共查询到20条相似文献,搜索用时 31 毫秒
1.
E. N. Pavlovskii 《Siberian Mathematical Journal》2008,49(3):512-523
We estimate the algorithmic complexity of the index set of some natural classes of computable models: finite computable models (Σ 2 0 -complete), computable models with ω-categorical theories (Δ ω 0 -complex Π ω+2 0 -set), prime models (Δ ω 0 -complex Π ω+2 0 -set), models with ω 1-categorical theories (Δ ω 0 -complex Σ ω+1 0 -set. We obtain a universal lower bound for the model-theoretic properties preserved by Marker’s extensions (Δ ω 0 . 相似文献
2.
Index sets of decidable models 总被引:1,自引:1,他引:0
E. B. Fokina 《Siberian Mathematical Journal》2007,48(5):939-948
We study the index sets of the class of d-decidable structures and of the class of d-decidable countably categorical structures, where d is an arbitrary arithmetical Turing degree. It is proved that the first of them is m-complete ∑ 3 0, d , and the second is m-complete ∑ 3 0, d \∑ 3 0, d in the universal computable numbering of computable structures for the language with one binary predicate. 相似文献
3.
F. M. Korkmasov 《Vestnik St. Petersburg University: Mathematics》2007,40(2):138-151
It is shown that if P m α,β (x) (α, β > ?1, m = 0, 1, 2, …) are the classical Jaboci polynomials, then the system of polynomials of two variables {Ψ mn α,β (x, y)} m,n=0 r = {P m α,β (x)P n α,β (y)} m, n=0 r (r = m + n ≤ N ? 1) is an orthogonal system on the set Ω N×N = ?ub;(x i , y i ) i,j=0 N , where x i and y i are the zeros of the Jacobi polynomial P n α,β (x). Given an arbitrary continuous function f(x, y) on the square [?1, 1]2, we construct the discrete partial Fourier-Jacobi sums of the rectangular type S m, n, N α,β (f; x, y) by the orthogonal system introduced above. We prove that the order of the Lebesgue constants ∥S m, n, N α,β ∥ of the discrete sums S m, n, N α,β (f; x, y) for ?1/2 < α, β < 1/2, m + n ≤ N ? 1 is O((mn) q + 1/2), where q = max?ub;α,β?ub;. As a consequence of this result, several approximate properties of the discrete sums S m, n, N α,β (f; x, y) are considered. 相似文献
4.
We consider the problem of representing a solution to the Cauchy problem for an ordinary differential equation as a Fourier series in polynomials l r,k α (x) (k = 0, 1,...) that are Sobolev-orthonormal with respect to the inner product , and generated by the classical orthogonal Laguerre polynomials L k α (x) (k = 0, 1,...). The polynomials l r,k α (x) are represented as expressions containing the Laguerre polynomials L n α?r (x). An explicit form of the polynomials l r,k+r α (x) is established as an expansion in the powers x r+l , l = 0,..., k. These results can be used to study the asymptotic properties of the polynomials l r,k α (x) as k→∞and the approximation properties of the partial sums of Fourier series in these polynomials.
相似文献
$$\left\langle {f,g} \right\rangle = \sum\limits_{v = 0}^{r - 1} {{f^{(v)}}(0){g^{(v)}}} (0) + \int\limits_0^\infty {{f^{(r)}}(t)} {g^{(r)}}(t){t^\alpha }{e^{ - t}}dt$$
5.
S. V. Pchelintsev 《Siberian Mathematical Journal》2016,57(4):666-678
We prove that the isotopes of the alternative monster and the Skosyrsky algebra satisfy the identity Пi=14 [xi, yi] = 0. Hence, the algebras themselves satisfy the identity Пi=14 (c, xi, yi) = 0. We also show that none of the identities Пi=1n(c, xi, yi) = 0 holds in all commutative alternative nil-algebras of index 3. Thus, we refute the Grishkov–Shestakov hypothesis about the structure of the free finitely generated commutative alternative nil-algebras of index 3. 相似文献
6.
In the L p -spaces, we study the complex powers of the operator where δ is the Laplace operator. The complex powers G λ ?α/2 , Reα > 0, are realized as potential type operators B λ α with a nonstandard metric. We obtain L p → L p + L s -estimates for the operator B λ α . By using the method of approximate inverse operators, we construct the inversion of the potentials B λ α φ with L p -densities and describe the range B λ α (L p ) in terms of the inversion constructions.
