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1.
利用曲面的局部微分性质给出二元函数极值存在的必要条件和充分条件,并将之运用于具有明显几何特征的曲面对应的二元函数极值的判别问题中. 相似文献
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Peter Franek 《Advances in Applied Clifford Algebras》2007,17(3):469-480
In this paper, we show the existence of a sequence of invariant differential operators on a particular homogeneous model G/P of a Cartan geometry. The first operator in this sequence is locally the Dirac operator in 2 Clifford variables, D = (D
1, D
2), where D
i
= ∑
j
e
j
. ∂
ij
. It follows from the construction that this operator is invariant with respect to the action of the group G. There are 2 other G-invariant differential operators following it so that the sequence of operators is exact. We compute the local expression
of these operators and show that it coincides with the operators described in [2, 5, 6] by the tools of Clifford analysis.
However, it follows from our approach that the operators are invariant.
The work presented here was supported by the grants GAUK 447/2004 and GA ČR 201/05/H005. 相似文献
3.
An Exploration of a Quantitative Reasoning Instructional Approach to Linear Equations in Two Variables With Community College Students 下载免费PDF全文
Paul T. Belue Laurie Overman Cavey Margaret T. Kinzel 《School science and mathematics》2017,117(5):183-193
In this exploratory study, we examined the effects of a quantitative reasoning instructional approach to linear equations in two variables on community college students’ conceptual understanding, procedural fluency, and reasoning ability. This was done in comparison to the use of a traditional procedural approach for instruction on the same topic. Data were gathered from a common unit assessment that included procedural and conceptual questions. Results demonstrate that small changes in instruction focused on quantitative reasoning can lead to significant differences in students’ ability to demonstrate conceptual understanding compared to a procedural approach. The results also indicate that a quantitative reasoning approach does not appear to diminish students’ procedural skills, but that additional work is needed to understand how to best support students’ understanding of linear relationships. 相似文献
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Antonio Causa 《代数通讯》2013,41(3):1041-1058
We give a general geometrical procedure to construct nilpotent morphisms Φ : F → F(d), with F a vector bundle on ?1, obtaining an analog of the Jordan canonical form. We investigate the possible splitting types of F in dependence on the degeneration behavior of Φ. Applications to nilpotent matrices with an arbitrary number of variables are also given. 相似文献
7.
We present various new inequalities involving the logarithmic mean L(x,y)=(x-y)/(logx-logy) L(x,y)=(x-y)/(\log{x}-\log{y}) , the identric mean I(x,y)=(1/e)(xx/yy)1/(x-y) I(x,y)=(1/e)(x^x/y^y)^{1/(x-y)} , and the classical arithmetic and geometric means, A(x,y)=(x+y)/2 A(x,y)=(x+y)/2 and G(x,y)=?{xy} G(x,y)=\sqrt{xy} . In particular, we prove the following conjecture, which was published in 1986 in this journal. If Mr(x,y) = (xr/2+yr/2)1/r(r 1 0) M_r(x,y)= (x^r/2+y^r/2)^{1/r}(r\neq{0}) denotes the power mean of order r, then $ M_c(x,y)<\frac{1}{2}(L(x,y)+I(x,y)) {(x,y>0,\, x\neq{y})} $ M_c(x,y)<\frac{1}{2}(L(x,y)+I(x,y)) {(x,y>0,\, x\neq{y})} with the best possible parameter c=(log2)/(1+log2) c=(\log{2})/(1+\log{2}) . 相似文献
8.
利用Rademacher随机变量,本文讨论了学习函数f的亏损函数及f的样本误差的估计问题,给出了f的亏损函数及样本误差的估计,同时也给出了f的亏损函数的期望值的估计,这些估计都是O(m-1/2),这里m为样本容量. 相似文献
9.
研究典型相关分析的原理、典型成分的计算方法及计算步骤.把两组变量X与Y转化为具有最大相关性的若干对典型成分,直到两组变量的相关性被分解.通过典型相关系数及其显著性检验.选择典型成分分析两组变量的相关性.实例表明只有第一个典型相关系数能通过显著性检验,而其它两个典型相关系数显著为零,故应选取第一对典型成分F1和G1做分析... 相似文献
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Fred Ames Shelton 《The Journal of the Operational Research Society》1987,38(3):269-275
Acceptance of the adaptive-filtering parameter-estimation process has been mixed. Much of the variability between studies may result from the particular learning factor selected and may be further affected by the type of standardization used. The author presents a modification of the Makridakis and Wheelwright adaptive-filtering algorithm. This modified algorithm provides superior performance and simplifies the selection of the learning factor when used with simple autoregressive processes. 相似文献
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《Optimization》2012,61(3):511-537
We study both the continuous and discrete problems of maximizing the product of two linear functions subject to all variables being between 0 and 1. We first give linear and low-order polynomial algorithms for the solution of the continuous problem. In addition, we describe penalties that help to fix variables in the discrete problem. Extensive computational tests demonstrate the effectiveness of these results. 相似文献
13.
利用图论和代数的方法研究离散几何中的两个铺砌问题:1)给出1×2长方形铺砌多米诺骨牌的充分必要条件;2)对高维空间盒子的情形,给出m_1×m_2×…×m_n砖能够铺砌a_1×a_2×…×a_n盒子的一些必要条件和充要条件. 相似文献
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The Penrose transform is used to construct a complex starting with the Dirac operator in two Clifford variables. The corresponding
relative BGG complex and its direct image is computed for cohomology with values in line bundles induced by representations
in singular infinitesimal character. The limit of the induced spectral sequence is computed in cases connected with the Dirac
operator in two Clifford variables.
The work presented here is a part of the research project MSM 0021620839 and was supported also by the grants GAUK 447/2004
and GA ČR 201/05/2117. 相似文献
17.
GRAVES-MORRIS P. R.; JONES R. HUGHES; MAKINSON G. J. 《IMA Journal of Applied Mathematics》1974,13(3):311-320
Chisholm has shown how rational approximants may be definedfor functions of two variables, which reduce to diagonal Pad?Approximants when one variable is zero. We extend the idea toallow for different maximum powers in numerator and denominator,and state the relevant theorems. We discuss numerical difficultiesand possible singularities occurring in the construction ofthe approximants; approximants to the Beta function are calculatedand discussed in detail. 相似文献
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多复变数星形映照的两类子族 总被引:3,自引:0,他引:3
本文首先讨论有界星形圆型域上星形映照的一个子族---次星形映照,着重研究其几何性质,包括增长定理与掩盖定理.然后,在有界凸圆型域上讨论星形映照的另一类子族---α次的γ-凸映照.讨论它与星形映照,β次星形映照以及凸映照的关系. 相似文献
19.
George Haiman 《Methodology and Computing in Applied Probability》2012,14(3):445-458
We provide a method to construct a 1-dependent stationary sequence provided some mixing condition on the joint distribution of two consecutive random variables. Two illustrations of computational benefits of the method are given. We obtain analytical formulas to compute the expectation and variance of the number of occurrences of a word in a sequence of letters from a finite alphabet generated by the 1-dependent model.We also obtain an approximation formula for the distribution of the longest success run in a Bernoulli sequence generated by our model. 相似文献