Articles tagged with Number Theory
Wataru Takeda has completely solved the polynomial analogue of the long-standing Brocard–Ramanujan problem, a breakthrough 150 years after its original proposal. The study resolves the problem for polynomials over finite fields and was published in the journal Finite Fields and Their Applications.
Ken Ono, a renowned number theorist, has been named a Cozzarelli Prize finalist for his research on prime numbers and partitions. His paper, 'Partitions Detect Primes,' reveals a new way of understanding prime numbers using the mathematical concept of partitions.
Researchers have developed big algebras, a new mathematical tool that connects abstract algebra and geometry, enabling unprecedented insights into symmetry groups. This breakthrough has the potential to strengthen the connection between quantum physics and number theory.
Researchers discovered a deep connection between the sums-of-digits function from number theory and phenotype mutational robustness in genetics. The maximum robustness is proportional to the logarithm of the fraction of all possible sequences that map to a phenotype, with a correction given by the sums of digits function s_k(n).
Brandon Levin, an assistant professor of mathematics at Rice University, has won a prestigious National Science Foundation CAREER Award to pursue his research on major unsolved problems in number theory. He aims to build theoretical bridges between arithmetic world and representation theory.
A recent study by Tokyo University of Science researchers provides theoretical foundations for effective parameter tuning in the Bernoulli shift map. They used modular arithmetic to determine optimal parameter values for preserving chaos, with implications for other chaotic maps like the tent and logistic maps.
A Tel Aviv University study challenges the widely-held assumption that COVID-19 originated from bats, instead highlighting their highly effective immune system. The researchers found that many reported findings on bat-borne viruses are based on antibody presence or PCR tests rather than actual virus isolation.
A new study published in PLOS One suggests that the number of people believing in conspiracy theories has not increased over time. The research, conducted by University of Miami academics and supported by a U-LINK grant, analyzed data from polls dating back to the 1960s and found no significant increase in belief in these theories. Des...
Researchers reexamined hundreds of experiments on neural activity and consciousness, finding that experiment parameters determine results. The study used artificial intelligence to predict which theory would be supported by each experiment with 80% success.
A RUDN University physicist simplified the Einstein-Lovelock theory for black holes by presenting its geometry in a compact form with a limited number of terms, sufficient to describe observed values. This simplification could aid in studying black holes in theories with quantum corrections.
Gordon examines secure computation to leverage user data without compromising privacy. He investigates three key tasks: handling large volumes of data with few parties, interacting with a large number of parties, and storing dynamic data in a distributed plane.
Researchers at FAU have decoded the structure and process behind formation of highly ordered clusters. They discovered over 25 different magic number colloidal clusters with unique shapes and symmetries.
The Biophysical Society has announced the winners of its Outstanding Poster Award, recognizing outstanding scientific achievements in biophysics. The student winners were selected for their research on HERG kinetics, while the postdoctoral winner was recognized for her work on cardiac resynchronization therapy.
A team of physicists has calculated the size of scale-free and small-world networks, which have six degrees of separation. This method can be applied to modeling complex networks and predicting their capacity to tolerate faults.
The Mathematical Association of America (MAA) has awarded the Euler Book Prize to Matt Parker for his book 'Things to Make and Do in the Fourth Dimension' and the Beckenbach Book Prize to Roland van der Veen and Jan van de Craats for their book 'The Riemann Hypothesis: A Million Dollar Problem',
A new study by Loris Ferrari examines the practical consequences of two entropy theories in small systems. The research finds that certain quantities can be measured experimentally to assess which theory is more accurate, resolving a long-standing debate between Ludwig Boltzmann and Willard Gibbs.
A new computational framework allows working with infinities and infinitesimals numerically, giving unexpected answers to two long-standing Hilbert problems. The Infinity Computer supercomputer enables numerical computations with infinite and infinitesimal numbers, previously only symbolically represented.
Researchers propose a new type of traveling wave pattern that can adapt to varying system sizes, shedding light on bacterial cell division processes. The 'stretchable map' theory offers insights into protein self-organization and surface mapping on growing cells.
