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85,800 | During her Ph.D. she worked on Lewis acids. Morse joined the faculty of Utah State University in 1968 in the department of chemistry and biochemistry, and subsequently became the department head, the dean, and was named provost in 1989. | Karen Morse (chemist) | 0.782808 |
85,801 | The crystal structure of ice IV was elucidated by Engelhardt and Kamb in 1981 by low-temperature single-crystal X-ray diffraction. Its structure is described by a rhombohedral unit cell with a space group of R-3c. The hydrogen geometry had been suggested to be completely disordered as IR and Raman spectra consist only ... | Ice IV | 0.782806 |
85,802 | Harris's research focuses on arithmetic geometry, automorphic forms, L-functions, and motives. He has developed the theory of coherent cohomology of Shimura varieties and applied it to number theoretic problems on special values of L-functions, Galois representations, and the theta correspondence. His later work focuse... | Michael Harris (mathematician) | 0.782805 |
85,803 | Since 2021, Harris has written the newsletter Silicon Reckoner exploring questions and issues related to the mechanization of mathematics and artificial intelligence. | Michael Harris (mathematician) | 0.782805 |
85,804 | Michael Howard Harris (born 1954) is an American mathematician known for his work in number theory. He is a professor of mathematics at Columbia University and professor emeritus of mathematics at Université Paris Cité. | Michael Harris (mathematician) | 0.782805 |
85,805 | The Fritz Zwicky Prize for Astrophysics and Cosmology is awarded biennially to a living person who, in the estimation of the judges, "has obtained fundamental and outstanding results related to astrophysics and/or cosmology". These results may constitute a body of work over a period of time or may be a single specific ... | Fritz Zwicky Prize for Astrophysics and Cosmology | 0.782802 |
85,806 | Later operating systems, including Eldon 2 at the University of Leeds, and COTAN, developed by UKAEA Culham Laboratories with the collaboration of Glasgow University, were fully interactive multi-access systems, with PDP-8 front ends to handle the terminals. The Kidsgrove and Whetstone Algol 60 compilers were among the... | English Electric KDF9 | 0.782802 |
85,807 | SageManifolds (following styling of SageMath) is an extension fully integrated into SageMath, to be used as a package for differential geometry and tensor calculus. The official page for the project is sagemanifolds.obspm.fr. It can be used on CoCalc. SageManifolds deals with differentiable manifolds of arbitrary dimen... | Sage Manifolds | 0.7828 |
85,808 | The R symbol was introduced by 19th-century French chemist Charles Frédéric Gerhardt, who advocated its adoption on the grounds that it would be widely recognizable and intelligible given its correspondence in multiple European languages to the initial letter of "root" or "residue": French racine ("root") and résidu ("... | Side chain | 0.7828 |
85,809 | In organic chemistry and biochemistry, a side chain is a chemical group that is attached to a core part of the molecule called the "main chain" or backbone. The side chain is a hydrocarbon branching element of a molecule that is attached to a larger hydrocarbon backbone. It is one factor in determining a molecule's pro... | Side chain | 0.7828 |
85,810 | Vortices in quantum fluids support Kelvin waves, which are helical perturbations of a vortex line away from its straight configuration that rotate at an angular velocity ω {\displaystyle \omega } , with ω ≈ κ k 2 4 π ln ( 1 k a 0 ) {\displaystyle \omega \approx {\frac {\kappa k^{2}}{4\pi }}\ln {\left({\frac {1}{ka_{0... | Quantum turbulence | 0.7828 |
85,811 | This leads to the idea of the Rankine vortex as shown in fig 2, which combines solid body rotation for small r {\displaystyle r} and vortex motion for large values of r {\displaystyle r} , and is a more realistic model of ordinary classical vortices. Many similarities can be drawn with vortices in classical fluids, for... | Quantum turbulence | 0.7828 |
85,812 | The circulation Γ {\displaystyle \Gamma } is defined to be the line integral along a simple closed path C {\displaystyle C} within the fluid Γ = ∮ C v ⋅ d r {\displaystyle \Gamma =\oint _{C}\mathbf {v} \cdot \mathbf {dr} } For a simply-connected surface S {\displaystyle S} , Stokes theorem holds, and the circulation va... | Quantum turbulence | 0.7828 |
