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heated and then allowed to cool, promoting the crystallization process. Once formed, crystals are best observed under polarized light with a 200–1,000-fold magnification. This method requires basic laboratory equipment, including a microscope equipped for polarized light, test tubes, pipettes, a micro spirit-lamp or mi... | {
"page_id": 73473030,
"title": "Microcrystallization"
} |
and when rotated between crossed polarizers, they alternate between bright and dark every 90°. The extinction angle is the angle between a specific crystal axis and the filter's polarization plane when the crystal appears dark (in extinction). For instance, this method can be employed to distinguish between perlatolic ... | {
"page_id": 73473030,
"title": "Microcrystallization"
} |
The molecular formula C10H22O (molar mass: 158.28 g/mol, exact mass: 158.1671 u) may refer to: 1-Decanol 2-Propylheptanol (2PH) | {
"page_id": 23993352,
"title": "C10H22O"
} |
The instant center of rotation (also known as instantaneous velocity center, instantaneous center, or pole of planar displacement) of a body undergoing planar movement is a point that has zero velocity at a particular instant of time. At this instant, the velocity vectors of the other points in the body generate a circ... | {
"page_id": 18947076,
"title": "Instant centre of rotation"
} |
points A and B in the moving body and locate the corresponding points in the two positions; see the illustration. Construct the perpendicular bisectors to the two segments A1A2 and B1B2. The intersection P of these two bisectors is the pole of the planar displacement. Notice that A1 and A2 lie on a circle around P. Thi... | {
"page_id": 18947076,
"title": "Instant centre of rotation"
} |
2 − A y 1 A x 2 − A x 1 , tan τ B = B y 2 − B y 1 B x 2 − B x 1 {\displaystyle \tan \tau _{A}={\frac {A_{y}^{2}-A_{y}^{1}}{A_{x}^{2}-A_{x}^{1}}},\quad \tan \tau _{B}={\frac {B_{y}^{2}-B_{y}^{1}}{B_{x}^{2}-B_{x}^{1}}}} Find the position of P ( P x , P y ) {\displaystyle P\left(P_{x},P_{y}\right)} Method 1: Taking the ... | {
"page_id": 18947076,
"title": "Instant centre of rotation"
} |
center of the rotation are the first two components of the solution vector ( P x P y d A d B ) = 1 sin ( τ A − τ B ) ( ( B y m − A y m ) sin τ A sin τ B + B x m sin τ A cos τ B − A x m cos τ A sin τ B ( A x m − B x m ) cos τ A cos τ B + A y m sin τ A cos τ B − B y m cos τ A sin τ B ( B x m − A... | {
"page_id": 18947076,
"title": "Instant centre of rotation"
} |
The equation of the bisector of B1B2 is y − B y m = tan τ B ( x − B x m ) {\displaystyle y-B_{y}^{m}=\tan \tau _{B}\left(x-B_{x}^{m}\right)} These two bisectors intersect at P ( P x , P y ) {\displaystyle P\left(P_{x},P_{y}\right)} so a system of 2 equations with 2 unknowns and coefficients can be written { P y − A y... | {
"page_id": 18947076,
"title": "Instant centre of rotation"
} |
wheel rolling without slipping == Consider the planar movement of a circular wheel rolling without slipping on a linear road; see sketch 3. The wheel rotates around its axis M, which translates in a direction parallel to the road. The point of contact P of the wheel with road does not slip, which means the point P has ... | {
"page_id": 18947076,
"title": "Instant centre of rotation"
} |
All points that are a distance equal to the radius of the wheel 'r' from point P move at the same speed as the point M but in different directions. This is shown for a point on the wheel that has the same speed as M but moves in the direction tangent to the circle around P. == Relative center of rotation for two contac... | {
"page_id": 18947076,
"title": "Instant centre of rotation"
} |
Considering first link P1-A: all points on this link, including point A, rotate around point P1. Since P1 is the only point not moving in the given plane it may be called the instant center of rotation for this link. Point A, at distance P1-A from P1, moves in a circular motion in a direction perpendicular to the link ... | {
"page_id": 18947076,
"title": "Instant centre of rotation"
} |
perpendicular to this connection. The speed is proportional to the distance to point P. Continuing this approach with the two links P1-A and P2-B rotating around their own instant centers of rotation the centrode for instant center of rotation P may be determined. From this the path of movement for C or any other point... | {
"page_id": 18947076,
"title": "Instant centre of rotation"
} |
Plakophilin are proteins of the cytoskeleton. They are involved in regulating the adhesive activity of cadherin. The three types of plakophilin proteins found in humans are PKP1, PKP2, and PKP3; all exhibiting dual localization in the nucleus as well as desmosomes. Genes include: PKP1 PKP2 PKP3 == See also == List of c... | {
