Simple 3-designs and PSL(2, q) with q ≡ 1 (mod 4)

In this paper, we consider the action of (2, q) on the finite projective line for q ≡ 1 (mod 4) and construct several infinite families of simple 3-designs which admit PSL(2, q) as an automorphism group. Some of the designs are also minimal. We also indicate a general outline to obtain some other algebraic constructions of simple 3-designs.      

Some new 3-designs from PSL(2, q) with q ≡ 1 (mod4)

We determine the sizes of orbits from the action of subgroups of PSL(2,q) on projective line X = GF(q) ∪ {∞} with q a prime power and congruent to 1 modulo 4.As an example of its application,we construct some new families of simple 3-designs admitting PSL(2,q) as automorphism group.     

Some identities associated with mock theta functions $$\omega (q)$$ ω ( q ) and $$\nu (q)$$ ν ( q )

The Ramanujan Journal - Recently, Andrews, Dixit, and Yee defined two partition functions $$p_{\omega }(n)$$ and $$p_{\nu }(n)$$ that are related with Ramanujan’s mock theta functions...     

多色经典Ramsey数(Rn{q,q,…,q)的下界

提出了探求n色经典Ramsey数(Rn{q,q,…,q)的下界的一种方法,并用这种方法借助计算机求得6个新的下界:R4(4)≥458,R3(5)≥242,R3(6)≥1 070,R3(7)≥1 214,R3(8)≥2 834以及R3(9)≥5 282.     

(p,q)-John椭球

本文主要研究(p,q)-John椭球.经典的John椭球和L_p John椭球均是(p,q)-John椭球的特殊情形.首先讨论(p,q)-John椭球的充分必要条件和连续性.得到了关于(p,q)-John椭球的不等式和包含关系,所得到的不等式和包含关系分别类似于Ball体积比不等式和John包含关系.     

ОцЕНкА (ε, δ)-ЁНтРОпИИ к лАссА цЕлых ФУНкцИИ В ИНтЕгРАльНОИ МЕтРИ кЕ

LetB _σ be the class of entire functions of exponential type σ, real valued and bounded in modulus by 1 in the real line. A setG of functions defined on the segment [-T-r, T+r], wherer is a fixed positive number, is called an (ε, δ)-net of the classB _σ on the segment [-т, т] if for any f?B _σ there existsg?G such that for anyx?[-T,T] $$\left| {f(x) - g(x)} \right| \leqq \frac{\varepsilon }{{2r}}\int\limits_{x - r}^{x + r} {\left| {f(t)} \right|dt + \delta .} $$ The main result consists in the following: For any positive σ, r, ε≦1, δ≦1 and sufficiently largeT we have $$H_{\varepsilon ,\delta } (B_\sigma ,T) \leqq \frac{{2\sigma T}}{\pi }\log \frac{{c(\sigma r)}}{{\max (\varepsilon ,\delta )}},$$ where c(σr) depends only on the product σr. The main tool of the proof of this inequality is the following estimate of the derivative of a polynomialP(x) with real coefficients: $$\left\| {P'(x)} \right\|_{L_p ( - {1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2},{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}) \leqq } c\left( {q + 1 + \sum\limits_{i = 1}^{n - q} {\frac{1}{{\left| {a_i } \right|^2 }}} } \right)\left\| {P(x} \right\|_{L_p ( - 1,1)} ,$$ whereq is the number of roots of the polynomialP(x) lying in the disk ¦z¦<1; a₁, ..., a_n?g are the other roots, с is an absolute constant, and 1≦p≦∞.     

ELEMENTARY ASPECTS OF B_(p,q)~S(K_n) AND F_(p,q)~S(K_n) SPACFS

In the first part of this paper,we discuss some properties of S~Ω(K_n),L_p~Ω(K_n) andL_p~Ω(K~n;l_a) spaces,give the Plancherel-Polya-Nikol'skij type inequalities and some multipli-er theorems.In the second part of this paper,using the results of Part I we prove some prelimi-nary results for the spaces B_(p,q)~s(K_n) and F_(p,q)~s(K_n).     

Classification of Flag-Transitive Primitive Symmetric(v,k, λ) Designs with PSL(2, q) as Socle

Let D be a nontrivial symmetric(v, k, λ) design, and G be a subgroup of the full automorphism group of D. In this paper we prove that if G acts flag-transitively, pointprimitively on D and Soc(G) = PSL(2, q), then D has parameters(7, 3, 1),(7, 4, 2),(11, 5, 2),(11, 6, 3) or(15, 8, 4).     

