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5,900 | Epigenetic repression of DDR genes occurs more frequently than gene mutation in many types of cancer (see Cancer epigenetics). Thus, epigenetic repression often plays a more important role than mutation in reducing expression of DDR genes. This reduced expression of DDR genes is likely an important driver of carcinogen... | Cancer genomics | 0.825211 |
5,901 | Microbiology Spectrum is a peer-reviewed scientific journal published by the American Society for Microbiology. Topics the journal covers include: archaea, food microbiology, bacterial genetics, cell biology, physiology, clinical microbiology, environmental microbiology, ecology, eukaryotic microbes, genomics, computat... | Microbiology Spectrum | 0.825202 |
5,902 | Ion Torrent Systems Inc. (now owned by Life Technologies) developed a system based on using standard sequencing chemistry, but with a novel, semiconductor-based detection system. This method of sequencing is based on the detection of hydrogen ions that are released during the polymerisation of DNA, as opposed to the op... | Dye terminator sequencing | 0.8252 |
5,903 | Natural logarithm Common logarithm Binary logarithm Power functions: raise a variable number to a fixed power; also known as Allometric functions; note: if the power is a rational number it is not strictly a transcendental function. Periodic functions Trigonometric functions: sine, cosine, tangent, cotangent, secant, c... | List of mathematical functions | 0.825194 |
5,904 | Transcendental functions are functions that are not algebraic. Exponential function: raises a fixed number to a variable power. Hyperbolic functions: formally similar to the trigonometric functions. Logarithms: the inverses of exponential functions; useful to solve equations involving exponentials. | List of mathematical functions | 0.825194 |
5,905 | Gamma function: A generalization of the factorial function. Barnes G-function Beta function: Corresponding binomial coefficient analogue. Digamma function, Polygamma function Incomplete beta function Incomplete gamma function K-function Multivariate gamma function: A generalization of the Gamma function useful in multi... | List of mathematical functions | 0.825194 |
5,906 | Algebraic functions are functions that can be expressed as the solution of a polynomial equation with integer coefficients. Polynomials: Can be generated solely by addition, multiplication, and raising to the power of a positive integer. Constant function: polynomial of degree zero, graph is a horizontal straight line ... | List of mathematical functions | 0.825194 |
5,907 | Logarithmic integral function: Integral of the reciprocal of the logarithm, important in the prime number theorem. Exponential integral Trigonometric integral: Including Sine Integral and Cosine Integral Inverse tangent integral Error function: An integral important for normal random variables. Fresnel integral: relate... | List of mathematical functions | 0.825194 |
5,908 | In mathematics, some functions or groups of functions are important enough to deserve their own names. This is a listing of articles which explain some of these functions in more detail. There is a large theory of special functions which developed out of statistics and mathematical physics. A modern, abstract point of ... | List of mathematical functions | 0.825194 |
5,909 | The theory of R ≤ {\displaystyle {\mathcal {R}}^{\leq }} has quantifier elimination. Thus the definable sets are Boolean combinations of solutions to polynomial equalities and inequalities; these are called semi-algebraic sets. Generalizing this property of the real line leads to the study of o-minimality. | Definable set | 0.825193 |
5,910 | Scientific journals exclusively or predominantly concerned with vision science include: Investigative Ophthalmology & Vision Science (IOVS) Ophthalmology JAMA Ophthalmology American Journal of Ophthalmology British Journal of Ophthalmology Progress in Retinal and Eye Research Current Opinion in Ophthalmology Survey of ... | Vision sciences | 0.825182 |
5,911 | This notion has made it possible to use the methods of graph theory in universal algebra and several other directions of discrete mathematics and computer science. Graph algebras have been used, for example, in constructions concerning dualities, equational theories, flatness, groupoid rings, topologies, varieties, fin... | Graph algebra | 0.82518 |
