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Longer titles found: Direct product of groups (view), Semidirect product (view), Subdirect product (view)

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alternate case: direct product

Matrix multiplication (6,456 words) [view diff] no match in snippet view article find links to article

In mathematics, particularly in linear algebra, matrix multiplication is a binary operation that produces a matrix from two matrices. For matrix multiplication

byproduct of the evolution of some other characteristic, rather than a direct product of adaptive selection. Stephen Jay Gould and Richard Lewontin brought

Okinawa, Japan. It is made from long grain indica rice, and is not a direct product of brewing (like sake) but of distillation (like shōchū). The majority

in previous versions. On July 30, 2009, Apple discontinued Shake. No direct product replacement was announced by Apple, but some features are now available

is also called the direct product, Kronecker product, categorical product, cardinal product, relational product, weak direct product, or conjunction. As

In mathematics, the restricted product is a construction in the theory of topological groups. Let I {\displaystyle I} be an index set; S {\displaystyle

genus 4. The full group of symmetries (including reflections) is the direct product S 5 × Z 2 {\displaystyle S_{5}\times \mathbb {Z} _{2}} , which has order

Internet. MECW also gains revenue from live events, product licensing, and direct product sales. Jason Daniel is also the President of the company and head booker

with naïve realism. The latter is the idea that knowledge must be a direct product of contact between an investigator and an independently existing reality

prior to purchase or consumption. Consumers rely on prior experience, direct product inspection and other information search activities to locate information

The tensor product of two fields is sometimes a field, and often a direct product of fields; In some cases, it can contain non-zero nilpotent elements

). The full automorphism group (including reflections) is the semi-direct product G L 2 ( 3 ) ⋊ Z 2 {\displaystyle GL_{2}(3)\rtimes \mathbb {Z} _{2}}

the US and that are the direct product of US technology or software, or they are developed from a plant that is the direct product of US technology or software

different operation. The Kronecker product is also sometimes called matrix direct product. The Kronecker product is named after the German mathematician Leopold

as the tensor product Kn × K2, as the complement of the Cartesian direct product of Kn and K2, or as a bipartite Kneser graph Hn,1 representing the 1-item

relations studies and defense analyses assume that military power is a direct product of material resources, often measured in terms of the size of a state's

index set A. Its algebraic and topological structures are the group direct product and product topology over the cyclic group of order 2 (which is itself

trademark boxed-section vehicle frames. Land Rover used boxed frames in a direct product bloodline until the termination of the original Defender in 2016; and

Paris in December 2015 and became effective in November 2016. Another direct product of the Climate Summit 2014 was the New York Declaration on Forests.

denying that racism exists). Internalized racism as a phenomenon is a direct product of a racial classification system, and is found across different racial

it transforms under Lorentz transformations as a tensor product, or direct product in physics parlance, of one-particle states as prescribed by equation

normal subgroup of G, called the "Frobenius kernel", and G is the semi-direct product of H and N (Frobenius' theorem). Lyndon, Roger C.; Schupp, Paul E. (2001)

eiφ leaves the norm invariant. Thus U(3) can be decomposed into a direct product U(1)×SU(3)/Z3. Because of this additional constraint, SU(3) has dimension

always Artinian rings; in particular they are isomorphic to a finite direct product of principal Artinian local rings. A local Artinian principal ring is

Software Group (the business unit responsible for marketing the Connect:Direct product and other file transfer products sourced from the pre-1993 Sterling

Software Group (the business unit responsible for marketing the Connect:Direct product and other file transfer products sourced from the pre-1993 Sterling

homomorphic image of a PI-ring is a PI-ring. A finite direct product of PI-rings is a PI-ring. A direct product of PI-rings, satisfying the same identity, is

and on the roots of unity, giving a non-abelian Galois group as semi-direct product. The Kummer theory gives a complete description of the abelian extension

directed to certain groups of, using tools like direct emailing, or direct product demonstrations for a specific group of people, like giving away vitamin

and it has also been suggested that the Ulster White was either the direct product of selective breeding of the Old Irish or of early 19th century crosses

2014. "DC Direct product page". DC Comics. Archived from the original on August 25, 2011. Retrieved October 28, 2014. "DC Direct product page". DC Comics

