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991.
We study the functional equation with \(x,y\in \mathbb {R}^d\) and \(b_i,c_i\in {GL}(d,\mathbb {R})\), both in the classical context of continuous complex-valued functions and in the framework of complex-valued Schwartz distributions, where these equations are properly introduced in two different ways. The solution sets are, typically, exponential polynomials and, in some particular cases, related to the so called characterization problem of the normal distribution in Probability Theory, they reduce to ordinary polynomials.
相似文献
$$\begin{aligned} \sum _{i=1}^mf_i(b_ix+c_iy)= \sum _{k=1}^nu_k(y)v_k(x) \end{aligned}$$
992.
Mikhail P. Shushpanov 《Algebra Universalis》2017,78(3):377-387
We consider a lattice generated by three elements, one of which is completely modular. The free lattice with this property is proved to be finite. It is not modular and contains exactly 39 elements. We have also found a finite set of defining relations for the generating elements of this lattice. 相似文献
993.
Fuchs called a partially-ordered integral domain, say D, division closed if it has the property that whenever a > 0 and ab > 0, then b > 0. He showed that if D is a lattice-ordered division closed field, then D is totally ordered. In fact, it is known that for a lattice-ordered division ring, the following three conditions are equivalent: a) squares are positive, b) the order is total, and c) the ring is division closed. In the present article, our aim is to study \({\ell}\)-rings that possibly possess zerodivisors and focus on a natural generalization of the property of being division closed, what we call regular division closed. Our investigations lead us to the concept of a positive separating element in an \({\ell}\)-ring, which is related to the well-known concept of a positive d-element. 相似文献
994.
V. I. Maksimov 《Proceedings of the Steklov Institute of Mathematics》2017,297(1):147-158
We discuss the problem of guaranteed guidance of a linear control system by a fixed time under the assumption that the system is subject to an unknown disturbance. We consider the case when a part of state coordinates are measured and the set of unknown initial states is finite. We specify a solution algorithm based on the combination of the package approach, the theory of dynamic inversion, and the extremal shift method. 相似文献
995.
Javier Cilleruelo D. S. Ramana O. Ramaré 《Proceedings of the Steklov Institute of Mathematics》2017,296(1):52-64
We study the cardinalities of A/A and AA for thin subsets A of the set of the first n positive integers. In particular, we consider the typical size of these quantities for random sets A of zero density and compare them with the sizes of A/A and AA for subsets of the shifted primes and the set of sums of two integral squares. 相似文献
996.
A. G. Chentsov 《Proceedings of the Steklov Institute of Mathematics》2017,296(1):43-59
Let a sequence of d-dimensional vectors n k = (n k 1 , n k 2 ,..., n k d ) with positive integer coordinates satisfy the condition n k j = α j m k +O(1), k ∈ ?, 1 ≤ j ≤ d, where α 1 > 0,..., α d > 0 and {m k } k=1 ∞ is an increasing sequence of positive integers. Under some conditions on a function φ: [0,+∞) → [0,+∞), it is proved that, if the sequence of Fourier sums \({S_{{m_k}}}\) (g, x) converges almost everywhere for any function g ∈ φ(L)([0, 2π)), then, for any d ∈ ? and f ∈ φ(L)(ln+ L) d?1([0, 2π) d ), the sequence \({S_{{n_k}}}\) (f, x) of rectangular partial sums of the multiple trigonometric Fourier series of the function f and the corresponding sequences of partial sums of all conjugate series converge almost everywhere. 相似文献
997.
M. R. Gabdullin 《Proceedings of the Steklov Institute of Mathematics》2017,297(1):81-87
We show the unimprovability of a theorem on sufficient convergence conditions for the trigonometric Fourier series of a function in classes ?(L) in the case when the class ?(L) is “close” to L. 相似文献
998.
Yu. N. Subbotin 《Proceedings of the Steklov Institute of Mathematics》2017,297(1):182-185
We consider problems of approximating the curvature of plane curves from smooth classes by the curvature of elements of smooth finite-dimensional function spaces (trigonometric polynomials, splines with equidistant knots) in the uniform norm. 相似文献
999.
K. S. Kobylkin 《Proceedings of the Steklov Institute of Mathematics》2017,299(1):106-112
We study the computational complexity of the vertex cover problem in the class of planar graphs (planar triangulations) admitting a plane representation whose faces are triangles. It is shown that the problem is strongly NP-hard in the class of 4-connected planar triangulations in which the degrees of vertices are of order O(log n), where n is the number of vertices, and in the class of plane 4-connected Delaunay triangulations based on the Minkowski triangular distance. A pair of vertices in such a triangulation is adjacent if and only if there is an equilateral triangle ?(p, λ) with p ∈ R2 and λ > 0 whose interior does not contain triangulation vertices and whose boundary contains this pair of vertices and only it, where ?(p, λ) = p + λ? = {x ∈ R2: x = p + λa, a ∈ ?}; here ? is the equilateral triangle with unit sides such that its barycenter is the origin and one of the vertices belongs to the negative y-axis. Keywords: computational complexity, Delaunay triangulation, Delaunay TD-triangulation. 相似文献
1000.
We continue the study of approximation properties of alternative duality schemes for improper problems of linear programming. The schemes are based on the use of the classical Lagrange function regularized simultaneously in primal and dual variables. The earlier results on the connection of its saddle points with the lexicographic correction of the right-hand sides of constraints in improper problems of the first and second kind are transferred to a more general type of improperness. Convergence theorems are presented and an informal interpretation of the obtained generalized solution is given. 相似文献