85,813 | For temperatures low enough for quantum mechanical effects to govern the fluid, quantum turbulence is a seemingly chaotic tangle of vortex lines with a highly knotted topology, which move each other and reconnect when they collide. In a pure superfluid, there is no normal component to carry the entropy of the system an... | Quantum turbulence | 0.7828 |
85,814 | Quantum turbulence is the name given to the turbulent flow – the chaotic motion of a fluid at high flow rates – of quantum fluids, such as superfluids. The idea that a form of turbulence might be possible in a superfluid via the quantized vortex lines was first suggested by Richard Feynman. The dynamics of quantum flui... | Quantum turbulence | 0.7828 |
85,815 | The Advanced Light Source (ALS) in Berkeley, California, is home to XM-1, a full-field soft X-ray microscope operated by the Center for X-ray Optics and dedicated to various applications in modern nanoscience, such as nanomagnetic materials, environmental and materials sciences and biology. XM-1 uses an X-ray lens to f... | X-ray microscopy | 0.782793 |
85,816 | For example, many human actions are done out of self-preservation instincts, which is realistic but not ethical; feeding such data to the computer cannot guarantee that the computer captures the ideal behavior. Furthermore, the data fed to an artificial intelligence must be carefully selected to avoid producing undesir... | Advanced driver assistance systems | 0.782786 |
85,817 | For instance, the artificial intelligence approach allows computers to learn human ethics by feeding them data regarding human actions. Such a method is useful when the rules cannot be articulated because the computer can learn and identify the ethical elements on its own without precisely programming whether an action... | Advanced driver assistance systems | 0.782786 |
85,818 | Auto liability and physical damage – This insurance covers third-party injuries and technology damage. Cyber liability – This insurance will protect companies from any lawsuits from third parties and penalties from regulators regarding cybersecurity. Directors and officers – This insurance protects a company's balance ... | Advanced driver assistance systems | 0.782786 |
85,819 | The Friedmann Prize is a Soviet and Russian physics prize, awarded for outstanding work in cosmology and gravity. It is named after the Russian cosmologist Alexander Alexandrovich Friedmann. Between 1972 and 1990 the prize was awarded by the USSR Academy of Sciences for the best scientific work in the field of meteorol... | Friedmann Prize | 0.782785 |
85,820 | He constructed a water clock in Toledo, discovered that the Sun's apogee moves slowly relative to the fixed stars, and obtained a good estimate of its motion for its rate of change. Nasir al-Din al-Tusi (1201–1274) wrote an important revision to Ptolemy's 2nd-century celestial model. When Tusi became Helagu's astrologe... | Islamic technology | 0.782783 |
85,821 | Astronomy became a major discipline within Islamic science. Astronomers devoted effort both towards understanding the nature of the cosmos and to practical purposes. One application involved determining the Qibla, the direction to face during prayer. Another was astrology, predicting events affecting human life and sel... | Islamic technology | 0.782783 |
85,822 | Advances in botany and chemistry in the Islamic world encouraged developments in pharmacology. Muhammad ibn Zakarīya Rāzi (Rhazes) (865–915) promoted the medical uses of chemical compounds. Abu al-Qasim al-Zahrawi (Abulcasis) (936–1013) pioneered the preparation of medicines by sublimation and distillation. His Liber s... | Islamic technology | 0.782783 |
85,823 | Al-Biruni, Avicenna and others described the preparation of hundreds of drugs made from medicinal plants and chemical compounds. Islamic physicists such as Ibn Al-Haytham, Al-Bīrūnī and others studied optics and mechanics as well as astronomy, and criticised Aristotle's view of motion. During the Middle Ages, Islamic s... | Islamic technology | 0.782783 |
85,824 | For example, astronomy was useful for determining the Qibla, the direction in which to pray, botany had practical application in agriculture, as in the works of Ibn Bassal and Ibn al-'Awwam, and geography enabled Abu Zayd al-Balkhi to make accurate maps. Islamic mathematicians such as Al-Khwarizmi, Avicenna and Jamshīd... | Islamic technology | 0.782783 |
