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Genome informatics-Applications-Biomolecular systems that can process information are sought for computational applications, because of their potential for parallelism and miniaturization and because their biocompatibility also makes them suitable for future biomedical applications. DNA has been used to design machines... | milkshake721/2.1M-wiki-STEM |
Projective Set (game)-Projective Set (game)-Projective Set (sometimes shortened to ProSet) is a real-time card game derived from the older game Set.
The deck contains cards consisting of colored dots; some cards are laid out on the table and players attempt to find "Sets" among them.
The word projective comes from the ... | milkshake721/2.1M-wiki-STEM |
Projective Set (game)-Rules-A Projective Set card has six binary attributes, or bits, generally represented by colored dots. For each color of dot, each card either has that dot or does not.
There is one card for each possible combination of dots except the combination of no dots at all, making 63 cards total.
Three c... | milkshake721/2.1M-wiki-STEM |
Projective Set (game)-Mathematics-The cards of a Projective Set deck can be thought of as nonzero vectors in the finite vector space F26 The collection of all such vectors is the finite projective space with order 2 and dimension 5.
Three cards form a set if and only if the corresponding points are collinear in that sp... | milkshake721/2.1M-wiki-STEM |
TOLLIP-TOLLIP-Toll interacting protein, also known as TOLLIP, is an inhibitory adaptor protein that in humans is encoded by the TOLLIP gene. | milkshake721/2.1M-wiki-STEM |
TOLLIP-Function and regulation-It is an inhibitory adaptor protein within Toll-like receptors (TLR). The TLR pathway is a part of the innate immune system that recognizes structurally conserved molecular patterns of microbial pathogens, leading to an inflammatory immune response. Tollip interacts with cellular and sub... | milkshake721/2.1M-wiki-STEM |
TOLLIP-Clinical significance-Polymorphisms in TLR genes have been implicated in various diseases like atopic dermatitis. Recently, variations in the TOLLIP gene have been associated with tuberculosis and idiopathic pulmonary fibrosis. | milkshake721/2.1M-wiki-STEM |
TOLLIP-Interactions-TOLLIP has been shown to interact with TOM1, TLR 2, TLR 4 and IL1RAP. | milkshake721/2.1M-wiki-STEM |
VyOS-VyOS-VyOS is an open source network operating system based on Debian.VyOS provides a free routing platform that competes directly with other commercially available solutions from well-known network providers. Because VyOS is run on standard amd64 systems, it can be used as a router and firewall platform for cloud ... | milkshake721/2.1M-wiki-STEM |
VyOS-History-After Brocade Communications stopped development of the Vyatta Core Edition of the Vyatta Routing software, a small group of enthusiasts in 2013 took the last Community Edition, and worked on building an Open Source fork to live on in place of the end of life VC. | milkshake721/2.1M-wiki-STEM |
VyOS-Features-BGP (IPv4 and IPv6), OSPF (v2 and v3), RIP and RIPng, policy-based routing.
IPsec, VTI, VXLAN, L2TPv3, L2TP/IPsec and PPTP servers, tunnel interfaces (GRE, IPIP, SIT), OpenVPN in client, server, or site-to-site modes, WireGuard.
Stateful firewall, zone-based firewall, all types of source and destination N... | milkshake721/2.1M-wiki-STEM |
VyOS-Releases-VyOS version 1.0.0 (Hydrogen) was released on December 22, 2013. On October 9, 2014, version 1.1.0 (Helium) was released. All versions released thus far have been based on Debian 6.0 (Squeeze), and are available as a 32-bit images and 64-bit images for both physical and virtual machines.On January 28, 201... | milkshake721/2.1M-wiki-STEM |
VyOS-Releases-While version 1.0 and 1.1 were named after elements, a new naming scheme based on constellations is used from version 1.2.
Release History VMware Support The VyOS OVA image for VMware was released with the February 3, 2014 maintenance release.