相似文献
$G_\lambda = m^2 I + \Delta - i\lambda \frac{{\partial ^2 }}{{\partial x_1^2 }},0 < \lambda < 1,m > 0,$
7.
Commutator of Riesz potential in <Emphasis Type="Italic">p</Emphasis>-adic generalized Morrey spaces
Suppose that I p α is the p-adic Riesz potential. In this paper, we established the boundedness of I p α on the p-adic generalized Morrey spaces, as well as the boundedness of the commutators generated by the p-adic Riesz potential I p α and p-adic generalized Campanato functions. 相似文献
8.
D. V. Zakablukov 《Moscow University Mathematics Bulletin》2016,71(3):89-97
The paper discusses the asymptotic depth of a reversible circuits consisting of NOT, CNOT and 2-CNOT gates. The reversible circuit depth function D(n, q) is introduced for a circuit implementing a mapping f: Z2n → Z2n as a function of n and the number q of additional inputs. It is proved that for the case of implementation of a permutation from A(Z2n) with a reversible circuit having no additional inputs the depth is bounded as D(n, 0) ? 2n/(3log2n). It is also proved that for the case of transformation f: Z2n → Z2n with a reversible circuit having q0 ~ 2n additional inputs the depth is bounded as D(n,q0) ? 3n. 相似文献
9.
N. L. Grigorenko D. V. Kamzolkin L. N. Luk’yanova 《Proceedings of the Steklov Institute of Mathematics》2011,273(1):49-58
Let {φ n (α,β) (z)} n=0 ∞ be a system of Jacobi polynomials orthonormal on the circle |z| = 1 with respect to the weight (1 ? cos τ)α+1/2(1 + cos τ)β+1/2 (α, β > ?1), and let \(\psi _n^{\left( {\alpha ,\beta } \right)*} \left( z \right): = z^n \overline {\psi _n^{\left( {\alpha ,\beta } \right)} \left( {{1 \mathord{\left/ {\vphantom {1 {\bar z}}} \right. \kern-\nulldelimiterspace} {\bar z}}} \right)}\)). We establish relations between the polynomial φ n (α,?1/2) (z) and the nth (C, α ? 1/2)-mean of the Maclaurin series for the function (1 ? z)?α?3/2 and also between the polynomial φ n (α,?1/2)* (z) and the nth (C, α + 1/2)-mean of the Maclaurin series for the function (1 ? z)?α?1/2. We use these relations to derive an asymptotic formula for φ n (α,?1/2) (z); the formula is uniform inside the disk |z| < 1. It follows that φ n (α,?1/2) (z) ≠ 0 in the disk |z| ≤ ρ for fixed φ ∈ (0, 1) and α > ?1 if n is sufficiently large. 相似文献
10.
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
11.
The renormalized coupling constants g 2k that enter the equation of state and determine nonlinear susceptibilities of the system have universal values g 2k * at the Curie point. We use the pseudo-ε-expansion approach to calculate them together with the ratios R 2k = g 2k /g 4 k-1 for the three-dimensional scalar λ ? 4 field theory. We derive pseudo-ε-expansions for g 6 * , g 8 * , R 6 * , and R 8 * in the five-loop approximation and present numerical estimates for R 6 * and R 8 * . The higher-order coefficients of the pseudo-ε-expansions for g 6 * and R 6 * are so small that simple Padé approximants turn out to suffice for very good numerical results. Using them gives R 6 * = 1.650, while the recent lattice calculation gave R 6 * = 1.649(2). The pseudo-ε-expansions of g 8 * and R 8 * are less favorable from the numerical standpoint. Nevertheless, Padé–Borel summation of the series for R 8 * gives the estimate R 8 * = 0.890, differing only slightly from the values R 8 * = 0.871 and R 8 * = 0.857 extracted from the results of lattice and field theory calculations. 相似文献
12.
We consider the families of polynomials P = { P n (x)} n=0 ∞ and Q = { Q n (x)} n=0 ∞ orthogonal on the real line with respect to the respective probability measures μ and ν. We assume that { Q n (x)} n=0 ∞ and {P n (x)} n=0 ∞ are connected by linear relations. In the case k = 2, we describe all pairs (P,Q) for which the algebras A P and A Q of generalized oscillators generated by { Qn(x)} n=0 ∞ and { Pn(x)} n=0 ∞ coincide. We construct generalized oscillators corresponding to pairs (P,Q) for arbitrary k ≥ 1. 相似文献
13.
