Showing papers in "Acta Applicandae Mathematicae in 1992"
TL;DR: A finite subset (code) is characterized by the minimal distance d(W) between its distinct elements, the number l(W), and the maximal strength τ (W) of the design generated by the code.
Abstract: Finite and infinite metric spaces % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWefv3ySLgzgj% xyRrxDYbqeguuDJXwAKbIrYf2A0vNCaGqbaiab-Xa8nbaa!427C!\[\mathfrak{M}\] that are polynomial with respect to a monotone substitution of variable t(d) are considered A finite subset (code) W % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGGipm0dc9vqaqpepu0xbbG8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyOHI0maaa!36D8!\[ \subseteq \] % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWefv3ySLgzgj% xyRrxDYbqeguuDJXwAKbIrYf2A0vNCaGqbaiab-Xa8nbaa!427C!\[\mathfrak{M}\] is characterized by the minimal distance d(W) between its distinct elements, by the number l(W) of distances between its distinct elements and by the maximal strength τ(W) of the design generated by the code W A code W % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGGipm0dc9vqaqpepu0xbbG8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyOHI0maaa!36D8!\[ \subseteq \] % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWefv3ySLgzgj% xyRrxDYbqeguuDJXwAKbIrYf2A0vNCaGqbaiab-Xa8nbaa!427C!\[\mathfrak{M}\] is called a maximum one if it has the greatest cardinality among subsets of % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWefv3ySLgzgj% xyRrxDYbqeguuDJXwAKbIrYf2A0vNCaGqbaiab-Xa8nbaa!427C!\[\mathfrak{M}\] with minimal distance at least d(W), and diametrical if the diameter of W is equal to the diameter of the whole space % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWefv3ySLgzgj% xyRrxDYbqeguuDJXwAKbIrYf2A0vNCaGqbaiab-Xa8nbaa!427C!\[\mathfrak{M}\] Delsarte codes are codes W % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGGipm0dc9vqaqpepu0xbbG8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyOHI0maaa!36D8!\[ \subseteq \] % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWefv3ySLgzgj% xyRrxDYbqeguuDJXwAKbIrYf2A0vNCaGqbaiab-Xa8nbaa!427C!\[\mathfrak{M}\] with τ(W)≥2l(W)−1 or τ(W)=2l(W)−2>0 and W is a diametrical code It is shown that all parameters of Delsarte codes W) % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGGipm0dc9vqaqpepu0xbbG8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyOHI0maaa!36D8!\[ \subseteq \] % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWefv3ySLgzgj% xyRrxDYbqeguuDJXwAKbIrYf2A0vNCaGqbaiab-Xa8nbaa!427C!\[\mathfrak{M}\] are uniquely determined by their cardinality |W| or minimal distance d(W) and that the minimal polynomials of the Delsarte codes W % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGGipm0dc9vqaqpepu0xbbG8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyOHI0maaa!36D8!\[ \subseteq \] % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWefv3ySLgzgj% xyRrxDYbqeguuDJXwAKbIrYf2A0vNCaGqbaiab-Xa8nbaa!427C!\[\mathfrak{M}\] are expansible with positive coefficients in an orthogonal system of polynomials {Q
i(t)} corresponding to % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWefv3ySLgzgj% xyRrxDYbqeguuDJXwAKbIrYf2A0vNCaGqbaiab-Xa8nbaa!427C!\[\mathfrak{M}\] The main results of the present paper consist in a proof of maximality of all Delsarte codes provided that the system {Q
i)} satisfies some condition and of a new proof confirming in this case the validity of all the results on the upper bounds for the maximum cardinality of codes W % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGGipm0dc9vqaqpepu0xbbG8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyOHI0maaa!36D8!\[ \subseteq \]% MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWefv3ySLgzgj% xyRrxDYbqeguuDJXwAKbIrYf2A0vNCaGqbaiab-Xa8nbaa!427C!\[\mathfrak{M}\] with a given minimal distance, announced by the author in 1978 Moreover, it appeared that this condition is satisfied for all infinite polynomial metric spaces as well as for distance-regular graphs, decomposable in a sense defined below It is also proved that with one exception all classical distance-regular graphs are decomposable In addition for decomposable distance-regular graphs an improvement of the absolute Delsarte bound for diametrical codes is obtained For the Hamming and Johnson spaces, Euclidean sphere, real and complex projective spaces, tables containing parameters of known Delsarte codes are presented Moreover, for each of the above-mentioned infinite spaces infinite sequences (of maximum) Delsarte codes not belonging to tight designs are indicated
150 citations
TL;DR: In this paper, the authors survey results of the authors and others conceming estimates for the Hausdorff dimension of strange attractors, particularly in the case of (generalized) Lorenz systems and Rossler systems.
