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In mathematics a polydivisible number (or magic number ) is a number in a given number base with digits abcde... that has the following properties: [ 1 ]
Let n {\displaystyle n} be a positive integer, and let k = ⌊ log b n ⌋ + 1 {\displaystyle k=\lfloor \log _{b}{n}\rfloor +1} be the number of digits in n written in... | https://en.wikipedia.org/wiki/Polydivisible_number |
Polydnaviriformidae ( / p ɒ ˈ l ɪ d n ə v ɪ r ə ˌ f ɔː m ɪ d ɛ / PDV ) [ 1 ] is a family of insect viriforms ; members are known as polydnaviruses . There are two genera in the family: Bracoform and Ichnoviriform . Polydnaviruses form a symbiotic relationship with parasitoid wasps . Ichnoviriforms (IV) occur in Ichneum... | https://en.wikipedia.org/wiki/Polydnaviriformidae |
Polyelectrolytes are polymers whose repeating units bear an electrolyte group. Polycations and polyanions are polyelectrolytes. These groups dissociate in aqueous solutions (water), making the polymers charged . Polyelectrolyte properties are thus similar to both electrolytes ( salts ) and polymers (high molecular weig... | https://en.wikipedia.org/wiki/Polyelectrolyte |
Adsorption of polyelectrolytes on solid substrates is a surface phenomenon where long-chained polymer molecules with charged groups (dubbed polyelectrolytes ) bind to a surface that is charged in the opposite polarity. On the molecular level, the polymers do not actually bond to the surface, but tend to "stick" to the... | https://en.wikipedia.org/wiki/Polyelectrolyte_adsorption |
Polyester resins are synthetic resins formed by the reaction of dibasic organic acids and polyhydric alcohols . Maleic anhydride is a commonly used raw material with diacid functionality in unsaturated polyester resins. [ 1 ] Unsaturated polyester resins are used in sheet moulding compound , bulk moulding compound and ... | https://en.wikipedia.org/wiki/Polyester_resin |
Polyesteramides are a class of synthetic polymers connected by ester and amide bonds. [ 1 ]
Common polyesteramides can be separated in to two different types. [ 2 ]
According to Rainer Höfer, nylon-type polyesteramides can be synthesized through the polymerisation of caprolactam or caprolactone , or through polyconde... | https://en.wikipedia.org/wiki/Polyesteramide |
Polyether block amide or PEBA is a thermoplastic elastomer (TPE). It is known under the tradename of PEBAX® ( Arkema ) and VESTAMID® E ( Evonik Industries ). It is a block copolymer obtained by polycondensation of a carboxylic acid polyamide ( PA6 , PA11 , PA12 ) with an alcohol termination polyether ( Polytetramethyl... | https://en.wikipedia.org/wiki/Polyether_block_amide |
Polyetherketones (PEK for short) are polymers whose molecular backbone contain alternating ketone (R-CO-R) and Ether (R-O-R) functionalities. The most common are Polyaryletherketones (PAEK), in which there is an aryl group linked in the (1–4)-position between each of the functional groups. The backbone, which is thus v... | https://en.wikipedia.org/wiki/Polyetherketones |
Polyethylene glycol ( PEG ; / ˌ p ɒ l i ˈ ɛ θ əl ˌ iː n ˈ ɡ l aɪ ˌ k ɒ l , - ˈ ɛ θ ɪ l -, - ˌ k ɔː l / ) is a polyether compound derived from petroleum with many applications, from industrial manufacturing to medicine . PEG is also known as polyethylene oxide ( PEO ) or polyoxyethylene ( POE ), depending on its molecul... | https://en.wikipedia.org/wiki/Polyethylene_glycol |
Polyethylene terephthalate (or poly(ethylene terephthalate) , [ 5 ] PET , PETE , or the obsolete PETP or PET-P ), is the most common thermoplastic polymer resin of the polyester family and is used in fibres for clothing, containers for liquids and foods, and thermoforming for manufacturing, and in combination with glas... | https://en.wikipedia.org/wiki/Polyethylene_terephthalate |
Polyethylenimine ( PEI ) or polyaziridine is a polymer with repeating units composed of the amine group and two carbon aliphatic CH 2 CH 2 spacers. Linear polyethyleneimines contain all secondary amines , in contrast to branched PEIs which contain primary, secondary and tertiary amino groups. Totally branched, dendrime... | https://en.wikipedia.org/wiki/Polyethylenimine |
Polyferrocenes are polymers containing ferrocene units. Ferrocene offers many advantages over pure hydrocarbons when used as a building block of macromolecular chemistry . The variety of possible substitutions at the ferrocene parent body results in a multitude of accessible polymers with interesting electronic and pho... | https://en.wikipedia.org/wiki/Polyferrocenes |
Polyfluorene is a polymer with formula (C 13 H 8 ) n , consisting of fluorene units linked in a linear chain — specifically, at carbon atoms 2 and 7 in the standard fluorene numbering. It can also be described as a chain of benzene rings linked in para positions (a polyparaphenylene ) with an extra methylene bridge co... | https://en.wikipedia.org/wiki/Polyfluorene |
Polyfullerene is a basic polymer of the C 60 monomer group, in which fullerene segments are connected via covalent bonds into a polymeric chain without side or bridging groups. They are called intrinsic polymeric fullerenes , or more often all C 60 polymers .
