scholarly journals On the consistency problem for modular lattices and related structures

2016 ◽  
Vol 26 (08) ◽  
pp. 1573-1595 ◽  
Author(s):  
Christian Herrmann ◽  
Yasuyuki Tsukamoto ◽  
Martin Ziegler
Keyword(s):  
Nauk Sssr ◽  
Arbitrary Field ◽  
Relation Algebras ◽  
Finite Rings ◽  
Modular Lattices ◽  
Finite Dimensional ◽  
Akad Nauk Sssr ◽  
Profinite Completions ◽  
Consistency Problem ◽  
Grassmann Cayley Algebra

The consistency problem for a class of algebraic structures asks for an algorithm to decide, for any given conjunction of equations, whether it admits a non-trivial satisfying assignment within some member of the class. For the variety of all groups, this is the complement of the triviality problem, shown undecidable by by Adyan [Algorithmic unsolvability of problems of recognition of certain properties of groups. (Russian) Dokl. Akad. Nauk SSSR (N.S.) 103 (1955) 533–535] and Rabin [Recursive unsolvability of group theoretic problems, Ann. of Math. (2) 67 (1958) 172–194]. For the class of finite groups, it amounts to the triviality problem for profinite completions, shown undecidable by Bridson and Wilton [The triviality problem for profinite completions, Invent. Math. 202 (2015) 839–874]. We derive unsolvability of the consistency problem for the class of (finite) modular lattices and various subclasses; in particular, the class of all subspace lattices of finite-dimensional vector spaces over a fixed or arbitrary field of characteristic [Formula: see text] and expansions thereof, e.g. the class of subspace ortholattices of finite-dimensional Hilbert spaces. The lattice results are used to prove unsolvability of the consistency problem for (finite) rings with unit and (finite) representable relation algebras. These results in turn apply to equations between simple expressions in Grassmann–Cayley algebra and to functional and embedded multivalued dependencies in databases.

An inverse problem for the Vlasov–Poisson system

2015 ◽  
Vol 23 (4) ◽  
Author(s):  
Fikret Gölgeleyen ◽  
Masahiro Yamamoto
Keyword(s):  
Boundary Condition ◽  
Inverse Problem ◽  
Specular Reflection ◽  
Nauk Sssr ◽  
Poisson System ◽  
Local Uniqueness ◽  
Electrical Field ◽  
Stability Theorems ◽  
Akad Nauk Sssr ◽  
Reflection Boundary

AbstractIn this paper, we discuss an inverse problem for the Vlasov–Poisson system. We prove local uniqueness and stability theorems by using the method in Anikonov and Amirov [Dokl. Akad. Nauk SSSR 272 (1983), 1292–1293] under the specular reflection boundary condition and with a prescribed outward electrical field at the boundary.

On the Vanishing of a (G, σ) Product in a (G, σ) Space

1970 ◽  
Vol 22 (2) ◽  
pp. 363-371 ◽  
Author(s):  
K. Singh
Keyword(s):  
Vector Space ◽  
Multiplicative Group ◽  
Cartesian Product ◽  
Arbitrary Field ◽  
Necessary And Sufficient Condition ◽  
Tensor Space ◽  
Linear Character ◽  
Finite Dimensional Vector Space ◽  
Finite Dimensional ◽  
Necessary And Sufficient

In this paper, we shall construct a vector space, called the (G, σ) space, which generalizes the tensor space, the Grassman space, and the symmetric space. Then we shall determine a necessary and sufficient condition that the (G, σ) product of the vectors x1, x2, …, xn is zero.1. Let G be a permutation group on I = {1, 2, …, n} and F, an arbitrary field. Let σ be a linear character of G, i.e., σ is a homomorphism of G into the multiplicative group F* of F.For each i ∈ I, let Vi be a finite-dimensional vector space over F. Consider the Cartesian product W = V1 × V2 × … × Vn.1.1. Definition. W is called a G-set if and only if Vi = Vg(i) for all i ∊ I, and for all g ∊ G.

On Some Invariants of a Bilinear Form

1961 ◽  
Vol 4 (3) ◽  
pp. 261-264
Author(s):  
Jonathan Wild
Keyword(s):  
Vector Space ◽  
Bilinear Form ◽  
Arbitrary Field ◽  
Dimensional Vector ◽  
Dimensional Vector Space ◽  
Finite Dimensional Vector Space ◽  
Finite Dimensional ◽  
Special Cases ◽  
Orthogonal Subspace

Let E be a finite dimensional vector space over an arbitrary field. In E a bilinear form is given. It associates with every sub s pa ce V its right orthogonal sub space V* and its left orthogonal subspace *V. In general we cannot expect that dim V* = dim *V. However this relation will hold in some interesting special cases.

