Monotone convergence of iterative methods for (n,p) and (p,n) boundary value problems

We provide sufficient conditions so that the Picard iterative scheme for (n, p) and (p, n) boundary value problems converges monotonically. An example which illustrates the usefulness of this technique is also included.     

A class of ((p n−p m)(p n−1), p n−p m)-arcs in PG(2, p n)

A (k, d)-arc in PG(2, q) is a set of k points such that some d, but no d+1, of them are collinear. An outstanding problem is to find the maximum value of k for which a (k, d)-arc exists. A construction is given for a class of (k, p ⁿ–p ^m)-arcs in PG(2, p ⁿ). These arcs constitute a lower bound on the maximum possible value of k, and a subset of them is shown to be optimal.     

Study of levels in51Cr through51V (p,nγ) reaction

The low lying levels in⁵¹Cr have been populated by⁵¹V (p, ny)⁵¹Cr reaction. The angular distribution of the ground state electromagnetic transitions from 1165, 1353, 1479 and 1557 keV states have been measured. The results are compared with the Hauser-Feshbach model of the statistical theory of nuclear reactions. The spins for the levels at 1165, 1479 and 1557 keV are shown to be 9/2^?, 11/2^? and 5/2^? respectively.     

Not all graded identities for Mn(E) come from Mn,n

We introduce here two classes of infinite dimensional Lie Algebras called potentially nilpotent and potentially solvable and we define the notion of Fine Lie Algebra. The study of the Fine Lie Algebras allows to obtain their complete classification in the natural or standard graded cases.     

Incidence Structures of Type (p, n)

Every incidence structure (understood as a triple of sets (G, M, I), I G×M) admits for every positive integer p an incidence structure where G ^p (M ^p) consists of all independent p-element subsets in G (M) and I ^p is determined by some bijections. In the paper such incidence structures are investigated the 's of which have their incidence graphs of the simple join form. Some concrete illustrations are included with small sets G and M.     

A braidlike presentation of Sp(n,p)

Forn even andp an odd prime a symplectic group Sp(n, p) is a quotient of the Artin braid groupB _n+1. Ifs ₁, …,s _n are standard generators ofB _n+1 then the kernel of the corresponding epimorphism is the normal closure of just four elements:s ₁ ^p ,(s ₁ s ₂)⁶,s ₁ ^(p+1)/2 s ₂ ⁴ s ₁ ^(p−1)/2 s ₂ ⁻² s ₁ ⁻¹ s ₂ ² and (s ₁ s ₂ s ₃)⁴ A ⁻¹ s ₁ ⁻² A, whereA=s ₂ s ₃ ⁻¹ s ₂ ^(p−1)/2 s ₄ s ₃ ² s ₄, all of them lying in the subgroupB ₅. Sp(n, p) acts on a vector space and the image of the subgroupB _n ofB _n+1 in Sp(n, p), denoted Sp(n−1,p), is a stabilizer of one vector. A sequence of inclusions …B _k+1·B _k … induces a sequence of inclusions …Sp(k,p)·Sp(k−1,p)…, which can be used to study some finite-valued invariants of knots and links in the 3-sphere via the Markov theorem. Partially supported by the Technion VPR-Fund.     

Correlations for paths in random orientations of G(n,p) and G(n,m)

We study random graphs, both G( n,p) and G( n,m), with random orientations on the edges. For three fixed distinct vertices s,a,b we study the correlation, in the combine probability space, of the events $\{a\to s\}$ and $\{s\to b\}$ . For G(n,p), we prove that there is a $pc = 1/2$ such that for a fixed $p < pc$ the correlation is negative for large enough n and for $p > pc$ the correlation is positive for large enough n. We conjecture that for a fixed $n \ge 27$ the correlation changes sign three times for three critical values of p. For G(n,m) it is similarly proved that, with $p=m/({{n}\atop {2}})$ , there is a critical pc that is the solution to a certain equation and approximately equal to 0.7993. A lemma, which computes the probability of non existence of any $\ell$ directed edges in G(n,m), is thought to be of independent interest. We present exact recursions to compute \input amssym $\Bbb{P}(a\to s)$ and \input amssym $\Bbb{P}(a\to s, s\to b)$ . We also briefly discuss the corresponding question in the quenched version of the problem. © 2011 Wiley Periodicals, Inc. Random Struct. Alg., 2011     

B(n,p)总体下函数f(p)无偏估计的存在性

总体服从二项分布B(n,p),p为未知参数,应用麦克劳林公式,得出了只有当f(p)=a1p a2p2 ... anpn时,函数f(p)才存在无偏估计,并给出了无偏估计量.     

Costruzione di una soluzione fondamentale per operatori differenziali ( p n )-ipoellittici,p=1, …, n

Riassunto è costruita una soluzione fondamentale per un operatore differenziale ( _p ⁿ )-ipoellittico,p=1, …,n, con coefficienti costanti. Tale soluzione fondamentale soddisfa a condizioni di Gevrey nei due semi-spazi {x _n <0}, {x _n >0}.

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Summary A constructive procedure of a fundamental solution to a linear ( _p ⁿ )-hypoelliptic,p=1, …,n, differential operator inR ⁿ with constant coefficients is exhibited. Such a fundamental solution satisfies Gevrey conditions in the two half-spaces {x _n >0}, {x _n <0}.

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Lavoro eseguito nell’ambito dell’attività del Gruppo Nazionale per l’Analisi Funzionale e le sue Applicazioni.     

关于图B（m,n,p）的优美性

在［１］［２］中已证明“除去三种特殊情形，连结两个顶点的三条独立路所成简单图Ｂ（ｍ，ｎ，ｐ）是优美图”，并猜想：对除去的三种情形，Ｂ（ｍ，ｎ，ｐ）也是优美的。本文证实了上术猜想。这样一来，也就证明了［３］中的猜想：有－ｈ－链弦的圈是优美的（ｈ≥２）。     

On the first Cartan invariant of the groupSp(4,p n )

The purpose of this paper is to obtain a formula for computing the first Cartan invariantC ₁₁ ⁽ⁿ⁾ of the groupSp(4,p ⁿ ). The main results are as follows: