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613. OCLC 1159631475. Kittel, Charles (1971). | Wikipedia - Introduction to Solid State Physics | null | null | null |
Introduction to solid state physics (4th ed.). New York: John Wiley & Sons. p. | Wikipedia - Introduction to Solid State Physics | null | null | null |
766. ISBN 978-0-471-49021-0. OCLC 802643946. | Wikipedia - Introduction to Solid State Physics | null | null | null |
Kittel, Charles (1976). Introduction to solid state physics (5th ed.). New York: Wiley. | Wikipedia - Introduction to Solid State Physics | null | null | null |
p. 673. ISBN 978-0-471-49024-1. | Wikipedia - Introduction to Solid State Physics | null | null | null |
OCLC 908887143. Kittel, Charles (1986). Introduction to solid state physics (6th ed.). | Wikipedia - Introduction to Solid State Physics | null | null | null |
New York: Wiley. p. 646. | Wikipedia - Introduction to Solid State Physics | null | null | null |
ISBN 978-0-471-87474-4. OCLC 797201261. Kittel, Charles (1996). | Wikipedia - Introduction to Solid State Physics | null | null | null |
Introduction to solid state physics (7th ed.). New York: Wiley. p. | Wikipedia - Introduction to Solid State Physics | null | null | null |
673. ISBN 978-0-471-11181-8. OCLC 263625446. | Wikipedia - Introduction to Solid State Physics | null | null | null |
Kittel, Charles (2005). Introduction to solid state physics (8th ed.). New York: Wiley. | Wikipedia - Introduction to Solid State Physics | null | null | null |
p. 680. ISBN 978-0-471-68057-4. | Wikipedia - Introduction to Solid State Physics | null | null | null |
OCLC 787838554. Kittel, Charles; McEuen, Paul (2018). Introduction to solid state physics (Global ed.,9th ed.). | Wikipedia - Introduction to Solid State Physics | null | null | null |
New Jersey: Wiley. p. 692. ISBN 978-1-119-45416-8. OCLC 1097548279. | Wikipedia - Introduction to Solid State Physics | null | null | null |
Kittel, Charles (1954) . Introduction to solid state physics (1st ed.). New York: John Wiley and Sons. p. | Wikipedia - Introduction to Solid State Physics | null | null | null |
396. OCLC 1123251585. Kittel, Charles (1967). | Wikipedia - Introduction to Solid State Physics | null | null | null |
Introduction to solid state physics (3rd ed.). New York: Wiley. p. | Wikipedia - Introduction to Solid State Physics | null | null | null |
648. OCLC 230149869. Kittel, Charles (1987). | Wikipedia - Introduction to Solid State Physics | null | null | null |
Introduction to solid state physics (6th ed.). New delhi: Wiley Eastern Ltd. p. | Wikipedia - Introduction to Solid State Physics | null | null | null |
599. OCLC 772488914. Kittel, Charles (2011). | Wikipedia - Introduction to Solid State Physics | null | null | null |
Introduction to solid state physics (8th ed.). Hoboken, NJ: Wiley. p. | Wikipedia - Introduction to Solid State Physics | null | null | null |
680. ISBN 978-0-471-41526-8. OCLC 730010889. | Wikipedia - Introduction to Solid State Physics | null | null | null |
Kittel, Charles (2013). Introduction to solid state physics (8th ed.). New Jersey: Wiley. | Wikipedia - Introduction to Solid State Physics | null | null | null |
p. 680. ISBN 978-0-471-41526-8. | Wikipedia - Introduction to Solid State Physics | null | null | null |
OCLC 820453856. Kittel, Charles; McEuen, Paul (2015). Introduction to solid state physics (8th ed.). | Wikipedia - Introduction to Solid State Physics | null | null | null |
New Delhi: Wiley. p. 680. ISBN 978-81-265-3518-7. OCLC 987438137. | Wikipedia - Introduction to Solid State Physics | null | null | null |
Kitti's hog-nosed bat roosts in caves in limestone hills, far from the entrance. While many caves contain only 10 to 15 individuals, the average group size is 100, with a maximum of about 500. Individuals roost high on walls or roof domes, far apart from each other. | Wikipedia - Bumblebee bat | null | null | null |
Bats also undertake seasonal migration between caves. Kitti's hog-nosed bat has a brief activity period, leaving its roost for only 30 minutes in the evening and 20 minutes at dawn. These short flights are easily interrupted by heavy rain or cold temperatures. | Wikipedia - Bumblebee bat | null | null | null |