85,825 | Science in the medieval Islamic world was the science developed and practised during the Islamic Golden Age under the Umayyads of Córdoba, the Abbadids of Seville, the Samanids, the Ziyarids, the Buyids in Persia, the Abbasid Caliphate and beyond, spanning the period roughly between 786 and 1258. Islamic scientific ach... | Islamic technology | 0.782783 |
85,826 | Given an operator A, the resolvent may be defined as R ( z ; A ) = ( A − z I ) − 1 . {\displaystyle R(z;A)=(A-zI)^{-1}~.} Among other uses, the resolvent may be used to solve the inhomogeneous Fredholm integral equations; a commonly used approach is a series solution, the Liouville–Neumann series. The resolvent of A ca... | Resolvent formalism | 0.782782 |
85,827 | In mathematics, the resolvent formalism is a technique for applying concepts from complex analysis to the study of the spectrum of operators on Banach spaces and more general spaces. Formal justification for the manipulations can be found in the framework of holomorphic functional calculus. The resolvent captures the s... | Resolvent formalism | 0.782782 |
85,828 | The theorem is also useful on a more microscopic scale, in biology. Living systems, such as cells, can be analyzed thermodynamically. They are rather complex systems, where many energy transformations occur, and they often waste heat. Hence, the Gouy-Stodola theorem may be useful, in certain situations, to perform exer... | Gouy-Stodola theorem | 0.782782 |
85,829 | The theorem also holds for adiabatic processes. That is, for closed systems, which are not in thermal contact with any heat reservoirs. Similarly to the non-adiabatic case, the lost work is measured relative to some reference reservoir T 0 {\displaystyle T_{0}} . Even though the process itself is adiabatic, the corresp... | Gouy-Stodola theorem | 0.782782 |
85,830 | In the above equations, W ˙ l o s t {\displaystyle {\dot {W}}_{lost}} is defined in reference to the environment reservoir, at T 0 {\displaystyle T_{0}} . When comparing the actual process to an ideal, reversible process between the same endpoints (in order to evaluate W r e v {\displaystyle W_{rev}} , so as to find th... | Gouy-Stodola theorem | 0.782782 |
85,831 | Time derivatives are denoted by dots. The theorem, as stated above, holds only for the entire thermodynamic universe - the system along with its surroundings, together:where the index "tot" denotes the total quantities produced within or by the entire universe. Note that W ˙ l o s t {\displaystyle {\dot {W}}_{lost}} is... | Gouy-Stodola theorem | 0.782782 |
85,832 | The reversible work is the maximal useful work which can be obtained, W r e v = W m a x {\displaystyle W_{rev}=W_{max}} , and can only be fully utilized in an ideal reversible process. An irreversible process produces some work W a c t u a l {\displaystyle W_{actual}} , which is less than W r e v {\displaystyle W_{rev}... | Gouy-Stodola theorem | 0.782782 |
85,833 | Thus, the exergy formulation of the theorem is less limited, as it can be applied on different regions separately. Nevertheless, the work form is used more often. The proof of the theorem, in both forms, uses the first law of thermodynamics, writing out the terms W ˙ l o s t {\displaystyle {\dot {W}}_{lost}} , ψ ˙ d {\... | Gouy-Stodola theorem | 0.782782 |
85,834 | As above, time derivatives are denoted by dots. Unlike the lost work formulation, this version of the theorem holds for both the system (the control volume) and for its surroundings (the environment and the thermal reservoirs) separately:andwhere the index "sys" denotes quantities produced within or by the system itsel... | Gouy-Stodola theorem | 0.782782 |
85,835 | The exergy of the system is the maximal amount of useful work that the system can generate, during a process which brings it to equilibrium with its environment, or the amount of energy available. During an irreversible process, such as heat exchanges with reservoirs, exergy is destroyed. Generally, the theorem states ... | Gouy-Stodola theorem | 0.782782 |
85,836 | The theoretical specific entropy and enthalpy after this ideal, isentropic process are given by s 2 , r e v {\displaystyle s_{2,rev}} and h 2 , r e v {\displaystyle h_{2,rev}} , respectively. When the actual process is compared to this theoretical reversible process and W ˙ l o s t {\displaystyle {\dot {W}}_{lost}} is ... | Gouy-Stodola theorem | 0.782782 |