It allows a convenient setup of VyOS on a VMware platform and ... | milkshake721/2.1M-wiki-STEM |
VyOS-Releases-The OVA image can be downloaded from the standard download site Amazon EC2 Support Starting with version 1.0.2, Amazon EC2 customers can select a VyOS AMI image. (deprecated, will be removed in February 2018) Starting with version 1.1.7, AWS customers should use new marketplace VyOS AMIStarting with versi... | milkshake721/2.1M-wiki-STEM |
Midpoint method-Midpoint method-In numerical analysis, a branch of applied mathematics, the midpoint method is a one-step method for numerically solving the differential equation, y′(t)=f(t,y(t)),y(t0)=y0.
The explicit midpoint method is given by the formula the implicit midpoint method by for n=0,1,2,… Here, h is th... | milkshake721/2.1M-wiki-STEM |
Midpoint method-Midpoint method-A geometric interpretation may give a better intuitive understanding of the method (see figure at right). In the basic Euler's method, the tangent of the curve at (tn,yn) is computed using f(tn,yn) . The next value yn+1 is found where the tangent intersects the vertical line t=tn+1 .... | milkshake721/2.1M-wiki-STEM |
Midpoint method-Midpoint method-The local error at each step of the midpoint method is of order O(h3) , giving a global error of order O(h2) . Thus, while more computationally intensive than Euler's method, the midpoint method's error generally decreases faster as h→0 The methods are examples of a class of higher-or... | milkshake721/2.1M-wiki-STEM |
Midpoint method-Derivation of the midpoint method-The midpoint method is a refinement of the Euler method yn+1=yn+hf(tn,yn), and is derived in a similar manner. The key to deriving Euler's method is the approximate equality which is obtained from the slope formula and keeping in mind that y′=f(t,y). | milkshake721/2.1M-wiki-STEM |
Midpoint method-Derivation of the midpoint method-For the midpoint methods, one replaces (3) with the more accurate y′(t+h2)≈y(t+h)−y(t)h when instead of (2) we find One cannot use this equation to find y(t+h) as one does not know y at t+h/2 . The solution is then to use a Taylor series expansion exactly as if using... | milkshake721/2.1M-wiki-STEM |
Midpoint method-Derivation of the midpoint method-The implicit method (1i) is obtained by approximating the value at the half step t+h/2 by the midpoint of the line segment from y(t) to y(t+h) y(t+h2)≈12(y(t)+y(t+h)) and thus y(t+h)−y(t)h≈y′(t+h2)≈k=f(t+h2,12(y(t)+y(t+h))) Inserting the approximation yn+hk for y(t... | milkshake721/2.1M-wiki-STEM |
Perlite-Perlite-Perlite is an amorphous volcanic glass that has a relatively high water content, typically formed by the hydration of obsidian. It occurs naturally and has the unusual property of greatly expanding when heated sufficiently. It is an industrial mineral, suitable "as ceramic flux to lower the sintering te... | milkshake721/2.1M-wiki-STEM |
Perlite-Properties-Perlite softens when it reaches temperatures of 850–900 °C (1,560–1,650 °F). Water trapped in the structure of the material vaporises and escapes, and this causes the expansion of the material to 7–16 times its original volume. The expanded material is a brilliant white, due to the reflectivity of th... | milkshake721/2.1M-wiki-STEM |
Perlite-Typical analysis-70–75% silicon dioxide: SiO2 12–15% aluminium oxide: Al2O3 3–4% sodium oxide: Na2O 3–5% potassium oxide: K2O 0.5-2% iron oxide: Fe2O3 0.2–0.7% magnesium oxide: MgO 0.5–1.5% calcium oxide: CaO 3–5% loss on ignition (chemical / combined water) | milkshake721/2.1M-wiki-STEM |
Perlite-Sources and production-Perlite is a non-renewable resource. The world reserves of perlite are estimated at 700 million tonnes.The confirmed resources of perlite existing in Armenia amount to 150 million m3, whereas the total amount of projected resources reaches up to 3 billion m3. Considering specific density ... | milkshake721/2.1M-wiki-STEM |
Perlite-Uses-Because of its low density and relatively low price (about US$150 per tonne of unexpanded perlite), many commercial applications for perlite have been developed. | milkshake721/2.1M-wiki-STEM |