During this period, the bat forages within fields of cassava and kapok or around the tops of bamboo clumps and teak trees, within one kilometre of the roosting site. The wings seem to be shaped for hovering flight, and the gut contents of specimens include spiders and insects that are presumably gleaned off foliage. Ne... | Wikipedia - Bumblebee bat | null | null | null |
Kitâb al-kusuf ("Book of Solar Eclipses") Kitāb an-nabāt yufadiluh al-‘ulamā' fī ta’līfih (كتاب النبات يفضله العلماء في تأليفه), ‘Plants, valued by scholars for its composition' Kitāb Al-Anwā (كتاب الانواء) 'Tempest' (weather) Kitāb Al-qiblah wa'z-zawāl (كتاب القبلة والزوال) "Book of Astral Orientations" Kitāb ḥisāb ad... | Wikipedia - Abu Hanifa Dinawari | null | null | null |
Kiwix: A free and open-source offline web browser created for the purpose of allowing users download Wikipedia entire content and use for offline learning, later was expanded with repositories for Wikimedia Foundation, public domain texts from Project Gutenberg, many of the Stack Exchange sites, and many other resource... | Wikipedia - List of free and open-source software packages | null | null | null |
Kleene algebras are a particular case of closed semirings, also called quasi-regular semirings or Lehmann semirings, which are semirings in which every element has at least one quasi-inverse satisfying the equation: a* = aa* + 1 = a*a + 1. This quasi-inverse is not necessarily unique. In a Kleene algebra, a* is the lea... | Wikipedia - Regular algebra | null | null | null |
Kleene's "(strong) logic of indeterminacy" K3 (sometimes K 3 S {\displaystyle K_{3}^{S}} ) and Priest's "logic of paradox" add a third "undefined" or "indeterminate" truth value I. The truth functions for negation (¬), conjunction (∧), disjunction (∨), implication (→K), and biconditional (↔K) are given by: The differen... | Wikipedia - Many-valued logic | null | null | null |
Kleiber's law relating animal metabolism to size, and allometric laws in general The two-thirds power law, relating speed to curvature in the human motor system. The Taylor's law relating mean population size and variance of populations sizes in ecology Neuronal avalanches The species richness (number of species) in cl... | Wikipedia - Broken power law | null | null | null |
Klein and Gordon papers: Klein, O. (1926). "Quantentheorie und fünfdimensionale Relativitätstheorie". Z. Phys. | Wikipedia - List of important publications in physics | null | null | null |
37 (12): 895–906. Bibcode:1926ZPhy...37..895K. doi:10.1007/BF01397481. | Wikipedia - List of important publications in physics | null | null | null |
Gordon, O. (1926). "Der Comptoneffekt nach der Schrödingerschen Theorie". | Wikipedia - List of important publications in physics | null | null | null |
Z. Phys. 40 (1–2): 117–133. Bibcode:1926ZPhy...40..117G. | Wikipedia - List of important publications in physics | null | null | null |
doi:10.1007/bf01390840. S2CID 122254400.The publications formulate what became known as the Klein–Gordon equation as the first relativistically invariant Schrödinger equation (however the equation was considered contemporaneously by Schrödinger - in his personal notes - and Fock, among others).Dirac equation: Dirac, P.... | Wikipedia - List of important publications in physics | null | null | null |
"The Quantum Theory of the Electron". Proceedings of the Royal Society A. 117 (778): 610–624. | Wikipedia - List of important publications in physics | null | null | null |
Bibcode:1928RSPSA.117..610D. doi:10.1098/rspa.1928.0023. Dirac, P. A. M. | Wikipedia - List of important publications in physics | null | null | null |
(1930). "A Theory of Electrons and Protons". Proceedings of the Royal Society A. | Wikipedia - List of important publications in physics | null | null | null |
126 (801): 360–365. Bibcode:1930RSPSA.126..360D. doi:10.1098/rspa.1930.0013. | Wikipedia - List of important publications in physics | null | null | null |
JSTOR 95359.In these papers, Dirac formulates and derives the Dirac equation, which won him a Nobel Prize (1933) in Physics.Feynman, Richard P. (1949). "Space-Time Approach to Quantum Electrodynamics". | Wikipedia - List of important publications in physics | null | null | null |
Physical Review. 76 (6): 769–789. Bibcode:1949PhRv...76..769F. | Wikipedia - List of important publications in physics | null | null | null |