Fullerene can be part of a polymer chain in many different ... | https://en.wikipedia.org/wiki/Polyfullerene |
Polygenic adaptation describes a process in which a population adapts through small changes in allele frequencies at hundreds or thousands of loci . [ 1 ]
Many traits in humans and other species are highly polygenic , i.e., affected by standing genetic variation at hundreds or thousands of loci. Under normal condition... | https://en.wikipedia.org/wiki/Polygenic_adaptation |
Polygons are used in computer graphics to compose images that are three-dimensional in appearance, [ 1 ] and are one of the most popular geometric building blocks in computer graphics. [ 2 ] Polygons are built up of vertices , and are typically used as triangles.
A model 's polygons can be rendered and seen simply in ... | https://en.wikipedia.org/wiki/Polygon_(computer_graphics) |
A polygon soup is a set of unorganized polygons, typically triangles, before the application of any structuring operation, such as e.g. octree grouping. [ 1 ]
The term must not to be confused with the "PolySoup" [ 2 ] operation available in the 3D package Houdini , whose goal is to optimize the storage space needed by... | https://en.wikipedia.org/wiki/Polygon_soup |
In chemistry the polyhedral skeletal electron pair theory (PSEPT) provides electron counting rules useful for predicting the structures of clusters such as borane and carborane clusters. The electron counting rules were originally formulated by Kenneth Wade , [ 1 ] and were further developed by others including Michael... | https://en.wikipedia.org/wiki/Polyhedral_skeletal_electron_pair_theory |
The polyhedral symbol is sometimes used in coordination chemistry to indicate the approximate geometry of the coordinating atoms around the central atom. One or more italicised letters indicate the geometry, e.g. TP -3 which is followed by a number that gives the coordination number of the central atom. [ 1 ] The polyh... | https://en.wikipedia.org/wiki/Polyhedral_symbol |
Polyhedron is a peer-reviewed scientific journal covering the field of inorganic chemistry . It was established in 1955 as the Journal of Inorganic and Nuclear Chemistry and is published by Elsevier .
Polyhedron is abstracted and indexed in:
According to the Journal Citation Reports , the journal has a 2020 impact fa... | https://en.wikipedia.org/wiki/Polyhedron_(journal) |
A polyhedron model is a physical construction of a polyhedron , constructed from cardboard, plastic board, wood board or other panel material, or, less commonly, solid material.
Since there are 75 uniform polyhedra , including the five regular convex polyhedra , five polyhedral compounds , four Kepler-Poinsot polyhedr... | https://en.wikipedia.org/wiki/Polyhedron_model |
Polyhexanide ( polyhexamethylene biguanide , PHMB ) is a polymer used as a disinfectant and antiseptic . In dermatological use, [ 4 ] it is spelled polihexanide ( INN ) and sold under various brand names. [ 5 ] PHMB has been shown to be effective against Pseudomonas aeruginosa , Staphylococcus aureus , Escherichia coli... | https://en.wikipedia.org/wiki/Polyhexanide |
Polyimide foam is a foam originally designed for NASA by Inspec Foams Inc. under the brand name Solimide. [ 1 ] Its primary purposes are as an insulator (such as for rocket fuels ) and acoustic damper. NASA engineered the product to have relatively low outgassing (a problem in vacuum and aboard spacecraft), desirable t... | https://en.wikipedia.org/wiki/Polyimide_foam |
Polyimines are classified as polymer materials that contain imine groups, which are characterised by a double bond between a carbon and nitrogen atom. [ 1 ] The term polyimine can also be found occasionally in covalent organic frameworks (COFs). In (older) literature, polyimines are sometimes also referred to as poly(a... | https://en.wikipedia.org/wiki/Polyimine |
Polyisobuteneamine ( PIBA ) is a polymer derived from the reaction of polyisobutylene (PIB) with ammonia or primary amines . This polymeric compound is known for its excellent adhesive and dispersant properties and is commonly used as an additive in lubricants , fuel, and other industrial applications.
