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1.
Construction of noniterated boolean functions in the basis {&;, ∨, −} and estimation of their number
O. V. Zubkov 《Russian Mathematics (Iz VUZ)》2008,52(10):13-19
In this paper we consider noniterated Boolean functions in the basis {&;, ∨, ?}. We obtain the canonical form of the formula for a noniterated function in this basis. We construct the set of such formulas with respect to variables x 1, …, x n and calculate the number of its elements. Based on these results, we obtain the upper and lower bounds for the number of noniterated Boolean functions of n variables in the basis under consideration. 相似文献
2.
S. E. Bubnov A. A. Voronenko D. V. Chistikov 《Computational Mathematics and Modeling》2010,21(2):196-205
Testing relative to a nonrepeating alternative in a conjunction-disjunction basis is considered. A lower bound on the test
length is established for all nonrepeating functions in this basis. A subsequence of easily testable functions is constructed
and the corresponding tests are described. Individual lower test length bounds are proved for functions of a special form;
minimality of the tests is established for the functions of the constructed subsequence. 相似文献
3.
Yu. V. Borodina 《Moscow University Mathematics Bulletin》2007,62(4):163-167
A new method for synthesis of easy tested diagrams of functional elements in the basis {&;, ∨, ?} is proposed for systems of m Boolean functions differing from constants and representable as disjunctive normal forms containing l variables x 1,...,x l , l > 0, without negations and the other variables x l+1,...,x n with negations only. All faults are assumed to be stack-at-1 faults at the outputs of elements. It is proved that the length of a complete verification test is not greater than min {m, l} for such diagrams. 相似文献
4.
We give a Schwarz-Pick estimate for bounded holomorphic functions on unit ball in Cn, and generalize some early work of Schwarz-Pick estimates for bounded holomorphic functions on unit disk in C. 相似文献
5.
6.
Aicheng Geng Fucai You Chunyuan Zhao Shuhui Shi Jianhua Wang Xinfeng Huang 《Mathematical Notes》2016,99(5-6):652-662
Some issues concerning expansions of functions in Fourier–Legendre series is considered in L2[?1, 1]. In particular, the rate of their convergence in the classes of functions characterized by the generalized modulus of continuity are estimated, and estimates of the remainder terms are obtained. 相似文献
7.
V. A. Makarichev 《Mathematical Notes》2011,89(5-6):689-705
We study the basis functions φ n,k and ψ n,p of generalized Taylor series for the classH ρ,2 and obtain asymptotic expansions of the functions φ n,0 (l) and $\psi _{n,2 \cdot 4^n - 1}^{(l)} $ . We prove the existence of an asymptotics for the functions φ n,k and ψ n,p for k ≠ 0 and p ≠ 2·4 n ? 1. The first term of the asymptotic expansions of these functions is obtained. 相似文献
8.
We utilize the method of Bellman functions to derive new -estimates of Littlewood–Paley type involving . Among the applications to singular integrals we improve the bounds for the Ahlfors–Beurling operator on when . In addition, dimensionless estimates of Riesz transforms in the classical as well as in the Ornstein–Uhlenbeck setting are attained. To cite this article: O. Dragi?evi?, A. Volberg, C. R. Acad. Sci. Paris, Ser. I 340 (2005). 相似文献
9.
This study proposes a deterministic model to solve the two-dimensional cutting stock problem (2DCSP) using a much smaller number of binary variables and thereby reducing the complexity of 2DCSP. Expressing a 2DCSP with $m$ stocks and $n$ cutting rectangles requires $2n^{2}+n(m+1)$ binary variables in the traditional model. In contrast, the proposed model uses $n^{2}+n\lceil {\log _2 m}\rceil $ binary variables to express the 2DCSP. Experimental results showed that the proposed model is more efficient than the existing model. 相似文献
10.
V. V. Chugunova 《Mathematical Notes》2011,89(3-4):421-437
We prove that, in the basis {x 1 & x 2 & x 3, x 1 ∨ x 2 ∨ x 3, $ \bar x_1 $ }, for inverse faults at the inputs of functional elements, all Boolean functions f(x 1, x 2, ..., x n ) can be realized by asymptotically optimally reliable circuits operating with unreliability asymptotically (as ? → 0) equal to: ? 3 for the constants 0 and 1, ? for the functions $ \bar x_i $ , and 3? for f(x 1, x 2, ..., x n ) ≠ 0, 1, $ \bar x_i $ , x i , where ? is the error probability at each input of the functional element and i = 1, ..., n. The functions xi, i = 1, ..., n, can be realized absolutely reliably. The complexity of asymptotically optimally reliable circuits is equal in order to the complexity of minimal circuits constructed only from reliable elements. 相似文献
11.
V. I. Masol 《Ukrainian Mathematical Journal》1991,43(9):1110-1116
There are investigated the joint distribution of random variables kn(1),..., kn(s), and distributions of some functionals of kn(), for n. Here kn(), 1ln–1 is the number of -steps in a binary sequence (b.s.), selected randomly and equiprobably from the totality of all n-dimensional b.s. that have a prescribed number of ones and k 1-steps. By an -step of a b.s. we understand a configuration of the form 1...0, where the ellipsis stands for an ( –1)-dimensional b.s.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 43, No. 9, pp. 1186–1193, September, 1991. 相似文献
12.