2-(v,k,1)设计和PSL(3,q)(q是奇数)

§ 1　 IntroductionA2 -(v,k,1 ) design D=(S,B) consists ofa finite set Sof v points and a collection Bof some subsets of S,called blocks,such that any two points lie on exactly one blockand each block contains exactly k points.A flag of Dis a pair(α,B) such thatα∈S,B∈Bandα∈B,the set of all flags is denoted by F.We assume that2≤k≤v.An automorphism of Dis a permutation of the points which leaves the set Binvari-ant,all the automorphisms form a group Aut D.Let G be a subgroup of A…     

On the Size of a Cap in PG(n,q) with q Even and n ≥ 3

Let m2(n,q), m2(n,q) be, respectively, the maximum value, the second largest value of k for which there exists a complete k-cap in PG(n,q). In this paper, the known upper bound on m2(3,q), q even, q 8, is improved. This new upper bound on m2(3,q) is then used to improve the upper bounds on m2(n,q), q even, q 8 and n 4.     

多色经典Ramsey数R( q,q,…,q )(n个)的下界 *

提出了探求n色经典Ramsey数R(q ,q ,… ,q) =R_n(q)的下界的一种方法 ,并用这种方法借助计算机求得6个新的下界:R₄(4)≥ 458,R₃ ( 5 )≥242 ,R₃ ( 6 )≥1 070 ,R₃ (7)≥ 1 214,R₃ (8)≥ 2 834以及R₃ (9)≥ 5 282 .     

Partial regularity for variational integrals with (s,\mu ,q)–Growth

We introduce integrands of –type, which are, roughly speaking, of lower (upper) growth rate ) satisfying in addition for some . Then, if , we prove partial –regularity of local minimizers by the way including integrands f being controlled by some N–function and also integrands of anisotropic power growth. Moreover, we extend the known results up to a certain limit and present examples which are not covered by the standard theory. Received: 17 February 2000 / Accepted: 23 January 2001 / Published online: 4 May 2001     

On Split δ-Jordan Lie Triple Systems

The aim of this article is to study the structures of arbitrary split δ-Jordan Lie triple systems, which are a generalization of split Lie triple systems. By developing techniques of connections of roots for this kind of triple systems, we show that any of such δ-Jordan Lie triple systems T with a symmetric root system is of the form ■with U a subspace of T0 and any I[α] a well described ideal of T, satisfying■ .     

Mode Dependent H∞ Filtering for Discrete-Time Networked Systems with Random Measurement Missing and Delays

The article investigates the H_∞ filtering problem for a class of discrete-time networked systems with random measurement losses and delays. Markov chain is used here to model measurement losses and delays in a unified framework. Based on the mode-dependent Lyapunov function approach, the necessary and sufficient conditions are derived to guarantee the exponential stability with a prescribed H_∞ disturbance attenuation performance for the filtering error system. By using a novel design scheme, the explicit expressions of mode dependent filter parameters are given in the form of linear matrix inequalities (LMIs) which can be readily solved by using the LMI TOOLBOX in MATLAB. At last, a numerical example is given to illustrate the feasibility and effectiveness of the proposed method.     

一般投影线性群PGL(2,q)和4-(q+1,5,λ)设计

本文主要考虑了一般投影线性群PGL(2,q)区传递作用下的4-(q+1,5,λ)设计的存在性问题。经讨论知λ的可能值是4。     

Generalized Steiner Systems GS(2, 4, v, 2) with v a Prime Power ≡ 7 (mod 12)

Generalized Steiner systems GS(2, 4, v, g) were first introduced by Etzion and were used to construct optimal constant weight codes over an alphabet of size g + 1 with minimum Hamming distance 5, in which each codeword has length v and weight 4. Etzion conjectured that the necessary conditions v 1 (mod 3) and v ; 7 are also sufficient for the existence of a GS(2,4,v,2). Except for the example of a GS(2,4,10,2) and some recursive constructions given by Etzion, nothing else is known about this conjecture. In this paper, Weil's theorem on character sum estimates is used to show that the conjecture is true for any prime power v 7 (mod 12) except v = 7, for which there does not exist a GS(2,4,7,2).     

On an Isomorphism Problem of Some Dual Hyperovals in PG(2d + 1, q) with q even

Let q = 2^l with l≥ 1 and d ≥ 2. We prove that any automorphism of the d-dimensional dual hyperoval over GF(q), constructed in [3] for any (d + 1)-dimensional GF(q)-vector subspace V in GF(qⁿ) with n≥ d + 1 and for any generator σ of the Galois group of GF(qⁿ) over GF(q), always fixes the special member X(∞). Moreover, we prove that, in case V = GF(q^d+1), two dual hyperovals and in PG(2d + 1,q), where σ and τ are generators of the Galois group of GF(q^d+1) over GF(q), are isomorphic if and only if (1) σ = τ or (2) σ τ = id. Therefore, we have proved that, even in the case q > 2, there exist non isomorphic d-dimensional dual hyperovals in PG(2d + 1,q) for d ≥ 3.