共查询到20条相似文献,搜索用时 15 毫秒
1.
Numerical Algorithms - Quasi-Newton methods for solving nonlinear systems of equations are generally defined in order to satisfy a “direct secant equation” or an “inverse secant... 相似文献
2.
A. S. Gordienko 《Journal of Mathematical Sciences》2010,164(2):188-194
Let A be a finite-dimensional associative algebra over a field of characteristic 0. Then there exist C ∈ ℚ+ and t ∈ ℤ+ such that gc
n
(A) ∼ Cn
t
d
n
as n → ∞, where d = PIexp(A). In particular, Amitsur’s and Regev’s conjectures hold for the codimensions gc
n
(A) of generalized polynomial identities. 相似文献
3.
Eugenio P. Balanzario Jorge Sánchez-Ortiz 《Statistics & probability letters》2010,80(23-24):1713-1719
We present two sufficient conditions for an absolutely continuous random variable to obey Benford’s law for the distribution of the first significant digit. These two sufficient conditions suggest that Benford’s law will not often be observed in everyday sets of numerical data. On the other hand, we recall that there are two processes by way of which a random variable can come close to following Benford’s law. The first of these is the multiplication of independent random variables and the second is the exponentiation of a random variable to a large power. Our working tool is the Poisson sum formula of Fourier analysis. Like the central limit theorem, Benford’s law has an asymptotic nature. 相似文献
4.
Let \(x_{n,k}^{(\alpha ,\beta )}\) , \(k=1,\ldots ,n\) , be the zeros of Jacobi polynomials \(P_{n}^{(\alpha ,\beta )}(x)\) arranged in decreasing order on \((-1,1)\) , where \(\alpha ,\beta >-1\) , and \(\theta _{n,k}^{(\alpha ,\beta )}=\arccos x_{n,k}^{(\alpha ,\beta )}\) . Gautschi, in a series of recent papers, conjectured that the inequalities $$n\theta_{n,k}^{(\alpha,\beta)}<(n+1)\theta_{n+1,k}^{(\alpha,\beta)} $$ and $$(n+(\alpha+\beta+3)/2)\theta_{n+1,k}^{(\alpha,\beta)}<(n+(\alpha+\beta+1)/2)\theta_{n,k}^{(\alpha,\beta)}, $$ hold for all \(n\geq 1\) , \(k=1,\ldots ,n\) , and certain values of the parameters \(\alpha \) and \(\beta \) . We establish these conjectures for large domains of the \((\alpha ,\beta )\) -plane by using a Sturmian approach. 相似文献
5.
We extend Prasad’s results on the existence of trilinear forms on representations of GL
2 of a local field, by permitting one or more of the representations to be reducible principal series, with infinite-dimensional
irreducible quotient. We apply this in a global setting to compute (unconditionally) the dimensions of the subspaces of motivic
cohomology of the product of two modular curves constructed by Beilinson.
Received February 24, 2000 / final version received September 12, 2000?Published online November 8, 2000 相似文献
6.
Jianbei An 《Israel Journal of Mathematics》1999,112(1):109-134
This paper is part of a program to study Alperin’s weight conjecture and Dade’s conjecture on counting ordinary characters
in blocks for several finite groups. The classifications of radical subgroups and certain radical chains and their local structures
of the simple Conway’s third group have been obtained by using the computer algebra system CAYLEY. The Alperin weight conjecture
and the Dade final conjecture have been confirmed for the group. 相似文献
7.
In Ax (Ann. Math. 93(2):252–268, 1971), J. Ax proved a transcendency theorem for certain differential fields of characteristic zero : the differential counterpart of the still open Schanuel conjecture about the exponential function over ${\mathbb{C}}$ (Lang, Introduction to transcendental numbers, 1966). In this article, we derive from Ax’s theorem transcendency results in the context of differential valued exponential fields. In particular, we obtain results for exponential Hardy fields, Logarithmic-Exponential power series fields, and Exponential-Logarithmic power series fields. 相似文献
8.
In this work, we first present new bijections for the composition analogues of the partition theorems of Euler, Glaisher, and Franklin respectively. Then we generalize one composition analogue of Beck’s conjectures found by Huang recently, and give a purely combinatorial proof applying our bijection. Finally, a new and general composition analogue of Beck’s conjectures is established. 相似文献
9.
We propose a very weak type of generalized distances called a weak τ-function and use it to weaken the assumptions about lower semicontinuity in existing versions of Ekeland’s variational principle and equivalent formulations. 相似文献
10.
In this paper, we investigate Green’s functions for various stationary problems with nonlocal boundary conditions. We express
the Green’s function per Green’s function for a problem with classical boundary conditions. This property is illustrated by
various examples. Properties of Green’s functions with nonlocal boundary conditions are compared with those for classical
problems.
The research was partially supported by the Lithuanian State Science and Studies Foundation, grant No. T-73/09. 相似文献
11.
Sadao Ikeda 《Annals of the Institute of Statistical Mathematics》1962,14(1):107-118
Summary Two types of necessary conditions are given for the convergence of Kullback-Leibler’s mean information, one of which is connected
with an asymptotic equivalence of two sequences of probability measures, and in special cases, with convergence of a sequence
of probability distributions. The other is given in terms of the generalized probability density functions. 相似文献
12.