doi:10.1103/PhysRev.76.769.Introduction of the Feynman diagrams approach to quantum electrodynamics.Yang, C. N.; Mills, R. (1954). "Conservation of Isotopic Spin and Isotopic Gauge Invariance". | Wikipedia - List of important publications in physics | null | null | null |
Physical Review. 96 (1): 191–195. Bibcode:1954PhRv...96..191Y. | Wikipedia - List of important publications in physics | null | null | null |
doi:10.1103/PhysRev.96.191.Extended the concept of gauge theory for abelian groups, e.g. quantum electrodynamics, to nonabelian groups to provide an explanation for strong interactions by use of what are now known as the Yang–Mills equations.Electroweak unification papers: S.L. Glashow (1961). "Partial-symmetries of we... | Wikipedia - List of important publications in physics | null | null | null |
Nuclear Physics. 22 (4): 579–588. Bibcode:1961NucPh..22..579G. | Wikipedia - List of important publications in physics | null | null | null |
doi:10.1016/0029-5582(61)90469-2. S. Weinberg (1967). "A Model of Leptons". | Wikipedia - List of important publications in physics | null | null | null |
Physical Review Letters. 19 (21): 1264–1266. Bibcode:1967PhRvL..19.1264W. | Wikipedia - List of important publications in physics | null | null | null |
doi:10.1103/PhysRevLett.19.1264. A. Salam (1968). "Weak and Electromagnetic Interactions". | Wikipedia - List of important publications in physics | null | null | null |
In N. Svartholm (ed.). Elementary Particle Physics: Relativistic Groups and Analyticity. Eighth Nobel Symposium at Lerum, Sweden. | Wikipedia - List of important publications in physics | null | null | null |
Conf. Proc. C680519 (1968). | Wikipedia - List of important publications in physics | null | null | null |
Stockholm: Almquvist and Wiksell. pp. 367–77.Combined the electromagnetic and weak interactions (through the use of the Higgs mechanism) into an electro-weak theory, and won the trio the Nobel Physics Prize (1979). | Wikipedia - List of important publications in physics | null | null | null |
Also seen as a step towards the Standard Model of particle physics.Higgs et al. 1964 papers: F. Englert, R. Brout; Brout (1964). "Broken Symmetry and the Mass of Gauge Vector Mesons". Physical Review Letters. | Wikipedia - List of important publications in physics | null | null | null |
13 (9): 321–323. Bibcode:1964PhRvL..13..321E. doi:10.1103/PhysRevLett.13.321. | Wikipedia - List of important publications in physics | null | null | null |
P.W. Higgs (1964). | Wikipedia - List of important publications in physics | null | null | null |
"Broken Symmetries and the Masses of Gauge Bosons". Physical Review Letters. 13 (16): 508–509. | Wikipedia - List of important publications in physics | null | null | null |
Bibcode:1964PhRvL..13..508H. doi:10.1103/PhysRevLett.13.508. | Wikipedia - List of important publications in physics | null | null | null |
G.S. Guralnik; Hagen; Kibble (1964). | Wikipedia - List of important publications in physics | null | null | null |
"Global Conservation Laws and Massless Particles". Physical Review Letters. 13 (20): 585–587. | Wikipedia - List of important publications in physics | null | null | null |
Bibcode:1964PhRvL..13..585G. doi:10.1103/PhysRevLett.13.585.Collectively these three papers (called the 1964 PRL symmetry breaking papers) formulated the concept of the Higgs mechanism. Also important later work done by t'Hooft.Gross, Wilczek & Politzer 1973 papers: Won the three researchers the Nobel Physics (2004) pr... | Wikipedia - List of important publications in physics | null | null | null |
(1995). An Introduction to Quantum Field Theory. Addison-Wesley Advanced Book Program. ISBN 978-0-201-50397-5.Standard graduate textbook in quantum field theory. | Wikipedia - List of important publications in physics | null | null | null |
Klein geometry, Erlangen programme symmetric space space form Maurer–Cartan form Examples hyperbolic space Gauss–Bolyai–Lobachevsky space Grassmannian Complex projective space Real projective space Euclidean space Stiefel manifold Upper half-plane Sphere | Wikipedia - List of differential geometry topics | null | null | null |