85,837 | Additionally, modifications may change the reversible process to which the real process is compared in calculating W ˙ l o s t {\displaystyle {\dot {W}}_{lost}} . The modified theorem then readswhere T e f f {\displaystyle T_{eff}} is the effective temperature. For a flow process, let s 1 {\displaystyle s_{1}} denote t... | Gouy-Stodola theorem | 0.782782 |
85,838 | In many cases, it is preferable to use a slightly modified version of the Gouy-Stodola theorem in work form, where T 0 {\displaystyle T_{0}} is replaced by some effective temperature. When this is done, it often enlarges the scope of the theorem, and adapts it to be applicable to more systems or situations. For example... | Gouy-Stodola theorem | 0.782782 |
85,839 | In general, the Gouy-Stodola theorem is used to quantify irreversibilities in a system and to perform exergy analysis. That is, it allows one to take a thermodynamic system and better understand how inefficient it is (energy-wise), how much work is lost, how much room there is for improvement and where. The second law ... | Gouy-Stodola theorem | 0.782782 |
85,840 | A variational principle in physics, such as the principle of least action or Fermat's principle in optics, allows one to describe the system in a global manner and to solve it using the calculus of variations. In thermodynamics, such a principle would allow a Lagrangian formulation. The Gouy-Stodola theorem can be used... | Gouy-Stodola theorem | 0.782782 |
85,841 | A flow process is a type of thermodynamic process, where matter flows in and out of an open system called the control volume. Such a process may be steady, meaning that the matter and energy flowing into and out of the system are constant through time. It can also be unsteady, or transient, meaning that the flows may c... | Gouy-Stodola theorem | 0.782782 |
85,842 | It is in contact with multiple reservoirs, of which one, that at temperature T 0 {\displaystyle T_{0}} , is the environment reservoir. During the process, the system produces work and generates entropy. Under these conditions, the theorem has two general forms. | Gouy-Stodola theorem | 0.782782 |
85,843 | The Gouy-Stodola theorem is often applied upon an open thermodynamic system, which can exchange heat with some thermal reservoirs. It holds both for systems which cannot exchange mass, and systems which mass can enter and leave. Observe such a system, as sketched in the image shown, as it is going through some process. | Gouy-Stodola theorem | 0.782782 |
85,844 | It can be used to find at which temperatures the performance is optimal, or what size system should be constructed. Overall, that is, the Gouy-Stodola theorem is a tool to find and quantify inefficiencies in a system, and can point to how to minimize them - this is the goal of exergy analysis. When the theorem is used ... | Gouy-Stodola theorem | 0.782782 |
85,845 | The Gouy-Stodola theorem is often applied to refrigeration cycles. These are thermodynamic cycles or mechanical systems where external work can be used to move heat from low temperature sources to high temperature sinks, or vice versa. Specifically, the theorem is useful in analyzing vapor compression and vapor absorpt... | Gouy-Stodola theorem | 0.782782 |
85,846 | Macroscopically, the theorem may be useful environmentally, in ecophysics. An ecosystem is a complex system, where many factors and components interact, some biotic and some abiotic. The Gouy-Stodola theorem can find how much entropy is generated by each part of the system, or how much work is lost. Where there is huma... | Gouy-Stodola theorem | 0.782782 |
85,847 | In thermodynamics and thermal physics, the Gouy-Stodola theorem is an important theorem for the quantification of irreversibilities in an open system, and aids in the exergy analysis of thermodynamic processes. It asserts that the rate at which work is lost during a process, or at which exergy is destroyed, is proporti... | Gouy-Stodola theorem | 0.782782 |
85,848 | The core of the research is based silicon and III-V nano-electronics, nanomagnetism (spintronics), micro- and nano-photonics (III-V and silicon photonics), and nanosystems (manufacturing and characterization.) It has four main divisions: Photonics department, Materials Department, Nanoelectronics Department, Microsyste... | Centre for Nanosciences and Nanotechnologies | 0.782779 |