T ) {\displaystyle o(S)\oplus o(T)} , while the ordinal type of the direct product is o ( S ) ⊗ o ( T ) {\displaystyle o(S)\otimes o(T)} . The natural

group of symmetries of X {\displaystyle {\mathcal {X}}} is the semi-direct product: Diff ( X ) = G ⋊ Diff ( M ) {\displaystyle {\text{Diff}}({\mathcal

monoidal category, is symmetric monoidal. The tensor product is the direct product of objects, and any terminal object (empty product) is the unit object

 1–145, MR 1878882 Takesaki, Masamichi (1964), "On the cross-norm of the direct product of C*-algebras", The Tohoku Mathematical Journal, Second Series, 16:

exist in either the α- or β-anomeric form. In glycogenolysis, it is the direct product of the reaction in which glycogen phosphorylase cleaves off a molecule

This decomposition of the orthogonal symmetric Lie algebra yields a direct product decomposition of the corresponding compact symmetric space H / K when

that minimizes distance on each interval) then it is isometric to a direct product of the real line and a complete (n-1)-dimensional Riemannian manifold

ignorance and lethargy in the life of poor and dispossessed are the direct product of the whole situation of economic, social, and political domination

modular forms is concerned with the study of certain functions on the direct product H n {\displaystyle {\mathcal {H}}^{n}} of n {\displaystyle n} copies

direct product of nonzero objects. Some typical examples are the following. The category of all finite abelian groups under the usual direct product operation

profiles of G {\displaystyle G} . A solution concept is an element of the direct product Π G ∈ Γ 2 S G ; {\displaystyle \Pi _{G\in \Gamma }2^{S_{G}};} i.e.,

{\displaystyle \rho _{\text{pseudo}}} is a direct product of group homomorphisms; it is the direct product of the fundamental homomorphism on SO ( n )

also an R-algebra. Direct products The direct product of a family of R-algebras is the ring-theoretic direct product. This becomes an R-algebra with the

declined to 14% of the population of Missouri (5,595,211). This shift is a direct product of the small geographic size of St. Louis City, which is nearly unique

D2h (that of a cuboid), of type Dih2 × Z2 = Z2 × Z2 × Z2. It is the direct product of the normal subgroup of T (see above) with Ci. The quotient group

labor will lead to an increase in productivity. Decentralized industry, direct product exchange, integration of labor, the combination of mental and physical

because the Lorentz group is simple, while the Galilean group is a semi-direct product of rotations and Galilean boosts. This means that the Lorentz group

validity is the same as above, replacing the direct product of the fields Fq[x]/fi by the direct product of their subfields with q elements. The complexity

bio-mechanical model predicts that morphological variation in torus size is the direct product of differential tension caused by mastication, as indicated by an increase

{Z} /n_{k}\mathbb {Z} } between the ring of integers modulo N and the direct product of the rings of integers modulo the ni. This means that for doing a

group A semigroup which is left simple and right cancellative. The direct product of a left zero semigroup and an abelian group. C&P p. 37, 38 Right zero

i {\textstyle \prod _{i\subseteq \Sigma }{\mathcal {M}}_{i}} be the direct product of the structures and I {\displaystyle I} be the collection of finite

(x_{0},\lambda _{0})=(0,0).} Let us split Y {\displaystyle Y} into the direct product Y = Y 1 ⊕ Y 2 {\displaystyle Y=Y_{1}\oplus Y_{2}} , where dim ⁡ Y 2

isomorphic to H × H {\displaystyle \mathbb {H} \times \mathbb {H} } , the direct product of two quaternion algebras. The center of that ring is R × R {\displaystyle

of this ring. Tate (1950) defined the ring of adeles as a restricted direct product, though he called its elements "valuation vectors" rather than adeles

g. Social Media). (See references below, Brand Ecosystems) Not only direct product experience, but also any stimulus provided by traditional marketing

roots obtained by replacing αi by −α0. In the first case it is the direct product of the circle group generated by Xi and a semisimple compact group with

\mathbb {F} _{2}} . The reduced cohomology ring of wedge sums is the direct product of their reduced cohomology rings. The cohomology ring of suspensions

to the acceptance of Tobler's law, and Tobler's law can be seen as a direct product of the quantitative revolution. In 2003, the American Association of

ring is a terminal object in Ring. The product in Ring is given by the direct product of rings. This is just the cartesian product of the underlying sets

certain charming simplicity in his character because it was the clear and direct product of his nature, unhelped by outside influences." Later in his life, his

accepted by the Commission in 2013. In addition, the DC Circulator was a direct product of NCPC planning and advising. Current efforts include the Pennsylvania

note in a 1988 interview with Flipside magazine that they were not a direct product of Gilman, having been established as a band years before the launch

