Articles tagged with Integral Equations
Comprehensive exploration of living organisms, biological systems, and life processes across all scales from molecules to ecosystems. Encompasses cutting-edge research in biology, genetics, molecular biology, ecology, biochemistry, microbiology, botany, zoology, evolutionary biology, genomics, and biotechnology. Investigates cellular mechanisms, organism development, genetic inheritance, biodiversity conservation, metabolic processes, protein synthesis, DNA sequencing, CRISPR gene editing, stem cell research, and the fundamental principles governing all forms of life on Earth.
Comprehensive medical research, clinical studies, and healthcare sciences focused on disease prevention, diagnosis, and treatment. Encompasses clinical medicine, public health, pharmacology, epidemiology, medical specialties, disease mechanisms, therapeutic interventions, healthcare innovation, precision medicine, telemedicine, medical devices, drug development, clinical trials, patient care, mental health, nutrition science, health policy, and the application of medical science to improve human health, wellbeing, and quality of life across diverse populations.
Comprehensive investigation of human society, behavior, relationships, and social structures through systematic research and analysis. Encompasses psychology, sociology, anthropology, economics, political science, linguistics, education, demography, communications, and social research methodologies. Examines human cognition, social interactions, cultural phenomena, economic systems, political institutions, language and communication, educational processes, population dynamics, and the complex social, cultural, economic, and political forces shaping human societies, communities, and civilizations throughout history and across the contemporary world.
Fundamental study of the non-living natural world, matter, energy, and physical phenomena governing the universe. Encompasses physics, chemistry, earth sciences, atmospheric sciences, oceanography, materials science, and the investigation of physical laws, chemical reactions, geological processes, climate systems, and planetary dynamics. Explores everything from subatomic particles and quantum mechanics to planetary systems and cosmic phenomena, including energy transformations, molecular interactions, elemental properties, weather patterns, tectonic activity, and the fundamental forces and principles underlying the physical nature of reality.
Practical application of scientific knowledge and engineering principles to solve real-world problems and develop innovative technologies. Encompasses all engineering disciplines, technology development, computer science, artificial intelligence, environmental sciences, agriculture, materials applications, energy systems, and industrial innovation. Bridges theoretical research with tangible solutions for infrastructure, manufacturing, computing, communications, transportation, construction, sustainable development, and emerging technologies that advance human capabilities, improve quality of life, and address societal challenges through scientific innovation and technological progress.
Study of the practice, culture, infrastructure, and social dimensions of science itself. Addresses how science is conducted, organized, communicated, and integrated into society. Encompasses research funding mechanisms, scientific publishing systems, peer review processes, academic ethics, science policy, research institutions, scientific collaboration networks, science education, career development, research programs, scientific methods, science communication, and the sociology of scientific discovery. Examines the human, institutional, and cultural aspects of scientific enterprise, knowledge production, and the translation of research into societal benefit.
Comprehensive study of the universe beyond Earth, encompassing celestial objects, cosmic phenomena, and space exploration. Includes astronomy, astrophysics, planetary science, cosmology, space physics, astrobiology, and space technology. Investigates stars, galaxies, planets, moons, asteroids, comets, black holes, nebulae, exoplanets, dark matter, dark energy, cosmic microwave background, stellar evolution, planetary formation, space weather, solar system dynamics, the search for extraterrestrial life, and humanity's efforts to explore, understand, and unlock the mysteries of the cosmos through observation, theory, and space missions.
Comprehensive examination of tools, techniques, methodologies, and approaches used across scientific disciplines to conduct research, collect data, and analyze results. Encompasses experimental procedures, analytical methods, measurement techniques, instrumentation, imaging technologies, spectroscopic methods, laboratory protocols, observational studies, statistical analysis, computational methods, data visualization, quality control, and methodological innovations. Addresses the practical techniques and theoretical frameworks enabling scientists to investigate phenomena, test hypotheses, gather evidence, ensure reproducibility, and generate reliable knowledge through systematic, rigorous investigation across all areas of scientific inquiry.
Study of abstract structures, patterns, quantities, relationships, and logical reasoning through pure and applied mathematical disciplines. Encompasses algebra, calculus, geometry, topology, number theory, analysis, discrete mathematics, mathematical logic, set theory, probability, statistics, and computational mathematics. Investigates mathematical structures, theorems, proofs, algorithms, functions, equations, and the rigorous logical frameworks underlying quantitative reasoning. Provides the foundational language and tools for all scientific fields, enabling precise description of natural phenomena, modeling of complex systems, and the development of technologies across physics, engineering, computer science, economics, and all quantitative sciences.
Mathematicians from RUDN University have proved a unique continuation theorem for a one dimensional solution to a fractional order diffusion problem, which can help calculate water movement in porous rock. The results of their work are needed for more accurate analysis and numerical simulation of solutions.
Researchers at the University of Pennsylvania have demonstrated a device that uses metamaterials to solve integral equations, a common problem in science and engineering. The device operates as an analog computer with light, solving problems orders of magnitude faster than digital computers.
Researchers used molecular dynamics simulations and integral equation theoretical calculations to study the phase separation of active and passive particles. The introduction of activity was found to enhance phase separation in some cases, contrary to previous assumptions.
Gennadi Henkin has received the 2011 Stefan Bergman Prize for his fundamental contributions to theory of functions on complex manifolds, integral representations in several complex variables, and multidimensional Cauchy-Riemann equations. He is recognized as a leading scientific researcher with over 130 publications in various fields.
Daan Huybrechs, a postdoctoral fellow at Belgium's Katholieke Universiteit Leuven, will receive the Richard C. DiPrima Prize for his dissertation on multiscale and hybrid methods for solving oscillatory integral equations. The prize recognizes his outstanding research in applied mathematics and computational science.