Variational Problem of Some Quadratic Functionals in Complex Analysis

SummaryHeat inactivation of thrombin at 54° C followed first order kinetics with a rate constant of 1.0 min−1 approximately. Addition of heparin resulted in protection against thermal denaturation and, at the same time, rendered denaturation kinetics more complex. Analysis of the biphasic curve of heat inactivation in the presence of heparin revealed that the rate constants of the second phase changed systematically with heparin concentrations. Namely, at 4.5 × 10−6M, 9 × 10−6M, 1.8 × 10−5M and 3.6 × 10−5M heparin concentrations, the rate constants were 0.27 min−1, 0.17 min−1, 0.11 min−1 and 0.06 min−1, respectively.Sulfate as well as phosphate ions displayed also enzyme protection against heat inactivation, however, the same effect was obtained already at a heparin concentration, lower by three orders of magnitude.The kinetics of enzyme denaturation was not affected by calcium ions, whereas in the presence of heparin the inactivation rate of thrombin changed, i. e. calcium ions abolished the biphasic character of time course of thermal denaturation.Thus, the data suggest that calcium ions contribute to the effect of heparin on thrombin.

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Complex analysis of prognostic factors in chronic lymphocytic leukemia

Orvosi Hetilap ◽

10.1556/oh.2007.27943 ◽

2007 ◽

Vol 148 (16) ◽

pp. 737-743

Author(s):

Béla Kajtár ◽

Pál Jáksó ◽

László Kereskai ◽

Ágnes Lacza ◽

Gábor Méhes ◽

...

Keyword(s):

Prognostic Factors ◽

Chronic Lymphocytic Leukemia ◽

Complex Analysis ◽

Lymphocytic Leukemia

Bevezetés: Az utóbbi években felfedezett számos új prognosztikai faktor segítséget nyújthat a várható túlélés meghatározásához krónikus lymphocytás leukémia esetében. Célok: Jelen tanulmány célja e prognosztikai faktorok gyakoriságának, valamint egymással való összefüggésének meghatározása volt 419 beteg mintáin. Módszerek: 160 esetben végezték el az immunglobulin-nehézláncgén mutációs vizsgálatát. Eredmények: Az esetek 62%-ában nem mutált immunglobulin gént találtak, a nehézlánc géncsaládok használata különbözött a mutációs státusz függvényében. A CD38 expresszió 78%-os konkordanciát mutatott a mutációs státusszal, a ZAP-70-expresszió tekintetében korrelációt nem figyeltek meg. Citogenetikai abnormalitást 76%-ban láttak, a leggyakoribb eltérések a del(13q) (57%), a 12-es triszómia (15%), a del(11q) (12%) és a del(17p) (6%) voltak. A del(11q)-t hordozó esetek 95%-a nem mutált, az egyedül del(13q)-t hordozó esetek 74%-a mutált IgH-gént tartalmazott. Következtetések: A vizsgált paraméterek nem függetlenek egymástól, ezért alkalmazásuk a klinikai gyakorlatban gondos tervezést igényel.

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Immune Complex Analysis in Active Lyme Disease

Forum on Immunopathological Diseases and Therapeutics ◽

10.1615/forumimmundisther.2017019621 ◽

2016 ◽

Vol 7 (3-4) ◽

pp. 213-224

Author(s):

Steven E. Schutzer ◽

P. K. Coyle

Keyword(s):

Lyme Disease ◽

Immune Complex ◽

Complex Analysis

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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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