Chantix/Champix (varenicline) to treat nicotine addiction, which recorded direct product revenues of more than $1 billion in 2019, $919 million in 2020, and

automorphism group of the Tutte 12-cage is of order 12,096 and is a semi-direct product of the projective special unitary group PSU(3,3) with the cyclic group

zymology, feedback serves as regulation of activity of an enzyme by its direct product(s) or downstream metabolite(s) in the metabolic pathway (see Allosteric

the perushim community in Safed. Believing that the catastrophe was a direct product of their neglect of Jerusalem, the surviving members of the perushim

Recent results, however, show that HAO does not produce nitrite as a direct product of catalysis. This enzyme instead produces nitric oxide and three electrons

x}1&0\\0&0\end{pmatrix}}={\begin{pmatrix}0&0\\0&0\end{pmatrix}}.} A direct product of two or more nonzero rings always has nonzero zero divisors. For example

eastward at about 2 cm/year (0.79 in/year). This rifting was not the direct product of hotspot interaction as it occurred over a cooler than normal mantle

actions commute by associativity. This can be extended to Rn (the n-fold direct product of R). Any two-sided ideal of a ring R is an R-R-bimodule, with the

minimal prime ideals of A, then the total ring of fractions K of A is the direct product of the residue fields κ ( p i ) = Q ( A / p i ) {\displaystyle \kappa

smash product of two pointed spaces is essentially the quotient of the direct product and the wedge sum. We would like to say that the smash product turns

cogenerator allows one to express every object as a subobject of a direct product of copies of the cogenerator. One is often interested in projective

value-added chemicals from biomass which included glucaric acid—the direct product of the oxidation of glucuronic acid. The first biosynthetic production

"The bootlegging and gang killings...are not the by-product but the direct product of the Volstead Act, and the supporters of this crime breeding legislation

Hence G {\displaystyle G} is abelian and in fact isomorphic to the direct product of two cyclic groups each of order p . {\displaystyle p.} More generally

"The bootlegging and gang killings...are not the by-product but the direct product of the Volstead Act, and the supporters of this crime breeding legislation

selfish determinants of collective action are, according to Popkin, a direct product of the inherent instability of peasant life. The goal of a laborer,

components of r, and the spin-2 representation of the 4d orbitals. This direct product, a 45-dimensional representation of SU(2), is not an irreducible representation

semi-direct product of groups using the topology of fibrations and properties of Eilenberg-Maclane spaces. Recall that for a semi-direct product of groups

identifying a vector with its coordinate vector) to identify V with the direct product R × R = R2, and the equivalence relation becomes (x, y) ~ (w, z) if

are almost always single-molecule products. Consumer products include direct product sales of chemicals such as soaps, detergents, and cosmetics. Typical

P_{\mathrm {TNL} }} both equal to 1. Not all neutrons are emitted as a direct product of fission; some are instead due to the radioactive decay of some of

of Michelle Obama, etc.' to know who Obama is. (6) However is not a direct product of the theses. Kripke notes "(6) need not be a thesis of the theory

M} (in étale topology or fppf topology) π {\displaystyle \pi } is a direct product π | U : G × U → U {\displaystyle \pi |_{U}:G\times U\to U} . A G-gerbe

with his wife, Clara Schumann. Hence, this symphony can be seen as a direct product of his shift of compositional strategy and counterpoint study. The symphony

would have affected the characters in Kesey's novel. The novel is a direct product of Kesey's time working the graveyard shift as an orderly at a mental

produced by both walks. This is equivalent to doing random walks on the direct product of the pair of graphs, and from this, a kernel can be derived that can

economy which replaced market relationships by direct calculation and direct product exchange, has nowhere been established [...]. Cottrell, Allin; Cockshott

relatively hyperbolic, relative to some free abelian subgroups. The semi-direct product of a free group by an infinite cyclic group is relatively hyperbolic

the Franklin graph is of order 48 and is isomorphic to Z/2Z×S4, the direct product of the cyclic group Z/2Z and the symmetric group S4. It acts transitively

coordinate z {\displaystyle z} is inessential; our spacetime is the direct product of a factor R with a signature −++ three-manifold. Suppressing z {\displaystyle