"page_id": 19209229,
"title": "Plakophilin"
} |
In metallurgy, alpha case is the oxygen-enriched surface phase that occurs when titanium and its alloys are exposed to heated air or oxygen. Alpha case is hard and brittle, and tends to create a series of microcracks that will reduce the metal's performance and its fatigue properties. Alpha case can be minimized or avo... | {
"page_id": 25828373,
"title": "Alpha case"
} |
In genetics, macrosatellites are the largest of the tandem repeats within DNA. Each macrosatellite repeat typically is several thousand base pairs in length, and the entire repeat array often spans hundreds of kilobases. Reduced number of repeats on chromosome 4 (D4Z4 repeats) causes euchromatization of local DNA and i... | {
"page_id": 67509276,
"title": "Macrosatellite"
} |
In electrochemistry, the working electrode is the electrode in an electrochemical system on which the reaction of interest is occurring. The working electrode is often used in conjunction with an auxiliary electrode, and a reference electrode in a three-electrode system. Depending on whether the reaction on the electro... | {
"page_id": 14097440,
"title": "Working electrode"
} |
AdaBoost (short for Adaptive Boosting) is a statistical classification meta-algorithm formulated by Yoav Freund and Robert Schapire in 1995, who won the 2003 Gödel Prize for their work. It can be used in conjunction with many types of learning algorithm to improve performance. The output of multiple weak learners is co... | {
"page_id": 1645603,
"title": "AdaBoost"
} |
( x ) = ∑ t = 1 T f t ( x ) {\displaystyle F_{T}(x)=\sum _{t=1}^{T}f_{t}(x)} where each f t {\displaystyle f_{t}} is a weak learner that takes an object x {\displaystyle x} as input and returns a value indicating the class of the object. For example, in the two-class problem, the sign of the weak learner's output ident... | {
"page_id": 1645603,
"title": "AdaBoost"
} |
of samples with large weights. == Derivation == This derivation follows Rojas (2009): Suppose we have a data set { ( x 1 , y 1 ) , … , ( x N , y N ) } {\displaystyle \{(x_{1},y_{1}),\ldots ,(x_{N},y_{N})\}} where each item x i {\displaystyle x_{i}} has an associated class y i ∈ { − 1 , 1 } {\displaystyle y_{i}\in \{-1,... | {
"page_id": 1645603,
"title": "AdaBoost"
} |
C_{m}} as the sum of its exponential loss on each data point, given as follows: E = ∑ i = 1 N e − y i C m ( x i ) = ∑ i = 1 N e − y i C ( m − 1 ) ( x i ) e − y i α m k m ( x i ) {\displaystyle E=\sum _{i=1}^{N}e^{-y_{i}C_{m}(x_{i})}=\sum _{i=1}^{N}e^{-y_{i}C_{(m-1)}(x_{i})}e^{-y_{i}\alpha _{m}k_{m}(x_{i})}} Letting w i... | {
"page_id": 1645603,
"title": "AdaBoost"
} |
k_{m}} is ∑ y i ≠ k m ( x i ) w i ( m ) {\textstyle \sum _{y_{i}\neq k_{m}(x_{i})}w_{i}^{(m)}} , we see that the k m {\displaystyle k_{m}} that minimizes E {\displaystyle E} is the one in the set { k 1 , … , k L } {\displaystyle \{k_{1},\ldots ,k_{L}\}} that minimizes ∑ y i ≠ k m ( x i ) w i ( m ) {\textstyle \sum _{y_... | {
"page_id": 1645603,
"title": "AdaBoost"
} |
∑ i = 1 N w i ( m ) {\displaystyle \epsilon _{m}={\frac {\sum _{y_{i}\neq k_{m}(x_{i})}w_{i}^{(m)}}{\sum _{i=1}^{N}w_{i}^{(m)}}}} , so it follows that: α m = 1 2 ln ( 1 − ϵ m ϵ m ) {\displaystyle \alpha _{m}={\frac {1}{2}}\ln \left({\frac {1-\epsilon _{m}}{\epsilon _{m}}}\right)} which is the negative logit function ... | {
"page_id": 1645603,
"title": "AdaBoost"
} |
ϵ m ) {\displaystyle \alpha _{m}={\frac {1}{2}}\ln \left({\frac {1-\epsilon _{m}}{\epsilon _{m}}}\right)} , and finally use this to improve the boosted classifier C m − 1 {\displaystyle C_{m-1}} to C m = C ( m − 1 ) + α m k m {\displaystyle C_{m}=C_{(m-1)}+\alpha _{m}k_{m}} . == Statistical understanding of boosting ==... | {
"page_id": 1645603,
"title": "AdaBoost"
} |
equivalent to recalculating the error on F t ( x ) {\displaystyle F_{t}(x)} after each stage. There is a lot of flexibility allowed in the choice of loss function. As long as the loss function is monotonic and continuously differentiable, the classifier is always driven toward purer solutions. Zhang (2004) provides a l... | {
"page_id": 1645603,
"title": "AdaBoost"
} |
gradient descent analogy, the output of the classifier for each training point is considered a point ( F t ( x 1 ) , … , F t ( x n ) ) {\displaystyle \left(F_{t}(x_{1}),\dots ,F_{t}(x_{n})\right)} in n-dimensional space, where each axis corresponds to a training sample, each weak learner h ( x ) {\displaystyle h(x)} co... | {
"page_id": 1645603,
"title": "AdaBoost"
} |
