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1. |
Record Nr. |
UNINA9910794062503321 |
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Autore |
Lombardi Henri |
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Titolo |
An elementary recursive bound for effective positivstellensatz and Hilbert's 17th problem / / Henri Lombardi, Daniel Perrucci, Marie-Françoise Roy |
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Pubbl/distr/stampa |
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Providence, Rhode Island : , : American Mathematical Society, , 2020 |
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ISBN |
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Descrizione fisica |
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1 online resource (138 pages) |
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Collana |
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Memoirs of the American Mathematical Society ; ; Volume 263 |
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Classificazione |
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Disciplina |
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Soggetti |
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Polynomials |
Algebraic fields |
Recursive functions |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Nota di bibliografia |
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Includes bibliographical references. |
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Nota di contenuto |
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Weak inference and weak existence -- Intermediate value theorem -- Fundamental theorem of algebra -- Hermite's theory -- Elimination of one variable -- Proof of the main theorems -- Annex. |
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Sommario/riassunto |
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"We prove an elementary recursive bound on the degrees for Hilbert's 17th problem. More precisely we express a nonnegative polynomial as a sum of squares of rational functions, and we obtain as degree estimates for the numerators and denominators the following tower of five exponentials 222d4k where d is the degree and k is the number of variables of the input polynomial. Our method is based on the proof of an elementary recursive bound on the degrees for Stengle's Positivstellensatz. More precisely we give an algebraic certificate of the emptyness of the realization of a system of sign conditions and we obtain as degree bounds for this certificate a tower of five exponentials, namely 2²(2max{2,d}4k+s2kmax{2,d}16kbit(d)) where d is a bound on the degrees, s is the number of polynomials and k is the number of variables of the input polynomials-- |
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2. |
Record Nr. |
UNINA9910164048503321 |
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Autore |
Anderson Peggy |
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Titolo |
Great Quotes from Great Leaders : Words from the Leaders Who Shaped the World |
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Pubbl/distr/stampa |
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Naperville : , : Sourcebooks, Incorporated, , 2017 |
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©2017 |
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ISBN |
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9781492660484 |
1492660485 |
9781492660439 |
1492660434 |
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Edizione |
[1st ed.] |
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Descrizione fisica |
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1 online resource (352 p.) : ill |
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Disciplina |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Nota di contenuto |
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Front Cover -- Title Page -- Copyright -- Contents -- Introduction -- Mother Teresa -- Winston Churchill -- Walt Disney -- Albert Einstein -- Dwight D. Eisenhower -- Henry Ford -- Benjamin Franklin -- Mahatma Gandhi -- Ruth Bader Ginsburg -- Andrew Jackson -- Thomas Jefferson -- Helen Keller -- John F. Kennedy -- Dr. Martin Luther King Jr. -- Ray Kroc -- Abraham Lincoln -- Vince Lombardi -- Douglas MacArthur -- Nelson Mandela -- Golda Meir -- Michelle Obama -- George S. Patton -- Ronald Reagan -- Eleanor Roosevelt -- Franklin Roosevelt -- Theodore Roosevelt -- Albert Schweitzer -- Margaret Thatcher -- Harry S. Truman -- Sam Walton -- Booker T. Washington -- George Washington -- John Wooden -- Pope John Paul II -- Back Cover. |
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Sommario/riassunto |
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A comprehensive anthology presenting quotes that capture the essence of leadership, strategy, wisdom, and human spirit from world-class leaders such as Ruth Bader Ginsburg, Mother Teresa, Nelson Mandela, Mahatma Gandhi, Martin Luther King Jr., Eleanor Roosevelt, and many more.Each quote in Great Quotes from Great Leaders is thoughtfully selected to enlighten and inspire. They offer valuable lessons on leadership, determination, resilience, and the power of belief.Key |
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Features:Comprehensive Collection: Offers a vast compilation of inspiring and thought-provoking quotes from the world's most influential leaders.Historical Context: Includes brief bios for each leader, providing context for their quotes.Diverse Perspectives: Features leaders from various fields and across different eras, encompassing a wide array of perspectives on leadership.Valuable Lessons: Provides insights on leadership, determination, resilience, and belief, which can guide personal and professional development.Updated Edition: This expanded version includes even more leaders and their iconic quotes.Resourceful: Serves as a valuable resource for students, professionals, and entrepreneurs seeking inspiration and guidance.Dive into Great Quotes from Great Leaders and let the wisdom of history's greatest leaders guide your path towards leadership and personal growth. |
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