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1.

Ajeet Kumar Yadav Rajendra M. Pawale Mohan S. Shrikhande 《组合设计杂志》2020,28(9):670-687

Let

X

be a finite set with

v

elements, called points and

β

be a family of subsets of

X

, called blocks. A pair

(X, β)

is called

λ

‐design whenever

∣ β ∣ = ∣ X ∣

and

1. for all $B_{i}, B_{j} \in β, i \neq j, ∣ B_{i} \cap B_{j} ∣ = λ$ ;
2. for all $B_{j} \in β, ∣ B_{j} ∣ = k_{j} > λ$ , and not all $k_{j}$ are equal.

The only known examples of

λ

‐designs are so‐called type‐1 designs, which are obtained from symmetric designs by a certain complementation procedure. Ryser and Woodall had independently conjectured that all

λ

‐designs are type‐1. Let

r, r^{*} ? (r > r^{*})

be replication numbers of a

λ

‐design

D = (X, β)

and

g = gcd (r ? 1, r^{*} ? 1), m = gcd ((r ? r^{*}) ∕ g, λ)

, and

m' = m

, if

m

is odd and

m' = m ∕ 2

, otherwise. For distinct points

x

and

y

of

D

, let

λ (x, y)

denote the number of blocks of

X

containing

x

and

y

. We strengthen a lemma of S.S. Shrikhande and N.M. Singhi and use it to prove that if

\frac{r (r ? 1)}{(v ? 1)} ? \frac{k (r ? r^{*})}{m' (v ? 1)}

are not integers for

k = 1, 2, …, m' ? 1

, then

D

is type‐1. As an application of these results, we show that for fixed positive integer

θ

there are finitely many nontype‐1

λ

‐designs with

r = r^{*} + θ

. If

r ? r^{*} = 27

or

r ? r^{*} = 4 p

and

r^{*} \neq {(p ? 1)}^{2}

, or

v = 7 p + 1

such that

p ? 1, 13 (\mod 21)

and

p ? 4, 9, 19, 24 (\mod 35)

, where

p

is a positive prime, then

D

is type‐1. We further obtain several inequalities involving

λ (x, y)

, where equality holds if and only if D is type‐1. 相似文献

2.

Naushad Pasha Puliyambalath Ákos Seress Iván Weisz 《组合设计杂志》2012,20(9):408-431

A λ‐design is a family of subsets of such that for all and not all are of the same size. Ryser's and Woodall's λ‐design conjecture states that each λ‐design can be obtained from a symmetric block design by a certain complementation procedure. Our main result is that the conjecture is true when λ < 63. © 2012 Wiley Periodicals, Inc. J. Combin. Designs 20: 408–431, 2012 相似文献

3.

Non Deterministic Classical Logic: The λμ++ ‐calculus

Karim Nour 《Mathematical Logic Quarterly》2002,48(3):357-366

In this paper, we present an extension of λμ‐calculus called λμ⁺⁺‐calculus which has the following properties: subject reduction, strong normalization, unicity of the representation of data and thus confluence only on data types. This calculus allows also to program the parallel‐or. 相似文献

4.

Grace Piper 《Mathematical Logic Quarterly》2009,55(5):562-568

We develop the theory of C_{κ, λ}ⁱ, a strongly normal filter over ??_κλ for Mahlo κ. We prove a minimality result, showing that any strongly normal filter containing {x ∈ ??_κλ: |x | = |x ∩ κ | and |x | is inaccessible} also contains C_{κ, λ}ⁱ. We also show that functions can be used to obtain a basis for C_{κ, λ}ⁱ (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献

5.

N. S. Mendelsohn M. Liang 《组合设计杂志》2003,11(1):1-23

We are already familiar with (υ, k, λ)‐difference sets and (υ, k, λ)‐designs. In this paper, we will introduce a new class of difference sets and designs: (υ, k, [λ₁, λ₂, … , λ_m])‐difference sets and (υ, k, [λ₁,λ₂, … , λ_m])‐designs. We will mainly study designs with a relationship we call λ‐equivalence and use them to produce other designs. Some existence or nonexistence theorems will be given. © 2002 Wiley Periodicals, Inc. J Combin Designs 11: 1–23, 2003; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/jcd.10031 相似文献

6.

Elena Toscano Calogero Vetro 《Mathematical Methods in the Applied Sciences》2017,40(5):1438-1447

We prove some convergence theorems for α‐ψ‐pseudocontractive operators in real Hilbert spaces, by using the concept of admissible perturbation. Our results extend and complement some theorems in the existing literature. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献

7.