A. V. Rozhdestvenskii 《Proceedings of the Steklov Institute of Mathematics》2007,256(1):263-274
For a periodic function f with a given decrease of the moduli of its Fourier coefficients, we analyze the solvability of the equation \(w(T_\alpha x) - w(x) = f(x) - \smallint _{\mathbb{T}^d } f(t) dt\) and the asymptotic behavior of the Birkhoff sums Σ s=0 n?1 f(T α s x) for almost every α. The results obtained are applied to the study of ergodic properties of a cylindrical cascade and of a special flow on the torus. 相似文献
14.
A k-total coloring of a graph G is a mapping ?: V (G) ? E(G) → {1; 2,..., k} such that no two adjacent or incident elements in V (G) ? E(G) receive the same color. Let f(v) denote the sum of the color on the vertex v and the colors on all edges incident with v: We say that ? is a k-neighbor sum distinguishing total coloring of G if f(u) 6 ≠ f(v) for each edge uv ∈ E(G): Denote χ Σ ″ (G) the smallest value k in such a coloring of G: Pil?niak and Wo?niak conjectured that for any simple graph with maximum degree Δ(G), χ Σ ″ ≤ Δ(G)+3. In this paper, by using the famous Combinatorial Nullstellensatz, we prove that for K 4-minor free graph G with Δ(G) > 5; χ Σ ″ = Δ(G) + 1 if G contains no two adjacent Δ-vertices, otherwise, χ Σ ″ (G) = Δ(G) + 2. 相似文献
15.
On the Fekete and Szegö problem for starlike mappings of order <Emphasis Type="Italic">α</Emphasis> 下载免费PDF全文
Let S α * be the familiar class of normalized starlike functions of order α in the unit disk. In this paper, we establish the Fekete and Szegö inequality for the class S α * , and then we generalize this result to the unit ball in a complex Banach space or on the unit polydisk in C n . 相似文献
16.
In our previous papers, we introduced the notion of a generalized solution to the initial-boundary value problem for the wave equation with a boundary function µ(t) such that the integral ∫ 0 T (T ? t)|µ(t)| p dt exists. Here we prove that this solution is a unique solution to the problem in L p that satisfies the corresponding integral identity. 相似文献
17.
Victor Kreiman 《Journal of Algebraic Combinatorics》2008,27(3):351-382
The Richardson variety X α γ in the Grassmannian is defined to be the intersection of the Schubert variety X γ and opposite Schubert variety X α . We give an explicit Gröbner basis for the ideal of the tangent cone at any T-fixed point of X α γ , thus generalizing a result of Kodiyalam-Raghavan (J. Algebra 270(1):28–54, 2003) and Kreiman-Lakshmibai (Algebra, Arithmetic and Geometry with Applications, 2004). Our proof is based on a generalization of the Robinson-Schensted-Knuth (RSK) correspondence, which we call the bounded RSK (BRSK). We use the Gröbner basis result to deduce a formula which computes the multiplicity of X α γ at any T-fixed point by counting families of nonintersecting lattice paths, thus generalizing a result first proved by Krattenthaler (Sém. Lothar. Comb. 45:B45c, 2000/2001; J. Algebr. Comb. 22:273–288, 2005). 相似文献
18.
Let {c j } j=0 n be a sequence of matrix moments associated with a matrix of measures supported on the unit circle, and let {P j } j=0 n be its corresponding sequence of monic matrix orthogonal polynomials. In this contribution, we consider a perturbation on the moments and find an explicit relation for the perturbed orthogonal polynomials in terms of {P j } j=0 n . We also obtain an expression for the corresponding second kind polynomials. 相似文献
19.
We show that for every ? > 0 there exist δ > 0 and n0 ∈ ? such that every 3-uniform hypergraph on n ≥ n0 vertices with the property that every k-vertex subset, where k ≥ δn, induces at least \(\left( {\frac{1}{2} + \varepsilon } \right)\left( {\begin{array}{*{20}c} k \\ 3 \\ \end{array} } \right)\) edges, contains K4? as a subgraph, where K4? is the 3-uniform hypergraph on 4 vertices with 3 edges. This question was originally raised by Erd?s and Sós. The constant 1/4 is the best possible. 相似文献
20.
Let H 2 = (?Δ)2 + V 2 be the Schrödinger type operator, where V satisfies reverse Hölder inequality. In this paper, we establish the L p boundedness for V 2 H 2 ?1 , H 2 ?1 V 2, VH 2 ?1/2 and H 2 ?1 V 2, and that of their commutators. We also prove that H 2 ?1 V 2,VH 2 ?1/2 are bounded from BMO L to BMO L . 相似文献