5,912 | Let D = (V, E) be a directed graph, and 0 an element not in V. The graph algebra associated with D has underlying set V ∪ { 0 } {\displaystyle V\cup \{0\}} , and is equipped with a multiplication defined by the rules xy = x if x , y ∈ V {\displaystyle x,y\in V} and ( x , y ) ∈ E {\displaystyle (x,y)\in E} , xy = 0 if x... | Graph algebra | 0.82518 |
5,913 | In mathematics, especially in the fields of universal algebra and graph theory, a graph algebra is a way of giving a directed graph an algebraic structure. It was introduced by McNulty and Shallon, and has seen many uses in the field of universal algebra since then. | Graph algebra | 0.82518 |
5,914 | In mathematics, a ternary equivalence relation is a kind of ternary relation analogous to a binary equivalence relation. A ternary equivalence relation is symmetric, reflexive, and transitive. The classic example is the relation of collinearity among three points in Euclidean space. In an abstract set, a ternary equiva... | Ternary equivalence relation | 0.825177 |
5,915 | The WCD concept also offers really defining the set of statistical parameters to choose as worst-case, being a perfect measure to start an optimization. However, a very important limitation is on just finding the WCD point, i.e. the set of statistical variable values which hits the spec-region, because even small real-... | Worst-case distance | 0.825173 |
5,916 | As real-world designs can be very complex and highly nonlinear, there are also examples where the WCD can be much more wrong, e.g. in case of an ADC or DAC and e.g. specifications on differential nonlinearity (DNL). Also for CMOS timing analysis a WCD analysis is very difficult. On the other hand: Although the WCD migh... | Worst-case distance | 0.825173 |
5,917 | WCD allows to simplify yield problems, but it is not the only way to do this. A simpler way is not to find the margin in terms of sigma in the space of statistical variables, but just to evaluate the performance margin(s) itself (like the Cpk does). The worst-case performance margin WPM is much easier to obtain, but he... | Worst-case distance | 0.825173 |
5,918 | The concept of worst-case distance (WCD) extends this simple idea for applying it to more complex problems (like having non-normal distributions, multiple specs, etc.). The WCD is a metric originally applied in electronic design for yield optimization and design centering, nowadays also applied as a metric for quantify... | Worst-case distance | 0.825173 |
5,919 | In design environments the WCD calculation is not done analytically but in a numerical way. Most WCD algorithms start with a short Monte-Carlo analysis, and use then optimization techniques to find the point in the statistical variable space which hits the specification border with minimum vector length. For cases with... | Worst-case distance | 0.825173 |
5,920 | It has been suggested that the Casimir forces have application in nanotechnology, in particular silicon integrated circuit technology based micro- and nanoelectromechanical systems, and so-called Casimir oscillators.The Casimir effect shows that quantum field theory allows the energy density in certain regions of space... | Casimir forces | 0.825157 |
5,921 | Nevertheless, the formal sciences play an important role in the empirical sciences. Calculus, for example, was initially invented to understand motion in physics. Natural and social sciences that rely heavily on mathematical applications include mathematical physics, chemistry, biology, finance, and economics. | General science | 0.825148 |
5,922 | Formal science is an area of study that generates knowledge using formal systems. A formal system is an abstract structure used for inferring theorems from axioms according to a set of rules. It includes mathematics, systems theory, and theoretical computer science. | General science | 0.825148 |
5,923 | The Human Genome Project was completed in 2003 by identifying and mapping all of the genes of the human genome. The first induced pluripotent human stem cells were made in 2006, allowing adult cells to be transformed into stem cells and turn to any cell type found in the body. With the affirmation of the Higgs boson di... | General science | 0.825148 |
5,924 | : 4–5 Experimentation is especially important in science to help establish causal relationships to avoid the correlation fallacy, though in some sciences such as astronomy or geology, a predicted observation might be more appropriate.When a hypothesis proves unsatisfactory, it is modified or discarded. If the hypothesi... | General science | 0.825148 |