85,849 | The Centre for Nanosciences and Nanotechnologies (Centre de Nanosciences et de Nanotechnologies de l'université Paris-Saclay) or C2N, is a nanotechnology laboratory created as a collaboration between the University of Paris-Saclay and the French National Centre for Scientific Research (CNRS. )CNRS and the university an... | Centre for Nanosciences and Nanotechnologies | 0.782779 |
85,850 | In 1973, he proved this conjecture false, though the concept that image textures could be modeled based on low-order statistics remained. In 1981, he originated the Texton Theory, which states that textons, composed of local image features, are "the putative units of pre-attentive human texture perception".In 1989, he ... | Julesz conjecture | 0.782777 |
85,851 | Later, Christopher Tyler, a former student of Julesz, used the principles of random-dot stereograms to invent autostereograms, which create the same effect using a single image instead of two. Julesz made important contributions to the theory of human visual perception of texture. In 1962 he originated the Julesz Conje... | Julesz conjecture | 0.782777 |
85,852 | Béla Julesz (also Bela Julesz in English; February 19, 1928 – December 31, 2003) was a Hungarian-born American visual neuroscientist and experimental psychologist in the fields of visual and auditory perception. Julesz was the originator of random dot stereograms which led to the creation of autostereograms. He also wa... | Julesz conjecture | 0.782777 |
85,853 | 1956 - Ph.D., Hungarian Academy of Sciences 1950 - Electrical Engineering, Technical University, Budapest | Julesz conjecture | 0.782777 |
85,854 | Julesz was a State of New Jersey Professor who received a variety of awards throughout his illustrious career, including a 1983 MacArthur Fellowship ("genius award") for his work in Experimental Psychology and Artificial Intelligence. He was elected to the American Academy of Arts and Sciences in 1980, the National Aca... | Julesz conjecture | 0.782777 |
85,855 | Social robots A social robot can either connect to the cloud or fog robot server depending upon the availability of information. For instance, it can make a robot working at an airport to communicate with other robots for effective communication with the help of fog robotics. | Fog robotics | 0.782776 |
85,856 | For fog and cloud robotics, it is the first robot operating system with algorithm-level collaborative computing. ElasticROS develops elastic collaborative computing to achieve adaptability to dynamic conditions. The collaborative computing algorithm is the core and challenge of ElasticROS. | Fog robotics | 0.782776 |
85,857 | Fog robotics mainly consists of a fog robot server and the cloud. It acts as a companion to cloud by shoving the data near to the user with the help of a local server. Moreover, these servers are adaptable, consists of processing power for computation, network capability, and secured by sharing the outcomes to other ro... | Fog robotics | 0.782776 |
85,858 | Fog robotics can be defined as an architecture which consists of storage, networking functions, control with fog computing closer to robots. | Fog robotics | 0.782776 |
85,859 | As part of this project, a real-time application of fog-assisted robotics is explored. Also, remote monitoring of robots and fleet formation for coordinated movement is being investigated.Fog Computing for Robotics and Industrial AutomationThis project focusses on designing novel programming models for Fog applications... | Fog robotics | 0.782776 |
85,860 | Fog Robotics This project promotes the applicability of fog robotics with regards to human-robot interaction scenarios. It utilises fog robot servers, cloud, and the robots for evaluation of fog robotics architecture.Secure Fog Robotics Using the Global Data PlaneTo improve the security and performance of robotic/machi... | Fog robotics | 0.782776 |
85,861 | The first two (purple) in their narrowest sense are generally treated as hypernyms of the others (red and blue), although in less precise usage the red and blue have often been treated as synonyms of the purple. At least one reference holds "EHEC" to be mutually exclusive of "VTEC" and "STEC", but this does not match c... | Shiga-like toxin-producing Escherichia coli | 0.782776 |
85,862 | .NET Bio was originally built and released by Microsoft Research under the name Microsoft Biology Foundation (MBF) and was later repackaged and released by the Outercurve Foundation as a fully public and open source project under the Apache License 2.0. | .NET Bio | 0.782775 |