The history of ... | https://en.wikipedia.org/wiki/Polyisobuteneamine |
In statistics , a polykay , or generalised k-statistic , (denoted k r , s {\displaystyle k_{r,s}} ) is a statistic defined as a linear combination of sample moments . [ 1 ]
The word polykay was coined by American mathematician John Tukey in 1956, from poly , "many" or "much", and kay , the phonetic spelling of the let... | https://en.wikipedia.org/wiki/Polykay |
In mathematics , a polylogarithmic function in n is a polynomial in the logarithm of n , [ 1 ]
The notation log k n is often used as a shorthand for (log n ) k , analogous to sin 2 θ for (sin θ ) 2 .
In computer science , polylogarithmic functions occur as the order of time for some data structure operations. Additio... | https://en.wikipedia.org/wiki/Polylogarithmic_function |
Polylogism is the belief that different groups of people reason in fundamentally different ways (coined from Greek poly 'many' + logos ' logic '). [ 1 ] The term is attributed to Ludwig von Mises , [ 2 ] who used it to refer to Nazism , Marxism and other class based social philosophies , [ 3 ] before the writings of Th... | https://en.wikipedia.org/wiki/Polylogism |
Polylysine refers to several types of lysine homopolymers , which may differ from each other in terms of stereochemistry (D/L; the L form is natural and usually assumed) and link position (α/ε). Of these types, only ε-poly-L-lysine is produced naturally.
The precursor amino acid lysine contains two amino groups , one ... | https://en.wikipedia.org/wiki/Polylysine |
polymake is a software for the algorithmic treatment of convex polyhedra . [ 1 ]
Albeit primarily a tool to study the combinatorics and the geometry of convex polytopes and polyhedra , [ 2 ] it is by now also capable of dealing with simplicial complexes , matroids , polyhedral fans, graphs , tropical objects, toric va... | https://en.wikipedia.org/wiki/Polymake |
Polymelia is a birth defect in which an affected individual has more than the usual number of limbs. It is a type of dysmelia . In humans and most land-dwelling vertebrates, this means having five or more limbs. The extra limb is most commonly shrunken and/or deformed. The term is from Greek πολυ- "many", μέλεα "limbs"... | https://en.wikipedia.org/wiki/Polymelia |
A polymer -based battery uses organic materials instead of bulk metals to form a battery. [ 1 ] Currently accepted metal-based batteries pose many challenges due to limited resources, negative environmental impact, and the approaching limit of progress. Redox active polymers are attractive options for electrodes in bat... | https://en.wikipedia.org/wiki/Polymer-based_battery |
Polymer-bonded explosives , also called PBX or plastic-bonded explosives , are explosive materials in which explosive powder is bound together in a matrix using small quantities (typically 5–10% by weight) of a synthetic polymer . PBXs are normally used for explosive materials that are not easily melted into a casting,... | https://en.wikipedia.org/wiki/Polymer-bonded_explosive |
Polymer-fullerene bulk heterojunction solar cells are a type of solar cell researched in academic laboratories. Polymer-fullerene solar cells are a subset of organic solar cells, also known as organic photovoltaic (OPV) cells, which use organic materials as their active component to convert solar radiation into electri... | https://en.wikipedia.org/wiki/Polymer-fullerene_bulk_heterojunction_solar_cell |
Polymer-protein hybrids are a class of nanostructure composed of protein - polymer conjugates (i.e. complexes composed of one protein attached to one or more polymer chains ). [ 1 ] [ 2 ] The protein component generally gives the advantages of biocompatibility and biodegradability , as many proteins are produced natura... | https://en.wikipedia.org/wiki/Polymer-protein_hybrid |
The Polymer Battery Experiment ( PBEX ) demonstrates the charging and discharging characteristics of polymer batteries in the space environment. PBEX validates use of lightweight, flexible battery technology to decrease cost and weight for future military and commercial space systems. PBEX was developed by Johns Hopkin... | https://en.wikipedia.org/wiki/Polymer_Battery_Experiment |
The Interdisciplinary Research Centre in Polymer Science and Technology is a consortium of research groups, formed in 1989 from the Universities of Durham , Leeds and Bradford , all of whom are involved research in polymer science and technology. [ 1 ] The University of Sheffield joined in 2004. The Polymer IRC has com... | https://en.wikipedia.org/wiki/Polymer_Interdisciplinary_Research_Centre |
Adsorption is the adhesion of ions or molecules onto the surface of another phase. [ 1 ] Adsorption may occur via physisorption and chemisorption . Ions and molecules can adsorb to many types of surfaces including polymer surfaces. A polymer is a large molecule composed of repeating subunits bound together by covalent ... | https://en.wikipedia.org/wiki/Polymer_adsorption |
Polymer architecture in polymer science relates to the way branching leads to a deviation from a strictly linear polymer chain. [ 1 ] Branching may occur randomly or reactions may be designed so that specific architectures are targeted. [ 1 ] It is an important microstructural feature. A polymer's architecture affects ... | https://en.wikipedia.org/wiki/Polymer_architecture |
Main chain or Backbone That linear chain to which all other chains, long or short or both, may be regarded as being pendant.
