More projective geometry associated with unramified double covers of curves of genus four

Sunto Sia : YY un rivestimento doppio non diramato di una curva di genere quattro definita su C e a moduli generali. Sia il punto di 2-divisione associate a . In questa nota si studia il sistema 2 delle quardriche di contatto al modello canonico di Y, associato al dato rivestimento.e si esplicita una biezione tra l'insieme delle theta-caratteristiche dispari di Y che diffeiscono per e l'insieme dell theta caratteristiche dispari dell curve di genere tre la cui Jacobiana e isomorfa (come v.a.p.p.) alla varieta di Prym P(f Y Y)     

A problem arising in finite population sampling theory

A probability sampling design is a probability functionp(s) on subsetss of [1, ..., i, ..., N. Let _ij denote the joint inclusion probability fori andj. The problem is to determine conditions under which a fixed size (n) sampling designp exists so that _ij (x _i –x _j )² for a vector of real numbersx=(x ₁, ...,x _N ), or equivalently, so that for some order of the coefficients _ik = _ij + _jk . Some necessary conditions for the proportionality to hold are obtained, and it is conjectured that it is satisfied only in special circumstances.     

Finite presentability of Steinberg groups over group rings

LetA be a finitely generated commutative -algebra with Krull dimensiond, and let be an arbitrary finite group. It is proved that the Steinberg groupSt _n (A) is finitely presented whenevern4. If, in addition,nd+3, andK ₁ (A) andK ₂ (A) are finitely generated, thenE _n (A) andGL _n (A) are finitely presented.The Project supported by National Natural Science Foundation of China.     

Lower central series and derived series of net subgroups of the general linear group

Over a commutative ring R with invertible element 2 and with radical , nets (i.e., tables =(_ij) of ideals _ij such that _{irrj ij}) such that _ii are considered. Such nets are called pseudoradical. The groups of the lower central series and the derived series are explicitly constructed for the corresponding net subgroups G () (of the general linear group GL (n,R)) in terms of .Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 114, pp. 180–186, 1982.     

Points cônes du mouvement brownien plan,le cas critique

Summary LetB=(B _t,t0) be a planar Brownian motion and let >0. For anyt0, the pointz=B _t is called a one-sided cone point with angle if there exist >0 and a wedgeW(,z) with vertexz and angle such thatB _sW(,z) for everys[t, t+]. Burdzy and Shimura have shown independently that one-sided cone points with angle exist when >/2 but not when      

Best one-sided approximation of certain classes of functions

This considers the question of the best one-sided approximation of certain classes of continuous periodic functions by means of trigonometric polynomials of order n-1 in the metric L ₂ ^p (1p<). Precise upper bounds are obtained for the best one-sided approximation of classes of 2/n-periodic functions H_,n [having arbitrary prescribed modulus of continuity (t)] in the metric L ₂ ^p , as well as of classes of 2-periodic functions H [having prescribed modulus of continuity (t) with definite limits] in the metric L ₂ ¹ .Translated from Matematicheskie Zametki, Vol. 10, No. 6, pp. 615–626, December, 1971.The author warmly thanks N. P. Korneichuk for his constant attention to this work.     

The likelihood ratio for densities with singularities

Let t_n be the Bayesian estimator of the parameter constructed from independent observations in the case of infinite information and probability distribution density with some singularities. It is shown that under certain conditions on the behavior of the densities near their singularities, the normalizing factor (n) ensuring that _n=(n) (t_n-) has a nontriviallimiting distribution for n is regularly varying in Karamata's sense. The limiting distribution of _n is determined.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 74, pp. 66–82, 1977.I would like to acknowledge the guidance of I. A. Ibragimov in the course of this research.     

Transposition generation of alternating permutations

A permutation _{1 2}... _n is alternating if ₁< ₂> ₃< ₄.... Alternating permutations are counted by the Euler numbers. Here we show that alternating permutations can be listed so that successive permutations differ by a transposition, ifn is odd. Extensions and open problems are mentioned.Research supported by the Natural Sciences and Engineering Research Council of Canada under grant A3379.     

Elastic properties of honeycomb sandwich plates with nontraditional cell forms

A method for correcting the elastic properties of honeycomb sandwich plates by changing the cell shape is described. Compact and convenient analytical expressions (1) are proposed for calculating the reduced elastic parameters of the honeycomb sandwich plates. The acceptable range of changes in the size of the honeycombs is restricted by the cell elongation region [0.5;2] and the region of variation of the angle between cell walls [/6; 5/6]. The results of the calculation experiment showed that the traditional cell shape (=/3, =1) is not effective as an optimum structure (Table 1).Institute of Transport Systems and Technologies (Transmag), National Academy of Sciences of Ukraine, Dnepropetrovsk, Ukraine. Translated from Mekhanika Kompozitnykh Materialov, Vol. 33, No. 2, pp. 187–191, March–April, 1997.     

227-01227-01227-01-property and normal subgroups

Summary D-property (=set of primes) in finite groups is not in general inherited by subgroups. In this paper, as evidence in favor of the following conjecture (F. Gross): (o) If a finite group G satisfies D then its normal subgroups satisfy D-property as well. the Author shows that if the D and the D-properties (=set of the primes not in ) hold together in a finite group G, then both are inherited by the normal subgroups of G. As a corollary, the characterization of the groups satisfying both the properties D and D is given in terms of the composition factors.     