5,925 | Their theory was set out in detail in Darwin's book On the Origin of Species, published in 1859. Separately, Gregor Mendel presented his paper, "Experiments on Plant Hybridization" in 1865, which outlined the principles of biological inheritance, serving as the basis for modern genetics.Early in the 19th century, John ... | General science | 0.825148 |
5,926 | Due to the collapse of the Western Roman Empire, the 5th century saw an intellectual decline and knowledge of Greek conceptions of the world deteriorated in Western Europe. : 194 During the period, Latin encyclopedists such as Isidore of Seville preserved the majority of general ancient knowledge. In contrast, because ... | General science | 0.825148 |
5,927 | Scientific research involves using the scientific method, which seeks to objectively explain the events of nature in a reproducible way. Scientists usually take for granted a set of basic assumptions that are needed to justify the scientific method: there is an objective reality shared by all rational observers; this o... | General science | 0.825148 |
5,928 | Science education for the general public is embedded in the school curriculum, and is supplemented by online pedagogical content (for example, YouTube and Khan Academy), museums, and science magazines and blogs. Scientific literacy is chiefly concerned with an understanding of the scientific method, units and methods o... | General science | 0.825148 |
5,929 | Interdisciplinary science involves the combination of two or more disciplines into one, such as bioinformatics, a combination of biology and computer science or cognitive sciences. The concept has existed since the ancient Greek and it became popular again in the 20th century. | General science | 0.825148 |
5,930 | The applied sciences are often contrasted with the basic sciences, which are focused on advancing scientific theories and laws that explain and predict events in the natural world.Computational science applies computing power to simulate real-world situations, enabling a better understanding of scientific problems than... | General science | 0.825148 |
5,931 | By contrast, a computer worm does not need a host program, as it is an independent program or code chunk. Therefore, it is not restricted by the host program, but can run independently and actively carry out attacks.Virus writers use social engineering deceptions and exploit detailed knowledge of security vulnerabiliti... | Virus signature | 0.825146 |
5,932 | (For projective homogeneous varieties, the cells are called Schubert cells, and their closures are called Schubert varieties.) Cellular varieties are very special among all algebraic varieties. For example, a cellular variety is rational, and (for k = C) the Hodge theory of a smooth projective cellular variety is trivi... | Quadric (algebraic geometry) | 0.825144 |
5,933 | To indicate the significance of the spinor bundles: Mikhail Kapranov showed that the bounded derived category of coherent sheaves on a split quadric X over a field k has a full exceptional collection involving the spinor bundles, along with the "obvious" line bundles O(j) restricted from projective space: D b ( X ) = ⟨... | Quadric (algebraic geometry) | 0.825144 |
5,934 | The action of SO(2m + 1) on this projective space does not come from a linear representation of SO(2m+1) over k, but rather from a representation of its simply connected double cover, the spin group Spin(2m + 1) over k. This is called the spin representation of Spin(2m + 1), of dimension 2 m {\displaystyle 2^{m}} . Ove... | Quadric (algebraic geometry) | 0.825144 |
5,935 | The space of r-planes in a smooth n-dimensional quadric (like the quadric itself) is a projective homogeneous variety, known as the isotropic Grassmannian or orthogonal Grassmannian OGr(r + 1, n + 2). (The numbering refers to the dimensions of the corresponding vector spaces. In the case of middle-dimensional linear su... | Quadric (algebraic geometry) | 0.825144 |
5,936 | In particular, every quadric over an algebraically closed field is rational. A quadric over a field k is called isotropic if it has a k-rational point. An example of an anisotropic quadric is the quadric x 0 2 + x 1 2 + ⋯ + x n + 1 2 = 0 {\displaystyle x_{0}^{2}+x_{1}^{2}+\cdots +x_{n+1}^{2}=0} in projective space P n ... | Quadric (algebraic geometry) | 0.825144 |
