Articles tagged with Differential 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.
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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.
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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.
Researchers from OIST and universities provided a new proof for the BBL inequality using heat and diffusion equations, taking an unconventional approach. The study offers fresh insights on the concept, which has vast applications across many fields, including computer science, medical imaging, and resource distribution.
Researchers designed urinals using physics and differential equations to minimize splashback, improving hygiene and accessibility. The Nautilus design fits various urination heights, making it accessible for children and people with wheelchairs.
Researchers developed an algorithm that uses stochastic differential equations to identify key data points in noisy data, improving early warning signal accuracy. The approach can be applied to various domains, including ecology and mental health, and has been validated through simulations.
Politecnico researchers developed a new type of neural network called Latent Dynamics Network (LDNet) that can accurately predict the evolution of complex systems in low-dimensional spaces. This approach offers significant innovations over traditional methods, enabling up to 5 times more accurate results with a reduction of over 90% in...
Researchers are combining biology, physics, computer science, and engineering to design electric circuits that mimic the brain's adaptive behavior. The goal is to create a more efficient AI application that can learn from history and adapt without significant energy consumption.
Researchers developed a new mathematical model to study circadian rhythm resilience and develop ways to improve it in individuals with weak internal clocks. Sustained disruptions can lead to disorders like diabetes and memory loss.
Researchers at Ohio State University created a mathematical model that assesses the efficacy of immunomodulatory drugs in treating myocardial infarctions. The study found that certain combinations of these drug inhibitors were more efficient at reducing inflammation, offering new possibilities for improving patient outcomes.
Experts in the field have long believed that uniform convexity of domains was essential for the optimal transport map to be smooth. The new study removes this condition, reducing the regularity assumption and providing a significant breakthrough in the field.
Researchers successfully connected two crucial equations, bridging relativity and quantum mechanics. Prof. Chen's work introduces bold ideas to solve previously unsolved equations.
Scientists have successfully predicted the dynamics of binding and unbinding processes on a time scale of seconds to half a minute in pharmacologically relevant test systems. The new dissipation-corrected targeted MD approach reduces computational power by a factor of ten.
Researchers have identified two scenarios in which minority languages can survive: linguistic diversity and mixed speaker populations. By applying mathematical modeling, the authors propose a new framework for understanding language coexistence, shedding light on the complexities of minority language preservation.
A research team developed a method for constructing an aggregated model of a power network that can efficiently analyze and control generator groups. The symmetry of the network in graph theory is the fundamental principle for realizing the synchronization of generator groups. This achievement aims to develop analysis and control metho...
Researchers from Russia and Italy have created a more accurate method to solve Navier-Stokes equations for incompressible plane motion. The new scheme allows for efficient numerical solutions and has been verified through computing experiments, outperforming existing methods in terms of precision and stability.
Numerical simulations by Everton Santos Medeiros provide a better understanding of the characteristics of tipping points in natural and social systems. The study highlights the persistence of system dynamics after irreversibility, masking the transition itself.
Simon's seminal paper on singularities has had a profound impact on analysis and geometry, with hundreds of papers built upon its insights. His work unifies and generalizes earlier research, providing powerful tools for differential equations and beyond.
Researchers developed a method to ensure fractional order stochastic differential inclusions can be controlled. This breakthrough applies to complex systems like financial markets and quantum systems. The team demonstrated controllability for both convex and nonconvex cases, enhancing device design and functionality.
Researchers at MIT developed a new compiler that translates human-written instructions into low-level specifications for analog computers. The compiler enables efficient simulation of biological systems using differential equations, which describe cell dynamics and chemical reactions.
Francis Clarke of Université Claude Bernard is the recipient of the 2015 W.T. and Idalia Reid Prize, awarded by the Society for Industrial and Applied Mathematics (SIAM). He received a cash prize of $10,000, an engraved medal, and delivered a prize lecture on definitions and hypotheses in control theory.
Dr. Tyrone Duncan will receive the W. T. and Idalia Reid Prize for his fundamental contributions to nonlinear filtering, stochastic control, and probability geometry. The prize recognizes his work in differential geometry, probability, stochastic control, and statistics.
The Clay Mathematics Institute awards Dr. Perelman the Millennium Prize for resolving the Poincaré conjecture, a century-long quest in mathematics. Perelman's breakthrough proof uses the Ricci flow method and introduces new ideas and techniques.