Perlite-Uses-Construction and manufacturing In the construction and manufacturing fields, it is used in lightweight plasters, concrete and mortar, insulation and ceiling tiles. It may also be used to build composite materials that are sandwich-structured or to create syntactic foam.Perlite filters are fairly commonplac... | milkshake721/2.1M-wiki-STEM |
Perlite-Uses-Aquatic filtration Perlite is currently used in commercial pool filtration technology, as a replacement to diatomaceous earth filters. Perlite is an excellent filtration aid and is used extensively as an alternative to diatomaceous earth. The popularity of perlite usage as a filter medium is growing consid... | milkshake721/2.1M-wiki-STEM |
Perlite-Uses-Biotechnology Due to thermal and mechanical stability, non-toxicity, and high resistance against microbial attacks and organic solvents, perlite is widely used in biotechnological applications. Perlite was found to be an excellent support for immobilization of biocatalysts such as enzymes for bioremediatio... | milkshake721/2.1M-wiki-STEM |
Perlite-Occupational safety-As perlite contains silicon dioxide, goggles and silica filtering masks are recommended when handling large quantities. | milkshake721/2.1M-wiki-STEM |
Perlite-Occupational safety-United States The Occupational Safety and Health Administration (OSHA) has set the legal limit (permissible exposure limit) for perlite exposure in the workplace as 15 mg/m3 total exposure and 5 mg/m3 respiratory exposure over an 8-hour workday. The National Institute for Occupational Safety... | milkshake721/2.1M-wiki-STEM |
GNU Scientific Library-GNU Scientific Library-The GNU Scientific Library (or GSL) is a software library for numerical computations in applied mathematics and science. The GSL is written in C; wrappers are available for other programming languages. The GSL is part of the GNU Project and is distributed under the GNU Gene... | milkshake721/2.1M-wiki-STEM |
GNU Scientific Library-Project history-The GSL project was initiated in 1996 by physicists Mark Galassi and James Theiler of Los Alamos National Laboratory. They aimed at writing a modern replacement for widely used but somewhat outdated Fortran libraries such as Netlib. They carried out the overall design and wrote ea... | milkshake721/2.1M-wiki-STEM |
GNU Scientific Library-Project history-The "overall development of the library and the design and implementation of the major modules" was carried out by Brian Gough and Gerard Jungman. Other major contributors were Jim Davies, Reid Priedhorsky, M. Booth, and F. Rossi.Version 1.0 was released in 2001. In the following ... | milkshake721/2.1M-wiki-STEM |
GNU Scientific Library-Project history-Vigorous development resumed with publication of version 2.0 in October 2015. The latest version 2.7 was released in June 2021. | milkshake721/2.1M-wiki-STEM |
GNU Scientific Library-Example-The following example program calculates the value of the Bessel function of the first kind and order zero for 5: The example program has to be linked to the GSL library upon compilation: The output is shown below and should be correct to double-precision accuracy: | milkshake721/2.1M-wiki-STEM |
GNU Scientific Library-Features-The software library provides facilities for: Programming-language bindings Since the GSL is written in C, it is straightforward to provide wrappers for other programming languages. Such wrappers currently exist for AMPL C++ Fortran Haskell Java Julia Common Lisp OCaml Octave Perl Data L... | milkshake721/2.1M-wiki-STEM |
GNU Scientific Library-Features-C++ wrappers for GSL are available. Not all of these are regularly maintained. They do offer access to matrix and vector classes without having to use GSL's interface to malloc and free functions. Some also offer support for also creating workspaces that behave like Smart pointer classes... | milkshake721/2.1M-wiki-STEM |
GNU Scientific Library-Features-While not strictly wrappers, there are some C++ classes that allow C++ users to use the Gnu Scientific Library with wrapper features. | milkshake721/2.1M-wiki-STEM |