A_{i}\in \mathbb {F} ^{n_{i}\times m_{i}}} . Kronecker product (matrix direct product resulting in a block matrix) Jordan normal form (canonical form of a

Majority of terpenes found in cannabis are hydrocarbons, which are a direct product of terpene synthase (TPS) enzymes. The molecular make up of terpenes

perspective, a peer universe can also contain companies that are not only direct product competitors but are subject to similar cycles, suppliers and other external

and thus SMIC may have violated the Department of Commerce’s Foreign Direct Product Rule." On 14 November 2019, SMIC announced that volume production of

perspective, a peer universe can also contain companies that are not only direct product competitors but are subject to similar cycles, suppliers and other external

carefully and was not always given. In many periods "replicas were the direct product of collecting, as collectors have always preferred recognizable masterpieces

necessarily have finite uniform dimension. For example, an infinite direct product of nonzero rings is a finitely generated (cyclic!) module over itself

are isomorphic rings: take R to be the group ring of the restricted direct product of infinitely many copies of A ⨯ B. The proof of the Cantor–Bernstein–Schroeder

"astonishing" song "may be Queen's greatest song of all". He felt it was "a direct product of [Mercury's] hedonism and promiscuity: an unrepentant, joyous, utterly

effective host to possess sufficient verbal skills to mask this lack of direct product knowledge. What A Great Idea It Turned Out To Be Selling Can Openers

Herzberg-Teller scattering, if the symmetry of the mode is contained in the direct product of the two electronic state symmetries. Resonance enhancement is most

clarifying price and risks and making it easier for consumers to make direct product comparisons." In 2012, many stay-at-home spouses complained that because

anyone's social, economic, or class level. Inclusivity in education is a direct product of intersectionality, as it takes into consideration elements of peoples'

US$10.761 million, although the individual claims—$2.261 million in direct product damage; $4.3 million in emotional, reputational, and financial distress;

under certain assumptions, the symmetries of the S-matrix must be a direct product of the Poincaré group with a compact internal symmetry group or if there

dioxide in the first dark reaction of photosynthesis (Figure 3). The direct product of RuBP carboxylase reaction is glyceraldehyde-3-phosphate; these are

ISSN 1420-8954. S2CID 1126187. Murnaghan, D. (1938). "The Analysis of the Direct Product of Irreducible Representations of the Symmetric Groups". Amer. J. Math

RR43 (≈252 km). Brown and colleagues proposed that the family were a direct product of the impact that removed Haumea's ice mantle, but a second proposal

algebraic structure is said to be doubly graded if the index set is a direct product of sets; the pairs may be called "bidegrees" (e.g. see Spectral sequence)

special, every quasigroup Q induces a semisymmetric quasigroup QΔ on the direct product cube Q3 via the following operation: (x1, x2, x3) ⋅ (y1, y2, y3) = (y3

semisimple ring, so by the Artin–Wedderburn theorem it decomposes as a direct product of matrix rings. The Fourier transform on finite groups explicitly exhibits

grounds of Art. 138 under its own national law infringement by the direct product of a patented process patent term, 20 years from the filing date All

each with uncountable chromatic number, but with countably chromatic direct product. That is, Hedetniemi's conjecture fails for infinite graphs. In a paper

been known for producing ads that invoke surreal images in lieu of direct product details, in partnership with Swedish ad agency Paradiset DDB, Stockholm

restriction since the disks and the equipment to make them were not a direct product of any American semiconductor technology or software. In April 2023

Gibbs. New Haven: Yale University Press. The dot product is called "direct product", and cross product is called "skew product". A History of Vector Analysis