Klein's inequality states that the quantum relative entropy S ( ρ ‖ σ ) = Tr ρ ( log ρ − log σ ) . {\displaystyle S(\rho \|\sigma )=\operatorname {Tr} \rho (\log \rho -\log \sigma ).} is non-negative in general. It is zero if and only if ρ = σ. Proof Let ρ and σ have spectral decompositions ρ = ∑ i p i v i v i ∗ ... | Wikipedia - Quantum relative entropy | null | null | null |
{\displaystyle \rho =\sum _{i}p_{i}v_{i}v_{i}^{*}\;,\;\sigma =\sum _{i}q_{i}w_{i}w_{i}^{*}.} So log ρ = ∑ i ( log p i ) v i v i ∗ , log σ = ∑ i ( log q i ) w i w i ∗ . {\displaystyle \log \rho =\sum _{i}(\log p_{i})v_{i}v_{i}^{*}\;,\;\log \sigma =\sum _{i}(\log q_{i})w_{i}w_{i}^{*}.} | Wikipedia - Quantum relative entropy | null | null | null |
Direct calculation gives S ( ρ ‖ σ ) = ∑ k p k log p k − ∑ i , j ( p i log q j ) | v i ∗ w j | 2 {\displaystyle S(\rho \|\sigma )=\sum _{k}p_{k}\log p_{k}-\sum _{i,j}(p_{i}\log q_{j})|v_{i}^{*}w_{j}|^{2}} = ∑ i p i ( log p i − ∑ j log q j | v i ∗ w j | 2 ) {\displaystyle \qquad \quad \;=\sum _{i}p_{i}(\log p_{i... | Wikipedia - Quantum relative entropy | null | null | null |
Define ri = Σjqj Pi j. Then {ri} is a probability distribution. From the non-negativity of classical relative entropy, we have S ( ρ ‖ σ ) ≥ ∑ i p i log p i r i ≥ 0. {\displaystyle S(\rho \|\sigma )\geq \sum _{i}p_{i}\log {\frac {p_{i}}{r_{i}}}\geq 0.} The second part of the claim follows from the fact that, since -l... | Wikipedia - Quantum relative entropy | null | null | null |
Klinefelter syndrome: Klinefelter syndrome is caused by the presence of one or more extra copies of the X chromosome in a male's cells. Males with Klinefelter syndrome typically have one extra copy of the X chromosome in each cell, for a total of two X chromosomes and one Y chromosome (47,XXY). It is less common for af... | Wikipedia - Human X chromosome | null | null | null |
Each extra X chromosome lowers the child's IQ by about 15 points, which means that the average IQ in Klinefelter syndrome is in general in the normal range, although below average. When additional X and/or Y chromosomes are present in 48,XXXY, 48,XXYY, or 49,XXXXY, developmental delays and cognitive difficulties can be... | Wikipedia - Human X chromosome | null | null | null |
These cases are called mosaic 46,XY/47,XXY.Triple X syndrome (also called 47,XXX or trisomy X): This syndrome results from an extra copy of the X chromosome in each of a female's cells. Females with trisomy X have three X chromosomes, for a total of 47 chromosomes per cell. | Wikipedia - Human X chromosome | null | null | null |
The average IQ of females with this syndrome is 90, while the average IQ of unaffected siblings is 100. Their stature on average is taller than normal females. They are fertile and their children do not inherit the condition. | Wikipedia - Human X chromosome | null | null | null |
Females with more than one extra copy of the X chromosome (48, XXXX syndrome or 49, XXXXX syndrome) have been identified, but these conditions are rare.Turner syndrome: This results when each of a female's cells has one normal X chromosome and the other sex chromosome is missing or altered. The missing genetic material... | Wikipedia - Human X chromosome | null | null | null |
Turner syndrome can also occur if one of the sex chromosomes is partially missing or rearranged rather than completely missing. Some women with Turner syndrome have a chromosomal change in only some of their cells. These cases are called Turner syndrome mosaics (45,X/46,XX). | Wikipedia - Human X chromosome | null | null | null |
Klingons possess a robust and enduring biology as well as large and muscular statures. Klingons have been seen on multiple occasions possessing physical strength equal to or superior to that of Jem'Hadar and Hirogen, two other races possessing immense strength, and the half-human B'Elanna Torres proves more than a matc... | Wikipedia - Klingon | null | null | null |
Their rapid metabolism allows injured Klingons to heal quickly. All of this makes Klingons extremely hardy and difficult to kill, as necessitated by their aggressive nature, and resistant to physical trauma, environmental exposure, and illness. | Wikipedia - Klingon | null | null | null |