85,863 | .NET Bio is an open source bioinformatics and genomics library created to enable simple loading, saving and analysis of biological data. It was designed for .NET Standard 2.0 and was part of the Microsoft Biology Initiative in the eScience division. | .NET Bio | 0.782775 |
85,864 | Each of these transitions yields a fluorescent photon with a characteristic energy equal to the difference in energy of the initial and final orbital. The wavelength of this fluorescent radiation can be calculated from Planck's Law: λ = h c E {\displaystyle \lambda ={\frac {hc}{E}}} The fluorescent radiation can be ana... | X-ray fluorescence spectroscopy | 0.782774 |
85,865 | The Rowland circle geometry ensures that the slits are both in focus, but in order for the Bragg condition to be met at all points, the crystal must first be bent to a radius of 2R (where R is the radius of the Rowland circle), then ground to a radius of R. This arrangement allows higher intensities (typically 8-fold) ... | X-ray fluorescence spectroscopy | 0.782774 |
85,866 | Because there is only one monochromator, the tube-sample-crystal distances can be kept very short, resulting in minimal loss of detected intensity. The obvious disadvantage is relatively long analysis time, particularly when many elements are being analysed, not only because the elements are measured in sequence, but a... | X-ray fluorescence spectroscopy | 0.782774 |
85,867 | "Sequential" spectrometers have a single variable-geometry monochromator (but usually with an arrangement for selecting from a choice of crystals), a single detector assembly (but usually with more than one detector arranged in tandem), and a single electronic pack. The instrument is programmed to move through a sequen... | X-ray fluorescence spectroscopy | 0.782774 |
85,868 | In wavelength dispersive spectrometers (WDX or WDS), the photons are separated by diffraction on a single crystal before being detected. Although wavelength dispersive spectrometers are occasionally used to scan a wide range of wavelengths, producing a spectrum plot as in EDS, they are usually set up to make measuremen... | X-ray fluorescence spectroscopy | 0.782774 |
85,869 | X-ray fluorescence (XRF) is the emission of characteristic "secondary" (or fluorescent) X-rays from a material that has been excited by being bombarded with high-energy X-rays or gamma rays. The phenomenon is widely used for elemental analysis and chemical analysis, particularly in the investigation of metals, glass, c... | X-ray fluorescence spectroscopy | 0.782774 |
85,870 | A Söller collimator is a stack of parallel metal plates, spaced a few tenths of a millimeter apart. To improve angular resolution, one must lengthen the collimator, and/or reduce the plate spacing. This arrangement has the advantage of simplicity and relatively low cost, but the collimators reduce intensity and increas... | X-ray fluorescence spectroscopy | 0.782774 |
85,871 | In order to keep the geometry of the tube-sample-detector assembly constant, the sample is normally prepared as a flat disc, typically of diameter 20–50 mm. This is located at a standardized, small distance from the tube window. Because the X-ray intensity follows an inverse-square law, the tolerances for this placemen... | X-ray fluorescence spectroscopy | 0.782774 |
85,872 | In statistics, Welch's t-test, or unequal variances t-test, is a two-sample location test which is used to test the (null) hypothesis that two populations have equal means. It is named for its creator, Bernard Lewis Welch, is an adaptation of Student's t-test, and is more reliable when the two samples have unequal vari... | Welch's t test | 0.78277 |
85,873 | In mathematical finite group theory, the Brauer–Fowler theorem, proved by Brauer & Fowler (1955), states that if a group G has even order g > 2 then it has a proper subgroup of order greater than g1/3. The technique of the proof is to count involutions (elements of order 2) in G. Perhaps more important is another resul... | Brauer–Fowler theorem | 0.782769 |
85,874 | Suppose X1, ..., Xn are independent and identically distributed, and are normally distributed with unknown expected value μ and known variance 1. Let X ¯ n = X 1 + ⋯ + X n n {\displaystyle {\overline {X}}_{n}={\frac {X_{1}+\,\cdots \,+X_{n}}{n}}} be the sample mean. The following statistical measures of dispersion of t... | Ancillary statistic | 0.782769 |
