This book provides a comprehensive analysis of the existence of weak solutions of unsteady problems with variable exponents. The central motivation is the weak solvability of the unsteady p(.,.)-Navier–Stokes equations describing the motion of an incompressible electro-rheological fluid. Due to the variable dependence of the power-law index p(.,.) in this system, the classical weak existence analysis based on the pseudo-monotone operator theory in the framework of Bochner–Lebesgue spaces is not applicable. As a substitute for Bochner–Lebesgue spaces, variable Bochner–Lebesgue spaces are introduced and analyzed. In the mathematical framework of this substitute, the theory of pseudo-monotone operators is extended to unsteady problems with variable exponents, leading to the weak solvability of the unsteady p(.,.)-Navier–Stokes equations under general assumptions. Aimed primarily at graduate readers, the book develops the material step-by-step, starting with the basics of PDE theory and non-linear functional analysis. The concise introductions at the beginning of each chapter, together with illustrative examples, graphics, detailed derivations of all results and a short summary of the functional analytic prerequisites, will ease newcomers into the subject.
This book provides a comprehensive analysis of the existence of weak solutions of unsteady problems with variable exponents. The central motivation is the weak solvability of the unsteady p(.,.)-Navier–Stokes equations describing the motion of an incompressible electro-rheological fluid. Due to the variable dependence of the power-law index p(.,.) in this system, the classical weak existence analysis based on the pseudo-monotone operator theory in the framework of Bochner–Lebesgue spaces is not applicable. As a substitute for Bochner–Lebesgue spaces, variable Bochner–Lebesgue spaces are introduced and analyzed. In the mathematical framework of this substitute, the theory of pseudo-monotone operators is extended to unsteady problems with variable exponents, leading to the weak solvability of the unsteady p(.,.)-Navier–Stokes equations under general assumptions. Aimed primarily at graduate readers, the book develops the material step-by-step, starting with the basics of PDE theory and non-linear functional analysis. The concise introductions at the beginning of each chapter, together with illustrative examples, graphics, detailed derivations of all results and a short summary of the functional analytic prerequisites, will ease newcomers into the subject.
Undoubtedly growing up during the Vietnam War, water gate and gas shortages can have a profound effect on a child. Also being the son of immigrant parents most certainly can lead to a traumatizing clash of cultures and the understanding of right and wrong. With that being said the Remington Company gave me the honor of a lifetime by letting me express my thoughts in unison with telling the brilliant stories of professionals around the world. As I wrote endlessly 24 hours a day I realized that our world is full of hope and real promise. I realized that it wasnt about war, ideology and the pursuit of global domination. I realized that in the pages of this great book great things were about to happen if only these stories can be made public. I realized that I had the opportunity of a lifetime by expressing the Humanitarian attributes that these professionals continually made. After many years of writing I realized that the Remington Company had a distinct and noble purpose and perhaps we could not change the present but we could certainly try to change our future. With that we created our Mentorship Program which gets these prolific stories out to the children. We wrote the stories with zest but never crossed the line of respect or dignity. We wished to capture the hearts of our audience and prove to them that giving was not an option but more so our duty as life forms on our planet. Today our book has a theme Inspiring the youth of America. This theme was our way of telling the world Lets hold hands and prepare our children for a better life. today I continue to write for the Registry. My life has irrevocably changed for the better. I volunteer for any thing all the time. I enjoy moments of quiet and the appreciation of our environment. I read these biographies in amazement as everyone else does and it never seems to get uneventful. Either way I sincerely hope you enjoy these biographies and use them to strengthen your spirit and confidence about our existence as a species on this planet. I patiently wait for divine intervention in order to write my next biography and am happy to serve the brilliant members of the Remington Registry of Outstanding Professionals.
Marshall McLuhan (1911–1980) is best known as a media theorist—many consider him the founder of media studies—but he was also an important theorist of art. Though a near-household name for decades due to magazine interviews and TV specials, McLuhan remains an underappreciated yet fascinating figure in art history. His connections with the art of his own time were largely unexplored, until now. In Distant Early Warning, art historian Alex Kitnick delves into these rich connections and argues both that McLuhan was influenced by art and artists and, more surprisingly, that McLuhan’s work directly influenced the art and artists of his time. Kitnick builds the story of McLuhan’s entanglement with artists by carefully drawing out the connections among McLuhan, his theories, and the artists themselves. The story is packed with big names: Marcel Duchamp, Niki de Saint Phalle, Jasper Johns, Andy Warhol, Nam June Paik, and others. Kitnick masterfully weaves this history with McLuhan’s own words and his provocative ideas about what art is and what artists should do, revealing McLuhan’s influence on the avant-garde through the confluence of art and theory. The illuminating result sheds light on new aspects of McLuhan, showing him not just as a theorist, or an influencer, but as a richly multifaceted figure who, among his many other accolades, affected multiple generations of artists and their works. The book finishes with Kitnick overlaying McLuhan’s ethos onto the state of contemporary and post-internet art. This final channeling of McLuhan is a swift and beautiful analysis, with a personal touch, of art’s recent transgressions and what its future may hold.
Practical General Practice is a highly practical manual, specifically designed for use during the consultation process. Containing over 1000 conditions, the unique underlying structure of the book allows the GP to see immediately what treatment is recommended and why. All recommendations are highly specific - giving a firm guide to the GP during the consultation process rather than a list of possibilities that the GP might wish to consider. Bullet points for action which give the GP an immediate summary of the issues that must be covered in the consultation. Bullet points of the key evidence which justifies those recommendations. All chapters thoroughly revised, to reflect changes in the evidence, and in major guidelines, since the last edition. NNT values provided when available
With a focus on case studies of R&D programs in a variety of disease areas, the book highlights fundamental productivity issues the pharmaceutical industry has been facing and explores potential ways of improving research effectiveness and efficiency. Takes a comprehensive and holistic approach to the problems and potential solutions to drug compound attrition Tackles a problem that adds billions of dollars to drug development programs and health care costs Guides discovery and development scientists through R&D stages, teaching requirements and reasons why drugs can fail Discusses potential ways forward utilizing new approaches and opportunities to reduce attrition
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