Taxine alkaloids-Taxine alkaloids-Taxine alkaloids, which are often named under the collective title of taxines, are the toxic chemicals that can be isolated from the yew tree. The amount of taxine alkaloids depends on the species of yew, with Taxus baccata and Taxus cuspidata containing the most. The major taxine alka... | milkshake721/2.1M-wiki-STEM |
Taxine alkaloids-Provenance-Taxine can be found in Taxus species: Taxus cuspidata, T. baccata (English yew), Taxus x media, Taxus canadensis, Taxus floridana, and Taxus brevifolia (Pacific or western yew). All of these species contain taxine in every part of the plant except in the aril, the fleshy covering of the seed... | milkshake721/2.1M-wiki-STEM |
Taxine alkaloids-History-The toxic nature of yew trees has been known for millennia. Greek and Roman writers have recorded examples of poisonings, including Julius Caesar's account of Cativolcus, king of Eburones, who committed suicide using the “juice of the yew”. The first attempt to extract the poisonous substance i... | milkshake721/2.1M-wiki-STEM |
Taxine alkaloids-Toxicity in humans-Almost all parts of Taxus baccata, perhaps the best-known Taxus species, contain taxines.Taxines are cardiotoxic calcium and sodium channel antagonists. If any leaves or seeds of the plant are ingested, urgent medical attention is recommended as well as observation for at least 6 hou... | milkshake721/2.1M-wiki-STEM |
Taxine alkaloids-Toxicity in humans-Clinical signs Cardiac and cardiovascular effects: Arrhythmia – Irregular heartbeats leading to lower cardiac output; itself a very severe symptom. Ventricular arrhythmias can lead to circulatory collapse (via cardiac arrest) very quickly if not treated.
Bradycardia – Fewer heart bea... | milkshake721/2.1M-wiki-STEM |
Taxine alkaloids-Toxicity in humans-Diagnosis Diagnosis of yew poisoning is very important if the patient is not already aware of having ingested parts of the yew tree. The method of diagnosis is the determination of 3,5-dimethoxyphenol, a product of the hydrolysis of the glycosidic bond in taxine, in the blood, the ga... | milkshake721/2.1M-wiki-STEM |
Taxine alkaloids-Toxicity in humans-Treatment There are no specific antidotes for taxine, so patients can only receive treatment for their symptoms. | milkshake721/2.1M-wiki-STEM |
Taxine alkaloids-Toxicity in humans-It is also important to control blood pressure and heart rate to treat the heart problems. Atropine has been used successfully in humans to treat bradycardias and arrhythmias caused by taxine. It is more effective if administrated early, but it is also necessary to be cautious with a... | milkshake721/2.1M-wiki-STEM |
Taxine alkaloids-Toxicity in humans-Other treatments are useful to treat the other symptoms of poisoning: positive pressure ventilation if respiratory distress is present, fluid therapy to support blood pressure and maintain hydration and renal function, and gastrointestinal protectants. It may also be necessary to con... | milkshake721/2.1M-wiki-STEM |
Taxine alkaloids-Toxicity in humans-Prevention The toxic effects of T. baccata have been known since ancient times. In most cases, poisoning is accidental, especially in cases involving children or animals. However, there are cases in which the poison is used as a suicide method.Because taxine poisoning is often only d... | milkshake721/2.1M-wiki-STEM |
Taxine alkaloids-Toxicity in animals-The effects of Taxine in humans are very similar to the effects on other animals. It has the same mechanisms of action, and most of the times the ingestion of yew material is diagnosed with the death of the animal. Moreover, clinical signs, diagnosis, treatment, and prevention are m... | milkshake721/2.1M-wiki-STEM |
Taxine alkaloids-Mechanism of action-The toxicity of the yew plant is due to a number of substances, the principal ones being toxic alkaloids (taxine B, paclitaxel, isotaxine B, taxine A), glycosides (taxicatine) and taxane derivates (taxol A, taxol B).There have been many studies about the toxicity of the taxine alkal... | milkshake721/2.1M-wiki-STEM |
Kyiv style-Kyiv style-The Kyiv Academic Style of Bandura Playing is a method of playing the Ukrainian folk instrument of bandura.