Note : Where two or more chains could equally be considered to be the main chain, that one is selected which leads to the simplest representation of the molecule. [ 1 ]
In polymer science , the... | https://en.wikipedia.org/wiki/Polymer_backbone |
Polymer banknotes are banknotes made from a synthetic polymer such as biaxially oriented polypropylene (BOPP) . Such notes incorporate many security features not available in paper banknotes, including the use of metameric inks . [ 1 ] Polymer banknotes last significantly longer than paper notes, causing a decrease in ... | https://en.wikipedia.org/wiki/Polymer_banknote |
In materials science , a polymer blend , or polymer mixture , is a member of a class of materials analogous to metal alloys , in which at least two polymers are blended together to create a new material with different physical properties. [ 1 ]
During the 1940s, '50s and '60s, the commercial development of new monomer... | https://en.wikipedia.org/wiki/Polymer_blend |
In materials science , a polymer brush is the name given to a surface coating consisting of polymers tethered to a surface. [ 1 ] The brush may be either in a solvated state, where the tethered polymer layer consists of polymer and solvent , or in a melt state, where the tethered chains completely fill up the space ava... | https://en.wikipedia.org/wiki/Polymer_brush |
Polymer characterization is the analytical branch of polymer science .
The discipline is concerned with the characterization of polymeric materials on a variety of levels. The characterization typically has as a goal to improve the performance of the material. As such, many characterization techniques should ideally b... | https://en.wikipedia.org/wiki/Polymer_characterization |
Polymer chemistry is a sub-discipline of chemistry that focuses on the structures, chemical synthesis , and chemical and physical properties of polymers and macromolecules . The principles and methods used within polymer chemistry are also applicable through a wide range of other chemistry sub-disciplines like organic ... | https://en.wikipedia.org/wiki/Polymer_chemistry |
Polymer degradation is the reduction in the physical properties of a polymer , such as strength, caused by changes in its chemical composition. Polymers and particularly plastics are subject to degradation at all stages of their product life cycle , including during their initial processing, use, disposal into the envi... | https://en.wikipedia.org/wiki/Polymer_degradation |
Polymer devolatilization , also known as polymer degassing, is the process of removing low-molecular-weight components such as residual monomers, solvents, reaction by-products and water from polymers. [ 1 ] : 1–12
When exiting a reactor after a polymerization reaction, many polymers still contain undesired low-molecu... | https://en.wikipedia.org/wiki/Polymer_devolatilization |
A polymer electrolyte is a polymer matrix capable of ion conduction . [ 1 ] Much like other types of electrolyte —liquid and solid-state —polymer electrolytes aid in movement of charge between the anode and cathode of a cell. [ 1 ] [ 2 ] [ 3 ] The use of polymers as an electrolyte was first demonstrated using dye-sensi... | https://en.wikipedia.org/wiki/Polymer_electrolytes |
Polymer engineering is generally an engineering field that designs, analyses, and modifies polymer materials. Polymer engineering covers aspects of the petrochemical industry , polymerization , structure and characterization of polymers, properties of polymers, compounding and processing of polymers and description of ... | https://en.wikipedia.org/wiki/Polymer_engineering |
Polymers are chainlike molecules that are made of the same repetition unit. With a few exceptions such as proteins , a polymer consists of a mix of molecules with different chain lengths. Therefore, average values are given for the molecular weight like the number average , the weight average or the viscosity average m... | https://en.wikipedia.org/wiki/Polymer_fractionation |
Polymer fume fever or fluoropolymer fever , also informally called Teflon flu , is an inhalation fever caused by the fumes released when polytetrafluoroethylene (PTFE, known under the trade name Teflon ) reaches temperatures of 300 °C (572 °F) to 450 °C (842 °F). [ 1 ]
When PTFE is heated above 450 °C the pyrolysis pr... | https://en.wikipedia.org/wiki/Polymer_fume_fever |