A. Guezane-Lakoud M.S. Jasmati A. Chaoui 《Nonlinear Analysis: Theory, Methods & Applications》2010,72(3-4):1522-1530
This work deals with an integrodifferential equation with initial, Newman and integral conditions. The existence and uniqueness of the weak solution in an appropriate sense is proved by the method of Rothe. 相似文献
13.
The Ramanujan Journal - In this paper, we give some extensions for Ramanujan’s circular summation formulas with the mixed products of two Jacobi’s theta functions. As applications, we... 相似文献
14.
Let u = (u
n
) be a sequence of real numbers whose generator sequence is Cesàro summable to a finite number. We prove that (u
n
) is slowly oscillating if the sequence of Cesàro means of (ω
n
(m−1)(u)) is increasing and the following two conditions are hold:
$\begin{gathered}
\left( {\lambda - 1} \right)\mathop {\lim \sup }\limits_n \left( {\frac{1}
{{\left[ {\lambda n} \right] - n}}\sum\limits_{k = n + 1}^{\left[ {\lambda n} \right]} {\left( {\omega _k^{\left( m \right)} \left( u \right)} \right)^q } } \right)^{\frac{1}
{q}} = o\left( 1 \right), \lambda \to 1^ + , q > 1, \hfill \\
\left( {1 - \lambda } \right)\mathop {\lim \sup }\limits_n \left( {\frac{1}
{{n - \left[ {\lambda n} \right]}}\sum\limits_{k = \left[ {\lambda n} \right] + 1}^n {\left( {\omega _k^{\left( m \right)} \left( u \right)} \right)^q } } \right)^{\frac{1}
{q}} = o\left( 1 \right), \lambda \to 1^ - , q > 1, \hfill \\
\end{gathered}$\begin{gathered}
\left( {\lambda - 1} \right)\mathop {\lim \sup }\limits_n \left( {\frac{1}
{{\left[ {\lambda n} \right] - n}}\sum\limits_{k = n + 1}^{\left[ {\lambda n} \right]} {\left( {\omega _k^{\left( m \right)} \left( u \right)} \right)^q } } \right)^{\frac{1}
{q}} = o\left( 1 \right), \lambda \to 1^ + , q > 1, \hfill \\
\left( {1 - \lambda } \right)\mathop {\lim \sup }\limits_n \left( {\frac{1}
{{n - \left[ {\lambda n} \right]}}\sum\limits_{k = \left[ {\lambda n} \right] + 1}^n {\left( {\omega _k^{\left( m \right)} \left( u \right)} \right)^q } } \right)^{\frac{1}
{q}} = o\left( 1 \right), \lambda \to 1^ - , q > 1, \hfill \\
\end{gathered} 相似文献
15.
16.
In this paper, we consider gradient estimates for positive solutions to the following weighted nonlinear parabolic equations on a complete smooth metric measure space with only Bakry-E′mery Ricci tensor bounded below: One is u_t=Δ_fu + aulogu+bu with a, b two real constants, and another is u_t = Δ_fu+λu~α with λ, α two real constants. We obtain local Hamilton-Souplet-Zhang type gradient estimates for the above two nonlinear parabolic equations. In particular, our estimates do not depend on any assumption on f. 相似文献
17.
Michael I. Gil’ 《Central European Journal of Mathematics》2011,9(5):1156-1163
We consider a linear nonautonomous higher order ordinary differential equation and establish the positivity conditions and
two-sided bounds for Green’s function for the two-point boundary value problem. Applications of the obtained results to nonlinear
equations are also discussed. 相似文献
18.
We consider the d-dimensional Jensen inequality $$ T[\varphi(f_1, \dots, f_d)]\, \ge \, \varphi(T[f_1], \dots, T[f_d])\quad\quad(\ast)$$ T [ φ ( f 1 , … , f d ) ] ≥ φ ( T [ f 1 ] , … , T [ f d ] ) ( * ) as it was established by McShane in 1937r. Here T is a functional, φ is a convex function defined on a closed convex set ${K\subset \mathbb{R}^d}$ K ? R d , and f 1, . . . , f d are from some linear space of functions. Our aim is to find necessary and sufficient conditions for the validity of (*). In particular, we show that if we exclude three types of convex sets K, then Jensen’s inequality holds for a sublinear functional T if and only if T is linear, positive, and satisfies T[1] = 1. Furthermore, for each of the excluded types of convex sets, we present nonlinear, sublinear functionals T for which Jensen’s inequality holds. Thus the conditions on K are optimal. Our contributions generalize or complete several known results. 相似文献
19.
In this paper, we present some new variants of Ostrowski’s method with order of convergence eight. For each iteration the new methods require three evaluations of the function and one evaluation of its first derivative and therefore they have the efficiency index equal to 1.682. Numerical tests verifying the theory are also given. 相似文献
20.
Thomas Mejstrik 《Czechoslovak Mathematical Journal》2012,62(1):235-242
We provide a simpler proof for a recent generalization of Nagumo’s uniqueness theorem by A. Constantin: On Nagumo’s theorem. Proc. Japan Acad., Ser. A 86 (2010), 41–44, for the differential equation x′ = f(t, x), x(0) = 0 and we show that not only is the solution unique but the Picard successive approximations converge to the unique solution.
The proof is based on an approach that was developed in Z. S. Athanassov: Uniqueness and convergence of successive approximations for ordinary differential equations. Math. Jap. 35 (1990), 351–367. Some classical existence and uniqueness results for initial-value problems for ordinary differential equations
are particular cases of our result. 相似文献
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