The instrument is held between the knees perpendicular to the body of the player. This means that the left hand is only able to play easily along the bass strings of the instrument. The righ... | milkshake721/2.1M-wiki-STEM |
Kyiv style-Kyiv style-The Kyiv style is based on the technique used by kobzari of the Chernihiv province such as Tereshko Parkhomenko. It became known as the Kyiv style because the Kyiv Bandurist Capella used it. Before World War II, most Kyiv banduras had diatonically tuned bass strings. Since World War II in Ukraine,... | milkshake721/2.1M-wiki-STEM |
Gateway Load Balancing Protocol-Gateway Load Balancing Protocol-Gateway Load Balancing Protocol (GLBP) is a Cisco proprietary protocol that attempts to overcome the limitations of existing redundant router protocols by adding basic load balancing functionality. | milkshake721/2.1M-wiki-STEM |
Gateway Load Balancing Protocol-Gateway Load Balancing Protocol-In addition to being able to set priorities on different gateway routers, GLBP allows a weighting parameter to be set. Based on this weighting (compared to others in the same virtual router group), ARP requests will be answered with MAC addresses pointing ... | milkshake721/2.1M-wiki-STEM |
Gateway Load Balancing Protocol-Gateway Load Balancing Protocol-GLBP elects one AVG (Active Virtual Gateway) for each group. Other group members act as backup in case of AVG failure. In case there are more than two members, the second best AVG is placed in the Standby state and all other members are placed in the Liste... | milkshake721/2.1M-wiki-STEM |
Gateway Load Balancing Protocol-Gateway Load Balancing Protocol-By default, GLBP routers use the local multicast address 224.0.0.102 to send hello packets to their peers every 3 seconds over UDP 3222 (source and destination).
Cisco implemented IPv6 support for GLBP in IOS release 12.2(33)SXI. | milkshake721/2.1M-wiki-STEM |
Descriptive phenomenological method in psychology-Descriptive phenomenological method in psychology-The descriptive phenomenological method in psychology was developed by the American psychologist Amedeo Giorgi in the early 1970s. Giorgi based his method on principles laid out by philosophers like Edmund Husserl and Ma... | milkshake721/2.1M-wiki-STEM |
Descriptive phenomenological method in psychology-Theoretical perspective-Giorgi promotes phenomenology as a theoretical movement that avoids certain simplified tendencies sustained by many modern approaches to psychological research. According to the phenomenological psychological perspective embraced by Giorgi, resea... | milkshake721/2.1M-wiki-STEM |
Descriptive phenomenological method in psychology-Theoretical perspective-An important aspect of the descriptive phenomenological method in psychology is the way by which it distinguishes itself from those approaches that are strictly interpretive. In this, Giorgi closely follows Husserl who proposes that "being given ... | milkshake721/2.1M-wiki-STEM |
Descriptive phenomenological method in psychology-Theoretical perspective-Another form of Descriptive phenomenological method in psychology was proposed by Paul Colaizzi. This method follows a distinctive seven step process that stays close to the data while providing strong analysis. | milkshake721/2.1M-wiki-STEM |
Descriptive phenomenological method in psychology-Phenomenological intuition-The Descriptive Phenomenological Method involves neither deduction nor induction in order to find meaning, but instead asks the researcher to intuit what is essential to the phenomenon being studied. Intuition, in this sense (going along with ... | milkshake721/2.1M-wiki-STEM |
Descriptive phenomenological method in psychology-Data analysis-The phenomenological psychological attitude is to be assumed while analyzing the data in order to ensure that "the results reflect a careful description of precisely the features of the experienced phenomenon as they present themselves to the consciousness... | milkshake721/2.1M-wiki-STEM |
Descriptive phenomenological method in psychology-Data analysis-The Colaizzi method for data analysis proceeds as follows: Familiarization: The researcher reads the participants description multiple times until it is familiar.