Abstract: This paper surveys results of the authors and others conceming estimates for the Hausdorff dimension of strange attractors, particularly in the case of (generalized) Lorenz systems and Rossler systems. A key idea is the interpretation of Hausdorff measure as an analogue of a Lyapunov function.
102 citations
TL;DR: In this paper, the second-order differential invariants of the Euclid, Poincare, Galilei, conformal, and projective algebras are constructed.
Abstract: Functional bases of second-order differential invariants of the Euclid, Poincare, Galilei, conformal, and projective algebras are constructed. The results obtained allow us to describe new classes of nonlinear many-dimensional invariant equations.
35 citations
TL;DR: In this paper, the authors considered the problem of k-orbit reconstruction and its connections with combinatorics, and developed a technique based on the notion of co-orbit algebras associated with a given permutation group (G, W).
Abstract: Let (G, W) be a permutation group on a finite set W = {w
1,..., w
n}. We consider the natural action of G on the set of all subsets of W. Let h
0, h
1,..., h
N
be the orbits of this action. For each i, 1 ≤ i ≤ N, there exists k, 1 ≤ k ≤ n, such that h
i
is a set of k-element subsets of W. In this case h
i is called a symmetrized k-orbit of the group (G, W) or simply a k-orbit. With a k-orbit h
i
we associate a multiset H(h
i
) = % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGGipm0dc9vqaqpepu0xbbG8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyykJeoaaa!3690!\[\langle \]h
i
(1), h
i
(2),..., h
i
(k)% MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGGipm0dc9vqaqpepu0xbbG8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyOkJepaaa!36A1!\[\rangle \] of its (k − 1)-suborbits. Orbits h
i
and h
j
are called equivalent if H(h
i
) = H(h
j
). An orbit is reconstructible if it is equivalent to itself only. The paper concerns the k-orbit reconstruction problem and its connections with different problems in combinatorics. The technique developed is based on the notion of orbit and co-orbit algebras associated with a given permutation group (G, W).
33 citations
TL;DR: In this article, the authors present a proof of Baillon's Theorem on Maximal Regularity for abstract Cauchy problems, which is a negative result (it states that maximal regularity can occur only in very special cases).
Abstract: The aim of this note is to give a proof of Baillon’s Theorem on Maximal Regularity. Though it is in some sense a negative result (it states that for abstract Cauchy problems maximal regularity can occur only in very special cases), it is commonly accepted that it is important. Many people believe that its proof is very complicated. This might be due to the fact that Baillon’s note in the Comptes Rendus is rather short and sometimes difficult to understand. The proof outlined here follows basically Baillon’s lines. However it is simplified and (hopefully) easier to understand.
21 citations
TL;DR: Galerkin (finite elements) approximations of compensators/estimators for partially observed infinite-dimensional systems with unbounded control operators are considered in this paper.
Abstract: Galerkin (finite elements) approximations of compensators/estimators for partially observed infinite-dimensional systems with unbounded control operators are considered. It is shown that these approximations enjoy two features: (i) they provide a near-optimal performance, and (ii) they retain uniform asymptotic stability properties (uniform with respect to the parameter of discretization) of the entire closed loop system. Examples of hyperbolic equations with boundary controls and boundary observations are provided.
19 citations
TL;DR: A construction of a pair of strongly regular graphs of type L 2 n−1(4n−1) from skew-symmetric association schemes W, W′ of order 4n − 1 is presented in this paper.