x ) {\displaystyle h_{t}(x)} that minimizes ϵ t {\displaystyle \epsilon _{t}} , the weighted sum error for misclassified points ϵ t = ∑ h t ( x i ) ≠ y i i = 1 n w i , t {\displaystyle \epsilon _{t}=\sum _{\stackrel {i=1}{h_{t}(x_{i})\neq y_{i}}}^{n}w_{i,t}} Choose α t = 1 2 ln ( 1 − ϵ t ϵ t ) {\displaystyle \alpha _... | {
"page_id": 1645603,
"title": "AdaBoost"
} |
minimizer for e − y ( F t − 1 ( x ) + f t ( p ( x ) ) ) {\displaystyle e^{-y\left(F_{t-1}(x)+f_{t}(p(x))\right)}} for some fixed p ( x ) {\displaystyle p(x)} (typically chosen using weighted least squares error): f t ( x ) = 1 2 ln ( x 1 − x ) {\displaystyle f_{t}(x)={\frac {1}{2}}\ln \left({\frac {x}{1-x}}\right)} .... | {
"page_id": 1645603,
"title": "AdaBoost"
} |
p t ( x i ) ) {\displaystyle p_{t}(x_{i})(1-p_{t}(x_{i}))} becomes very small and the z term, which is large for misclassified samples, can become numerically unstable, due to machine precision rounding errors. This can be overcome by enforcing some limit on the absolute value of z and the minimum value of w === Gentle... | {
"page_id": 1645603,
"title": "AdaBoost"
} |
positive samples is mislabeled as negative, and all samples marked as negative after each stage are discarded. If 50% of negative samples are filtered out by each stage, only a very small number of objects would pass through the entire classifier, reducing computation effort. This method has since been generalized, wit... | {
"page_id": 1645603,
"title": "AdaBoost"
} |
margin-trimming: when the coefficient, or the contribution to the total test error, of some weak classifier falls below a certain threshold, that classifier is dropped. Margineantu & Dietterich suggested an alternative criterion for trimming: weak classifiers should be selected such that the diversity of the ensemble i... | {
"page_id": 1645603,
"title": "AdaBoost"
} |
Well-known inorganic and organometallic compounds and reagents that are named after individuals include: Adams' catalyst (proposed to be PtOx) Adamsite (NH(C6H4)2AsCl) Adkins catalyst (Cu2Cr2O5) Attenburrow's Oxide (MnO2) Arduengo carbene (class of compounds) Baeyer's reagent (KMnO4(aq)) Benedict's reagent Bobbitt's sa... | {
"page_id": 32709669,
"title": "List of inorganic compounds named after people"
} |
reagent (K2HgI4) Normant reagents (RMgX + CuX) Nugent's reagent (TiCp2Cl) Nysted reagent (ZnCH2(ZnBr)2.THF) Pearlman's catalyst (proposed to be Pd(OH)2/C) Péligot's salt (KCrO3Cl) Periana catalyst (Pt(2,2'-Bipyrimidine)Cl2) Petasis reagent (Cp2TiMe2) Peyrone's salt (cis-PtCl2(NH3)2) Piers' borane (HB(C6F5)2) Piers' cat... | {
"page_id": 32709669,
"title": "List of inorganic compounds named after people"
} |
Substructure search (SSS) is a method to retrieve from a database only those chemicals matching a pattern of atoms and bonds which a user specifies. It is an application of graph theory, specifically subgraph matching in which the query is a hydrogen-depleted molecular graph. The mathematical foundations for the method... | {
"page_id": 5643301,
"title": "Substructure search"
} |
for substances which contain three atoms and two single bonds connected as C–C–O. Propanol is a "hit", as is diethyl ether, with C–C–O–C–C. If a user wished to limit the hits to alcohols, then the query structure would have to be drawn with an "explicit hydrogen", as C–C–O–H and ether would no longer match. In mathemat... | {
"page_id": 5643301,
"title": "Substructure search"
} |
is identical for all these substances, as it encodes the molecular graph. == Query interfaces and search algorithms == Most substructure search systems present the user with a graphical user interface with a chemical structure drawing component. Query structures may contain bonding patterns such as "single/aromatic" or... | {
"page_id": 5643301,
"title": "Substructure search"
} |
chemicals can also be searched that way. Suppliers of chemicals as synthesis intermediates or for high-throughput screening routinely provide search interfaces. Currently, the largest database that can be freely searched by the public is the ZINC database, which is claimed to contain over 37 billion commercially availa... | {
"page_id": 5643301,
"title": "Substructure search"
} |
requirements had been partially met as early as 1881 when Friedrich Konrad Beilstein introduced the Handbuch der organischen Chemie (Handbook of Organic Chemistry) which carefully classified known chemicals in a very systematic manner so that all examples containing a given heterocycle would be located together. In 190... | {
"page_id": 5643301,
"title": "Substructure search"
} |