5,937 | It is common to assume that n ≥ 1 {\displaystyle n\geq 1} and q is irreducible, which excludes that special case. Here algebraic varieties over a field k are considered as a special class of schemes over k. When k is algebraically closed, one can also think of a projective variety in a more elementary way, as a subset ... | Quadric (algebraic geometry) | 0.825144 |
5,938 | A smooth quadric over a field k is a projective homogeneous variety for the orthogonal group (and for the special orthogonal group), viewed as linear algebraic groups over k. Like any projective homogeneous variety for a split reductive group, a split quadric X has an algebraic cell decomposition, known as the Bruhat d... | Quadric (algebraic geometry) | 0.825144 |
5,939 | If a quadric X over a field k is split, then it can be written (after a linear change of coordinates) as x 0 x 1 + x 2 x 3 + ⋯ + x 2 m − 2 x 2 m − 1 + x 2 m 2 = 0 {\displaystyle x_{0}x_{1}+x_{2}x_{3}+\cdots +x_{2m-2}x_{2m-1}+x_{2m}^{2}=0} if X has dimension 2m − 1, or x 0 x 1 + x 2 x 3 + ⋯ + x 2 m x 2 m + 1 = 0 {\displ... | Quadric (algebraic geometry) | 0.825144 |
5,940 | A central part of the geometry of quadrics is the study of the linear spaces that they contain. (In the context of projective geometry, a linear subspace of P N {\displaystyle {\mathbf {P} }^{N}} is isomorphic to P a {\displaystyle {\mathbf {P} }^{a}} for some a ≤ N {\displaystyle a\leq N} .) A key point is that every ... | Quadric (algebraic geometry) | 0.825144 |
5,941 | Namely, given a 4-dimensional vector space V with a symplectic form, the quadric 3-fold X can be identified with the space LGr(2,4) of 2-planes in V on which the form restricts to zero. Furthermore, the space of lines in the quadric 3-fold X is isomorphic to P 3 {\displaystyle \mathbf {P} ^{3}} .A split quadric 4-fold ... | Quadric (algebraic geometry) | 0.825144 |
5,942 | )A split quadric surface X is isomorphic to P 1 × P 1 {\displaystyle \mathbf {P} ^{1}\times \mathbf {P} ^{1}} , embedded in P 3 {\displaystyle \mathbf {P} ^{3}} by the Segre embedding. The space of lines in the quadric surface X has two connected components, each isomorphic to P 1 {\displaystyle \mathbf {P} ^{1}} .A sp... | Quadric (algebraic geometry) | 0.825144 |
5,943 | Let X be a split quadric over a field k. (In particular, X can be any smooth quadric over an algebraically closed field.) In low dimensions, X and the linear spaces it contains can be described as follows. | Quadric (algebraic geometry) | 0.825144 |
5,944 | An example is the quadric surface x y = z w {\displaystyle xy=zw} in projective space P 3 {\displaystyle {\mathbf {P} }^{3}} over the complex numbers C. A quadric has a natural action of the orthogonal group, and so the study of quadrics can be considered as a descendant of Euclidean geometry. Many properties of quadri... | Quadric (algebraic geometry) | 0.825144 |
5,945 | In mathematics, a quadric or quadric hypersurface is the subspace of N-dimensional space defined by a polynomial equation of degree 2 over a field. Quadrics are fundamental examples in algebraic geometry. The theory is simplified by working in projective space rather than affine space. | Quadric (algebraic geometry) | 0.825144 |
5,946 | "The findings break from the traditional interpretation of marine ecology found in textbooks, which states that nearly all sunlight in the ocean is captured by chlorophyll in algae. Instead, rhodopsin-equipped bacteria function like hybrid cars, powered by organic matter when available — as most bacteria are — and by s... | Marine microorganisms | 0.825136 |
5,947 | Some species are endosymbionts of marine animals and other protists, and play an important part in the biology of coral reefs. Others predate other protozoa, and a few forms are parasitic. Many dinoflagellates are mixotrophic and could also be classified as phytoplankton. | Marine microorganisms | 0.825135 |
5,948 | Mermaid's wineglass, a genus of subtropical green algae, is single-celled but remarkably large and complex in form with a single large nucleus, making it a model organism for studying cell biology. Another single-celled algae, Caulerpa taxifolia, has the appearance of a vascular plant including "leaves" arranged neatly... | Marine microorganisms | 0.825135 |
