answered up to now, so far as they can find in the literature. In addition they show that the distribution of X_αX_β is a generalized г-distribution.