An initial-boundary value problem for the sine-Gordon equation in laboratory coordinates

We consider the sine-Gordon equation in laboratory coordinates with both x and t in [0, ). We assume that u(x, 0), u_t(x, 0), u(0, t) are given, and that they satisfy u(x, 0)2q, u_t(x, 0)0, for large x, u(0, t)2p for large t, where q, p are integers. We also assume that u_x(x, 0), u_t(x, 0), u_t(0, t), u(0, t)-2p, u(x, 0)-2q L₂. We show that the solution of this initial-boundary value problem can be reduced to solving a linear integral equation which is always solvable. The asymptotic analysis of this integral equation for large t shows how the boundary conditions can generate solitons.The authors dedicate this paper to the memory of M. C. PolivanovDepartment of Mathematics and Computer Science; Institute for Nonlinear Studies, Clarkson University, Postdam, New York. Published in Teoreticheskaya i Matematicheskaya Fizika, Vol. 92, No. 3, pp. 387–403, September, 1992.     

Unbounded divergence of Fourier series of continuous functions

For any given set E [0, 2), of measure zero, a functionf(t) C (0, 2), is constructed whose Fourier series is unboundedly divergent on E. If E is closed, there is a function(t) C (0, 2), whose Fourier series diverges unboundedly on E and converges on [0, 2)E.Translated from Matematicheskie Zametki, Vol. 7, No. 1, pp. 7–18, January, 1970.I wish to thank P. L. Ul'yanov for posing the problem and for his useful comments on this work.     

Generating alternating permutations lexicographically

A permutation _{1 2} ... _n is alternating if ₁<₂>₃<₄ .... We present a constant average-time algorithm for generating all alternating permutations in lexicographic order. Ranking and unranking algorithms are also derived.Research supported by the Natural Sciences and Engineering Research Council of Canada under grant A3379.     

Durch graduierte Lie-Algebren definierte Paar-Algebren

Pair algebras which have a non degenerate (left- and right-) invariant bilinear form and for which the inner derivation algebra is completely reducible are characterised by pairs (C,), where C is a n×n matrix satisfying certain conditions and is a sequence of n integers equal to 0 or 1. They occur as pair algebras of type (S(C,)_–1,S(C,)₁), xuy=[[x,u],y], where (S(C,)_r)_r is the gradation induced by . in the Kac-Moody algebraS(C). If C is an affin Cartan matrix (as in the case of Lie triple systems), there exists a finite dimensional simple Lie algebrag and a Aut (g), ord =m< such that the pair algebra is isomorphic to the pair algebra (g _–1,g ₁), xuy=[[x,u],y] (product ing), whereg _i. is the eigenspace of of eigenvalue ⁱ, a primitive m-th root of unity.     

High-Energy Relations Between Elastic Scattering Amplitudes of Particles and Antiparticles

We find conditions under which the ratio of particle and antiparticle total scattering cross sections as s. If the forward elastic scattering amplitudes become purely real asymptotically, then their ratio tends to –1. We prove that /_–(s)1 for ₊(s)/m ², where m is the -meson mass. We show that the asymptotic relations obtained have finite-energy analogues for some processes.     

1-formes fermées singulières et groupe fondamental

Summary We study the influence of the ₁ of a closed manifoldM ⁿ (n3) on the foliations ofM defined by closed differential 1-forms with Morse singularities (of index 0,n). Every nonexact form is cohomologous to a weakly complete one, that is one whose leaf space is of the same type as that of a nonsingular form. Generically, a form has compact leaves or is weakly complete. If ₁ M has no quotient isomorphic to *, then every nonexact form onM is weakly complete. We also say a form is complete if every path inM is homotopic to either a path transverse to or a path contained in a leaf of . Completeness of depends only on its de R ham cohomology class. The set of complete cohomology classes depends only on ₁ M and is related to finitely generated normal subgroups of ₁ M with quotient . If ₁ M is nilpotent (or even polycyclic), every nonexact form onM is complete. On irreducible 3-manifolds, a form is complete iff it is cohomologous to a nonsingular one.     

Nielsensche Realisierungssätze für Seifertfaserungen

Let M be a closed aspherical manifold and A a finite subgroup of the outer automorphism group Out ₁M of ₁M. A necessary (and in many cases also sufficient) condition for realising A by the induced action of an isomorphic group of homeomorphisms of M is the existence of an extension 1₁MEA1 to the abstract kernel (A,₁M, AOut ₁M). If the center of ₁M is nontrivial, this condition need not be fulfilled ([14]). We showed in [25] however that one can always find a surjection BA of a finite group B with abelian kernel such that there exists an extension to the abstract kernel (B,₁M,BAOut₁M), and one can try to realize B instead of A. The main result of the present paper is a characterisation of all such groups B (for a given A) which can be realized by a group of homeomorphisms. The class of manifolds considered here consists of certain Seifert fiber spaces in arbitrary dimensions but the main result is purely algebraic and can be applied to other classes of manifolds, for example to flat Riemannian manifolds.     

Locally forced critical surface waves in channels of arbitrary cross section

Critical long surface waves forced by locally distributed external pressure applied on the free surface in channels of arbitrary cross section are studied in this paper. The fluid under consideration is inviscid and has constant density. The upstream flow is uniform and the upstream velocity is assumed to be near critical, i.e.,u ₀=u _c ++0(²), where 0<1 andu _c is the critical velocity determined by the geometry of the channel. The external pressure applied on the free surface as the forcing is ² P(x). Then the first order perturbation of the free surface elevation satisfies a forced Korteweg-de Vries equation (fK-dV). It is shown in this paper that: (i) If (supercritical), the stationaryfK-dV has two cusped solitary wave solutions; (ii) if (subcritical), the stationaryfK-dV has a downstream cnoidal wave solution; (iii) when= _L , the unique stationary solution of thefK-dV is a wave free hydraulic fall; (iv) if= _d =– _L , thefK-dV has a jump solution; and (v) if _L << _c , thefK-dV does not have stationary solutions. Some free surface profiles and bifurcation diagrams are presented.