Abstract: A construction of a pair of strongly regular graphs Гn and Г′n of type L
2n−1(4n−1) from a pair of skew-symmetric association schemes W, W′ of order 4n−1 is presented. Examples of graphs with the same parameters as Гn and Г′n, i.e., of type L
2n−1(4n−1), were known only if 4n−1=p
3, where p is a prime. The first new graph appearing in the series has parameters (v, k, λ)=(225, 98, 45). A 4-vertex condition for relations of a skew-symmetric association scheme (very similar to one for the strongly regular graphs) is introduced and is proved to hold in any case. This has allowed us to check the 4-vertex condition for Гn and Г′n, thus to prove that Гn and Г′n are not rank three graphs if n>2.
19 citations
TL;DR: The Ovsiannikov's orbit method for finding partially invariant solutions to compatibility systems is essentially based on such symmetries as mentioned in this paper, which is known as orbits of partially invariants and generic solutions involved in the Lie group foliation of differential equations.
Abstract: When symmetries of differential equations are applied, various types of associated systems of equations appear. Compatibility conditions of the associated systems expressed in the form of differential equations inherit Lie symmetries of the initial equations. Invariant solutions to compatibility systems are known as orbits of partially invariant and generic solutions involved in the Lie group foliation of differential equations and so on. In some cases Backlund transformations and differential substitutions connecting quotient equations for compatibility conditions and initial systems naturally arise. Besides, Ovsiannikov's orbit method for finding partially invariant solutions is essentially based on such symmetries.
18 citations
TL;DR: A survey of spectral properties of Krein operators can be found in this paper, where it is shown that every positive operator on a Krein space which is not a multiple of the identity operator has a nontrivial hyperinvariant subspace.
Abstract: A Krein operator is a positive operator, acting on a partially ordered Banach space, that carries positive elements to strong units. The purpose of this paper is to present a survey of the remarkable spectral properties (most of which were established by M.G. Krein) of these operators. The proofs presented here seem to be simpler than the ones existing in the literature. Some new results are also obtained. For instance, it is shown that every positive operator on a Krein space which is not a multiple of the identity operator has a nontrivial hyperinvariant subspace.
18 citations
TL;DR: In this paper, the main result of the present paper is an algorithm for finding among all tournaments the cyclic ones, and the running time of the algorithm is bounded by a polynomial function of the number of input tournament vertices.
Abstract: In [3] the problem of finding an efficient criterion for isomorphism testing of cyclic graphs was posed. In the context of the theory of computational complexity the problem reduces to that of the existence of a polynomial-time algorithm for recognizing their isomorphism. The main result of the present paper is an algorithm for finding among all tournaments the cyclic ones. For cyclic tournaments generators of the automorphism group and the set of canonical labels are constructed. The running time of the algorithm is bounded by a polynomial function of the number of input tournament vertices. Thus an affirmative answer to the above problem is obtained.
16 citations
TL;DR: In this article, the authors introduced variational principles of the type proposed by Morato for the stochastic action functional, for a dynamical system on curved manifolds, can be extended to the case of diffusion processes.
Abstract: The classical definition of the action functional, for a dynamical system on curved manifolds, can be extended to the case of diffusion processes. For the stochastic action functional so obtained, we introduce variational principles of the type proposed by Morato. In order to generalize the class of process variations, from the flat case originally given by Morato to general curved manifolds, we introduce the notion of stochastic differential systems. These give a synthetic characterization of the process and its variations as a generalized controlled stochastic process on the tangent bundle of the manifold. The resulting programming equations are equivalent to the quantum Schrodinger equation, where the wave function is coupled to an additional vector potential, satisfying a plasma-like equation with a peculiar dissipative behavior.
TL;DR: In this article, the authors study the characteristic speeds of systems of two conservation laws representing three-phase flow in a porous medium with gravity taken into account and show that for any choice of gravitational and viscosity parameters such regions shrinks to points where the characteristic speed is real and equal, provided that each relative permeability depends on its respective saturation only.
