共查询到20条相似文献,搜索用时 15 毫秒
1.
Vladimir I. Arnold 《Functional Analysis and Other Mathematics》2011,3(2):169-178
The complex Euler group is defined associating to an integer complex number z the multiplicative group of the complex integers residues modulo z, relatively prime to z. This group is calculated for z=(3+0i)
n
: it is isomorphic to the product of three cyclic group or orders (8, 3
n−1 and 3
n−1). 相似文献
2.
The Ramanujan Journal - In this paper, transformation formulas for the function $$\begin{aligned} A_{1}\left( z,s:\chi \right) =\sum \limits _{n=1}^{\infty }\sum \limits _{m=1} ^{\infty }\chi... 相似文献
3.
The bondage number of a graph is the smallest number of its edges whose removal results in a graph having a larger domination number. We provide constant upper bounds for the bondage number of graphs on topological surfaces, and improve upper bounds for the bondage number in terms of the maximum vertex degree and the orientable and non-orientable genera of graphs. Also, we present stronger upper bounds for graphs with no triangles and graphs with the number of vertices larger than a certain threshold in terms of graph genera. This settles Teschner’s Conjecture in affirmative for almost all graphs. As an auxiliary result, we show tight lower bounds for the number of vertices of graphs 2-cell embeddable on topological surfaces of a given genus. 相似文献
4.
This paper is concerned with a generalized Ky Fan’s inequality. We first give an existence result of generalized Ky Fan’s (weak) efficient points, and then establish a complete metric space. Based on these results, we obtain the sufficient and necessary conditions of upper semicontinuity of efficient solution mapping to a generalized Ky Fan’s inequality. We also obtain the sufficient conditions of lower semicontinuity and continuity of efficient solution mapping to a generalized Ky Fan’s inequality. Our results are new and different from the corresponding ones in the literature. 相似文献
5.
In this paper, we present an extention of Hyers–Ulam stability of Sahoo–Riedel’s points for real-valued differentiable functions on [a, b] and then we obtain stability results of Flett’s points for functions in the class of continuously differentiable functions on [a, b] with f′(a) = f′(b). 相似文献
6.
Mohammad Zarrin 《Archiv der Mathematik》2018,111(4):349-351
In 1979, Herzog put forward the following conjecture: if two simple groups have the same number of involutions, then they are of the same order. We give a counterexample to this conjecture. 相似文献
7.
In this article we study the regularity of stationary points of the knot energies E (α) introduced by O’Hara (Topology 30(2):241–247, 1991; Topol Appl 48(2):147–161, 1992; Topol Appl 56(1):45–61, 1994) in the range ${\alpha\in(2,3)}$ . In a first step we prove that E (α) is C 1 on the set of all regular embedded curves belonging to ${{H^{(\alpha+1)/2,2}(\mathbb {R}{/}\mathbb {Z}, \mathbb {R}^n)}}$ and calculate its derivative. After that we use the structure of the Euler-Lagrange equation to study the regularity of stationary points of E (α) plus a positive multiple of the length. We show that stationary points of finite energy are of class C ∞—so especially all local minimizers of E (α) among curves with fixed length are smooth. 相似文献
8.
Igor Mykolaiovych Velichko 《Journal of Mathematical Sciences》2013,192(4):459-473
The asymptotic formula for a summatory function of the number of representations of matrices from $ {M_2}\left( \mathbb{Z} \right) $ in the form C = A 1 A 2 A 3 under the condition det C ≤ x is constructed. The second moment of the error term of this asymptotic formula is estimated. 相似文献
9.
10.
In the study of the number of limit cycles of near-Hamiltonian systems, the first order Melnikov function plays an important role. This paper aims to generalize Horozov-Iliev’s method to estimate the upper bound of the number of zeros of the function.
相似文献11.
Carlo Gasbarri 《manuscripta mathematica》1999,98(4):453-475
Let K be a number field and its ring of integers. Let be a Hermitian vector bundle over . In the first part of this paper we estimate the number of points of bounded height in (generalizing a result by Schanuel). We give then some applications: we estimate the number of hyperplanes and hypersurfaces
of degree d>1 in of bounded height and containing a fixed linear subvariety and we estimate the number of points of height, with respect to
the anticanonical line bundle, less then T (when T goes to infinity) of ℙ
N
K
blown up at a linear subspace of codimension two.
Received: 20 February 1998 / Revised version: 9 November 1998 相似文献
12.