V. A. Abilov F. V. Abilova M. K. Kerimov 《Computational Mathematics and Mathematical Physics》2013,53(9):1231-1238
Given a function $\mathbb{L}_2 $ (?), its Fourier transform $g(x) = \hat f(x) = F[f](x) = \frac{1} {{\sqrt {2\pi } }}\int\limits_{ - \infty }^{ + \infty } {f(x)e^{ - ixt} dt} ,f(t) = F^{ - 1} [g](t) = \frac{1} {{\sqrt {2\pi } }}\int\limits_{ - \infty }^{ + \infty } {g(x)e^{ - ixt} dx} $ and the inverse Fourier transform are considered in the space f ε $\mathbb{L}_2 $ (?). New estimates are presented for the integral $\int\limits_{|t| \geqslant N} {|g(t)|^2 dt} = \int\limits_{|t| \geqslant N} {|\hat f(t)|^2 dt} ,N \geqslant 1,$ in the vase of f ε $\mathbb{L}_2 $ (?) characterized by the generalized modulus of continuity of the kth order constructed with the help of the Steklov function. Some other estimates associated with this integral are proved. 相似文献
13.
14.
Consideration of the analytic continuation of the Eisenstein series of weight 3/2 for the group 0(4) leads to a new proof of Mordell's formula connecting the values X()=
m=1
F(m)eim, Im > 0, and (–1/). The behavior of the function () for 0(4) is examined by the same method.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 64, pp. 69–79, 1976. 相似文献
15.
G. A. Kalyabin 《Proceedings of the Steklov Institute of Mathematics》2010,269(1):137-142
Explicit formulas are obtained for the maximum possible values of the derivatives f
(k)(x), x ∈ (−1, 1), k ∈ {0, 1, ..., r − 1}, for functions f that vanish together with their (absolutely continuous) derivatives of order up to ≤ r − 1 at the points ±1 and are such that $
\left\| {f^{\left( r \right)} } \right\|_{L_2 ( - 1,1)} \leqslant 1
$
\left\| {f^{\left( r \right)} } \right\|_{L_2 ( - 1,1)} \leqslant 1
. As a corollary, it is shown that the first eigenvalue λ
1,r
of the operator (−D
2)
r
with these boundary conditions is $
\sqrt 2
$
\sqrt 2
(2r)! (1 + O(1/r)), r → ∞. 相似文献
16.
M. V. Abilov M. K. Kerimov E. V. Selimkhanov 《Computational Mathematics and Mathematical Physics》2017,57(10):1559-1576
Some problems in computational mathematics and mathematical physics lead to Fourier series expansions of functions (solutions) in terms of special functions, i.e., to approximate representations of functions (solutions) by partial sums of corresponding expansions. However, the errors of these approximations are rarely estimated or minimized in certain classes of functions. In this paper, the convergence rate (of best approximations) of a Fourier series in terms of Jacobi polynomials is estimated in classes of bivariate functions characterized by a generalized modulus of continuity. An approximation method based on “spherical” partial sums of series is substantiated, and the introduction of a corresponding class of functions is justified. A two-sided estimate of the Kolmogorov N-width for bivariate functions is given. 相似文献
17.
We consider and study properties of the smoothness characteristics
, of functions f(x) that belong to the space S
p
, 1 ≤ p < ∞, introduced by Stepanets. Exact inequalities of the Jackson type are obtained, and the exact values of the widths of
the classes of functions defined by using Ωm(f,t)S
p are calculated.
__________
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 58, No. 3, pp. 303–316, March, 2006. 相似文献
18.
M. K. Kerimov E. V. Selimkhanov 《Computational Mathematics and Mathematical Physics》2016,56(5):717-729
The work is devoted to exact estimates of the convergence rate of Fourier series in the trigonometric system in the space of square summable 2π-periodic functions with the Euclidean norm on certain classes of functions characterized by the generalized modulus of continuity. Some N-widths of these classes are calculated, and the residual term of one quadrature formula over equally spaced nodes for a definite integral connected with the issues under consideration is found. 相似文献
19.
I. I. Sharapudinov 《Mathematical Notes》1997,62(4):501-512
Suppose that 0<δ≤1,N=1/δ, and α, ga≥0, is an integer. For the classical Meixner polynomials
orthonormal on the gird {0, δ, 2δ, ...} with weight ρ(x)=(1-e
−δ)αг(Nx+α+ 1)/г(Nx+1), the following asymptotic formula is obtained:
. The remainderv
n,N
α
(z) forn≤λN satisfies the estimate
where Λ
k
α
(x) are the Laguerre orthonormal polynomials. As a consequence, a weighted estimate, for the Meixner polynomial
on the semiaxis [0, ∞) is obtained.
Translated fromMatematicheskie Zametki, Vol. 62, No. 4, pp. 603–616, October, 1997.
Translated by N. K. Kulman 相似文献
20.
Manfred G. Madritsch 《The Ramanujan Journal》2010,21(2):181-210
We consider b-additive functions f where b is an algebraic integer over ℤ. In particular, let p be a polynomial, then we show that the asymptotic distribution of f(⌊ p(z)⌋), where ⌊⋅⌋ denotes the integer part with respect to basis b, when z runs through the elements of the ring ℤ[b] is the normal law. This is a generalization of results of Bassily and Kátai (for the integer case) and of Gittenberger and Thuswaldner (for the Gaussian integers). 相似文献