5,949 | A key consideration is that more accurate diagnosis is possible when the diagnosis is based on both the morphologic changes in tissues (traditional anatomic pathology) and on molecular testing.It is a scientific discipline that encompasses the development of molecular and genetic approaches to the diagnosis and classif... | Molecular pathology | 0.82513 |
5,950 | Molecular pathology is an emerging discipline within pathology which is focused in the study and diagnosis of disease through the examination of molecules within organs, tissues or bodily fluids. Molecular pathology shares some aspects of practice with both anatomic pathology and clinical pathology, molecular biology, ... | Molecular pathology | 0.82513 |
5,951 | The equations of a linear system are independent if none of the equations can be derived algebraically from the others. When the equations are independent, each equation contains new information about the variables, and removing any of the equations increases the size of the solution set. For linear equations, logical ... | Vector equation | 0.825125 |
5,952 | The following computation shows Gauss–Jordan elimination applied to the matrix above: ∼ ∼ ∼ ∼ ∼ ∼ ∼ . {\displaystyle {\begin{aligned}\left&\sim \left\sim \left\sim \left\\&\sim \left\sim \left\sim \left\sim \left.\end{aligned}}} The last matrix is in reduced row echelon form, and represents the system x = −15, ... | Vector equation | 0.825125 |
5,953 | Andreas Vesalius was the author of De humani corporis fabrica, an important book on human anatomy. Bacteria and microorganisms were first observed with a microscope by Antonie van Leeuwenhoek in 1676, initiating the scientific field microbiology. | Medicine | 0.825124 |
5,954 | This was the notion that because some prominent person in the past said something must be so, then that was the way it was, and anything one observed to the contrary was an anomaly (which was paralleled by a similar shift in European society in general – see Copernicus's rejection of Ptolemy's theories on astronomy). P... | Medicine | 0.825124 |
5,955 | A function f: I → R + {\displaystyle f:I\rightarrow \mathbb {R} ^{+}} is polynomial on μ {\displaystyle \mu } -average on spheres if there exists k ≥ 1 {\displaystyle k\geq 1} such that ∑ w ∈ I n f 1 / k ( w ) μ n ( w ) = O ( n ) {\displaystyle \sum _{w\in I_{n}}f^{1/k}(w)\mu _{n}(w)=O(n)} where { μ n } {\displaystyle ... | Generic-case complexity | 0.82512 |
5,956 | More precisely for a proper complexity function f, G e n ( f ) ⊊ G e n ( f 3 ) {\displaystyle Gen(f)\subsetneq Gen(f^{3})} . The next theorem shows that just as there are average case complete problems within distributional NP problems, there are also generic case complete problems. The arguments in the generic case ar... | Generic-case complexity | 0.82512 |
5,957 | A famous Rice's theorem states that if F is a subset of the set of partial computable functions from N {\displaystyle \mathbb {N} } to { 0 , 1 } {\displaystyle \{0,1\}} , then unless F or its complement is empty, the problem of deciding whether or not a particular Turing machine computes a function in F is undecidable.... | Generic-case complexity | 0.82512 |
5,958 | In this case it is often convenient to use spheres I n = { x ∈ I ∣ σ ( x ) = n } {\displaystyle I_{n}=\{x\in I\mid \sigma (x)=n\}} instead of balls and define ρ ′ ( X ) = lim | X ∩ I n | | I n | {\displaystyle \rho '(X)=\lim {\frac {|X\cap I_{n}|}{|I_{n}|}}} . An argument using Stolz theorem shows that ρ ( X ) {\displa... | Generic-case complexity | 0.82512 |
5,959 | The de novo protein synthesis theory of memory formation is a hypothesis about the formation of the physical correlates of memory in the brain. It is widely accepted that the physiological correlates for memories are stored at the synapse between various neurons. The relative strength of various synapses in a network o... | De novo protein synthesis theory of memory formation | 0.825096 |
5,960 | The goal of many graph representation learning techniques is to produce an embedded representation of each node based on the overall network topology. node2vec extends the word2vec training technique to nodes in a graph by using co-occurrence in random walks through the graph as the measure of association. Another appr... | Feature learning | 0.825094 |
5,961 | In machine learning, feature learning or representation learning is a set of techniques that allows a system to automatically discover the representations needed for feature detection or classification from raw data. This replaces manual feature engineering and allows a machine to both learn the features and use them t... | Feature learning | 0.825094 |