Polymer physics is the field of physics that studies polymers , their fluctuations, mechanical properties , as well as the kinetics of reactions involving degradation of polymers and polymerisation of monomers . [ 1 ] [ 2 ] [ 3 ] [ 4 ]
While it focuses on the perspective of condensed matter physics , polymer physics w... | https://en.wikipedia.org/wiki/Polymer_physics |
Polymer scattering experiments are one of the main scientific methods used in chemistry , physics and other sciences to study the characteristics of polymeric systems: solutions , gels, compounds and more. As in most scattering experiments, it involves subjecting a polymeric sample to incident particles (with defined w... | https://en.wikipedia.org/wiki/Polymer_scattering |
Polymer science or macromolecular science is a subfield of materials science concerned with polymers , primarily synthetic polymers such as plastics and elastomers . The field of polymer science includes researchers in multiple disciplines including chemistry , physics , and engineering .
This science comprises three... | https://en.wikipedia.org/wiki/Polymer_science |
Polymer soil stabilization refers to the addition of polymers to improve the physical properties of soils, most often for geotechnical engineering , construction, or agricultural projects. [ 1 ] Even at very small concentrations within soils, various polymers have been shown to increase water retention and reduce erosi... | https://en.wikipedia.org/wiki/Polymer_soil_stabilization |
Polymer solutions are solutions containing dissolved polymers . [ 1 ] These may be liquid solutions (e.g. in aqueous solution ), or solid solutions (e.g. a substance which has been plasticized). [ 2 ]
The introduction into the polymer of small amounts of a solvent ( plasticizer ) reduces the temperature of glass trans... | https://en.wikipedia.org/wiki/Polymer_solution |
Taking clues from spongy toddler toys that can absorb water and inflate to bigger sizes, [ 1 ] scientists at Mayo Clinical Research Centre, Rochester, Minnesota, United States have developed biodegradable polymer grafts that, when surgically placed in damaged vertebrae, intended to grow such that it is just the right s... | https://en.wikipedia.org/wiki/Polymer_sponge |
Polymers and plastics known as polymer substrates are used for banknotes and other everyday products. The banknote is more durable than paper, won't become soaked in liquids and is harder to counterfeit, though not impossible. Countries whose whole banknote production is in polymer are: Australia , Romania , Vietnam , ... | https://en.wikipedia.org/wiki/Polymer_substrate |
The polymerase chain reaction ( PCR ) is a method widely used to make millions to billions of copies of a specific DNA sample rapidly, allowing scientists to amplify a very small sample of DNA (or a part of it) sufficiently to enable detailed study. PCR was invented in 1983 by American biochemist Kary Mullis at Cetus C... | https://en.wikipedia.org/wiki/Polymerase_chain_reaction |
PCR inhibitors are any factor which prevent the amplification of nucleic acids through the polymerase chain reaction (PCR). [ 1 ] PCR inhibition is the most common cause of amplification failure when sufficient copies of DNA are present. [ 2 ] PCR inhibitors usually affect PCR through interaction with DNA or interferen... | https://en.wikipedia.org/wiki/Polymerase_chain_reaction_inhibitors |
The polymerase chain reaction (PCR) is a commonly used molecular biology tool for amplifying DNA, and various techniques for PCR optimization which have been developed by molecular biologists to improve PCR performance and minimize failure.
The PCR method is extremely sensitive, requiring only a few DNA molecules in a... | https://en.wikipedia.org/wiki/Polymerase_chain_reaction_optimization |
Polymerase cycling assembly (or PCA , also known as Assembly PCR ) is a method for the assembly of large DNA oligonucleotides from shorter fragments. The process uses the same technology as PCR , but takes advantage of DNA hybridization and annealing as well as DNA polymerase to amplify a complete sequence of DNA in a... | https://en.wikipedia.org/wiki/Polymerase_cycling_assembly |
Polymerase stuttering is the process by which a polymerase transcribes a nucleotide several times without progressing further on the mRNA chain. It is often used in addition of poly A tails or capping mRNA chains by less complex organisms such as viruses.