Ken Kesey's novel One Flew Over the Cuckoo's Nest; Kesey's novel is a direct product of his time working the graveyard shift as an orderly at a mental health

predecessor of and inspiration for the battlecruiser. The heavy cruiser was a direct product of the First London Naval Treaty of 1930, which divided cruisers into

abilities like learning and memory, and perhaps consciousness itself. A direct product of neuropsychopharmacological research is the knowledge base required

about a point on the line of reflection. It is isomorphic to a semi-direct product of Z and C2. Example pattern with this symmetry group: For any symmetry

increase their comfort levels. Therefore, according to Parker GDP is a direct product of the natural compensation of humans to their climate. Political geographers

p {\displaystyle K^{sep}} ). A ring is called Henselian if it is a direct product of a finite number of Henselian local rings. Assume that ( K , v ) {\displaystyle

of the Nauru graph is a group of order 144. It is isomorphic to the direct product of the symmetric groups S4 and S3 and acts transitively on the vertices

to define the Pontryagin product we first need a map which sends the direct product of the m-th and n-th homology group to the (m+n)-th homology group of

given the structure of an abelian group which is isomorphic to the direct product of Z {\displaystyle \mathbb {Z} } and the sandpile group (also referred

complete lattice L: L is completely distributive. L can be embedded into a direct product of chains [0,1] by an order embedding that preserves arbitrary meets

function f ( γ , t ) {\displaystyle f(\gamma ,\,t)} , defined on the direct product Γ × R 1 {\displaystyle \Gamma \,\times \,\mathbb {R} ^{1}} (where R

regard L 2 ( G ) {\displaystyle L^{2}(G)} as a representation of the direct product group G × G {\displaystyle G\times G} , with the two factors acting

The decision where to produce is based on many factors, not simply direct product costs. Marketing and operations are both affected greatly by producing

64(2) EPC. The EPC requires that national courts must consider the "direct product of a patented process" to be an infringement. Article 64(2) EPC reads:

determination of the representations of a group G which is the semi-direct product of an abelian group N by a group H that acts by automorphisms of N.

and every time only because God willed it to happen—the event was "a direct product of divine intervention as any more attention grabbing miracle". Averroes

Horton graph is of order 96 and is isomorphic to Z/2Z×Z/2Z×S4, the direct product of the Klein four-group and the symmetric group S4. The characteristic

matrices with real entries and determinant 1, and ⋉ denotes the semi-direct product. SL(n+1,R) ⋉ Rn+1 forms a Lie group. The affine normal line at a point

SO(3)/SU(2) over the complex numbers. Given two irreps, the tensor direct product can be reduced to a sum of irreps, giving rise to the Clebcsh-Gordon

decrease certain behaviours. Contingency management programs are a direct product of research from operant conditioning. Behavioural therapy based on

ideas about right and wrong, and fair and unfair, that are not the direct product of adult teaching and that are often maintained in the face of adult

Klavžar, Sandi; Zmazek, B. (1996), "On a Vizing-like conjecture for direct product graphs", Discrete Mathematics, 156 (1–3): 243–246, doi:10.1016/0012-365X(96)00032-5

it is still a G-set.) The ring structure on A(G) is induced by the direct product of G-sets; the multiplicative identity is the (isomorphism class of

the p-completion of a compact connected Lie group and BK is finite direct product of simple exotic p-compact groups i.e., simple p-compact groups whose

actors Inter-firm relations Competitive Collaborative Mode of production Direct product competition Differentiated, niche production Legal system Complete and

and irreducible otherwise. A reducible pair can be decomposed into a direct product of irreducible ones, and for many purposes, it is enough to restrict

competing factor is the computational speedup available when using the direct product of two one-dimensional grids. Despite this, the Lebedev grid still outperforms

integers. Polynomials in several variables simply take N to be the direct product of several copies of the monoid of non-negative integers. Several interesting

the full symmetry group of the spherical polyhedron is then just the direct product with reflection through the origin, which is the kernel on passage to

historical precedent. However, others dispute social emancipation as being a direct product of capitalism or question the emancipation that has resulted. The feminist

existence of moral support. The morals a person has as an adult, come as a direct product of their moral development. Literature surrounding this field of study

group's commercial success with their Top 40 debut, Ultimate Spinach, a direct product of the marketing campaign known as the Bosstown Sound. However, the