Identifying Significant Statements: The researcher Identifies all the relevant statements tha... | milkshake721/2.1M-wiki-STEM |
N-Methylconiine-N-Methylconiine-N-Methylconiine is a poisonous alkaloid found in poison hemlock in small quantities. | milkshake721/2.1M-wiki-STEM |
N-Methylconiine-Isolation and properties-The d-(+)-stereoisomer of N-methylconiine is reported to occur in hemlock in small quantities, and methods for its isolation are described by Wolffenstein and by von Braun. It is a colourless, oily, coniine-like liquid, specific rotation [α]D +81.33° at 24.3 °C. The salts are cr... | milkshake721/2.1M-wiki-STEM |
N-Methylconiine-Isolation and properties-The l-(−)-stereoisomer was obtained by Ahrens from residues left in the isolation of coniine as hydrobromide or by removing coniine as the nitroso-compound. It is a colourless, coniine-like liquid, bp. 175.6 °C/767 mmHg, specific rotation [α]D −81.92° at 20 °C. The monohydrochlo... | milkshake721/2.1M-wiki-STEM |
N-Methylconiine-Synthesis-N-Methyl-d-coniine was prepared by the action of potassium methyl sulfate on coniine by Passon. Hess and Eichel have shown that d-coniine with formaldehyde and formic acid yields an active N-methyl-d-coniine, and that methyl-isopelletierine hydrazone yields N-methyl-dl-coniine when heated with... | milkshake721/2.1M-wiki-STEM |
Dtella-Dtella-Dtella is a free and open-source, peer-to-peer file sharing client that connects to a distributed, decentralized DC++ Direct Connect network. Dtella allows the creation of a file-sharing intra-net with decentralized communication between clients. This lets clients on the same network share files without a... | milkshake721/2.1M-wiki-STEM |
Dtella-History-Dtella originated at Purdue from a need to share files on a network without being limited by Purdue's bandwidth limit (for residents of its residence halls) and to avoid anti-piracy take-down notices. Dtella started as a client for DCGate, which used a DC network linked via IRC directory nodes. DCGate or... | milkshake721/2.1M-wiki-STEM |
Dtella-Forks-Notable Forks Dtella@Purdue Dtella@Purdue The original Dtella hub. Active from 2004 to May 13, 2023.
One of the most active Dtella communitiesDtella@Berkeley Dtella@Berkeley Moved to UC Berkeley in Fall 2010 No longer a Dtella CommunityDtella@Home Dtella@Home For Home and off-campus use.
Other known Forks ... | milkshake721/2.1M-wiki-STEM |
Isometry-Isometry-In mathematics, an isometry (or congruence, or congruent transformation) is a distance-preserving transformation between metric spaces, usually assumed to be bijective. The word isometry is derived from the Ancient Greek: ἴσος isos meaning "equal", and μέτρον metron meaning "measure". | milkshake721/2.1M-wiki-STEM |
Isometry-Introduction-Given a metric space (loosely, a set and a scheme for assigning distances between elements of the set), an isometry is a transformation which maps elements to the same or another metric space such that the distance between the image elements in the new metric space is equal to the distance between... | milkshake721/2.1M-wiki-STEM |
Isometry-Introduction-Isometries are often used in constructions where one space is embedded in another space. For instance, the completion of a metric space M involves an isometry from M into M′, a quotient set of the space of Cauchy sequences on M. | milkshake721/2.1M-wiki-STEM |
Isometry-Introduction-The original space M is thus isometrically isomorphic to a subspace of a complete metric space, and it is usually identified with this subspace. Other embedding constructions show that every metric space is isometrically isomorphic to a closed subset of some normed vector space and that every co... | milkshake721/2.1M-wiki-STEM |
Isometry-Introduction-An isometric surjective linear operator on a Hilbert space is called a unitary operator. | milkshake721/2.1M-wiki-STEM |
Isometry-Definition-Let X and Y be metric spaces with metrics (e.g., distances) dX and dY.
