Denis, E. Yeramian, The representation of functions through the combined use of integral transforms and Pade approximants: Pade -- Laplace analysis of functions as sums of exponentials, Computer Physics Reports, vol. 9, pp. 247--299, 1989....
\small (b) Deduce from this result, and from Exercise 11, the Poisson integral representation formula from the Cauchy integral formula: If u is harmonic in the unit disc and continuous on its closure, then if z = re^{i\theta} one has u(z)=\frac{1}{2\pi}\int_0^{2\pi}P_r(\...
[16]Lecture 16_ Fejer’s Theorem and Convergence of Fourier Series.zh_en 1:21:23 [17]Lecture 17_ Minimizers, Orthogonal Complements and the Riesz Representation 1:16:04 [18]Lecture 18_ The Adjoint of a Bounded Linear Operator on a Hilbert Space ...
Features original articles, short communications, and critical reviews. Encompasses various topics, including string theory, non-Archimedean and noncommutative geometry, theory of finite fields and rings, representation theory, cognitive models, neural networks, and many more. ...
For uniqueness, suppose T',S'\in\mathcal L(\mathcal H,\mathcal H) form another self-adjoint representation of A. Set \tilde T:=T'-T and \tilde S:=S'-S. Then \tilde T,\tilde S are self-adjoint, and \tilde T+i\tilde S=(T'-T)+i(S'-S)\equiv 0. Hence 0=0^*\equiv ...
Social emotions such as guilt and gratitude serve adaptive functions critical to social interactions and relationships. Therefore, an ecologically valid approach to studying the psychological and neural mechanisms of social emotions is to elicit and measure them in social interactive contexts, where relevan...
Expected MSText representation of the expected value for the mean square.Q(source)represents a quadratic function ofsourceandV(source)represents the variance ofsource. MS denomDenominator of theF-statistic. d.f. denomDegrees of freedom for the denominator of theF-statistic. ...
Hierarchical clustering also allows you to experiment with different linkages. For example, clustering the iris data with single linkage, which tends to link together objects over larger distances than average distance does, gives a very different interpretation of the structure in the data. ...
broad的人估计是灌水太多,不忍再残害科学界,才花了大力气打造了一个颇具科学性的基因富集分析工具GSEA。 补充:普通富集分析的正式英文是Over-Representation Analysis;GSEA则称为Gene Set Enrichment Analysis。 Enrichment map是一个不错的结果展现方式。 待续~ 10 11...
Compactness theorems of measurable selections and integral representation theorem Charles Castaing, Michel Valadier Pages 125-161 Primitive of multifunctions and multivalued differential equations Charles Castaing, Michel Valadier Pages 163-194 Convex integrand on locally convex spaces. And its ...