Klingons alone have a natural resistance to "the Phage," which plagues the Vidiians of the Delta Quadrant. Like Cardassians, they avoid cold temperatures. Klingons also have a heightened sense of smell as suggested in "Birthright, Part II" in The Next Generation, when Worf and a Klingon boy go hunting and can track an ... | Wikipedia - Klingon | null | null | null |
KmPlot is a mathematical function plotter released under the free GPL license. Includes a powerful parser and precision printing in correct scale. Simultaneously plot multiple functions and combine function terms to build new functions. Supports functions with parameters and functions in polar coordinates. Several grid... | Wikipedia - List of interactive geometry software | null | null | null |
Knee osteoarthritis and other joint pain are common complaints amongst obese individuals and are often a reason as to why exercise prescriptions such as walking are not continued after prescribed. To determine why an obese person might have more joint problems than a non-obese individual, the biomechanical parameters m... | Wikipedia - Obesity and walking | null | null | null |
Knitro offers four different optimization algorithms for solving optimization problems. Two algorithms are of the interior point type, and two are of the active set type. These algorithms are known to have fundamentally different characteristics; for example, interior point methods follow a path through the interior of... | Wikipedia - Artelys Knitro | null | null | null |
Knitro provides tools for solving optimization models (both linear and nonlinear) with binary or integer variables. The Knitro mixed integer programming (MIP) code offers three algorithms for mixed-integer nonlinear programming (MINLP): Nonlinear Branch and Bound Quesada Grossman algorithm Mixed-Integer Sequential Quad... | Wikipedia - Artelys Knitro | null | null | null |
Knitted mathematical objects include the Platonic solids, Klein bottles and Boy's surface. The Lorenz manifold and the hyperbolic plane have been crafted using crochet. Knitted and crocheted tori have also been constructed depicting toroidal embeddings of the complete graph K7 and of the Heawood graph. The crocheting o... | Wikipedia - Mathematics and fiber arts | null | null | null |
Knot theory is the study of mathematical knots. While inspired by knots that appear in daily life in shoelaces and rope, a mathematician's knot differs in that the ends are joined so that it cannot be undone. In precise mathematical language, a knot is an embedding of a circle in 3-dimensional Euclidean space, R 3 {\di... | Wikipedia - Algebraic Topology | null | null | null |
Knott (1977) uses the bijection between stack-sortable permutations and binary trees to define a numerical rank for each binary tree, and to construct efficient algorithms for computing the rank of a tree ("ranking") and for computing the tree with a given rank ("unranking"). Micheli & Rossin (2006) defined two edit op... | Wikipedia - Stack-sortable permutation | null | null | null |
Knowing that facial recognition technology statically struggle to recognize black women or transgender people, Elwes set out to "Queer the Dataset" through an open-sourced generative adversarial network (GAN). Elwes added a dataset of 1,000 photos of drag kings and queens into the GAN's 70,000 faces collected in a data... | Wikipedia - Jake Elwes | null | null | null |
Knowing that the quantum Fisher information is the convex roof of the variance times four, we obtain the relation which is stronger than the Heisenberg uncertainty relation. For a particle of spin- j , {\displaystyle j,} the following uncertainty relation holds where J l {\displaystyle J_{l}} are angular momentum compo... | Wikipedia - Wigner–Yanase skew information | null | null | null |
Knowing that the trace is an invariant, the rotation angle α {\displaystyle \alpha } for a proper orthogonal 3×3 rotation matrix A {\displaystyle A} is found by α = cos − 1 ( A 11 + A 22 + A 33 − 1 2 ) {\displaystyle \alpha =\cos ^{-1}\left({\frac {A_{11}+A_{22}+A_{33}-1}{2}}\right)} Using the principal arc-cosine, t... | Wikipedia - Spin axis | null | null | null |
Accordingly, A v = v {\displaystyle Av=v} , and the rotation axis therefore corresponds to an eigenvector of the rotation matrix associated with an eigenvalue of 1. As long as the rotation angle α {\displaystyle \alpha } is nonzero (i.e., the rotation is not the identity tensor), there is one and only one such directio... | Wikipedia - Spin axis | null | null | null |