scholarly journals P1 or P\bar 1? Corrigendum

2000 ◽  
Vol 56 (4) ◽  
pp. 744-744 ◽  
Author(s):  
Richard E. Marsh
Keyword(s):  
Nauk Sssr ◽  
Monoclinic Space Group ◽  
Orthorhombic Space Group ◽  
Acta Cryst ◽  
Triclinic Space Group ◽  
Space Group ◽  
Akad Nauk Sssr

The structure of bis((phenyl-O,N,N-azoxy)oxy)methane, C_{13}H_{12}N_4O_4, originally reported as triclinic, space group P1 [Zyuzin et al. (1997). Isz. Akad. Nauk SSSR Ser. Khim. pp. 1486–1492; CSD refcode NIXQAM] was recently revised to monoclinic, space group C2 [Marsh (1999). Acta Cryst. B55, 931–936]. It is properly described as orthorhombic, space group Fdd2.

scholarly journals Reynolds number effect on the velocity derivative flatness factor

2018 ◽  
Vol 856 ◽  
pp. 426-443 ◽  
Author(s):  
M. Meldi ◽  
L. Djenidi ◽  
R. Antonia
Keyword(s):  
Reynolds Number ◽  
Isotropic Turbulence ◽  
Nauk Sssr ◽  
Quantitative Agreement ◽  
Homogeneous Isotropic Turbulence ◽  
Simulation Data ◽  
Akad Nauk Sssr ◽  
Analytic Expression ◽  
Velocity Derivative ◽  
Flatness Factor

This paper investigates the effect of a finite Reynolds number (FRN) on the flatness factor ($F$) of the velocity derivative in decaying homogeneous isotropic turbulence by applying the eddy damped quasi-normal Markovian (EDQNM) method to calculate all terms in an analytic expression for $F$ (Djenidi et al., Phys. Fluids, vol. 29 (5), 2017b, 051702). These terms and hence $F$ become constant when the Taylor microscale Reynolds number, $Re_{\unicode[STIX]{x1D706}}$ exceeds approximately $10^{4}$. For smaller values of $Re_{\unicode[STIX]{x1D706}}$, $F$, like the skewness $-S$, increases with $Re_{\unicode[STIX]{x1D706}}$; this behaviour is in quantitative agreement with experimental and direct numerical simulation data. These results indicate that one must first ensure that $Re_{\unicode[STIX]{x1D706}}$ is large enough for the FRN effect to be negligibly small before the hypotheses of Kolmogorov (Dokl. Akad. Nauk SSSR, vol. 30, 1941a, pp. 301–305; Dokl. Akad. Nauk SSSR, vol. 32, 1941b, pp. 16–18; J. Fluid Mech., vol. 13, 1962, pp. 82–85) can be assessed unambiguously. An obvious implication is that results from experiments and direct numerical simulations for which $Re_{\unicode[STIX]{x1D706}}$ is well below $10^{4}$ may not be immune from the FRN effect. Another implication is that a power-law increase of $F$ with respect to $Re_{\unicode[STIX]{x1D706}}$, as suggested by the Kolmogorov 1962 theory, is not tenable when $Re_{\unicode[STIX]{x1D706}}$ is large enough.

Best constants in norm inequalities for derivatives on a half-line

1985 ◽  
Vol 100 (1-2) ◽  
pp. 67-84 ◽  
Author(s):  
Z. M. Franco ◽  
Hans G. Kaper ◽  
Man Kam Kwong ◽  
A. Zettl
Keyword(s):  
Symmetric Operator ◽  
Nauk Sssr ◽  
Norm Inequality ◽  
Differentiation Operator ◽  
Maximal Domain ◽  
Large N ◽  
Asymptotic Expressions ◽  
The Best Possible Constant ◽  
Akad Nauk Sssr ◽  
Image Position

SynopsisLet K be the class of all operators T in a Banach space × which have the property that, for any pair of integers (n, k) with n ≧2 and l≦ k ≦ n – l, there exists a constant Cnk such thatfor all fϵdom Tn. If T ϵ K, then the best possible constant for the norm inequality (*) is the smallest non-negative value of the constant Cnk in (*). Any operator T which is the adjoint of a maximal symmetric operator in a Hilbert space belongs to the class K, as was shown by Ljubič [Izv. Akad. Nauk SSSR, Ser. Mat. 24 (1960), 825–864].This article is concerned with the computation of the best possible constant for the differentiation operator Tf=if′ on the maximal domain in L2(0, ∞). Three algorithms, proposed by Ljubič [ibid.] and Kupcov [Trudy Mat. Inst. Steklov. 138 (1975)], are discussed and related to one another, asymptotic expressions (valid for large n) and numerical values of the best possible constant are presented, and the extremals (i.e. the elements / ∈ dom Tn for which equality holds in (*) with the best possible constant) are given.

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