DeMarco's work on dynamical systems has led to the emergence of arithmetic dynamics, a field that connects number theory with mathematical structures. Her research has also shed light on connections between dynamical systems and elliptic curves in arithmetic geometry.
Henri Darmon receives 2017 AMS Cole Prize for his work on the Birch and Swinnerton-Dyer conjecture, a major open problem in mathematics. His research casts new light on the conjecture and possible extensions of complex multiplication theory.
Arthur receives prize 'for his fundamental contributions to number theory and harmonic analysis.' His work on the Arthur-Selberg trace formula has profound connections between properties of numbers and geometric shapes.
Researchers found that the moon's uppermost surface materials are completely turned over in approximately 80,000 years, much faster than previously estimated. This discovery has significant implications for future human exploration and development of the Moon.
Researchers analyzed 20 years of data on S\¼P 1,500 firms and found that a firm's efforts to promote gender diversity in management may need to redouble once initial progress is made. This could result in women remaining an isolated minority in top management.
Undergraduates at Wake Forest University will conduct original mathematical research under the guidance of Assistant Professor Jeremy Rouse and Visiting Assistant Professor Katherine Thompson. The program, WADE INTO Research, aims to develop students' skills in mathematics and prepare them for future careers.
A team of mathematicians has proved the Umbral Moonshine Conjecture, offering a finite calculation for this complex pattern. The conjecture has potential applications in various areas of math and physics.
Undergraduate Levent Alpoge is awarded the 2015 Morgan Prize for his contributions to number theory, probability, and combinatorics. He has authored seven research papers before even beginning graduate studies.
Researchers Jan Boeyens and Francis Thackeray found a connection between the Golden Ratio, space-time, and a biological species constant. The study suggests that concepts associated with relativity and quantum mechanics can be integrated through the number 1.618.
Mathematician Alex Eskin has been selected as a 2014 Simons Investigator to tackle long-term studies of fundamental questions in mathematics. He aims to understand the behavior of billiard balls in various polygons, shedding light on ergodicity and randomness.
Researchers find that a wide range of lock-free algorithms offer performance guarantees comparable to wait-free algorithms, even with complex scheduler variations. This discovery simplifies multicore chip programming, as programmers often program under the assumption of benevolent schedulers.
A recent study by Renato Gianella found that lottery numbers can be analyzed using a colored template based on Pascal's rule, allowing players to identify combinations with the highest probabilities of winning. The method was tested across multiple countries and demonstrated its effectiveness in predicting lottery results.
Physicists observed quantum chaos in ultracold atoms using a controlled environment to study complex systems. The team confirmed the universality of random matrix theory through statistical analysis and computer simulations, revealing new insights into ultracold gases and chemistry.
Researchers find fractal distribution of physical characteristics at edge of chaos, deviating from previously reported bell-curve shape. This discovery could improve understanding of chaotic natural phenomena.
Theorists Volker Koch and Dirk Andrae have devised formulas to calculate the polarizability of atomic ions as a function of their total charge number. This breakthrough enables accurate calculations for series of multi-electron ions, with implications for applications such as semiconductor manufacturing and planetary atmosphere modeling.
The new institute will offer sabbatical placements to top academics, advancing theoretical basic research and enhancing ETH's academic base. The fellows will work alongside experienced researchers, providing additional stimulation and enrichment.
A mathematician has proven that a formula for mock modular forms, developed by Indian mathematician Srinivasa Ramanujan, can be computed just as he predicted. The discovery may unlock secrets about black holes and has implications for number theory.
Vojtech Rödl and Mathias Schacht have been awarded the 2012 George Pólya Prize for their work on the regularity method for hypergraphs, producing key results such as the generalized hypergraph removal lemma. The prize recognizes their notable contributions to combinatorial theory.
A study found that unschooled adults from Papua New Guinea mapped numbers onto space but only used endpoints when placing numbers on a line. In contrast, educated individuals used the entire number line, demonstrating that this understanding can be learned through education and cultural practices.