to implementation of systems such as MACCS.: 73–77 This commercial system from MDL Information Systems made use of an algorithm specifically designed for storage and search within groups of chemicals that differed only in their stereochemistry. A review of the many systems available by the mid-1980s pointed out that "m... | {
"page_id": 5643301,
"title": "Substructure search"
} |
Anna Maria Stasto is a Polish particle physicist and a Professor of Physics at Pennsylvania State University. Stasto studied Physics at Jagiellonian University, graduating in 1996. She completed her PhD in 1999, which was awarded jointly by the Institute of Nuclear Physics of the Polish Academy of Sciences and Durham U... | {
"page_id": 79830055,
"title": "Anna Stasto"
} |
Jordan A. Goodman is an American physicist whose expertise is in particle astrophysics. He is the former Chair of Physics Department, at the University of Maryland. In 2009, Goodman was elected a fellow of the American Association for the Advancement of Science. In 2017 he was awarded the Yodh Prize. == Education == Un... | {
"page_id": 38280232,
"title": "Jordan A. Goodman"
} |
flux from neutralino annihilations in the Sun with the IceCube 22-string detector. (R. Abbasi et al.) Phys. Rev. Lett. 102:201302,(2009) Determination of the Atmospheric Neutrino Flux and Searches for New Physics with AMANDA-II. (R. Abbasi et al.) Phys. Rev. D 79:102005,(2009) Search for Point Sources of High Energy Ne... | {
"page_id": 38280232,
"title": "Jordan A. Goodman"
} |
Myconet was a peer-reviewed mycological journal intended for the documentation of selected mycosystematic files published on the Internet. The journal was published from 1997 to 2007. == References == | {
"page_id": 23469098,
"title": "Myconet"
} |
The UCSC Genome Browser is an online and downloadable genome browser hosted by the University of California, Santa Cruz (UCSC). It is an interactive website offering access to genome sequence data from a variety of vertebrate and invertebrate species and major model organisms, integrated with a large collection of alig... | {
"page_id": 24517676,
"title": "UCSC Genome Browser"
} |
to enhance sequence alignment and coordinate conversion between different genome assemblies. === Expansion and Feature Enhancements (2004–2010) === Between 2004 and 2010, the UCSC Genome Browser incorporated numerous additional genomes, including those of rat, chicken, dog, and chimpanzee, among others. The development... | {
"page_id": 24517676,
"title": "UCSC Genome Browser"
} |
spatial transcriptomics. The browser has also integrated data from the Genotype-Tissue Expression (GTEx) project, providing visualization resources for gene expression across various human tissues. The browser now hosts over 180 genome assemblies from more than 100 species, including the fully telomere-to-telomere huma... | {
"page_id": 24517676,
"title": "UCSC Genome Browser"
} |
and include assemblies that are not hosted natively on it. There, users can load and annotate unique assemblies for which UCSC does not provide an annotation database. A full list of species and their assemblies can be viewed in the GenArk Portal, including 2,589 assemblies hosted by both UCSC Genome Browser database a... | {
"page_id": 24517676,
"title": "UCSC Genome Browser"
} |
the locations of the mRNAs, gene predictions, etc. Blocks of color along the coordinate axis show the locations of the alignments of the various data types. The ability to show this large variety of data types on a single coordinate axis makes the browser a handy tool for the vertical integration of the data. To find a... | {
"page_id": 24517676,
"title": "UCSC Genome Browser"
} |
entire chromosome (human chr1 = 245 million bases, Mb) with full annotation tracks. Researchers can display a single gene, a single exon, or an entire chromosome band, showing dozens or hundreds of genes and any combination of the many annotations. A convenient drag-and-zoom feature allows the user to choose any region... | {
"page_id": 24517676,
"title": "UCSC Genome Browser"
} |
advanced configuration. === Tracks === Below the displayed images of the UCSC Genome browser are eleven categories of additional tracks that can be selected and displayed alongside the original data. Researchers can select tracks which best represent their query to allow for more applicable data to be displayed dependi... | {
"page_id": 24517676,
"title": "UCSC Genome Browser"
} |
all overlapping 11-mers stepping by 5 unless there are repeats. Using BLAT on protein finds sequences ≥ 80% similarity of amino acids of lengths ≥ 20. It indexes the genome in memory of all overlapping 4-mers stepping 5 unless there are repeats. BLAT was written by Jim Kent, more information about the software can be f... | {
"page_id": 24517676,
"title": "UCSC Genome Browser"
} |
