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41.
Alireza Bahadori Sohrab Zendehboudi 《Journal of Dispersion Science and Technology》2013,34(6):793-799
Calcium carbonate, or calcite, scale is frequently encountered in oilfield operations. In a reservoir, when brine is produced, it is disturbed because the brine is moved to lower temperature and pressure areas. The dissolved concentration of calcium carbonate is greatly influenced by temperature and the partial pressure of carbon dioxide gas over the water. The net result of a drop in temperature and pressure may therefore be an increase or a decrease in the calcium carbonate saturation ratio as determined by the temperature change relative to the pressure change. In this article, a simple Arrhenius-type function is developed to estimate the combined effect of temperature and carbon dioxide pressure on calcium carbonate dissolved concentration in oilfield brines. Estimations are found to be in excellent agreement with reported data in the literature with average absolute deviation being less than 2%. The tool developed in this study can be of immense practical value for engineers to have a quick check of combined effect of temperature and carbon dioxide pressure on calcium carbonate dissolved concentration at various conditions without opting for any field or experimental trials. In particular, engineers would find the approach to be user friendly with transparent calculations involving no complex expressions. 相似文献
42.
对文[1]中关于多项式不动点的主要定理进行了修正和发展,进而研究了多项式的广义(高阶)不动点,证明了对任意给定的n个点t_1≤t_2≤…≤t_n,存在唯一的首项系数为α∈R(α≠0)的n次多项式P(x)以它们为广义不动点. 相似文献
43.
H. W. GOULD 《数学研究及应用》2019,39(6):603-606
The Catalan numbers $1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862,\ldots$ are given by $C(n)=\frac{1}{n+1}\binom{2n}{n}$ for $n\geq 0$. They are named for Eugene Catalan who studied them as early as 1838. They were also found by Leonhard Euler (1758), Nicholas von Fuss (1795), and Andreas von Segner (1758). The Catalan numbers have the binomial generating function $$\mathbf{C}(z) = \sum_{n=0}^{\infty}C(n)z^n = \frac{1 - \sqrt{1-4z}}{2z}$$ It is known that powers of the generating function $\mathbf{C}(z)$ are given by $$\mathbf{C}^a(z) = \sum_{n=0}^{\infty}\frac{a}{a+2n}\binom{a+2n}{n}z^n.$$ The above formula is not as widely known as it should be. We observe that it is an immediate, simple consequence of expansions first studied by J. L. Lagrange. Such series were used later by Heinrich August Rothe in 1793 to find remarkable generalizations of the Vandermonde convolution. For the equation $x^3 - 3x + 1 =0$, the numbers $\frac{1}{2k+1}\binom{3k}{k}$ analogous to Catalan numbers occur of course. Here we discuss the history of these expansions. and formulas due to L. C. Hsu and the author. 相似文献
44.
Sheng-Liang Yang 《Discrete Applied Mathematics》2007,155(15):2025-2030
In this paper, we are going to study some additional relations between the Stirling matrix Sn and the Pascal matrix Pn. Also the representation for the matrix Tn and in terms of sn and Sn will be considered. Consequently, this will give an answer to an open problem proposed by EI-Mikkawy [On a connection between the Pascal, Vandermonde and Stirling matrices—II, Appl. Math. Comput. 146 (2003) 759-769]. 相似文献
45.
46.
47.
This short note describes new properties of the elementary symmetric polynomials, and reveals that the properties give an answer to the conjecture raised by El-Mikkawy in [M.E.A. El-Mikkawy, On a connection between the Pascal, Vandermonde and Stirling matrices—II, Appl. Math. Comput. 146 (2003) 759-769]. 相似文献
48.
Ren-Cang Li. 《Mathematics of Computation》2006,75(256):1987-1995
Lower bounds on the condition number of a real confluent Vandermonde matrix are established in terms of the dimension , or and the largest absolute value among all nodes that define the confluent Vandermonde matrix and the interval that contains the nodes. In particular, it is proved that for any modest (the largest multiplicity of distinct nodes), behaves no smaller than , or than if all nodes are nonnegative. It is not clear whether those bounds are asymptotically sharp for modest .
49.
G. A. Kalyabin 《Functional Analysis and Its Applications》2002,36(2):106-113
We describe the construction of extension operators with minimal possible norm m from the half-line to the entire real line for the spaces
and derive the asymptotic estimate
, where
The proof is based on the investigation of the maximum and minimum eigenvalues and the corresponding eigenvectors of some special matrices related to Vandermonde matrices and their inverses, which can be of interest in themselves. 相似文献
50.
Christopher J. Hillar Lionel Levine 《Proceedings of the American Mathematical Society》2007,135(6):1607-1618
Let be an algebraically closed field of characteristic zero and let . The -th cyclic resultant of is
Res
A generic monic polynomial is determined by its full sequence of cyclic resultants; however, the known techniques proving this result give no effective computational bounds. We prove that a generic monic polynomial of degree is determined by its first cyclic resultants and that a generic monic reciprocal polynomial of even degree is determined by its first of them. In addition, we show that cyclic resultants satisfy a polynomial recurrence of length . This result gives evidence supporting the conjecture of Sturmfels and Zworski that resultants determine . In the process, we establish two general results of independent interest: we show that certain Toeplitz determinants are sufficient to determine whether a sequence is linearly recurrent, and we give conditions under which a linearly recurrent sequence satisfies a polynomial recurrence of shorter length.