Abstract: We study the characteristic speeds of systems of two conservation laws representing three-phase flow in a porous medium with gravity taken into account. Generically hyperbolicity fails on open regions (elliptic regions) where the characteristic speeds assume complex values. The presence of such regions creates difficulties such as multiple solutions which indicate a modeling problem, according to some authors. The hyperbolicity of the models we study depends on the relative permeability functions. It is customary in oil engineering studies to suppose that the water and gas permeabilities depend only on their respective saturation, while the oil relative permeability changes with the gas and water saturations. Such a hypothesis on the oil relative permeability generically leads to elliptic regions. We define a set of three curves that surround elliptic regions of any model. By studying these curves, we indicate a procedure to locate the singularities and prove that for any choice of gravitational and viscosity parameters such regions shrinks to points where the characteristic speeds are real and equal, provided it is assumed that each relative permeability depends on its respective saturation only. Our results, together with a paper of Trangenstein, lead to the conclusion that in order to insure real wave speeds, such an assumption is necessary and sufficient when gravitational effects are considered in three-phase models.
TL;DR: In this paper, the Vlasov-Maxwell system is reduced to nonlinear elliptic equations in the stationary case and hyperbolic equations in nonstationary case, and theorems on the existence of solutions and sufficient conditions of Lyapunov stability are obtained.
Abstract: The study of the Vlasov-Maxwell system is reduced to nonlinear elliptic equations in the stationary case and hyperbolic equations in the nonstationary case On this basis, theorems on the existence of solutions and sufficient conditions of Lyapunov stability are obtained The cases are considered when electromagnetic fields and distribution functions can be constructed in an implicit form
TL;DR: In this article, the Equivariant Branching Lemma is extended to the case of non-linear (Lie-point) symmetries, and applied to gauge theories and gauge theoretic problems, and to nonlinear evolution PDE's.
Abstract: We review and recast the Equivariant Branching Lemma-which has proved a remarkable tool in linearly equivariant bifurcation theory-and consider its extension to the case of nonlinear (Lie-point) symmetries. This is then applied to gauge theories and gauge theoretic problems, and to nonlinear evolution PDE's; the paper also contains an original setting of Lie-point symmetries for evolution PDEs, modelled on the dynamical systems setting.
TL;DR: In this paper, numerically generated turbulence obtained by integrating the complete time-dependent three-dimensional Navier-Stokes equations is considered, which contains detailed information on spatial coherent flow structures as well as on the time-dependency and statistics of the 3D velocity and pressure fields.
Abstract: This paper considers numerically generated turbulence obtained by integrating the complete time-dependent three-dimensional Navier-Stokes equations. The simulated unidirectional turbulent flow, bounded by two parallel planes, is strongly inhomogeneous in the direction normal to the planes but homogeneous in the parallel directions. The resulting flow field, which is considered a numerical realization of fully developed turbulent channel flow, contains detailed information on spatial coherent flow structures as well as on the time-dependency and statistics of the three-dimensional velocity and pressure fields. Focussing here on the statistics of the numerically generated turbulence, second-moments and higher-moments are presented and compared with the most recent PTV and LDV laboratory measurements. It is concluded that direct numerical simulations are an invaluable approach to turbulence which complements field studies and laboratory investigations. Numerical experiments are now becoming a principal source of detailed and reliable information, which play a key role in the deepening of our understanding of turbulent flow phenomena.
TL;DR: In this article, the authors introduced two new classes of special functions, related to representations of groups of motions in the spaces of constant curvature as well as the unitary group of large ranks, which generalize a number of classical scalar special functions in one variable.
Abstract: This work is devoted to the construction and investigation of two new classes of special functions, related to representations of groups of motions in the spaces of constant curvature as well as the unitary group of large ranks. These are special functions with matrix indices and some types of orthogonal polynomials in several continuous and discrete variables. The functions introduced generalize a number of classical scalar special functions in one variable.
TL;DR: A survey of the progress in automorphism groups theory for free, solvable, modular, and profinite groups is given in this paper, with a focus on automorphisms.
Abstract: The survey presents classical assertions due to Nielsen, Whitehead, and others, well-known theorems on automorphisms included in monographs on group theory, and recent results in this area. Attention is focused on the progress in automorphism groups theory for free, solvable, modular, and profinite groups. New tools of investigation using graphs and geometrical ideas are also discussed.