not mapped, use the closest mapped base. == Python APIs == The UCSC Genome Browser provides Python-compatible interfaces that allow researchers to programmatically access genomic data and annotations. These APIs support automation, integration into computational workflows, and large-scale analysis tasks, enhancing acce... | {
"page_id": 24517676,
"title": "UCSC Genome Browser"
} |
MySQL or Table Browser advanced queries) No built-in authentication for sensitive data (e.g., private tracks) For large datasets or bulk analysis, users may still prefer downloading entire tracks or working with the UCSC Genome Browser database locally. === Resources and Documentation === UCSC Genome Browser REST API D... | {
"page_id": 24517676,
"title": "UCSC Genome Browser"
} |
Membrane-introduction mass spectrometry (MIMS) is a method of introducing analytes into the mass spectrometer's vacuum chamber via a semi-permeable membrane. Usually a thin, gas-permeable, hydrophobic membrane is used, for example polydimethylsiloxane. Samples can be almost any fluid including water, air or sometimes e... | {
"page_id": 2432047,
"title": "Membrane-introduction mass spectrometry"
} |
The α-factor is a dimensionless quantity used to predict the solid–liquid interface type of a material during solidification. It was introduced by physicist Kenneth A. Jackson in 1958. In his model, crystal growth with larger values of α is smooth, whereas crystals growing at smaller α (below the threshold value of 2) ... | {
"page_id": 32185392,
"title": "Alpha factor"
} |
Ten Horn's sign is a clinical sign used for diagnosing appendicitis, particularly in older adults. == Method == The patient lies on a couch. The examiner gently stretches the right spermatic cord using the thumb and index finger right about the testis in the right scrotum. For a patient with appendicitis, this causes p... | {
"page_id": 66919473,
"title": "Ten Horn's sign"
} |
In chemistry, transfer hydrogenation is a chemical reaction involving the addition of hydrogen to a compound from a source other than molecular H2. It is applied in laboratory and industrial organic synthesis to saturate organic compounds and reduce ketones to alcohols, and imines to amines. It avoids the need for high... | {
"page_id": 4856882,
"title": "Transfer hydrogenation"
} |
transition metal-based systems. The catalytic asymmetric hydrogenation of ketones was demonstrated with ruthenium-based complexes of BINAP. Even though the BINAP-Ru dihalide catalyst could reduce functionalized ketones, the hydrogenation of simple ketones remained unsolved. This challenge was solved with precatalysts o... | {
"page_id": 4856882,
"title": "Transfer hydrogenation"
} |
the biochemically relevant coenzyme NADH. In the catalytic cycle for this reaction the amine and the aldehyde first form an iminium ion, then proton transfer is followed by hydrolysis of the iminium bond regenerating the catalyst. By adopting a chiral imidazolidinone MacMillan organocatalyst an enantioselectivity of 81... | {
"page_id": 4856882,
"title": "Transfer hydrogenation"
} |
The word chemistry derives from the word alchemy, which is found in various forms in European languages. The word 'alchemy' itself derives from the Arabic word al-kīmiyāʾ (الكيمياء), wherein al- is the definite article 'the'. The ultimate origin of the word is uncertain, but the Arabic term kīmiyāʾ (كيمياء) is likely d... | {
"page_id": 7740467,
"title": "Etymology of chemistry"
} |
the Egyptologist Wallis Budge, the Arabic word al-kīmiyaʾ actually means "the Egyptian [science]", borrowing from the Coptic word for "Egypt", kēme (or its equivalent in the Mediaeval Bohairic dialect of Coptic, khēme). This Coptic word derives from Demotic kmỉ, itself from ancient Egyptian kmt. The ancient Egyptian wo... | {
"page_id": 7740467,
"title": "Etymology of chemistry"
} |
is the science of matter at the atomic to molecular scale, dealing primarily with collections of atoms, such as molecules, crystals, and metals. == From alchemy to chemistry == Later medieval Latin had alchimia / alchymia "alchemy", alchimicus "alchemical", and alchimista "alchemist". The mineralogist and humanist Geor... | {
"page_id": 7740467,
"title": "Etymology of chemistry"
} |
chemical, there was corresponding shift from alchimical to alchemical, which occurred in the early 19th century. In French, Italian, Spanish and Russian today it continues to be spelled with an i as in for example Italian chimica. == See also == History of chemistry History of science History of thermodynamics List of ... | {
"page_id": 7740467,
"title": "Etymology of chemistry"
} |
