共查询到20条相似文献,搜索用时 46 毫秒
1.
S. A. Vanstone D. R. Stinson P. J. Schellenberg A. Rosa R. Rees C. J. Colbourn M. W. Carter J. E. Carter 《Israel Journal of Mathematics》1993,83(3):305-319
Hanani triple systems onv≡1 (mod 6) elements are Steiner triple systems having (v−1)/2 pairwise disjoint almost parallel classes (sets of pairwise disjoint triples that spanv−1 elements), and the remaining triples form a partial parallel class. Hanani triple systems are one natural analogue of the
Kirkman triple systems onv≡3 (mod 6) elements, which form the solution of the celebrated Kirkman schoolgirl problem. We prove that a Hanani triple system
exists for allv≡1 (mod 6) except forv ∈ {7, 13}. 相似文献
2.
By a “reproducing” method forH =L
2(ℝ
n
) we mean the use of two countable families {e
α : α ∈A}, {f
α : α ∈A}, inH, so that the first “analyzes” a function h ∈H by forming the inner products {<h,e
α >: α ∈A} and the second “reconstructs” h from this information:h = Σα∈A <h,e
α >:f
α.
A variety of such systems have been used successfully in both pure and applied mathematics. They have the following feature
in common: they are generated by a single or a finite collection of functions by applying to the generators two countable
families of operators that consist of two of the following three actions: dilations, modulations, and translations. The Gabor
systems, for example, involve a countable collection of modulations and translations; the affine systems (that produce a variety
of wavelets) involve translations and dilations.
A considerable amount of research has been conducted in order to characterize those generators of such systems. In this article
we establish a result that “unifies” all of these characterizations by means of a relatively simple system of equalities.
Such unification has been presented in a work by one of the authors. One of the novelties here is the use of a different approach
that provides us with a considerably more general class of such reproducing systems; for example, in the affine case, we need
not to restrict the dilation matrices to ones that preserve the integer lattice and are expanding on ℝ
n
. Another novelty is a detailed analysis, in the case of affine and quasi-affine systems, of the characterizing equations
for different kinds of dilation matrices. 相似文献
3.
M. Yu. Yurkin 《Mathematical Notes》1995,58(5):1223-1226
A proof is given of the stability theorem for minimal systems of exponentialse(Λ) = {e
iλx
}λ∈Λ inL
p
[−π, π], where Λ ⊂ ℂ is a discrete subset. Geometric minimality conditions for such systems are obtained.
Translated fromMatematicheskie Zametki, Vol. 58, No. 5, pp. 773–777, November, 1995.
I wish to express gratitude to A. A. Shkalikov, who posed the problem and paid constant attention to this work. 相似文献
4.
V. I. Borzdyko 《Ukrainian Mathematical Journal》2010,62(1):15-30
We prove the existence of positive ω-periodic solutions for some “predator–prey” systems with continuous delay of the argument for the case where the parameters
of these systems are specified by ω-periodic continuous positive functions. 相似文献
5.
For dynamical systems defined by a covering map of a compact Hausdorff space and the corresponding transfer operator, the
associated crossed product C
*-algebras C(X)⋊
α,ℒℕ introduced by Exel and Vershik are considered. An important property for homeomorphism dynamical systems is topological
freeness. It can be extended in a natural way to in general non-invertible dynamical systems generated by covering maps. In
this article, it is shown that the following four properties are equivalent: the dynamical system generated by a covering
map is topologically free; the canonical embedding of C(X) into C(X)⋊
α,ℒℕ is a maximal abelian C
*-subalgebra of C(X)⋊
α,ℒℕ; any nontrivial two sided ideal of C(X)⋊
α,ℒℕ has non-zero intersection with the embedded copy of C(X); a certain natural representation of C(X)⋊
α,ℒℕ is faithful. This result is a generalization to non-invertible dynamics of the corresponding results for crossed product
C
*-algebras of homeomorphism dynamical systems. 相似文献
6.
7.
Floris Takens 《Bulletin of the Brazilian Mathematical Society》2002,33(2):231-262
The reconstruction theorem deals with dynamical systems which are given by a map ψ : M → M together with a read out function 𝒻 : M → ℝ. Restricting to the cases where ψ is a diffeomorphism, it states that for generic (ψ, 𝒻 ) there is a bijection between
elements x ∈ M and corresponding sequences (𝒻(x), 𝒻 (ψ(x)), . . . , 𝒻 (ψ
k
-1(x))) of k successive observations, at least for k sufficiently big. This statement turns out to be wrong in cases where ψ is an endomorphism.
In the present paper we derive a version of this theorem for endomorphisms (and which is equivalent to the original theorem
in the case of diffeomorphisms). It justifies, also for dynamical systems given by endomorphisms, the algorithms for estimating
dimensions and entropies of attractors from obervations.
Received: 20 June 2002 相似文献
8.
A. I. Kozko 《Journal of Mathematical Sciences》2006,139(6):7151-7164
We study the problem on the completeness of orthogonal systems in asymmetric spaces with sign-sensitive weight. Theorems of
general form are obtained. In particular, the necessary and sufficient conditions on α, β, q
1, and q
2 for which the known orthogonal systems are everywhere dense in asymmetric spaces L
(α,β);q ([0, 1]) are found.
