共查询到20条相似文献,搜索用时 31 毫秒
1.
V.M. Shelkovich 《PAMM》2007,7(1):2040039-2040040
Using the definitions of δ - and δ ′-shocks for some systems of conservation laws, the corresponding Rankine–Hugoniot conditions are derived. We also derive the balance laws describing area, volume, mass and momentum transportation between the area outside the wave front and the wave front. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
2.
Georg Peters Fernando Crespo Pawan Lingras Richard Weber 《International Journal of Approximate Reasoning》2013,54(2):307-322
Clustering is one of the most widely used approaches in data mining with real life applications in virtually any domain. The huge interest in clustering has led to a possibly three-digit number of algorithms with the k-means family probably the most widely used group of methods. Besides classic bivalent approaches, clustering algorithms belonging to the domain of soft computing have been proposed and successfully applied in the past four decades. Bezdek’s fuzzy c-means is a prominent example for such soft computing cluster algorithms with many effective real life applications. More recently, Lingras and West enriched this area by introducing rough k-means. In this article we compare k-means to fuzzy c-means and rough k-means as important representatives of soft clustering. On the basis of this comparison, we then survey important extensions and derivatives of these algorithms; our particular interest here is on hybrid clustering, merging fuzzy and rough concepts. We also give some examples where k-means, rough k-means, and fuzzy c-means have been used in studies. 相似文献
3.
S. Paszkowski 《Numerical Algorithms》1995,10(2):337-361
It is proved that some power series converging very slowly in a neighbourhood of the point 1 can be transformed intoquasipower series. The latter converge faster but are more complicated because they contain some hypergeometric series2
F
1. Standard methods of the values evaluation for needed hypergeometric series with the aid of recurrence relations are not sufficiently efficient for some variable values. Therefore a new method, formally similar to Levin's transforms, is proposed. More generally, this is a method of approximative evaluating of such a solution of an inhomogeneous recurrence relation of order one which has some particular asymptotic properties.The efficacity of the proposed methods is analyzed in detail for Euler's dilogarithm. This is a typical function whose power series is approached with difficulties ifz1. In particular, its Padé approximants are sufficiently accurate only for, sayx[–1, 1/2]. Hermite-Padé approximation is more effective. Resulting irrational approximants generalize in some sense partial sums of the quasipower series introduced here. 相似文献
4.
Transitivity and Chaos 总被引:1,自引:0,他引:1
Mat Jiehua 《东北数学》1998,(1)
Several different definitions of transitivity and their relationship are carefullydiscussed for general spaces, and it is proved that a continuous map on a metric space ischaotic in the sense of Devaney if and only if it is periodic orbit transitive or periodic orbitstrongly transitive. 相似文献
5.
AER-x.,Aiscalledanonnegative(nonPositive)matrixifau>O(a,jO(aiirtO),markedA>O(AO(i#j),auO,wecallp(A)=max{IA,l,lA,l'.-.,lAnl},(whereA,,A2,..',A"areeigenva1ueofA)asspectralradiusofA.LemmalIfAe7'.,thenareanonnegativesquarematrxBandapositivenumberksuchthatA=B-kI(whereIistheidentitymatrixofordern).ProofLetbti=… 相似文献
6.
《数学研究与评论》1992,(4)
Algebraic-geometry foundations for non-linear spline functions are estab-lished.The structure of algebraic spline curves and surfaces represented by implicitforms are investigated.The necessary and sufficient conditions for smooth connection ofalgebraic curves(or surfaces)are presented. 相似文献
7.
8.
If a continued fraction K
n=1∞
a
n
/b
n
is known to converge but its limit is not easy to determine, it may be easier to use an extension of K
n=1∞
a
n
/b
n
to find the limit. By an extension of K
n=1∞
a
n
/b
n
we mean a continued fraction K
n=1∞
c
n
/d
n
whose odd or even part is K
n=1∞
a
n
/b
n
. One can then possibly find the limit in one of three ways:
We apply these ideas to derive new proofs of certain continued fraction identities of Ramanujan and to prove a generalization
of an identity involving the Rogers-Ramanujan continued fraction, which was conjectured by Blecksmith and Brillhart.
