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Non‐negative residual matrix factorization: problem definition, fast solutions, and applications

Statistical Analysis and Data Mining: The ASA Data Science Journal, 2011
AbstractMatrix factorization is a very powerful tool to find graph patterns, e.g. communities, anomalies, etc. A recent trend is to improve the usability of the discovered graph patterns, by encoding some interpretation‐friendly properties (e.g., non‐negativity, sparseness, etc) in the factorization.
Tong, Hanghang, Lin, Ching-yung
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Evaluation of Real Definite Integrals by Means of Residues

1984
If n is a positive integer, then $$ \begin{gathered} L\left( n \right) = {\int\limits_0^{ + \infty } {\left( {\frac{{\sin x}}{x}} \right)} ^n}dx \hfill \\ = \left\{ {\begin{array}{*{20}{c}} {\frac{{{{\left( { - 1} \right)}^{n/2}}\pi {i^n}}}{{{2^n}\left( {n - 1} \right)!}}\sum\limits_{k = 0}^{\frac{n}{2} - 1} {{{\left( { - 1} \right)}^k}\left ...
Dragoslav S. Mitrinović   +1 more
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Residual algorithm for large-scale positive definite generalized eigenvalue problems

Computational Optimization and Applications, 2009
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Bello, Lenys   +2 more
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Evaluation of four irrational cosine definite integrals using residue theory

Applied Mathematics and Computation, 1989
For the four integrals \[ D_ j(a)=\int^{2\pi}_{0}(a+\cos^ j\theta)^{-1/2} d\theta,\quad N_ j(a)=\int^{2\pi}_{0}(a+\cos^ j\theta)^{1/2} d\theta,\quad j=1,2, \] Laurent series, convergent for sufficiently large values of \(| a|\), are ``derived'' by rather dubious calculations with residues which, miraculously, lead to correct results (although written ...
Evans, James D., Evans, Lori M.
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Computations of Definite Integrals Using the Residue Theorem

2011
We have seen in Chapter 5 how the fundamental theorem of calculus for line integrals, or Cauchy’s theorem, allow us to compute (in general real) definite integrals such as the Fresnel integrals. In that chapter no residues are computed. The approach in the present chapter is different. The main player is the residue theorem. There are numerous kinds of
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Evaluation of four irrational definite sine integrals using residue theory

Applied Mathematics and Computation, 1990
The integrals are \[ \int^{2\pi}_{0}(a+\sin \sigma)^{\pm} d\sigma \quad (a>1),\quad and\quad \] \[ \int^{2\pi}_{0}(a+\sin^ 2 \sigma)^{\pm} d\sigma \quad (a>0). \] The integrals, which are equivalent to the complete elliptic integrals of the second and first kinds, are evaluated as power series in \(a^{-2}\) and \((a+)^{-2}\) respectively.
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Objective definition of interaction degree between residues in globular proteins

Journal of Molecular Structure: THEOCHEM, 2004
Abstract A new measure of the interaction between two molecular fragments, contact intensity (ContI), is defined as the ratio X /( Y + Z ), where X is the average inter-fragment inter-atomic distance and Y and Z are the average intra-fragment inter-atomic distances.
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Fundamental Definitions in Residual Stress Analysis and Their Implications

Abstract The article provides detailed discussion on the definitions and implications for each of these seven subjects in residual stress analysis: preliminary concepts; loading and stress; displacement, deformation, and strain; constitutive equations and linear elasticity; material descriptors; methods; and diffraction. The article also
I. Cevdet Noyan, Darren C. Pagan
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[Salvage Surgery for Residual and Recurred Tumor after Definitive Chemoradiotherapy].

Kyobu geka. The Japanese journal of thoracic surgery, 2018
Standard treatment for clinical N2-locally advanced lung cancer is definitive chemoradiotherapy (CRT). For local recurrence or residual tumor after definitive CRT, salvage surgery may have effective treatment option with relatively high operative risk.To examine the prognosis and risk of salvage surgery.In 2001 to 2016, postoperative complications ...
Hiroyuki, Ito, Haruhiko, Nakayama
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