85,875 | An ancillary statistic is a measure of a sample whose distribution (or whose pmf or pdf) does not depend on the parameters of the model. An ancillary statistic is a pivotal quantity that is also a statistic. Ancillary statistics can be used to construct prediction intervals. They are also used in connection with Basu's... | Ancillary statistic | 0.782769 |
85,876 | Natural processes can have a distinct recurrent behaviour, e.g. periodicities (as seasonal or Milankovich cycles), but also irregular cyclicities (as El Niño Southern Oscillation, heart beat intervals). Moreover, the recurrence of states, in the meaning that states are again arbitrarily close after some time of diverge... | Recurrence plots | 0.782768 |
85,877 | Another strengthening of Steinitz's theorem, by Barnette and Grünbaum, states that for any polyhedral graph, any face of the graph, and any convex polygon representing that face, it is possible to find a polyhedral realization of the whole graph that has the specified shape for the designated face. This is related to a... | Steinitz theorem | 0.782768 |
85,878 | Indeed, even the problem of determining which complete graphs are the graphs of non-convex polyhedra (other than K 4 {\displaystyle K_{4}} for the tetrahedron and K 7 {\displaystyle K_{7}} for the Császár polyhedron) remains unsolved.Eberhard's theorem partially characterizes the multisets of polygons that can be combi... | Steinitz theorem | 0.782768 |
85,879 | Although Steinitz's original proof was not expressed in terms of graph theory, it can be rewritten in those terms, and involves finding a sequence of Δ-Y and Y-Δ transforms that reduce any 3-connected planar graph to K 4 {\displaystyle K_{4}} , the graph of the tetrahedron. A Y-Δ transform removes a degree-three vertex... | Steinitz theorem | 0.782768 |
85,880 | In any dimension higher than three, the algorithmic Steinitz problem consists of determining whether a given lattice is the face lattice of a convex polytope. It is unlikely to have polynomial time complexity, as it is NP-hard and more strongly complete for the existential theory of the reals, even for four-dimensional... | Steinitz theorem | 0.782768 |
85,881 | "The theorem appears in a 1922 publication of Ernst Steinitz, after whom it is named. It can be proven by mathematical induction (as Steinitz did), by finding the minimum-energy state of a two-dimensional spring system and lifting the result into three dimensions, or by using the circle packing theorem. Several extensi... | Steinitz theorem | 0.782768 |
85,882 | Additionally, it has been applied in graph drawing, as a way to construct three-dimensional visualizations of abstract graphs. Branko Grünbaum has called this theorem "the most important and deepest known result on 3-polytopes. | Steinitz theorem | 0.782768 |
85,883 | In polyhedral combinatorics, a branch of mathematics, Steinitz's theorem is a characterization of the undirected graphs formed by the edges and vertices of three-dimensional convex polyhedra: they are exactly the 3-vertex-connected planar graphs. That is, every convex polyhedron forms a 3-connected planar graph, and ev... | Steinitz theorem | 0.782768 |
85,884 | It is possible to prove a stronger form of Steinitz's theorem, that any polyhedral graph can be realized by a convex polyhedron whose coordinates are integers. For instance, Steinitz's original induction-based proof can be strengthened in this way. However, the integers that would result from Steinitz's construction ar... | Steinitz theorem | 0.782768 |
85,885 | The March of Dimes Prize in Developmental Biology is awarded once a year by the March of Dimes. It carries a $150,000 award "to scientific leaders who have pioneered research to advance our understanding of prenatal development and pregnancy". | March of Dimes Prize in Developmental Biology | 0.782767 |
85,886 | It is the smallest possible snark, and was the only known snark from 1898 until 1946. The snark theorem, a result conjectured by W. T. Tutte and announced in 2001 by Robertson, Sanders, Seymour, and Thomas, states that every snark has the Petersen graph as a minor. Additionally, the graph has fractional chromatic index... | Petersen graph | 0.782765 |