相似文献
(i) | Prove the extension converges and find its limit; |
(ii) | Prove the extension converges and find the limit of the other contraction (for example, the odd part, if K n=1∞ a n /b n is the even part); |
(iii) | Find the limit of the other contraction and show that the odd and even parts of the extension tend to the same limit. |
9.
Trial and error is a problem-solving strategy everyone uses at one time or another.In trial and error,you try ananswer.(The word trial comes from try.)If the answer is in error,you try something else.You keep trying untilyou get a correct answer.Trial and error is a particularly good strategy if a question has only a few possible answers. 相似文献
10.
《中学生数学》2006,(11)
Civilized man is surrounded on all sides, indoors and out, by a subtle, seldom-noticed conflict between two ancient ways of shaping things: the orthogonal and the round. Cars on circular wheels, guided by hand on circular steering wheels, move on streets that intersect like the lines of a rectangular lattice. Buildings and houses are made up mostly of right angles, relieved occasionally by circular domes and windows. At rectangular or circular tables, with rectangular napkins on our laps, we eat from circular plates and drink from glasses with circular cross sections. We light cylindrical cigarettes with matches torn from rectangular packs, and we pay the rectangular bill with rectangular bank notes and circular coins. 相似文献
11.
We present an easy proof that p-Hardy’s inequality implies uniform p-fatness of the boundary when p = n. The proof works also in metric space setting and demonstrates the self-improving phenomenon of the p-fatness. We also explore the relationship between p-fatness, p-Hardy inequality, and the uniform perfectness for all p ≥ 1, and demonstrate that in the Ahlfors Q-regular metric measure space setting with p = Q, these three properties are equivalent. When p ≠ 2, our results are new evenin the Euclidean setting. 相似文献
12.
Ath Kehagias 《Rendiconti del Circolo Matematico di Palermo》2003,52(2):322-350
In this paper we study two fuzzy hyperoperations, denoted by ⋎ (which can be seen as a generalization of ∨) and ⋏ (which can
be seen as a generalization of ∧). ⋎ is obtained from a family of crisp ∨;
p
hyperoperations and ⋏ is obtained from a family of crisp ∧
p
hyperoperations. The hyperstructure (X, ⋎, ∧) resembles ahyperlattice and the hyperstructure (X, ∨, ⋏) resembles adual hyperlattice 相似文献
13.
Dorit Patkin Avikam Gazit 《International Journal of Mathematical Education in Science & Technology》2013,44(8):1191-1200
The paper presents findings of a small scale study of a few items related to problem solving with squares and roots, for different teacher groups (pre-service and in-service mathematics teachers: elementary and junior high school). The research participants were asked to explain what would be the units digit of a natural number to be squared in order to obtain a certain units digit as a result. They were also asked to formulate a rule – an algorithm for calculating the square of a 2-digit number which is a multiple of 5. Based on this knowledge and estimation capability, they were required to find, without using calculators, the square roots of given natural numbers. The findings show that most of the participants had only partial intuition regarding the units’ digit of a number which is squared when the units’ digit of the square is known. At the same time, the participants manifested some evidence of creativity and flow of ideas in identifying the rule for calculating the square of a natural number whose units digit is 5. However, when asked to identify, by means of estimation and based on knowledge from previous items, the square roots of three natural numbers, only few of them managed to find the three roots by estimation. 相似文献
14.
《Journal of Pure and Applied Algebra》1987,47(1):1-33
Crossed complexes have longstanding uses, explicit and implicit, in homotopy theory and the cohomology of groups. It is here shown that the category of crossed complexes over groupoids has a symmetric monoidal closed structure in which the internal Hom functor is built from morphisms of crossed complexes, nonabelian chain homotopies between them and similar higher homotopies. The tensor product involves non-abelian constructions related to the commutator calculus and the homotopy addition lemma. This monoidal closed structure is derived from that on the equivalent category of ω-groupoids where the underlying cubical structure gives geometrically natural definitions of tensor products and homotopies. 相似文献
15.