A polymerase may undergo stuttering as a probability controlle... | https://en.wikipedia.org/wiki/Polymerase_stuttering |
A polymeric foam is a special foam , in liquid or solidified form, formed from polymers . [ 1 ]
Examples include: | https://en.wikipedia.org/wiki/Polymeric_foam |
Polymeric materials have widespread application due to their versatile characteristics, cost-effectiveness, and highly tailored production. The science of polymer synthesis allows for excellent control over the properties of a bulk polymer sample. However, surface interactions of polymer substrates are an essential are... | https://en.wikipedia.org/wiki/Polymeric_surface |
Polymerization-induced phase separation ( PIPS ) is the occurrence of phase separation in a multicomponent mixture induced by the polymerization of one or more components. [ 1 ] [ 2 ] The increase in molecular weight of the reactive component renders one or more components to be mutually immiscible in one another, resu... | https://en.wikipedia.org/wiki/Polymerization-induced_phase_separation |
Polymers of intrinsic microporosity ( PIMs ) are a unique class of microporous material developed by research efforts led by Neil McKeown , Peter Budd , et al. [ 1 ] PIMs contain a continuous network of interconnected intermolecular voids less than 2 nm in width. Classified as a porous organic polymer, PIMs generate po... | https://en.wikipedia.org/wiki/Polymers_of_intrinsic_microporosity |
In biotechnology , polymersomes [ 1 ] are a class of artificial vesicles , tiny hollow spheres that enclose a solution. Polymersomes are made using amphiphilic synthetic block copolymers to form the vesicle membrane, and have radii ranging from 50 nm to 5 μm or more. [ 2 ] Most reported polymersomes contain an aqueous ... | https://en.wikipedia.org/wiki/Polymersome |
Polymethylhydrosiloxane ( PMHS ) is a polymer with the general structure [−CH 3 (H)Si−O−] . It is used in organic chemistry as a mild and stable reducing agent easily transferring hydrides to metal centers and a number of other reducible functional groups. [ 1 ] [ 2 ] A variety of related materials are available under ... | https://en.wikipedia.org/wiki/Polymethylhydrosiloxane |
Many compound materials exhibit polymorphism , that is they can exist in different structures called polymorphs. Silicon carbide (SiC) is unique in this regard as more than 250 polymorphs of silicon carbide had been identified by 2006, [ 1 ] with some of them having a lattice constant as long as 301.5 nm, about one tho... | https://en.wikipedia.org/wiki/Polymorphs_of_silicon_carbide |
In mathematics , a polynomial Diophantine equation is an indeterminate polynomial equation for which one seeks solutions restricted to be polynomials in the indeterminate. A Diophantine equation , in general, is one where the solutions are restricted to some algebraic system, typically integers. (In another usage ) Di... | https://en.wikipedia.org/wiki/Polynomial_Diophantine_equation |
In signal processing, the polynomial Wigner–Ville distribution is a quasiprobability distribution that generalizes the Wigner distribution function . It was proposed by Boualem Boashash and Peter O'Shea in 1994.
Many signals in nature and in engineering applications can be modeled as z ( t ) = e j 2 π ϕ ( t ) {\displa... | https://en.wikipedia.org/wiki/Polynomial_Wigner–Ville_distribution |
In coding theory , a polynomial code is a type of linear code whose set of valid code words consists of those polynomials (usually of some fixed length) that are divisible by a given fixed polynomial (of shorter length, called the generator polynomial ).
Fix a finite field G F ( q ) {\displaystyle GF(q)} , whose eleme... | https://en.wikipedia.org/wiki/Polynomial_code |
In algebra , the ring of polynomial differential forms on the standard n -simplex is the differential graded algebra : [ 1 ]
Varying n , it determines the simplicial commutative dg algebra :
(each u : [ n ] → [ m ] {\displaystyle u:[n]\to [m]} induces the map Ω poly ∗ ( [ m ] ) → Ω poly ∗ ( [ n ] ) , t i ↦ ∑ u ( j ) ... | https://en.wikipedia.org/wiki/Polynomial_differential_form |
In mathematics and computer science , polynomial evaluation refers to computation of the value of a polynomial when its indeterminates are substituted for some values. In other words, evaluating the polynomial P ( x 1 , x 2 ) = 2 x 1 x 2 + x 1 3 + 4 {\displaystyle P(x_{1},x_{2})=2x_{1}x_{2}+x_{1}^{3}+4} at x 1 = 2 , x ... | https://en.wikipedia.org/wiki/Polynomial_evaluation |
In mathematics , an expansion of a product of sums expresses it as a sum of products by using the fact that multiplication distributes over addition. Expansion of a polynomial expression can be obtained by repeatedly replacing subexpressions that multiply two other subexpressions, at least one of which is an addition, ... | https://en.wikipedia.org/wiki/Polynomial_expansion |
In algebra, the greatest common divisor (frequently abbreviated as GCD) of two polynomials is a polynomial, of the highest possible degree, that is a factor of both the two original polynomials. This concept is analogous to the greatest common divisor of two integers.