TL;DR: In this article, a probability measure for scalar fields with exponential interaction on Riemann surfaces is presented, which is a mathematical realization of Polyakov's heuristic measure for bosonic strings in space-time dimensions 3≤d≤13.
Abstract: We construct a probability measure giving a mathematical realization of Polyakov's heuristic measure for bosonic strings in space-time dimensions 3≤d≤13, having as world sheet compact Riemann surfaces Λ of arbitrary genus. The measure involves the path space measures for scalar fields with exponential interaction on Λ and a measure on Teichmuller space.
TL;DR: In this paper, the authors consider various aspects of the following problem: Let T be a positive operator on a Banach lattice such that σ(T) = {1}. Does it follow that T ≥ 1?
Abstract: We consider various aspects of the following problem: Let T be a positive operator on a Banach lattice such that σ(T) = {1}. Does it follow that T ≥ 1?
TL;DR: Weakly compact operators and compact operators were investigated strongly in the last twenty years as discussed by the authors, and some of this knowledge has been collected and ordered in a recent survey, which includes comments, remarks and examples.
Abstract: The class of weakly compact operators is, as well as the class of compact operators, a fundamental operator ideal. They were investigated strongly in the last twenty years. In this survey, we have collected and ordered some of this (partly very new) knowledge. We have also included some comments, remarks and examples.
TL;DR: In this article, the authors consider a class of multitype particle systems in ℝ d undergoing spatial diffusion and critical stable multiitype branching, and show that for large classes of initial states, the particle process and the superprocess converge in distribution towards known equilibrium states as time tends to infinity.
Abstract: We consider a class of multitype particle systems in ℝ d undergoing spatial diffusion and critical stable multitype branching, and their limits known as critical stable multitype Dawson-Watanabe processes, or superprocesses. We show that for large classes of initial states, the particle process and the superprocess converge in distribution towards known equilibrium states as time tends to infinity. As an application we obtain the asymptotic behavior of a system of nonlinear partial differential equations whose solution is related to the distribution of both the particle process and the superprocess.
TL;DR: In this article, the authors present an approach to study groups acting on connected vertex-symmetric graphs of finite valency and prove the existence of non-simply connected spaces associated with a finitely generated group.
Abstract: The present paper was written at the request of one of the editors for a survey on some results of the author. The research presents an approach to studying groups acting on connected vertex-symmetric graphs of finite valency. This situation arises naturally when studying groups (the action of a group on its Cayley graph, the action of a primitive group on the corresponding permutation graphs, etc.) and also when studying certain applications (description of graphs with given symmetry properties and some other problems of algebraic combinatorics, crystallography, etc.). The paper consists of two parts. In Part I, the asymptotic properties of automorphisms of connected vertex-symmetric graphs of finite valency are investigated. A kind of structure theory for groups acting as automorphism groups on such graphs is developed. Part II is devoted to two applications. The first one is an affirmative answer to the L. van den Dries-A. Wilkie question on the existence of a non-simply connected space associated with a finitely generated group. The second application is a proof of an improved version of the C. Sims conjecture for primitive permutation groups. Comments (1)-(7) at the end of the paper are mainly of an illustrative nature.
TL;DR: In this paper, a general scheme is introduced which allows a unified approach to the weak coupling and singular coupling limits, and analogies and differences between the two are discussed; the main difference consists of the fact that, in the singular coupling limit, the use of a Hamiltonian unbounded below seems to be unavoidable, while this is not the case for weak coupling limit.
Abstract: After having recalled some definitions concerning quantum stochastic processes and, in particular, quantum Brownian motions, a general scheme is introduced which allows a unified approach to the weak coupling and singular coupling limits. The analogies and differences between the two are discussed. The main difference consists of the fact that, in the singular coupling limit, the use of a Hamiltonian unbounded below seems to be unavoidable, while this is not the case for the weak coupling limit.
TL;DR: In this paper, the authors obtained extensions of the Wiener-Young theorem for strongly continuous semigroups of positive operators in Banach lattices, which they used to obtain extensions to strongly continuous semi-continuous positive operators.