5,962 | The weights together with the connections define an energy function, based on which a joint distribution of visible and hidden nodes can be devised. Based on the topology of the RBM, the hidden (visible) variables are independent, conditioned on the visible (hidden) variables. Such conditional independence facilitates ... | Feature learning | 0.825094 |
5,963 | In self-supervised feature learning, features are learned using unlabeled data like unsupervised learning, however input-label pairs are constructed from each data point, which enables learning the structure of the data through supervised methods such as gradient descent. Classical examples include word embeddings and ... | Feature learning | 0.825094 |
5,964 | Examples include supervised neural networks, multilayer perceptron and (supervised) dictionary learning. In unsupervised feature learning, features are learned with unlabeled input data by analyzing the relationship between points in the dataset. Examples include dictionary learning, independent component analysis, mat... | Feature learning | 0.825094 |
5,965 | Joint constraints are rotational constraints on the joints of an artificial system. They are used in an inverse kinematics chain, in fields including 3D animation or robotics. Joint constraints can be implemented in a number of ways, but the most common method is to limit rotation about the X, Y and Z axis independentl... | Joint constraints | 0.825091 |
5,966 | The branches of science known informally as omics are various disciplines in biology whose names end in the suffix -omics, such as genomics, proteomics, metabolomics, metagenomics, phenomics and transcriptomics. Omics aims at the collective characterization and quantification of pools of biological molecules that trans... | Omics | 0.825091 |
5,967 | The word chromosome derives from the Greek stems χρωμ(ατ)- "colour" and σωμ(ατ)- "body". While σωμα "body" genuinely contains the -μα suffix, the preceding -ω- is not a stem-forming suffix but part of the word's root. Because genome refers to the complete genetic makeup of an organism, a neo-suffix -ome suggested itsel... | Omics | 0.825091 |
5,968 | The Oxford English Dictionary (OED) distinguishes three different fields of application for the -ome suffix: in medicine, forming nouns with the sense "swelling, tumour" in botany or zoology, forming nouns in the sense "a part of an animal or plant with a specified structure" in cellular and molecular biology, forming ... | Omics | 0.825091 |
5,969 | Nutritional genomics: A science studying the relationship between human genome, nutrition and health. Nutrigenetics studies the effect of genetic variations on the interaction between diet and health with implications to susceptible subgroups Nutrigenomics: Study of the effects of foods and food constituents on gene ex... | Omics | 0.825091 |
5,970 | Tomomics: A combination of tomography and omics methods to understand tissue or cell biochemistry at high spatial resolution, typically using imaging mass spectrometry data. Ethomics: The high-throughput machine measurement of animal behaviour. Videomics (or vide-omics): A video analysis paradigm inspired by genomics p... | Omics | 0.825091 |
5,971 | Connectomics: The study of the connectome, the totality of the neural connections in the brain. Microbiomics: The study of the genomes of the communities of microorganisms that live in a specific environmental niche. Cellomics: The quantitative cell analysis and study using bioimaging methods and bioinformatics. | Omics | 0.825091 |
5,972 | Mitointeractome Psychogenomics: Process of applying the powerful tools of genomics and proteomics to achieve a better understanding of the biological substrates of normal behavior and of diseases of the brain that manifest themselves as behavioral abnormalities. Applying psychogenomics to the study of drug addiction, t... | Omics | 0.825091 |
5,973 | Inspired by foundational questions in evolutionary biology, a Harvard team around Jean-Baptiste Michel and Erez Lieberman Aiden created the American neologism culturomics for the application of big data collection and analysis to cultural studies. | Omics | 0.825091 |
5,974 | Sex-linked interactionsSex-linked inheritance (gonosomal loci) Sex-limited phenotype expression (e.g., cryptorchism) Inheritance through the maternal line (in case of mitochondrial DNA loci) Inheritance through the paternal line (in case of Y-chromosomal loci)6. Locus–locus interactions Epistasis with other loci (e.g.,... | Biological inheritance | 0.825086 |
