A Fast Method of Lighting Estimate Using Multi-linear Algebra

SummaryA simple and fast method for the quantitative determination of protein C activity in plasma is here described. The first step consists in the conversion of protein C in the test sample into activated protein C by means of an activator isolated from Southern Copperhead venom. Subsequently, the degradation of factor Va, in presence of protein C-deficient plasma, is measured by the prolongation of the prothrombin time which is proportional to the amount of protein C in the sample. The dose-response curve showed a linear relationship from 6 to 150% protein C activity and the inter- and intra-assay reproducibility was 3.5% and 5.6% respectively. In normal subjects, a mean of protein C level of 98 ± 15% of normal pooled plasma was found. Comparison with the anticoagulant assay in samples of patients with oral anticoagulant, liver cirrhosis, disseminated intravascular coagulation and severe preeclampsia revealed an excellent correlation (r = 0.94, p <0.001). Also, a similar correlation (r = 0.93, p <0.001) existed between amidolytic assay and the method here proposed for all the samples studied without including the oral anticoagulant group. These results allowed us to infer that this method evaluates the ability of protein C to interact with protein S, phospholipids, calcium ions and factor Va.

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A fast method for contingency analysis based on P-Q decoupled model.

IEEJ Transactions on Power and Energy ◽

10.1541/ieejpes1972.107.9 ◽

1987 ◽

Vol 107 (1) ◽

pp. 9-16

Author(s):

Dong Jian Li ◽

Eiichi Tanaka ◽

Jun Hasegawa

Keyword(s):

Fast Method ◽

Contingency Analysis

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Numerical linear algebra and examples in control

10.23919/acc.1983.4788087 ◽

1983 ◽

Author(s):

Alan J. Laub

Keyword(s):

Linear Algebra ◽

Numerical Linear Algebra

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Matrix Completions, Moments, and Sums of Hermitian Squares

10.23943/princeton/9780691128894.001.0001 ◽

2011 ◽

Cited By ~ 7

Author(s):

Mihály Bakonyi ◽

Hugo J. Woerdeman

Keyword(s):

Linear Algebra ◽

Undergraduate Students ◽

Complex Analysis ◽

Measure Theory ◽

Complex Function ◽

Complex Function Theory ◽

Extensive Discussion ◽

The Subject ◽

Processing Control ◽

Developing Area

Intensive research in matrix completions, moments, and sums of Hermitian squares has yielded a multitude of results in recent decades. This book provides a comprehensive account of this quickly developing area of mathematics and applications and gives complete proofs of many recently solved problems. With MATLAB codes and more than two hundred exercises, the book is ideal for a special topics course for graduate or advanced undergraduate students in mathematics or engineering, and will also be a valuable resource for researchers. Often driven by questions from signal processing, control theory, and quantum information, the subject of this book has inspired mathematicians from many subdisciplines, including linear algebra, operator theory, measure theory, and complex function theory. In turn, the applications are being pursued by researchers in areas such as electrical engineering, computer science, and physics. The book is self-contained, has many examples, and for the most part requires only a basic background in undergraduate mathematics, primarily linear algebra and some complex analysis. The book also includes an extensive discussion of the literature, with close to six hundred references from books and journals from a wide variety of disciplines.

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Topics in Quaternion Linear Algebra

10.23943/princeton/9780691161853.001.0001 ◽

2014 ◽

Cited By ~ 19

Author(s):

Leiba Rodman

Keyword(s):

Linear Algebra ◽

Complex Analysis ◽

Dimensional Space ◽

Applied Mathematics ◽

Three Dimensional ◽

Number System ◽

Graduate Course ◽

Open Problems ◽

Unpublished Research ◽

Reference Tool

Quaternions are a number system that has become increasingly useful for representing the rotations of objects in three-dimensional space and has important applications in theoretical and applied mathematics, physics, computer science, and engineering. This is the first book to provide a systematic, accessible, and self-contained exposition of quaternion linear algebra. It features previously unpublished research results with complete proofs and many open problems at various levels, as well as more than 200 exercises to facilitate use by students and instructors. Applications presented in the book include numerical ranges, invariant semidefinite subspaces, differential equations with symmetries, and matrix equations. Designed for researchers and students across a variety of disciplines, the book can be read by anyone with a background in linear algebra, rudimentary complex analysis, and some multivariable calculus. Instructors will find it useful as a complementary text for undergraduate linear algebra courses or as a basis for a graduate course in linear algebra. The open problems can serve as research projects for undergraduates, topics for graduate students, or problems to be tackled by professional research mathematicians. The book is also an invaluable reference tool for researchers in fields where techniques based on quaternion analysis are used.

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