Qingde Kang Yanfang Zhang 《组合设计杂志》2002,10(3):151-159

Let G=(V(G),E(G)) be a graph. A (n,G, λ)‐GD is a partition of the edges of λK_n into subgraphs (G‐blocks), each of which is isomorphic to G. The (n,G,λ)‐GD is named as graph design for G or G‐decomposition. The large set of (n,G,λ)‐GD is denoted by (n,G,λ)‐LGD. In this work, we obtain the existence spectrum of (n,P₃,λ)‐LGD. © 2002 Wiley Periodicals, Inc. J Combin Designs 10: 151–159, 2002; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/jcd.10008 相似文献

8.

Paolo Lipparini 《Mathematical Logic Quarterly》2010,56(4):340-374

We prove, in ZFC alone, some new results on regularity and decomposability of ultrafilters; among them: (a) If m ≥ 1 and the ultrafilter D is (_m(λ⁺ⁿ), _m(λ⁺ⁿ))‐regular, then D is κ ‐decomposable for some κ with λ ≤ κ ≤ 2^λ (Theorem 4.3(a^')). (b) If λ is a strong limit cardinal and D is (_m(λ⁺ⁿ), _m(λ⁺ⁿ))‐regular, then either D is (cf λ, cf λ)‐regular or there are arbitrarily large κ < λ for which D is κ ‐decomposable (Theorem 4.3(b)). (c) Suppose that λ is singular, λ < κ, cf κ ≠ cf λ and D is (λ⁺, κ)‐regular. Then: (i) D is either (cf λ, cf λ)‐regular, or (λ^', κ)‐regular for some λ^' < λ (Theorem 2.2). (ii) If κ is regular, then D is either (λ, κ)‐regular, or (ω, κ^')‐regular for every κ^' < κ (Corollary 6.4). (iii) If either (1) λ is a strong limit cardinal and λ^<λ < 2^κ, or (2) λ^<λ < κ, then D is either λ ‐decomposable, or (λ^', κ)‐regular for some λ^' < λ (Theorem 6.5). (d) If λ is singular, D is (μ, cf λ)‐regular and there are arbitrarily large ν < λ for which D is ν ‐decomposable, then D is κ ‐decomposable for some κ with λ ≤ κ ≤ λ^<μ (Theorem 5.1; actually, our result is stronger and involves a covering number). (e) D × D^' is (λ, μ)‐regular if and only if there is a ν such that D is (ν, μ)‐regular and D^' is (λ, ν^')‐regular for all ν^～ < ν (Proposition 7.1). We also list some problems, and furnish applications to topological spaces and to extended logics (Corollar‐ies 4.6 and 4.8) (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献

9.

Shivani Rai Shakti Banerjee Sanpei Kageyama 《组合设计杂志》2004,12(6):466-470

10.

The basis decision problem in λ-calculus

Benedetto Intrigila 《Mathematical Logic Quarterly》1993,39(1):178-180

We show that the problem of deciding if a finite set of closed terms in normal form is a basis is recursively unsolvable. The restricted problem concerning one element sets is still recursively unsolvable. MSC: 03B40, 03D35. 相似文献

11.

Giuseppe Longo 《Mathematical Logic Quarterly》2000,46(2):257-266

The proofs of universally quantified statements, in mathematics, are given as “schemata” or as “prototypes” which may be applied to each specific instance of the quantified variable. Type Theory allows to turn into a rigorous notion this informal intuition described by many, including Herbrand. In this constructive approach where propositions are types, proofs are viewed as terms of λ‐calculus and act as “proof‐schemata”, as for universally quantified types. We examine here the critical case of Impredicative Type Theory, i. e. Girard's system F, where type‐quantification ranges over all types. Coherence and decidability properties are proved for prototype proofs in this impredicative context. 相似文献

12.

Pierre Matet 《Mathematical Logic Quarterly》2003,49(6):615-628

Given a regular infinite cardinal κ and a cardinal λ > κ, we study fine ideals H on P_κ(λ) that satisfy the square brackets partition relation , where μ is a cardinal ≥2. (© 2003 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献

13.

Hatice Gül &#x;nce &#x;larslan Hasan Erbay Ali Aral 《Mathematical Methods in the Applied Sciences》2019,42(18):6580-6587

相似文献

14.