5,975 | Correlation genotype–phenotype Dominant Intermediate (also called "codominant") Recessive Overdominant UnderdominantThese three categories are part of every exact description of a mode of inheritance in the above order. In addition, more specifications may be added as follows: 4. Coincidental and environmental interact... | Biological inheritance | 0.825086 |
5,976 | There is no doubt, however, that the synthesis was a great landmark in evolutionary biology. It cleared up many confusions, and was directly responsible for stimulating a great deal of research in the post-World War II era. Trofim Lysenko however caused a backlash of what is now called Lysenkoism in the Soviet Union wh... | Biological inheritance | 0.825086 |
5,977 | In plants, polyploidy must be included in any view of speciation. Formulations such as 'evolution consists primarily of changes in the frequencies of alleles between one generation and another' were proposed rather later. The traditional view is that developmental biology ('evo-devo') played little part in the synthesi... | Biological inheritance | 0.825086 |
5,978 | The role of genetic drift is equivocal; though strongly supported initially by Dobzhansky, it was downgraded later as results from ecological genetics were obtained. The primacy of population thinking: the genetic diversity carried in natural populations is a key factor in evolution. The strength of natural selection i... | Biological inheritance | 0.825086 |
5,979 | He also succeeded in secretly enabling a number of Jewish scientists to continue working in institutes of the KWG for several years. In 1936, his term as president of the KWG ended, and the Nazi government pressured him to refrain from seeking another term. As the political climate in Germany gradually became more host... | Max Planck | 0.825083 |
5,980 | Planck started a six-semester course of lectures on theoretical physics, "dry, somewhat impersonal" according to Lise Meitner, "using no notes, never making mistakes, never faltering; the best lecturer I ever heard" according to an English participant, James R. Partington, who continues: "There were always many standin... | Max Planck | 0.825083 |
5,981 | In 1889, he was named the successor to Kirchhoff's position at the Friedrich-Wilhelms-Universität in Berlin – presumably thanks to Helmholtz's intercession – and by 1892 became a full professor. In 1907 Planck was offered Boltzmann's position in Vienna, but turned it down to stay in Berlin. During 1909, as a University... | Max Planck | 0.825083 |
5,982 | Further work on entropy and its treatment, especially as applied in physical chemistry, followed. He published his Treatise on Thermodynamics in 1897. He proposed a thermodynamic basis for Svante Arrhenius's theory of electrolytic dissociation. | Max Planck | 0.825083 |
5,983 | With the completion of his habilitation thesis, Planck became an unpaid Privatdozent (German academic rank comparable to lecturer/assistant professor) in Munich, waiting until he was offered an academic position. Although he was initially ignored by the academic community, he furthered his work on the field of heat the... | Max Planck | 0.825083 |
5,984 | For example, he recast the theory in terms of classical action.Einstein's hypothesis of light quanta (photons), based on Heinrich Hertz's 1887 discovery (and further investigation by Philipp Lenard) of the photoelectric effect, was initially rejected by Planck. He was unwilling to discard completely Maxwell's theory of... | Max Planck | 0.825083 |
5,985 | So much the worse for the facts if they don't fit. "Max Born wrote about Planck: "He was, by nature, a conservative mind; he had nothing of the revolutionary and was thoroughly skeptical about speculations. Yet his belief in the compelling force of logical reasoning from facts was so strong that he did not flinch from ... | Max Planck | 0.825083 |
5,986 | Even several years later, other physicists like Rayleigh, Jeans, and Lorentz set Planck's constant to zero in order to align with classical physics, but Planck knew well that this constant had a precise nonzero value. "I am unable to understand Jeans' stubbornness – he is an example of a theoretician as should never be... | Max Planck | 0.825083 |