Theorem. Let α, β, q
1, q
2 ∈ [1,+∞]. The following orthogonal systems are dense in asymmetric spaces L
(α,β);q ([0, 1]) if and only if either max{α, β, q
1, q
2} < + ∞ or max {α, β} < +∞, q
1 = q
2 = +∞: trigonometric, algebraic, Haar’s system, Meyer’s system of wavelets, Shannon-Kotel’nikov wavelets, Stromberg and Lemarie-Battle
wavelets, the Walsh system, and the Franklin system.
__________
Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 24, Dynamical
Systems and Optimization, 2005. 相似文献
9.
A. V. Smirnov 《Theoretical and Mathematical Physics》2009,158(3):300-312
We show a relation between systems of integrable tops on the algebras sl(N, ℂ) and Calogero-Moser systems of N particles. We construct classical Lax operators corresponding to these systems. We show
that these operators are related to certain new trigonometric and rational solutions of the Yang-Baxter equations for the
algebras sl(N, ℂ) and give explicit formulas for N = 2, 3.
__________
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 158, No. 3, pp. 355–369, March, 2009. 相似文献
10.
A new relation between morphisms in a category is introduced—roughly speaking (accurately in the categories Set and Top), f ∥ g iff morphisms w:dom(f)→dom(g) never map subobjects of fibres of f non-constantly to fibres of g. (In the algebraic setting replace fibre with kernel.) This relation and a slight weakening of it are used to define “connectedness”
versus “disconnectedness” for morphisms. This parallels and generalises the classical treatment of connectedness versus disconnectedness
for objects in a category (in terms of constant morphisms). The central items of study are pairs (F,G)({\mathcal F},{\mathcal G}) of classes of morphisms which are corresponding fixed points of the polarity induced by the ∥-relation. Properties of such
pairs are examined and in particular their relation to (pre)factorisation systems is analysed. The main theorems characterise:
(a) |
factorisation systems which factor morphisms through a regular epimorphic “connected” morphism followed by a “disconnected”
morphism, and 相似文献
11.
Zhang Jinwen 《数学学报(英文版)》1988,4(1):72-75
In this paper we develop a sequenceZ
0, ...,Z
α,... of axiom systems for set theory, such that (1) the consistency of any system within the sequence is provable in its succeeding
systems, (2) the first system in the sequence is Zermelo's system Z and the union of all systems in the sequence is justZF. And we prove that for ordinal number α>1, there exists a sequence of ℵa+1 axiom systems between systemsZ
α andZ
α+1 such that these systems satisfy the above condition (1). 相似文献
12.
In a recent paper, the authors studied some algebraic hypersurfaces of the third order in the projective spacePG(5,q) and they called them ruled cubics, since they possess three systems of planes. Any two of these constitute a regular switching
set and furthermore, if Σ is a given regular spread ofPG(5,q), one of the three systems is contained in Σ.
The subject of this note is to prove, conversely, that every regular switching set (Φ, Φ′) with Φ ⊂ Σ is a ruled cubic and
to construct, for a generic choice of the projective reference system inP
G(5,q), the quasifield which coordinatizes the translation plane Π associated with the spread (Σ − Φ) ∪ Φ′.
The planes Π, of orderq
3, are a generalization of the finite Hall planes. 相似文献
13.
Branko Dragovich Zoran Rakić 《P-Adic Numbers, Ultrametric Analysis, and Applications》2010,2(4):322-340
Feynman’s path integrals in ordinary, p-adic and adelic quantum mechanics are considered. The corresponding probability amplitudes K(x″, t″; x′, t′) for two-dimensional systems with quadratic Lagrangians are evaluated analytically and obtained expressions are generalized
to any finite-dimensional spaces. These general formulas are presented in the form which is invariant under interchange of
the number fields ℝ ↔ ℚ
p
and ℚ ↔ ℚ
p
, p ≠ p′. According to this invariance we have that adelic path integral is a fundamental object in mathematical physics of quantum
phenomena. 相似文献
14.
Belén García Jesús S. Pérez Del Río Jaume Llibre 《Rendiconti del Circolo Matematico di Palermo》2006,55(3):420-440
In this work we classify the phase portraits of all quadratic polynomial differential systems having a polynomial first integral.
IfH(x, y) is a polynomial of degreen+1 then the differential systemx′=−∂H/∂y,y′=∂H/∂x is called a Hamiltonian system of degreen. We also prove that all the phase portraits that we obtain in this paper are realizable by Hamiltonian systems of degree
2. 相似文献
15.
V. M. Shelkovich 《Journal of Mathematical Sciences》2008,151(1):2781-2792
New definitions of δ-shock-wave-type solutions are introduced for two (one-dimensional) types of hyperbolic systems of conservation laws. The
corresponding Rankine-Hugoniot conditions for δ-shocks are derived and their geometrical interpretation is given. Balance laws connected with “area” mass and momentum transportation
for δ-shocks are derived.
__________
Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 12, No. 6, pp. 213–229, 2006. 相似文献
16.
