Search results for ""Author R. Swaminathan""

By using mathematical models to describe the physical, biological or chemical phenomena, one of the most common results is either a differential equation or a system of differential equations, together with the correct boundary and initial conditions. The determination and interpretation of their solution are at the base of applied mathematics. Hence the analytical and numerical study of the differential equation is very much essential for all theoretical and experimental researchers, and this book helps to develop skills in this area. Recently non-linear differential equations were widely used to model many of the interesting and relevant phenomena found in many fields of science and technology on a mathematical basis. This problem is to inspire them in various fields such as economics, medical biology, plasma physics, particle physics, differential geometry, engineering, signal processing, electrochemistry and materials science. This book contains seven chapters and practical applications to the problems of the real world. The first chapter is specifically for those with limited mathematical background. Chapter one presents the introduction of non-linear reaction-diffusion systems, various boundary conditions and examples. Real-life application of non-linear reaction-diffusion in different fields with some important non-linear equations is also discussed. In Chapter 2, mathematical preliminaries and various advanced methods of solving non-linear differential equations such as Homotopy perturbation method, variational iteration method, exponential function method etc. are described with examples. Steady and non-steady state reaction-diffusion equations in the plane sheet (chapter 3), cylinder (chapter 4) and spherical (chapter 5) are analyzed. The analytical results published by various researchers in referred journals during 2007-2020 have been addressed in these chapters 4 to 6, and this leads to conclusions and recommendations on what approaches to use on non-linear reaction-diffusion equations. Convection-diffusion problems arise very often in applied sciences and engineering. Non-linear convection-diffusion equations and corresponding analytical solutions in various fields of chemical sciences are discussed in chapter6. Numerical methods are used to provide approximate results for the non-linear problems, and their importance is felt when it is impossible or difficult to solve a given problem analytically. Chapter 7 identifies some of the numerical methods for finding solutions to non-linear differential equations.

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DNA and RNA fractions have been isolated from whole blood, serum, plasma, the surface of blood cells, and urine from both healthy persons and patients. Specific fragments have been identified as being related to particular disorders, for example, diabetes, cancer, myocardial infarction, and stroke. The ability to isolate these fractions and assess their relationship to specific diseases makes early noninvasive diagnosis possible. This volume reports on the most recent progress in this field, including chapters on developing protocols for nucleic acid extraction, determining the origin of the circulating nucleic acids, the capacity of these nucleic acids to enter cells and exhibit biological activity, isolating and testing fetal cells from maternal blood, and discussing the clinical implications of these discoveries and developing the techniques that will bring them into clinical application. NOTE: Annals volumes are available for sale as individual books or as a journal. For information on institutional journal subscriptions, please visit www.blackwellpublishing.com/nyas. ACADEMY MEMBERS: Please contact the New York Academy of Sciences directly to place your order (www.nyas.org). Members of the New York Academy of Science receive full-text access to the Annals online and discounts on print volumes. Please visit http://www.nyas.org/MemberCenter/Join.aspx for more information about becoming a member

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An accurate, inexpensive, and noninvasive method for the early diagnosis of cancer has been something of a holy grail among cancer researchers, but until recently a method meeting all three criteria has been elusive. Nucleic acids were first discovered in circulation in 1948, but it was not until the 1960s and 70s that patients with autoimmune disease and cancer were discovered to have higher levels of circulating DNA than were detected in in healthy persons. The focus in this volume is on three major applications of the circulating nucleic acids detection method: cancer, fetal medicine, and diseases such as diabetes, stroke, and myocardial infarction. In addition, there are reports on the biology and origins of circulating DNA and RNA and on improved methods for the detection of nucleic acids in plasma and serum. The circulating DNA found in cancer patients has many characteristics in common with their tumors, which made it an attractive candidate for use in the diagnosis and management of patients with malignancies. This method can also be applied to the assessment of the sublinical tumor burden in cancer patients, thus reducing the risk of unnecessary chemotherapy. Detection of nucleic acids circulating in maternal serum means that fetal diagnosis may be possible without resorting to the more dangerous and invasive methods now used (e.g., amniotic fluid and chorionic villus sampling). Detection of problems in the pregnancy such as preeclampsia and intrauterine growth retardation may also become possible through maternal blood samples. In diabetic patients, circulating nucleic acids can be used for the early detection of developments such as retinopathy. The benefits of using circulating nucleic acids in the diagnosis and management of cancer and chronic disease will be realized through earlier detection by means of this less expensive and less invasive testing technique and through its potential for closer monitoring of the disease. NOTE: Annals volumes are available for sale as individual books or as a journal. For information on institutional journal subscriptions, please visit www.blackwellpublishing.com/nyas. ACADEMY MEMBERS: Please contact the New York Academy of Sciences directly to place your order (www.nyas.org). Members of the New York Academy of Science receive full-text access to the Annals online and discounts on print volumes. Please visit http://www.nyas.org/MemberCenter/Join.aspx for more information about becoming a member

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