5,987 | The discovery of Planck's constant enabled him to define a new universal set of physical units (such as the Planck length and the Planck mass), all based on fundamental physical constants upon which much of quantum theory is based. In recognition of Planck's fundamental contribution to a new branch of physics, he was a... | Max Planck | 0.825083 |
5,988 | The total energy at that frequency is then equal to hν multiplied by the number of photons at that frequency. At first Planck considered that quantisation was only "a purely formal assumption ... actually I did not think much about it ..."; nowadays this assumption, incompatible with classical physics, is regarded as t... | Max Planck | 0.825083 |
5,989 | In November 1900 Planck revised this first version, now relying on Boltzmann's statistical interpretation of the second law of thermodynamics as a way of gaining a more fundamental understanding of the principles behind his radiation law. Planck was deeply suspicious of the philosophical and physical implications of su... | Max Planck | 0.825083 |
5,990 | The Rayleigh–Jeans law, another approach to the problem, agreed with experimental results at low frequencies, but created what was later known as the "ultraviolet catastrophe" at high frequencies, as predicted by classical physics. However, contrary to many textbooks, this was not a motivation for Planck.Planck's first... | Max Planck | 0.825083 |
5,991 | At the end of the 1920s, Bohr, Heisenberg and Pauli had worked out the Copenhagen interpretation of quantum mechanics, but it was rejected by Planck, and by Schrödinger, Laue, and Einstein as well. Planck expected that wave mechanics would soon render quantum theory – his own child – unnecessary. This was not to be the... | Max Planck | 0.825083 |
5,992 | In October 1878, Planck passed his qualifying exams and in February 1879 defended his dissertation Über den zweiten Hauptsatz der mechanischen Wärmetheorie (On the Second Law of Mechanical Heat Theory). He briefly taught mathematics and physics at his former school in Munich. By the year 1880, Planck had obtained the t... | Max Planck | 0.825083 |
5,993 | Under Jolly's supervision, Planck performed the only experiments of his scientific career, studying the diffusion of hydrogen through heated platinum, but transferred to theoretical physics. In 1877, he went to the Friedrich Wilhelms University in Berlin for a year of study with physicists Hermann von Helmholtz and Gus... | Max Planck | 0.825083 |
5,994 | However, instead of music he chose to study physics. The Munich physics professor Philipp von Jolly advised Planck against going into physics, saying, "In this field, almost everything is already discovered, and all that remains is to fill a few holes." Planck replied that he did not wish to discover new things, but on... | Max Planck | 0.825083 |
5,995 | This is how Planck first came in contact with the field of physics. Planck was gifted when it came to music. He took singing lessons and played piano, organ and cello, and composed songs and operas. | Max Planck | 0.825083 |
5,996 | In 1867 the family moved to Munich, and Planck enrolled in the Maximilians gymnasium school, where he came under the tutelage of Hermann Müller, a mathematician who took an interest in the youth, and taught him astronomy and mechanics as well as mathematics. It was from Müller that Planck first learned the principle of... | Max Planck | 0.825083 |
5,997 | Max Karl Ernst Ludwig Planck (English: , German: ; 23 April 1858 – 4 October 1947) was a German theoretical physicist whose discovery of energy quanta won him the Nobel Prize in Physics in 1918.Planck made many substantial contributions to theoretical physics, but his fame as a physicist rests primarily on his role as... | Max Planck | 0.825083 |
5,998 | In the turbulent post-war years, Planck, now the highest authority of German physics, issued the slogan "persevere and continue working" to his colleagues. In October 1920, he and Fritz Haber established the Notgemeinschaft der Deutschen Wissenschaft (Emergency Organization of German Science), aimed at providing financ... | Max Planck | 0.825083 |
5,999 | Chemogenomics integrates target and drug discovery by using active compounds, which function as ligands, as probes to characterize proteome functions. The interaction between a small compound and a protein induces a phenotype. Once the phenotype is characterized, we could associate a protein to a molecular event. Compa... | Chemical genomics | 0.825072 |
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