In thermodynamics, the entropy of mixing is the increase in the total entropy when several initially separate systems of different composition, each in a thermodynamic state of internal equilibrium, are mixed without chemical reaction by the thermodynamic operation of removal of impermeable partition(s) between them, f... | {
"page_id": 3021875,
"title": "Entropy of mixing"
} |
is done. The entropy of mixing is entirely accounted for by the diffusive expansion of each material into a final volume not initially accessible to it. In the general case of mixing non-ideal materials, however, the total final common volume may be different from the sum of the separate initial volumes, and there may ... | {
"page_id": 3021875,
"title": "Entropy of mixing"
} |
species. For example, two ideal gases, at the same temperature and pressure, are initially separated by a dividing partition. Upon removal of the dividing partition, they expand into a final common volume (the sum of the two initial volumes), and the entropy of mixing Δ S m i x {\displaystyle \Delta S_{mix}} is given b... | {
"page_id": 3021875,
"title": "Entropy of mixing"
} |
an ideal gas mixture or an ideal solution, there is no enthalpy of mixing ( Δ H mix {\displaystyle \Delta H_{\text{mix}}\,} ), so that the Gibbs free energy of mixing is given by the entropy term only: Δ G mix = − T Δ S mix {\displaystyle \Delta G_{\text{mix}}=-T\Delta S_{\text{mix}}} For an ideal solution, the Gibbs f... | {
"page_id": 3021875,
"title": "Entropy of mixing"
} |
the entropy of mixing Δ S mix {\displaystyle \Delta S_{\text{mix}}} is positive and favors mixing of the pure components. The curvature of Δ S mix {\displaystyle \Delta S_{\text{mix}}} as a function of x {\displaystyle x} is given by the second derivative ( ∂ 2 Δ S mix ∂ x 2 ) T , P = − n R ( 1 x + 1 1 − x ) {\displays... | {
"page_id": 3021875,
"title": "Entropy of mixing"
} |
negative for mixing of the two phases below 19 °C and positive above this temperature. Therefore, Δ S mix = − ( ∂ Δ G mix ∂ T ) P {\displaystyle \Delta S_{\text{mix}}=-\left({\frac {\partial \Delta G_{\text{mix}}}{\partial T}}\right)_{P}} is negative for mixing of these two equilibrium phases. This is due to the format... | {
"page_id": 3021875,
"title": "Entropy of mixing"
} |
do, including close packing.) This is a crystal-like conceptual model to identify the molecular centers of mass. If the two phases are liquids, there is no spatial uncertainty in each one individually. (This is, of course, an approximation. Liquids have a "free volume". This is why they are (usually) less dense than so... | {
"page_id": 3021875,
"title": "Entropy of mixing"
} |
k = m ln m − m + 1 ≈ m ln m − m {\displaystyle \ln m!=\sum _{k}\ln k\approx \int _{1}^{m}dk\ln k=m\ln m-m+1\approx m\ln m-m} , the result is Δ S m i x = − k B [ N 1 ln ( N 1 / N ) + N 2 ln ( N 2 / N ) ] = − k B N [ x 1 ln x 1 + x 2 ln x 2 ] {\displaystyle \Delta S_{mix}=-k_{\text{B}}[N_{1}\ln(N_{1}/N)+N_{2}... | {
"page_id": 3021875,
"title": "Entropy of mixing"
} |
x_{i}=-nR\sum _{i=1}^{r}x_{i}\ln x_{i}} The Flory–Huggins solution theory is an example of a more detailed model along these lines. === Relationship to information theory === The entropy of mixing is also proportional to the Shannon entropy or compositional uncertainty of information theory, which is defined without re... | {
"page_id": 3021875,
"title": "Entropy of mixing"
} |
again obtain the entropy of mixing on multiplying by the Boltzmann constant k B {\displaystyle k_{\text{B}}} . Δ S mix = − N k B ∑ i = 1 r x i ln x i {\displaystyle \Delta S_{\text{mix}}=-Nk_{\text{B}}\sum _{i=1}^{r}x_{i}\ln x_{i}} So thermodynamic entropy with r chemical species with a total of N particles has a par... | {
"page_id": 3021875,
"title": "Entropy of mixing"
} |
subset of occupied cells is not the same at different times. But only when there is real mixing and an occupied cell is found do we ask which kind of molecule is there. See also: Gibbs paradox, in which it would seem that "mixing" two samples of the same gas would produce entropy. === Application to solutions === If th... | {
"page_id": 3021875,
"title": "Entropy of mixing"
} |
the entropy of mixing at prescribed common temperature and pressure has nothing to do with mixing in the sense of intermingling and interactions of molecular species, but is only to do with expansion into the common volume.: 273 According to Fowler and Guggenheim (1939/1965), the conflating of the just-mentioned two me... | {
"page_id": 3021875,
"title": "Entropy of mixing"
} |
volume and changing partial volumes, with mechanically controlled varying pressure, and constant temperature ==== An experimental demonstration may be considered. The two distinct gases, in a cylinder of constant total volume, are at first separated by two contiguous pistons made respectively of two suitably specific i... | {