V.V. Rybakov 《Archive for Mathematical Logic》2003,42(2):179-200
In terms of formal deductive systems and multi-dimensional Kripke frames we study logical operations know, informed, common knowledge and common information. Based on [6] we introduce formal axiomatic systems for common information logics and prove that these systems are sound
and complete. Analyzing the common information operation we show that it can be understood as greatest open fixed points for
knowledge formulas. Using obtained results we explore monotonicity, omniscience problem, and inward monotonocity, describe
their connections and give dividing examples. Also we find algorithms recognizing these properties for some particular cases.
Received: 21 October 2000 / Published online: 2 September 2002
Key words or phrases: Multi-agent systems – Non-standard logic – Knowledge representation – Common knowledge – Common information – Fixed points,
Kripke models – Modal logic 相似文献
17.
B. Ruf 《Proceedings of the Steklov Institute of Mathematics》2006,255(1):234-243
We consider nonlinear elliptic equations of the form −Δu = g(u) in Ω, u = 0 on ∂Ω, and Hamiltonian-type systems of the form −Δu = g(v) in Ω, −Δv = f(u) in Ω, u = 0 and v = 0 on ∂Ω, where Ω is a bounded domain in ℝ2 and f, g ∈ C(ℝ) are superlinear nonlinearities. In two dimensions the maximal growth (= critical growth) of f and g (such that the problem can be treated variationally) is of exponential type, given by Pohozaev-Trudinger-type inequalities.
We discuss existence and nonexistence results related to the critical growth for the equation and the system. A natural framework
for such equations and systems is given by Sobolev spaces, which provide in most cases an adequate answer concerning the maximal
growth involved. However, we will see that for the system in dimension 2, the Sobolev embeddings are not sufficiently fine
to capture the true maximal growths. We will show that working in Lorentz spaces gives better results.
Dedicated to Professor S. Nikol’skii on the occasion of his 100th birthday 相似文献
18.
G. V. Shevchenko 《Computational Mathematics and Mathematical Physics》2011,51(4):537-549
Nonlinear systems with a stationary (i.e., explicitly time independent) right-hand side are considered. For time-optimal control
problems with such systems, an iterative method is proposed that is a generalization of one used to solve nonlinear time-optimal
control problems for systems divided by phase states and controls. The method is based on constructing finite sequences of
simplices with their vertices lying on the boundaries of attainability domains. Assuming that the system is controllable,
it is proved that the minimizing sequence converges to an ɛ-optimal solution after a finite number of iterations. A pair {T, u(·)} is called an ɛ-optimal solution if |T − T
opt| − ɛ, where T
opt is the optimal time required for moving the system from the initial state to the origin and u is an admissible control that moves the system to an ɛ-neighborhood of the origin over the time T. 相似文献
19.
V. I. Skrypnik 《Ukrainian Mathematical Journal》1997,49(5):770-778
Quantum systems of particles interacting via an effective electromagnetic potential with zero electrostatic component are
considered (magnetic interaction). It is assumed that the j th component of the effective potential for n particles equals the partial derivative with respect to the coordinate of the jth particle of “magnetic potential energy” of n particles almost everywhere. The reduced density matrices for small values of the activity are computed in the thermodynamic
limit for d-dimensional systems with short-range pair magnetic potentials and for one-dimensional systems with long-range pair magnetic
interaction, which is an analog of the interaction of three-dimensional Chern-Simons electrodynamics (“magnetic potential
energy” coincides with the one-dimensional Coulomb (electrostatic) potential energy).
Institute of Mathematics, Ukrainian Academy of Sciences, Kiev. Published in Ukrainskii Matematicheskii Zhurnal, Vol. 49, No.
5, pp. 691–698, May 1997. 相似文献
20.
In this paper, we consider a new class of random dynamical systems that contains, in particular, neural networks and complicated
circuits. For these systems, we consider the viability problem: we suppose that the system survives only the system state
is in a prescribed domain Π of the phase space. The approach developed here is based on some fundamental ideas proposed by
A. Kolmogorov, R. Thom, M. Gromov, L. Valiant, L. Van Valen, and others. Under some conditions it is shown that almost all
systems from this class with fixed parameters are unstable in the following sense: the probability P
t
to leave Π within the time interval [0, t] tends to 1 as t → ∞. However, it is allowed to change these parameters sometimes (“evolutionary” case), then it may happen that P
t
< 1 − δ < 1 for all t (“stable evolution”). Furthermore, we study the properties of such a stable evolution assuming that the system parameters
are encoded by a dicsrete code. This allows us to apply complexity theory, coding, algorithms, etc. Evolution is a Markov
process of modification of this code. Under some conditions we show that the stable evolution of unstable systems possesses
the following general fundamental property: the relative Kolmogorov complexity of the code cannot be bounded by a constant
as t → ∞. For circuit models, we define complexity characteristics of these circuits. We find that these complexities also have
a tendency to increase during stable evolution. We give concrete examples of stable evolution. Bibliography: 80 titles.
To the memory of A. N. Livshitz
Published in Zapiski Nauchnykh Seminarov POMI, Vol. 360, 2008, pp. 31–69. 相似文献
|