In the important case of univariate polynomials ov... | https://en.wikipedia.org/wiki/Polynomial_greatest_common_divisor |
In mathematics, polynomial identity testing (PIT) is the problem of efficiently determining whether two multivariate polynomials are identical. More formally, a PIT algorithm is given an arithmetic circuit that computes a polynomial p in a field , and decides whether p is the zero polynomial. Determining the computatio... | https://en.wikipedia.org/wiki/Polynomial_identity_testing |
In algebra , polynomial long division is an algorithm for dividing a polynomial by another polynomial of the same or lower degree , a generalized version of the familiar arithmetic technique called long division . It can be done easily by hand, because it separates an otherwise complex division problem into smaller one... | https://en.wikipedia.org/wiki/Polynomial_long_division |
In algebra , a polynomial map or polynomial mapping P : V → W {\displaystyle P:V\to W} between vector spaces over an infinite field k is a polynomial in linear functionals with coefficients in k ; i.e., it can be written as
where the λ i j : V → k {\displaystyle \lambda _{i_{j}}:V\to k} are linear functionals and the ... | https://en.wikipedia.org/wiki/Polynomial_mapping |
In mathematics , a polynomial matrix or matrix of polynomials is a matrix whose elements are univariate or multivariate polynomials . Equivalently, a polynomial matrix is a polynomial whose coefficients are matrices.
A univariate polynomial matrix P of degree p is defined as:
where A ( i ) {\displaystyle A(i)} denote... | https://en.wikipedia.org/wiki/Polynomial_matrix |
Polynomial Matrix Spectral Factorization or Matrix Fejer–Riesz Theorem is a tool used to study the matrix decomposition of polynomial matrices . Polynomial matrices are widely studied in the fields of systems theory and control theory and have seen other uses relating to stable polynomials . In stability theory , Spect... | https://en.wikipedia.org/wiki/Polynomial_matrix_spectral_factorization |
In mathematics, the polynomial method is an algebraic approach to combinatorics problems that involves capturing some combinatorial structure using polynomials and proceeding to argue about their algebraic properties. Recently (around 2016), the polynomial method has led to the development of remarkably simple solution... | https://en.wikipedia.org/wiki/Polynomial_method_in_combinatorics |
Finding the roots of polynomials is a long-standing problem that has been extensively studied throughout the history and substantially influenced the development of mathematics. It involves determining either a numerical approximation or a closed-form expression of the roots of a univariate polynomial, i.e., determinin... | https://en.wikipedia.org/wiki/Polynomial_root-finding |
In mathematics a P-recursive equation can be solved for polynomial solutions . Sergei A. Abramov in 1989 and Marko Petkovšek in 1992 described an algorithm which finds all polynomial solutions of those recurrence equations with polynomial coefficients. [ 1 ] [ 2 ] The algorithm computes a degree bound for the solution ... | https://en.wikipedia.org/wiki/Polynomial_solutions_of_P-recursive_equations |
In mathematics , a polynomial transformation consists of computing the polynomial whose roots are a given function of the roots of a polynomial. Polynomial transformations such as Tschirnhaus transformations are often used to simplify the solution of algebraic equations .
Let
be a polynomial, and
be its complex root... | https://en.wikipedia.org/wiki/Polynomial_transformation |
In organic chemistry , a polyol is an organic compound containing multiple hydroxyl groups ( −OH ). The term "polyol" can have slightly different meanings depending on whether it is used in food science or polymer chemistry . Polyols containing two, three and four hydroxyl groups are diols , [ 1 ] triols , [ 2 ] and te... | https://en.wikipedia.org/wiki/Polyol |
The polyol pathway is a two-step process that converts glucose to fructose. [ 1 ] In this pathway glucose is reduced to sorbitol, which is subsequently oxidized to fructose. It is also called the sorbitol-aldose reductase pathway .