Jiang Ming CHANG Ming Liang FANG 《数学学报(英文版)》2007,23(6):973-982
Let f be a nonconstant entire function; let k ≥ 2 be a positive integer; and let a be a nonzero complex number. If f(z) = a→f′(z) = a, and f′(z) = a →f^(k)(z) = a, then either f = Ce^λz + a or f = Ce^λz + a(λ - 1)/)λ, where C and ), are nonzero constants with λ^k-1 = 1. The proof is based on the Wiman-Vlairon theory and the theory of normal families in an essential way. 相似文献
16.
S. V. Nagaev 《Acta Appl Math》2007,97(1-3):151-162
Burkholder’s type inequality is stated for the special class of martingales, namely the product of independent random variables. The constants in the latter are much less than in the general case which is considered in Nagaev (Acta Appl. Math. 79, 35–46, 2003; Teor. Veroyatn. i Primenen. 51(2), 391–400, 2006). On the other hand, the moment inequality is proved, which extends these by Wittle (Teor. Veroyatn. i Primenen. 5(3), 331–334, 1960) and Dharmadhikari and Jogdeo (Ann. Math. Stat. 40(4), 1506–1508, 1969) to martingales. 相似文献
17.
We introduce a new map from polynomials orthogonal on the unit circle to polynomials orthogonal on the real axis. This map is closely related to the theory of CMV matrices. It contains an arbitrary parameter ?? which leads to a linear operator pencil. We show that the little and big ?1?Jacobi polynomials are naturally obtained under this map from the Jacobi polynomials on the unit circle. 相似文献
18.
Yuan Xu 《Constructive Approximation》2010,31(1):115-138
Several problems on Fourier series and trigonometric approximation on regular hexagonal and triangular domains are studied.
The results include Abel and Cesàro summability of Fourier series, degree of approximation, and best approximation by trigonometric
functions with both direct and inverse theorems. One of the objectives of this study is to demonstrate that Fourier series
on spectral sets enjoy a rich structure that permits an extensive theory for Fourier series and approximation. 相似文献
19.
We give necessary and sufficient conditions on a pair of positive radial functions V and W on a ball B of radius R in R n , n ≥ 1, so that the following inequalities hold for all \({u \in C_{0}^{\infty}(B)}\) : This characterization makes a very useful connection between Hardy-type inequalities and the oscillatory behaviour of certain ordinary differential equations, and helps in the identification of a large number of such couples (V, W)—that we call Bessel pairs—as well as the best constants in the corresponding inequalities. This allows us to improve, extend, and unify many results—old and new—about Hardy and Hardy–Rellich type inequalities, such as those obtained by Caffarelli et al. (Compos Math 53:259–275, 1984), Brezis and Vázquez (Revista Mat. Univ. Complutense Madrid 10:443–469, 1997), Wang and Willem (J Funct Anal 203:550–568, 2003), Adimurthi et al. (Proc Am Math Soc 130:489–505, 2002), and many others.
相似文献
$\label{one} \int\limits_{B}V(x)|\nabla u |^{2}dx \geq \int\limits_{B} W(x)u^2dx,$
$\label{two} \int\limits_{B}V(x)|\Delta u |^{2}dx \geq\int\limits_{B} W(x)|\nabla u|^{2}dx+(n-1)\int\limits_{B}\left(\frac{V(x)}{|x|^2}-\frac{V_r(|x|)}{|x|}\right)|\nabla u|^2dx.$
20.
In this paper, we establish the Fekete and Szeg inequality for a class of holomorphic functions in the unit disk, and then we extend this result to a class of holomorphic mappings on the unit ball in a complex Banach space or on the unit polydisk in C~n. 相似文献