A study published in PLoS ONE suggests that the number-line concept is not an innate human intuition but a culturally acquired tool. The research, conducted with indigenous Yupno adults in Papua New Guinea, found that precise number concepts can exist independently of linear spatial representations.
The American Mathematical Society will award numerous prestigious prizes to recognize outstanding achievements in mathematics. These awards include the AMS Steele Prize, which honors lifetime achievement and mathematical exposition.
A Princeton scientist has recast two well-known math problems as physics questions, providing new tools for solving challenges in data compression, gravitational waves, and more. The reformulation offers insights into the role of randomness and disorder.
The George Pólya Prize recognizes Emmanuel Candès and Terence Tao's work on compressive sensing and matrix completion. Their algorithms enable efficient reconstruction of sparse, high-dimensional data with few measurements.
The 2010 International Mathematical Union prizes were awarded to four mathematicians: Elon Lindenstrauss, Ngô Bảo Châu, Stanislav Smirnov, and Cédric Villani. Lindenstrauss received the Fields Medal for his work on measure rigidity in ergodic theory and its applications to number theory.
Ngô Bao Châu received the Fields Medal for his proof of the fundamental lemma in automorphic forms through new algebro-geometric methods. His work has relevance to high-energy physics, computer science, and cryptography, building on decades of mathematicians' contributions.
Research found that certain types of arousal can lead to unhealthy food choices and less-healthy decisions. Arousal interfered with the beneficial effect of positive mood on resistance to temptation, especially in situations requiring mental energy.
A new theory explains why some plants produce large seeds, while others produce small seeds in abundance. Helene Muller-Landau's tolerance-fecundity model reveals that plant species can coexist under different environmental stresses.
Research at Gothenburg University and Oxford University found that middle-aged men prefer younger women in lonely hearts ads. However, this contradicts the idea that men place more emphasis on attractive appearance than resources and social status. In contrast, younger women tend to prefer older men.
Researchers Daniel J. Madden and Lee W. Jacobi have found an infinite number of solutions to Euler's Equation of degree four, a centuries-old mathematical puzzle. They used elliptic curves to generate new solutions, which are more efficient than previous methods.
The intersection of mathematics and cryptography has significant implications for security and research, with mathematicians like Neal Koblitz contributing to the field. Koblitz's work highlights the challenges of 'provable security' in cryptography, as well as the influence of the National Security Agency on research.
Researchers at Rutgers University have developed a new theory that explains the physical and chemical properties of plutonium, which can help create safer and more versatile nuclear materials. The study finds that valence electrons in solid plutonium metal fluctuate among different orbitals on a short time scale.
Researchers at UW-Madison crack long-standing problem of mock theta functions using Harmonic Maass Forms. The discovery is invaluable in resolving open questions in number theory and enables applications to physics, chemistry, and mathematics.
The Society for Industrial and Applied Mathematics awarded the George Polya Prize to Gregory F. Lawler, Oded Schramm and Wendelin Werner for their groundbreaking work on stochastic Loewner evolution (SLE). Their research established the existence and conformal invariance of critical scaling limits of several 2D lattice models.
As early as 20 years from now, Germany's hours worked per capita may decrease by 8 percent due to the aging population. This shift requires a more flexible and evenly distributed workforce to maintain productivity.
Research at Harvard University reveals that preschool children have a basic understanding of number concepts and can perform addition before formal schooling. However, their ability to comprehend symbolic arithmetic is limited, suggesting that teaching methods may need to be revised.
Burger's work on number theory and mathematics education has earned him numerous awards, including the MAA Deborah and Franklin Tepper Haimo Award. His research focuses on Diophantine approximation and geometry of numbers, and he is also dedicated to making math accessible to everyone.
Researchers identified vulnerabilities in Wi-Fi networks that can drain battery life and disrupt communication infrastructure. A proposed solution involves reputation-based control systems to strengthen routing protocols against stealth attacks.