We use bounds of mixed character sums modulo a square-free integer q of a special structure to estimate the density of integer points on the hypersurface for some polynomials \(f_i \in {\mathbb {Z}}[X]\) and nonzero integers a and \(k_i\), \(i=1, \ldots , n\). In the case of the above hypersurface is known as the Markoff–Hurwitz hypersurface, while for it is known as the Dwork hypersurface. Our results are substantially stronger than those known for general hypersurfaces.
相似文献
$$\begin{aligned} f_1(x_1) + \cdots + f_n(x_n) =a x_1^{k_1} \ldots x_n^{k_n} \end{aligned}$$
$$\begin{aligned} f_1(X) = \cdots = f_n(X) = X^2\quad \text{ and }\quad k_1 = \cdots = k_n =1 \end{aligned}$$
$$\begin{aligned} f_1(X) = \cdots = f_n(X) = X^n\quad \text{ and }\quad k_1 = \cdots = k_n =1 \end{aligned}$$
13.
S. N. Preobrazhenskii 《Mathematical Notes》2011,89(1-2):277-290
We refine the upper bound for the Vinogradov integral. 相似文献
14.
15.
The probabilities of the state transitions of the initial value So in the S table of RC4 are described by a kind of bistochastic matrices, and then a computational formula for such bistochastic matrices is given, by which the mathematical expectation of the number of fixed points in the key extending algorithm of RC4 is obtained. As a result, a statistical weakness of the key extending algorithm of RC4 is presented. 相似文献
16.
József Beck 《Combinatorica》1981,1(4):319-325
Letg be a coloring of the set {1, ...,N} = [1,N] in red and blue. For each arithmetic progressionA in [1,N], consider the absolute value of the difference of the numbers of red and of blue members ofA. LetR(g) be the maximum of this number over all arithmetic progression (thediscrepancy ofg). Set
over all two-coloringsg. A remarkable result of K. F. Roth gives*R(N)≫N
1/4. On the other hand, Roth observed thatR(N)≪N
1/3+ɛ and suggested that this bound was nearly sharp. A. Sárk?zy disproved this by provingR(N)≪N
1/3+ɛ. We prove thatR(N)=N
1/4+o(1) thus showing that Roth’s original lower bound was essentially best possible.
Our result is more general. We introduce the notion ofdiscrepancy of hypergraphs and derive an upper bound from which the above result follows. 相似文献
17.
We present new sufficient conditions for the semilocal convergence of Newton’s method to a locally unique solution of an equation in a Banach space setting. Upper bounds on the limit points of majorizing sequences are also given. Numerical examples are provided, where our new results compare favorably to earlier ones such as Argyros (J Math Anal Appl 298:374–397, 2004), Argyros and Hilout (J Comput Appl Math 234:2993-3006, 2010, 2011), Ortega and Rheinboldt (1970) and Potra and Pták (1984). 相似文献
18.
We prove estimates for complete rational arithmetic sums of Bernoulli polynomials whose arguments are formed by the fractional parts of values of a polynomial with rational coefficients. The results are applied to the problem of finding the convergence exponent for the mean values of the sums under consideration. 相似文献
19.
B. O. Vasilevskiĭ 《Siberian Mathematical Journal》2013,54(6):994-1004
We consider a regular Riemann surface of finite genus and “generalized spectral data,” a special set of distinguished points on it. From them we construct a discrete analog of the Baker-Akhiezer function with a discrete operator that annihilates it. Under some extra conditions on the generalized spectral data, the operator takes the form of the discrete Cauchy-Riemann operator, and its restriction to the even lattice is annihilated by the corresponding Schrödinger operator. In this article we construct an explicit formula for the Green’s function of the indicated operator. The formula expresses the Green’s function in terms of the integral along a special contour of a differential constructed from the wave function and the extra spectral data. In result, the Green’s function with known asymptotics at infinity can be obtained at almost every point of the spectral curve. 相似文献
20.
K. Gelashvili 《Journal of Mathematical Sciences》2011,177(3):373-382
The problem of existence of an optimal control is solved on the basis of Weierstrass’s classical theorem if the set of admissible
controls belongs to the class of piecewise continuous functions. In the process of describing admissible controls, the main
assumption is that the number of switchings (points of discontinuity) is uniformly bounded and not just finite, as in the
main problem of optimal control theory. On the one hand, this assumption does not restrict the spectrum of optimal control
applications. On the other hand, it fits the Weierstrass’s theorem owing to the convenience in characterizing the sequential
compactness. The formulation of Weierstrass’s theorem, which asserts the existence of continuous function extrema on sequentially
compact sets, is customary, and its proof complies with the traditional scheme, whereas the concepts (convergent sequences
and some others) are adapted to the peculiarity of optimal problems. 相似文献