"page_id": 3021875,
"title": "Entropy of mixing"
} |
difference in constitutive properties between the two species yields a thermodynamically recognized process of transfer with mixing, and a possibly considerable entropy change, namely the entropy of mixing. The "paradox" arises because any detectable constitutive distinction, no matter how slight, can lead to a conside... | {
"page_id": 3021875,
"title": "Entropy of mixing"
} |
infinite time, in view of the nature of thermodynamic equilibrium. Even the slightest departure from ideality, as assessed over a finite time, would extend to utter non-ideality, as assessed over a practically infinite time. Such quantum phenomena as tunneling ensure that nature does not allow such membrane ideality as... | {
"page_id": 3021875,
"title": "Entropy of mixing"
} |
Synizesis refers to a phenomenon sometimes observed in one of the subphases of meiosis. This phenomenon, sometimes referred to as a "synizetic knot", and contrasted with the chromosome "bouquet" more typically observed, is characterized by the localization of the meiotic chromosomes in a tight clump on one side of the ... | {
"page_id": 28777526,
"title": "Synizesis (biology)"
} |
In bioinformatics, lncRNAdb is a biological database of Long non-coding RNAs The database focuses on those RNAs which have been experimentally characterised with a biological function. The database currently holds over 290 lncRNAs from around 60 species. Example lncRNAs in the database are HOTAIR and Xist. == Reference... | {
"page_id": 31202359,
"title": "LncRNAdb"
} |
In chemical physics and physical chemistry, chemical affinity is the electronic property by which dissimilar chemical species are capable of forming chemical compounds. Chemical affinity can also refer to the tendency of an atom or compound to combine by chemical reaction with atoms or compounds of unlike composition. ... | {
"page_id": 7225,
"title": "Chemical affinity"
} |
used in particular by the Swedish chemist Torbern Olof Bergman throughout his book De attractionibus electivis (1775). Affinity theories were used in one way or another by most chemists from around the middle of the 18th century into the 19th century to explain and organise the different combinations into which substan... | {
"page_id": 7225,
"title": "Chemical affinity"
} |
to students and its visual arrangement was often combined with other kinds diagrams. Joseph Black, for example, used the table in combination with chiastic and circlet diagrams to visualise the core principles of chemical affinity. Affinity tables were used throughout Europe until the early 19th century when they were ... | {
"page_id": 7225,
"title": "Chemical affinity"
} |
the Belgian mathematician and physicist Théophile de Donder derived a relation between affinity and the Gibbs free energy of a chemical reaction. Through a series of derivations, de Donder showed that if we consider a mixture of chemical species with the possibility of chemical reaction, it can be proven that the follo... | {
"page_id": 7225,
"title": "Chemical affinity"
} |
The molecular formula C6H4Cl2O could refer to: 2,3-Dichlorophenol 2,4-Dichlorophenol 2,5-Dichlorophenol 2,6-Dichlorophenol 3,4-Dichlorophenol 3,5-Dichlorophenol | {
"page_id": 23993412,
"title": "C6H4Cl2O"
} |
Mating pool is a concept used in evolutionary algorithms and means a population of parents for the next population. The mating pool is formed by candidate solutions that the selection operators deem to have the highest fitness in the current population. Solutions that are included in the mating pool are referred to as ... | {
"page_id": 1514566,
"title": "Mating pool"
} |
== Several methods can be applied to create a mating pool. All of these processes involve the selective breeding of a particular number of individuals within a population. There are multiple criteria that can be employed to determine which individuals make it into the mating pool and which are left behind. The selectio... | {
"page_id": 1514566,
"title": "Mating pool"
} |
as parents. In ranking selection all the individuals are sorted based on their fitness values. Then, the selection of the parents is made according to the rank of the candidates. Every individual has a chance of being chosen, but higher ranked ones are favored === Threshold based selection === The last type of selectio... | {
"page_id": 1514566,
"title": "Mating pool"
} |