A map f:X→Y is called an isometry or distance preserving if for any a,b∈X one has dX(a,b)=dY(f(a),f(b)).
An isometry is automatically injective; otherwise two distinct points, a and b, could be mapped to the same point, the... | milkshake721/2.1M-wiki-STEM |
Isometry-Definition-There is also the weaker notion of path isometry or arcwise isometry: A path isometry or arcwise isometry is a map which preserves the lengths of curves; such a map is not necessarily an isometry in the distance preserving sense, and it need not necessarily be bijective, or even injective. This ter... | milkshake721/2.1M-wiki-STEM |
Isometry-Definition-ExamplesAny reflection, translation and rotation is a global isometry on Euclidean spaces. See also Euclidean group and Euclidean space § Isometries.
The map x↦|x| in R is a path isometry but not a (general) isometry. Note that unlike an isometry, this path isometry does not need to be injective. | milkshake721/2.1M-wiki-STEM |
Isometry-Isometries between normed spaces-The following theorem is due to Mazur and Ulam. Definition: The midpoint of two elements x and y in a vector space is the vector 1/2(x + y).
Linear isometry Given two normed vector spaces V and W, a linear isometry is a linear map A:V→W that preserves the norms: ‖Av‖=‖v‖ fo... | milkshake721/2.1M-wiki-STEM |
Isometry-Manifold-An isometry of a manifold is any (smooth) mapping of that manifold into itself, or into another manifold that preserves the notion of distance between points. The definition of an isometry requires the notion of a metric on the manifold; a manifold with a (positive-definite) metric is a Riemannian ma... | milkshake721/2.1M-wiki-STEM |
Isometry-Manifold-A local isometry from one (pseudo-)Riemannian manifold to another is a map which pulls back the metric tensor on the second manifold to the metric tensor on the first. When such a map is also a diffeomorphism, such a map is called an isometry (or isometric isomorphism), and provides a notion of isomor... | milkshake721/2.1M-wiki-STEM |
Isometry-Manifold-Definition Let R=(M,g) and R′=(M′,g′) be two (pseudo-)Riemannian manifolds, and let f:R→R′ be a diffeomorphism. Then f is called an isometry (or isometric isomorphism) if g=f∗g′, where f∗g′ denotes the pullback of the rank (0, 2) metric tensor g′ by f.
Equivalently, in terms of the pushforward ... | milkshake721/2.1M-wiki-STEM |
Isometry-Manifold-Properties A collection of isometries typically form a group, the isometry group. When the group is a continuous group, the infinitesimal generators of the group are the Killing vector fields. The Myers–Steenrod theorem states that every isometry between two connected Riemannian manifolds is smooth (... | milkshake721/2.1M-wiki-STEM |
Isometry-Manifold-Riemannian manifolds that have isometries defined at every point are called symmetric spaces. | milkshake721/2.1M-wiki-STEM |
Isometry-Generalizations-Given a positive real number ε, an ε-isometry or almost isometry (also called a Hausdorff approximation) is a map f:X→Y between metric spaces such that for x,x′∈X one has |dY(f(x),f(x′))−dX(x,x′)|<ε, and for any point y∈Y there exists a point x∈X with dY(y,f(x))<ε That is, an ε-isometry p... | milkshake721/2.1M-wiki-STEM |
Isometry-Generalizations-Quasi-isometry is yet another useful generalization.
One may also define an element in an abstract unital C*-algebra to be an isometry: a∈A is an isometry if and only if a∗⋅a=1.