Knowing that 1 is an eigenvalue, it follows that the remaining two eigenvalues are complex conjugates of each other, but this does not imply that they are complex—they could be real with double multiplicity. In the degenerate case of a rotation angle α = 180 ∘ {\displaystyle \alpha =180^{\circ }} , the remaining two ei... | Wikipedia - Spin axis | null | null | null |
A spectral analysis is not required to find the rotation axis. If n {\displaystyle n} denotes the unit eigenvector aligned with the rotation axis, and if α {\displaystyle \alpha } denotes the rotation angle, then it can be shown that 2 sin ( α ) n = { A 32 − A 23 , A 13 − A 31 , A 21 − A 12 } {\displaystyle 2\sin(\al... | Wikipedia - Spin axis | null | null | null |
On the other hand, if this vector has a zero magnitude, it means that sin ( α ) = 0 {\displaystyle \sin(\alpha )=0} . In other words, this vector will be zero if and only if the rotation angle is 0 or 180 degrees, and the rotation axis may be assigned in this case by normalizing any column of A + I {\displaystyle A+I... | Wikipedia - Spin axis | null | null | null |
Knowing the eigenvectors and eigenvalues inside the material, one have to calculate E r → = ( E r x , E r y , 0 ) {\displaystyle {\vec {E_{r}}}=(E_{rx},E_{ry},0)} the reflected electromagnetic vector usually detected in experiments. We use the continuity equations for E → {\displaystyle {\vec {E}}} and H → {\displaysty... | Wikipedia - Voigt Effect | null | null | null |
Knowing when a speech sound should be accurately produced helps parents and professionals determine when child may have an articulation disorder. There have been two traditional methods used to compare a child's articulation of speech sounds to chronological age. The first is comparing the number of correct responses o... | Wikipedia - Speech acquisition | null | null | null |
The second method consists of comparing an individual sound a child produces with developmental norms for that individual sound. The second method can be difficult when considering the differing normative data and other factors that affect typical speech development. Many norms are based on age expectations in which a ... | Wikipedia - Speech acquisition | null | null | null |
Knowledge about dinosaurs is derived from a variety of fossil and non-fossil records, including fossilized bones, feces, trackways, gastroliths, feathers, impressions of skin, internal organs and other soft tissues. Many fields of study contribute to our understanding of dinosaurs, including physics (especially biomech... | Wikipedia - Dinosaur | null | null | null |
Knowledge about the pharmacokinetics of oral progesterone has been complicated by the use of flawed analytical techniques. When progesterone is taken orally, due to first-pass metabolism, very high levels of its metabolites occur. Most previous studies have used a method known as immunoassay (IA) to measure progesteron... | Wikipedia - Pharmacokinetics of progesterone | null | null | null |
As a result, studies that have assessed the pharmacokinetics of oral progesterone using IA have reported falsely high progesterone levels and inaccurate dependent pharmacokinetic parameters.Comparative studies using reliable and exact methods such as liquid chromatography–mass spectrometry (LC–MS) and IA in conjunction... | Wikipedia - Pharmacokinetics of progesterone | null | null | null |
Knowledge gained during lunar outpost missions will be highly relevant to successful establishment of a Martian outpost. If the challenges posed by the long transit to Mars and the extended period of microgravity exposure can be met, the outpost phase should represent a much lower risk by comparison, since lunar outpos... | Wikipedia - Physiological effects in space | null | null | null |
Knowledge gained from science translates into engineering. Four examples are the construction and maintenance of facilities on polar ice caps, the establishment of snow runways, the design of snow tires and ski sliding surfaces. Buildings on snow foundations – The US Army Cold Regions Research and Engineering Laborator... | Wikipedia - Snow science | null | null | null |
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