R. P. Anstee Farzin Barekat Zachary Pellegrin 《组合设计杂志》2020,28(6):445-457

In this paper we relate

t

‐designs to a forbidden configuration problem in extremal set theory. Let

1_{t} 0_{?}

denote a column of

t

1's on top of

?

0's. Let

q ? 1_{t} 0_{?}

denote the

(t + ?) \times q

matrix consisting of

t

rows of

q

1's and

?

rows of

q

0's. We consider extremal problems for matrices avoiding certain submatrices. Let

A

be a (0, 1)‐matrix forbidding any

(t + ?) \times (λ + 2)

submatrix

(λ + 2) ? 1_{t} 0_{?}

. Assume

A

is

m

‐rowed and only columns of sum

t + 1, t + 2, …, m ? ?

are allowed to be repeated. Assume that

A

has the maximum number of columns subject to the given restrictions. Assume

m

is sufficiently large. Then

A

has each column of sum

0, 1, …, t

and

m ? ? + 1, m ? ? + 2, …, m

exactly once and, given the appropriate divisibility condition, the columns of sum

t + 1

correspond to a

t

‐design with block size

t + 1

and parameter

λ

. The proof derives a basic upper bound on the number of columns of

A

by a pigeonhole argument and then a careful argument, for large m, reduces the bound by a substantial amount down to the value given by design‐based constructions. We extend in a few directions. 相似文献

15.

Guangzhou Chen Lijun Ji Jianguo Lei 《组合设计杂志》2014,22(8):323-342

Symmetric orthogonal arrays and mixed orthogonal arrays are useful in the design of various experiments. They are also a fundamental tool in the construction of various combinatorial configurations. In this paper, we investigated the mixed orthogonal arrays with four and five factors of strength two, and proved that the necessary conditions of such mixed orthogonal arrays are also sufficient with several exceptions and one possible exception. 相似文献

16.

Hiroki Tamura 《组合设计杂志》2006,14(6):451-462

We obtain new conditions on the existence of a square matrix whose Gram matrix has a block structure with certain properties, including D‐optimal designs of order , and investigate relations to group divisible designs. We also find a matrix with large determinant for n = 39. © 2006 Wiley Periodicals, Inc. J Combin Designs 14: 451–462, 2006 相似文献

17.

Xia Zhang BaoZheng Wang Ming Liu 《Mathematical Methods in the Applied Sciences》2019,42(16):5251-5257

A random normed module is a random generalization of an ordinary normed space, and it is the randomization that makes a random normed module possess rich stratification structures. On the basis of these stratification structures, this paper shows that either the kernel space N(f) for an L⁰‐linear function f from a random normed module S to the algebra is a closed submodule or N(f) on some specifical stratification is a dense proper submodule of S, which generalizes the classical case. In the meantime, a characterization for the kernel space N(f) to be closed is also given. 相似文献

18.

Jin Zhang 《Mathematical Methods in the Applied Sciences》2019,42(18):6139-6154

In this paper, we provide some geometric properties of λ‐symmetries of ordinary differential equations using vector fields and differential forms. According to the corresponding geometric representation of λ‐symmetries, we conclude that first integrals can also be derived if the equations do not possess enough symmetries. We also investigate the properties of λ‐symmetries in the sense of the deformed Lie derivative and differential operator. We show that λ‐symmetries have the exact analogous properties as standard symmetries if we take into consideration the deformed cases. 相似文献

19.

Zaihong Jiang Jishan Fan 《Mathematical Methods in the Applied Sciences》2014,37(6):838-845

We consider the long time behavior of solutions to the magnetohydrodynamics‐ α model in three spatial dimensions. Time decay rate in L²‐norm of the solution is obtained. Similar results for a generalized Leray‐ α‐magnetohydrodynamics model are also established. As a by‐product, an optimal time decay rate for the Navier–Stokes‐ α model is achieved. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献

20.

Shagufta Rahman Mohammad Mursaleen Ana Maria Acu 《Mathematical Methods in the Applied Sciences》2019,42(11):4042-4053

In the present article, Kantorovich variant of λ‐Bernstein operators with shifted knots are introduced. The advantage of using shifted knot is that one can do approximation on [0,1] as well as on its subinterval. In addition, it adds flexibility to operators for approximation. Some basic results for approximation as well as rate of convergence of the introduced operators are established. The r^th order generalization of the operator is also discussed. Further for comparisons, some graphics and error estimation tables are presented using MATLAB. 相似文献