Abstract: The purpose of this paper is to obtain extensions of the Wiener-Young theorem for strongly continuous semigroups of positive operators in Banach lattices.
TL;DR: A new proof of the Luxemburg-Schep theorem for lattice homomorphisms was given in this article, and the proof was later extended to the case of lattice classes.
Abstract: We give a new proof of the Luxemburg-Schep theorem for lattice homomorphisms. Mathematics Subject Classifications (1991): 46A40, 47B60
TL;DR: In this paper, the authors present an exposition of a fundamental result due to J.L. Krivine about the local structure of a Banach lattice, which they call below.
Abstract: In this paper we shall present an exposition of a fundamental result due to J.L. Krivine about the local structure of a Banach lattice. In [3] Krivine proved that £ p (1 ≤ p ≤ ∞) is finitely lattice representable in any infinite dimensional Banach lattice. At the end of the introduction of [3] it is then stated that a value of p for which this holds is given by, what we will call below, the upper index of the Banach lattice. He states that this follows from the methods of his paper and of the paper [5] of Maurey and Pisier. One can ask whether the theorem also holds for p equal to the lower index of the Banach lattice. At first glance this is not obvious from [3], since many theorems in [3] have as a hypothesis that the upper index of the Banach lattice is finite. This can e.g. also be seen from the book [6] of H.U. Schwarz, where only the result for the upper index is stated, while both indices are discussed. One purpose of this paper is clarify this point and to present an exposition of all the ingredients of a proof of Krivine’s theorem for both the upper and lower index of a Banach lattice. We first gather some definitions and state some properties of the indices of a Banach lattice. For a discussion of these indices we refer to the book of Zaanen[7].
TL;DR: The concept of phylon is introduced as a generalisation of derivative strings, differential strings and new tensors in this article, and the behaviour of phyla under change of coordinates is given by finite-dimensional algebraic representations of a very large group, the infinite phylon group.
Abstract: The concept of phylon is introduced as a generalisation of derivative strings, differential strings and new tensors. The behaviour of phyla under change of coordinates is given by finite-dimensional algebraic representations of a very large group, the infinite phylon group. These representations are studied from both the general and the matrix points of view. Various examples of phyla are given, mainly from a statistical context. The basic structure of these representations is given.
TL;DR: In this article, the authors give an explicit description of the Kac-Peterson-Lepowsky construction of the level one representations for the twisted affine Lie algebrasan(2) anddn(2).
Abstract: We give an explicit description of the Kac-Peterson-Lepowsky construction of the level one representations for the twisted affine Lie algebrasan(2) anddn(2). We assign to any conjugacy class of the Weyl group ofan anddn 1) an equivalent class of maximal Heisenberg subalgebras of the corresponding twisted affine Lie algebras, and 2) multicomponent charged and neutral free fermionic fields. The boson-fermion correspondence for these fields provides us with fermionic vertex operators, whose ‘normal ordered products’ give the (twisted) vertex operators of the Kac-Peterson-Lepowsky construction.
TL;DR: In this paper, the authors give a summary account of some results which characterize order bounded linear operators which are sums of lattice homomorphisms, or more generally of orthomorphisms.
Abstract: This paper gives a summary account, with minimal or no proofs, first of some results which characterize order bounded linear operators which are sums of lattice homomorphisms, or more generally of orthomorphisms; and secondly of theorems concerning extensions of vector lattice homomorphisms (theorems of Hahn—Banach type if you will). In all cases we assume that domain and range are vector lattices and that the range is Dedekind complete. The results vary from historical (pre-1940) to recent (1990). The most recent work, on sums of lattice homomorphisms, is covered in §1 and the more classical work on extension theorems is dealt with in §2.
TL;DR: In this article, the authors studied the subschemes of the Hamming scheme H(n, q) for q greater than or equal to 4 and proved that there are no nontrivial sub-schemes when q > 4.
Abstract: The subschemes of the Hamming schemes H(n, q) for q greater than or equal to 4 are studied. We prove that there are no nontrivial subschemes when q > 4 and there exists only one nontrivial subscheme when q = 4.