Moreover, Q m a x r ( R ) {\displaystyle Q_{max}^{r}(R)} is a finite direct product of full linear rings if and only if R has a nonsingular, faithful module

the Virasoro conformal algebra, a current conformal algebra or a semi-direct product of the two. There are also partial classifications of infinite subalgebras

group theory. The configuration 2p2 has the symmetry of the following direct product in the full rotation group: Γ(1) × Γ(1) = Γ(0) + [Γ(1)] + Γ(2), which

appeal to companies' target demographic. Avenues such as sponsorship or direct product placement and sampling are explored in turn. Unlike traditional event

is an integral manifold for T(i)M. Furthermore, Hol(M) splits as a direct product of the holonomy groups of each Mi, the maximal integral manifold of

products within the pre-assigned time frame shall be delivered, enabling direct product sale between customers and SHGs. Studies on economics of fishery enterprises

U_{i}U_{j}=-U_{j}U_{i}\,\,(i\neq j).} This is a projective representation of a direct product of N − 1 groups of order 2. (N is assumed to be greater than 1.) The

Z ) × {\displaystyle (\mathbb {Z} /q\mathbb {Z} )^{\times }} is the direct product of a cyclic group of order 2 (generated by −1) and a cyclic group of

(even infinitely many) injective modules is injective; conversely, if a direct product of modules is injective, then each module is injective (Lam 1999, p

A;M)} . Recall that the singular cohomology module of a space is the direct product of the singular cohomology modules of its path components. A nonempty

retrieved 2017-07-18 Murnaghan, F. D. (1938), "The Analysis of the Direct Product of Irreducible Representations of the Symmetric Groups", American Journal

right R {\displaystyle R} -module and M ∗ {\displaystyle M^{*}} is a direct product of copies of the right R {\displaystyle R} -modules R ∗ {\displaystyle

means they have loose joints allowing them to flatten their bodies; a direct product of their environment.  The introduction of new research techniques including

may also consider the following subspace of elements in the countable direct product of A {\displaystyle A} ℓ 2 ( A ) = H A = { ( a i ) | ∑ i = 1 ∞ a i ∗

matter which allowed Matei Călinescu to propose that Un om mare was a direct product of its author's experience with drugs. The same commentator, who deemed

differential algebra is an algebra together with a derivation. direct A direct product of a family of rings is a ring given by taking the cartesian product

national law, the EPC requires that national courts must consider the "direct product of a patented process" to be an infringement. The "extent of the protection"

child nutrition in industrialized countries. These disparities are a direct product of social inequalities and social inequalities are rising throughout

style and good writing" to produce stories. Wordsmith is sold as both a direct product and service to clients. In October 2015, the Wordsmith platform was

2 {\displaystyle \phi :A_{1}\to A_{2}} to be a subalgebroid of the direct product A 1 × A 2 {\displaystyle A_{1}\times A_{2}} (introduced below). Lie

in different sub-spaces of the Hilbert space, the entire field is a direct product of | n k l ⟩ {\displaystyle |n_{\mathbf {k} _{l}}\rangle } over all

#51 (I†*/C2;I/C2)†*, Conway ±1/60[I×I].2). It is isomorphic to the direct product of abstract groups: S5×C2. The chiral extended pentachoric group is

from the Stan Kenton orchestra and Robert Graettinger (1947–1953) is a direct product of the experimental American music scene of the post World War II era

industry. The signing of distribution agreements and the launch of direct product brands throughout the 1980s resulted in Anglia holding much more extensive

1969 theorem of Larson-Sweedler on Hopf modules and integrals. The direct product and tensor product of Frobenius algebras are Frobenius algebras. A finite-dimensional

problem for the fundamental group of the torus. However this group is the direct product of two infinite cyclic groups and so has a solvable word problem. In

Systems division. All these design and manufacture innovations were a direct product of Arthur Collins' creativity. The following are Patents held Solely

of phosphorus pentachloride on inorganic sulfites was regarded as a direct product of the reaction and which formed the only experimental evidence in favour

than the earlier LBA examples and Tylecote suggests that they may be a direct product of smelting. Theoretically such an ingot could be formed in the base

completion (equivalent to nearly $6 million in 2008). The bridge was a direct product of the City Beautiful Movement in Philadelphia in the early years of