Note that as mentioned in the introduction this is not necessarily a unitary element because one does not in general... | milkshake721/2.1M-wiki-STEM |
Cross-coupling reaction-Cross-coupling reaction-In organic chemistry, a cross-coupling reaction is a reaction where two different fragments are joined. Cross-couplings are a subset of the more general coupling reactions. Often cross-coupling reactions require metal catalysts. One important reaction type is this: R−M + ... | milkshake721/2.1M-wiki-STEM |
Cross-coupling reaction-Cross-coupling reaction-Richard F. Heck, Ei-ichi Negishi, and Akira Suzuki were awarded the 2010 Nobel Prize in Chemistry for developing palladium-catalyzed coupling reactions. | milkshake721/2.1M-wiki-STEM |
Cross-coupling reaction-Mechanism-Many mechanisms exist reflecting the myriad types of cross-couplings, including those that do not require metal catalysts. Often, however, cross-coupling refers to a metal-catalyzed reaction of a nucleophilic partner with an electrophilic partner. | milkshake721/2.1M-wiki-STEM |
Cross-coupling reaction-Mechanism-In such cases, the mechanism generally involves reductive elimination of R-R' from LnMR(R') (L = spectator ligand). This intermediate LnMR(R') is formed in a two step process from a low valence precursor LnM. The oxidative addition of an organic halide (RX) to LnM gives LnMR(X). Subseq... | milkshake721/2.1M-wiki-STEM |
Cross-coupling reaction-Mechanism-Catalysts Catalysts are often based on palladium, which is frequently selected due to high functional group tolerance. Organopalladium compounds are generally stable towards water and air. Palladium catalysts can be problematic for the pharmaceutical industry, which faces extensive reg... | milkshake721/2.1M-wiki-STEM |
Cross-coupling reaction-Mechanism-Leaving groups The leaving group X in the organic partner is usually a halide, although triflate, tosylate and other pseudohalide have been used. Chloride is an ideal group due to the low cost of organochlorine compounds. Frequently, however, C–Cl bonds are too inert, and bromide or io... | milkshake721/2.1M-wiki-STEM |
Cross-coupling reaction-Carbon–carbon cross-coupling-Many cross-couplings entail forming carbon–carbon bonds. | milkshake721/2.1M-wiki-STEM |
Cross-coupling reaction-Carbon–heteroatom coupling-Many cross-couplings entail forming carbon–heteroatom bonds (heteroatom = S, N, O). A popular method is the Buchwald–Hartwig reaction: | milkshake721/2.1M-wiki-STEM |
Cross-coupling reaction-Miscellaneous reactions-Palladium-catalyzes the cross-coupling of aryl halides with fluorinated arene. The process is unusual in that it involves C–H functionalisation at an electron deficient arene. | milkshake721/2.1M-wiki-STEM |
Cross-coupling reaction-Applications-Cross-coupling reactions are important for the production of pharmaceuticals, examples being montelukast, eletriptan, naproxen, varenicline, and resveratrol. with Suzuki coupling being most widely used. Some polymers and monomers are also prepared in this way. | milkshake721/2.1M-wiki-STEM |
Cross-coupling reaction-Reviews-Fortman, George C.; Nolan, Steven P. (2011). "N-Heterocyclic carbene (NHC) ligands and palladium in homogeneous cross-coupling catalysis: a perfect union". Chemical Society Reviews. 40 (10): 5151–69. doi:10.1039/c1cs15088j. PMID 21731956.
Yin; Liebscher, Jürgen (2007). "Carbon−Carbon Cou... | milkshake721/2.1M-wiki-STEM |
Home construction-Home construction-Home construction or residential construction is the process of constructing a house, apartment building, or similar residential building generally referred to as a 'home' when giving consideration to the people who might now or someday reside there. Beginning with simple pre-histori... | milkshake721/2.1M-wiki-STEM |
Home construction-Home construction-The cost of housing and access to it is often controlled by the modern realty trade, which frequently has a certain level of market force speculation. The level of economic activity in the home-construction section is reported as housing starts, though this is contrarily denominated ... | milkshake721/2.1M-wiki-STEM |
Home construction-Home construction-Global access to homes is not consistent around the world, with many economies not providing adequate support for the right to housing. Sustainable Development Goal 11 includes a goal to create "Adequate, safe, and affordable housing and basic services and upgrade slums". Based on cu... | milkshake721/2.1M-wiki-STEM |
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