The Santa Fe Trail problem is a genetic programming exercise in which artificial ants search for food pellets according to a programmed set of instructions. The layout of food pellets in the Santa Fe Trail problem has become a standard for comparing different genetic programming algorithms and solutions. One method for... | {
"page_id": 31726662,
"title": "Santa Fe Trail problem"
} |
The molecular formula C2Cl2F4 (molar mass: 170.92 g/mol) may refer to: 1,1-Dichlorotetrafluoroethane 1,2-Dichlorotetrafluoroethane | {
"page_id": 23993415,
"title": "C2Cl2F4"
} |
The Fradkin tensor, or Jauch-Hill-Fradkin tensor, named after Josef-Maria Jauch and Edward Lee Hill and David M. Fradkin, is a conservation law used in the treatment of the isotropic multidimensional harmonic oscillator in classical mechanics. For the treatment of the quantum harmonic oscillator in quantum mechanics, i... | {
"page_id": 77405256,
"title": "Fradkin tensor"
} |
: F i j L j = 0 {\displaystyle F_{ij}L_{j}=0} contracting the Fradkin tensor with the displacement vector gives the relationship x i F i j x j = E x → 2 − L → 2 2 m {\displaystyle x_{i}F_{ij}x_{j}=E{\vec {x}}^{2}-{\frac {{\vec {L}}^{2}}{2m}}} . The 5 independent components of the Fradkin tensor and the 3 components of ... | {
"page_id": 77405256,
"title": "Fradkin tensor"
} |
H}{\partial x_{k}}}\right)+{\frac {\partial A}{\partial t}}} , so for the Fradkin tensor of the harmonic oscillator, d F i j d t = 1 2 ω 2 ∑ k ( ( x j δ i k + x i δ j k ) p k − ( p j δ i k + p i δ j k ) x k ) = 0. {\displaystyle {\frac {\mathrm {d} F_{ij}}{\mathrm {d} t}}={\frac {1}{2}}\omega ^{2}\sum _{k}{\Big (}(x_{j... | {
"page_id": 77405256,
"title": "Fradkin tensor"
} |
Time–space compression (also known as space–time compression and time–space distanciation) is an idea referring to the altering of the qualities of space–time and the relationship between space and time that is a consequence of the expansion of capital. It is rooted in Karl Marx's notion of the "annihilation of space b... | {
"page_id": 3742793,
"title": "Time–space compression"
} |
World War, and the end of the 20th century. In both of these time periods, according to Jon May and Nigel Thrift, "there occurred a radical restructuring in the nature and experience of both time and space ... both periods saw a significant acceleration in the pace of life concomitant with a dissolution or collapse of ... | {
"page_id": 3742793,
"title": "Time–space compression"
} |
of such things as equal distribution or diversity are potentials of capitalism itself in its abundant and diverse productive powers. This initial perspective misfires however, when forms of society such as modernity and subsequently postmodernism take itself as the true whole of life for being oppositional to capitalis... | {
"page_id": 3742793,
"title": "Time–space compression"
} |
A decision stump is a machine learning model consisting of a one-level decision tree. That is, it is a decision tree with one internal node (the root) which is immediately connected to the terminal nodes (its leaves). A decision stump makes a prediction based on the value of just a single input feature. Sometimes they ... | {
"page_id": 9903179,
"title": "Decision stump"
} |
Continuous foam separation is a chemical process closely related to foam fractionation in which foam is used to separate components of a solution when they differ in surface activity. In any solution, surface active components tend to adsorb to gas-liquid interfaces while surface inactive components stay within the bul... | {
"page_id": 36052045,
"title": "Continuous foam separation"
} |
commonly used for decades. Protein skimmers are one example of foam separation used in saltwater aquariums. The earliest documents pertaining to foam separation is dated back to 1959, when Robert Schnepf and Elmer Gaden, Jr. studied the effects of pH and concentration on the separation of bovine serum albumin from solu... | {
"page_id": 36052045,
"title": "Continuous foam separation"
} |
increases; this increases surface tension at the liquid-vapor interface. Surface tension describes how difficult it is to extend the area of a surface. If surface tension is high, there is a large free energy required to increase the surface area. The surface of the bubbles will contract due to this increased surface t... | {
"page_id": 36052045,
"title": "Continuous foam separation"
} |
equation. The pressure is greater on the concave side of the liquid lamellae (the inside of the bubble) with radius, R, dependent on the pressure differential. For spherical bubbles in a wet foam and standard surface tension γ°, the equation for the change in pressure is as follows: Δ P = 2 γ ∘ R {\displaystyle \Delta ... | {
"page_id": 36052045,
"title": "Continuous foam separation"
} |
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