Farm Park have been in existence since 1972, when they emerged as a direct product of the environmental and community gardening movements of the 1970s

geodetically complete CAT(0) cubical complex X, then either X splits as a direct product of two unbounded convex subcomplexes, or G contains a rank-1 element

despite it being the most openly revolutionary work of its era and a direct product of the suppression Chernyshevsky had faced. The novel marked a significant

landscapes, including the ruins of the now-neglected Great Wall – a direct product of Tang's frontier policy. Han Chinese power during the tumultuous post-Tang

its custom web crawler, to search the web for prices, and it allows direct product feeds from retailers at no cost. The search engine's rapid growth has

theory for the understanding of environmental problems. This work was a direct product of his PhD research at the EUI in Florence, in the late 1980s under

definitions). Finally, some authors use the name Picard group to refer to the direct product of the sandpile group and Z {\displaystyle \mathbb {Z} } , which naturally

Stallings group is exactly the kernel of the homomorphism from the direct product of three copies of the free group F 2 {\displaystyle F_{2}} to the additive

these polities and the detail with which they have been recorded are a direct product of nineteenth- and twentieth-century history and the circumstances which

operates in a non-profit basis from 1 October 2011th. It occurs as a direct product of the development program EMvI MEDIA with a view to developing all

, {\displaystyle |z_{1}|=Q,} then I K {\displaystyle I_{K}} is the direct product of I K 1 {\displaystyle I_{K}^{1}} and the subgroup generated by z 1

Evolutionary ecology assumes that “behavioral variation itself is not the direct product of natural selection, rather, selection enters the explanation only

measurement aims to provide greater specificity. 11-Deoxycortisol is a direct product of 17α-hydroxyprogesterone, with 21-hydroxylase catalyzing the reaction

finitely generated groups commensurable with groups embeddable in a direct product of finitely many free groups, and Brough conjectured that every poly-context-free

prior to purchase or consumption. Consumers rely on prior experience, direct product inspection and other information search activities to locate information

21st century. As noted by Chris Allen, the EDL is nevertheless "not a direct product of the traditional far-right milieu" in Britain, differing from other

decomposition is intrinsic. When G is abelian, G {\displaystyle G} is then the direct product of the closed subgroup of the semisimple elements in G and that of unipotent

mentioned above. Thus a Higgs bundle may be thought of as an element of the direct product ( E , Φ ) ∈ H ˇ 1 ( X , G L ( r , C ) ) ⊕ H 0 ( X , End ⁡ ( E ) ⊗ Ω

how far our innate sense of self extends until we start to become a direct product of our surroundings and experiences. Can technology influence our mind

a product of order 3. The graph is connected unless the group has a direct product decomposition. The graphs corresponding to the smallest symmetric groups

example). Don Eleuterio despises the Puerto Rican culture, but is a direct product of it. His commentary on Puerto Rican culture is affected by his personal

p−1(b) = F for all points b from B and p−1(U) is homeomorphic to the direct product U × F where F is the fiber of B. Therefore, any set is actually a named

interest or the city of Boston. It was assumed that youth violence was the direct product of gangs involvement almost in every youth violence incident. Some gang

technical, this general construction is of enormous versatility for semi-direct product groups of the type R n ⋊ K {\displaystyle \mathbb {R} ^{n}\rtimes K}

{\displaystyle \ell } . A torus is said to be induced if it is the direct product of finitely many tori of the form considered in the previous paragraph

conditions. This is the topology induced by the natural map of C(X) into the direct product of the Banach spaces Cb(XN) of continuous bounded functions on XN. It

Flensted–Jensen's method uses the centraliser of SO(2) in SL(2,C) which splits as a direct product of SO(2) and the 1-parameter subgroup K1 of matrices g t = ( cosh ⁡

symmetry group of S-matrix is necessarily locally isomorphic to the direct product of an internal symmetry group and the Poincaré group. This means that

associative commutative algebra Ae is straightforward since it is a direct product. For c = Σ αi ei and d = Σ βi ei, the Bergman operator on Ae has determinant

to take up the central throne. Tatila Akufuna (son of Imbue) was a direct product of the Mbunda at Lukwakwa. This is a Mbunda Chieftainship related to

Third, Krach's State Department team succeeded in expanding the Foreign Direct Product Rule to prevent Huawei from "dodging" U.S. export controls. Senate Democratic

and choose your favorites before making a playlist of them. It is a direct product of the streaming era philosophy. Regardless, fans of DL will most certainly

data using XML or ASCII text ISO 28219:2009 Packaging - Labelling and direct product marking with linear bar code and two-dimensional symbols ISO 28238:2010

and data-driven approaches to studying geographic phenomena. It is a direct product of the quantitative revolution in geography. It was influenced by developments