85,887 | The Petersen graph has chromatic number 3, meaning that its vertices can be colored with three colors — but not with two — such that no edge connects vertices of the same color. It has a list coloring with 3 colors, by Brooks' theorem for list colorings. The Petersen graph has chromatic index 4; coloring the edges requ... | Petersen graph | 0.782765 |
85,888 | Kempe observed that its vertices can represent the ten lines of the Desargues configuration, and its edges represent pairs of lines that do not meet at one of the ten points of the configuration.Donald Knuth states that the Petersen graph is "a remarkable configuration that serves as a counterexample to many optimistic... | Petersen graph | 0.782765 |
85,889 | In the mathematical field of graph theory, the Petersen graph is an undirected graph with 10 vertices and 15 edges. It is a small graph that serves as a useful example and counterexample for many problems in graph theory. The Petersen graph is named after Julius Petersen, who in 1898 constructed it to be the smallest b... | Petersen graph | 0.782765 |
85,890 | Nonstandard finite difference schemes is a general set of methods in numerical analysis that gives numerical solutions to differential equations by constructing a discrete model. The general rules for such schemes are not precisely known. | Nonstandard finite difference scheme | 0.782764 |
85,891 | A domain wall is a term used in physics which can have similar meanings in optics, magnetism, or string theory. These phenomena can all be generically described as topological solitons which occur whenever a discrete symmetry is spontaneously broken.As of 2009, a phase-locked dark-dark vector soliton was observed only ... | Domain wall (optics) | 0.782763 |
85,892 | Dale Miller and Gopalan Nadathur have written the book Programming with higher-order logic, published by Cambridge University Press in June 2012. Amy Felty has written in a 1997 tutorial on lambda Prolog and its Applications to Theorem Proving. John Hannan has written a tutorial on Program Analysis in lambda Prolog for... | ΛProlog | 0.782763 |
85,893 | The system is described in a paper that appeared LPAR 2015. ELPI is also available as a Coq plugin: see Enrico Tassi's tutorial on this plugin. The Abella prover can be used to prove theorems about λProlog programs and specifications. | ΛProlog | 0.782763 |
85,894 | Since 1986, λProlog has received numerous implementations. As of 2023, the language and its implementations are still actively being developed. The Abella theorem prover has been designed to provide an interactive environment for proving theorems about the declarative core of λProlog. | ΛProlog | 0.782763 |
85,895 | In particle physics, a trigger is a system that uses criteria to rapidly decide which events in a particle detector to keep when only a small fraction of the total can be recorded. Trigger systems are necessary due to real-world limitations in computing power, data storage capacity and rates. Since experiments are typi... | Trigger (particle physics) | 0.782763 |
85,896 | Morrissey J and Sumich J (2011) Introduction to the Biology of Marine Life Jones & Bartlett Publishers. ISBN 9780763781606. Mladenov, Philip V., Marine Biology: A Very Short Introduction, 2nd edn (Oxford, 2020; online edn, Very Short Introductions online, Feb. 2020), http://dx.doi.org/10.1093/actrade/9780198841715.001.... | Marine creatures | 0.782762 |
85,897 | The organisms studied range from microscopic phytoplankton and zooplankton to huge cetaceans (whales) 25–32 meters (82–105 feet) in length. Marine ecology is the study of how marine organisms interact with each other and the environment. Marine life is a vast resource, providing food, medicine, and raw materials, in ad... | Marine creatures | 0.782762 |
85,898 | The ocean is a complex three-dimensional world covering approximately 71% of the Earth's surface. The habitats studied in marine biology include everything from the tiny layers of surface water in which organisms and abiotic items may be trapped in surface tension between the ocean and atmosphere, to the depths of the ... | Marine creatures | 0.782762 |
85,899 | Marine biology is the scientific study of the biology of marine life, organisms in the sea. Given that in biology many phyla, families and genera have some species that live in the sea and others that live on land, marine biology classifies species based on the environment rather than on taxonomy. A large proportion of... | Marine creatures | 0.782762 |
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