The pathway is implicated in diabetic complications, especially in microvascular damag... | https://en.wikipedia.org/wiki/Polyol_pathway |
Polyoxetane ( POX ), or poly(oxetane) , is synthetic organic heteroatomic thermoplastic polymer with molecular formula (–OCH 2 CH 2 CH 2 –) n . It is polymerized from oxetane monomer , which is a four-membered cyclic ether .
Needed chemistry was observed and developed through the 1930s and 1940s. The very first polyme... | https://en.wikipedia.org/wiki/Polyoxetane |
Polyoxins are a group of peptidyl nucleoside antibiotics . [ 1 ] [ 2 ] They are a complex produced by Streptomyces cacaoi var. asoensis and S . piomogenus. [ 3 ] Polyoxin compounds contain the same base structure but differ in the composition of certain functional groups. At least fifteen polyoxin compounds are known, ... | https://en.wikipedia.org/wiki/Polyoxins |
In chemistry , a polyoxometalate (abbreviated POM ) is a polyatomic ion , usually an anion , that consists of three or more transition metal oxyanions linked together by shared oxygen atoms to form closed 3-dimensional frameworks. The metal atoms are usually group 6 (Mo, W) or less commonly group 5 ( V , Nb , Ta ) and ... | https://en.wikipedia.org/wiki/Polyoxometalate |
Polypeptoids are a class of peptidomimetic polymers. They are based on an N-substituted glycine backbone, the side chains are attached directly to the polymer backbone via the nitrogen of the amide group , rather than at the α-carbon as in polypeptides. As opposed to polypeptides , polypeptoids have an achiral backbone... | https://en.wikipedia.org/wiki/Polypeptoids |
Feeding is the process by which organisms, typically animals , obtain food . Terminology often uses either the suffixes -vore, -vory, or -vorous from Latin vorare , meaning "to devour", or -phage, -phagy, or -phagous from Greek φαγεῖν ( phagein ), meaning "to eat".
The evolution of feeding is varied with some feeding ... | https://en.wikipedia.org/wiki/Polyphagy |
Polypharmacology is the design or use of pharmaceutical agents that act on multiple targets or disease pathways. [ 1 ]
Despite scientific advancements and an increase of global R&D spending, drugs are frequently withdrawn from markets. This is primarily due to their side effects or toxicities. Drug molecules often int... | https://en.wikipedia.org/wiki/Polypharmacology |
Polypharmacy (polypragmasia) is an umbrella term to describe the simultaneous use of multiple medicines by a patient for their conditions. [ 1 ] [ 2 ] [ 3 ] The term polypharmacy is often defined as regularly taking five or more medicines but there is no standard definition and the term has also been used in the contex... | https://en.wikipedia.org/wiki/Polypharmacy |
A polyphenic trait is a trait for which multiple, discrete phenotypes can arise from a single genotype as a result of differing environmental conditions. It is therefore a special case of phenotypic plasticity .
There are several types of polyphenism in animals, from having sex determined by the environment to the cas... | https://en.wikipedia.org/wiki/Polyphenism |
Polyphenylene sulfide (PPS) is an organic polymer consisting of aromatic rings linked by sulfides . Synthetic fiber and textiles derived from this polymer resist chemical and thermal attack. PPS is used in filter fabric for coal boilers , papermaking felts , electrical insulation , film capacitors , specialty membranes... | https://en.wikipedia.org/wiki/Polyphenylene_sulfide |
A polyphosphate is a salt or ester of polymeric oxyanions formed from tetrahedral PO 4 ( phosphate ) structural units linked together by sharing oxygen atoms. Polyphosphates can adopt linear or a cyclic (also called, ring) structures. In biology, the polyphosphate esters ADP and ATP are involved in energy storage. A va... | https://en.wikipedia.org/wiki/Polyphosphate |
Polyphosphate-accumulating organisms (PAOs) are a group of microorganisms that, under certain conditions, facilitate the removal of large amounts of phosphorus from their environments. The most studied example of this phenomenon is in polyphosphate-accumulating bacteria (PAB) found in a type of wastewater processing kn... | https://en.wikipedia.org/wiki/Polyphosphate-accumulating_organisms |
A polyphyletic group is an assemblage that includes organisms with mixed evolutionary origin but does not include their most recent common ancestor. [ 1 ] The term is often applied to groups that share similar features known as homoplasies , which are explained as a result of convergent evolution . The arrangement of t... | https://en.wikipedia.org/wiki/Polyphyly |
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