For United States expenditures under subsections ( A ), ( B ), ( D ), ( E ), ( F ), ( H ) through ( R ) of Section 104 of the Act or under any of such subsections, the rupee equivalent of $200 million.

For example, R. I. Pervo dates Acts to the first quarter of the 2nd century.

For example, the field extension R / Q, that is the field of real numbers as an extension of the field of rational numbers, is transcendental, while the field extensions C / R and Q (√ 2 )/ Q are algebraic, where C is the field of complex numbers.

For the case of a non-commutative base ring R and a right module M < sub > R </ sub > and a left module < sub > R </ sub > N, we can define a bilinear map, where T is an abelian group, such that for any n in N, is a group homomorphism, and for any m in M, is a group homomorphism too, and which also satisfies

From Comrade Semichastny's speech I learn that the government, ' would not put any obstacles in the way of my departure from the U. S. S. R .' For me this is impossible.

For example, an " X " is used to indicate a variable group amongst a class of compounds ( though usually a halogen ), while " R " is used for a radical, meaning a compound structure such as a hydrocarbon chain.

For example, intervals, where takes all integer values in Z, cover R but there is no finite subcover.

For any subset A of Euclidean space R < sup > n </ sup >, the following are equivalent:

For example, he believed ( as most Romans ) that his ancestor Appius Claudius Caecus had used the censorship to introduce the letter " R " and so used his own term to introduce his new letters.

For example, the Cyrillic letter Р is usually written as R in the Latin script, although in many cases it is not as simple as a one-for-one equivalence.

* For a more detailed account of Christine de Pizan ’ s rhetorical strategies refer to Jenny R. Redfern ’ s excerpt Christine de Pisan and The Treasure of the City of Ladies: A Medieval Rhetorician and Her Rhetoric ( in Reclaiming Rhetorica, ed.

For regions in R < sup > 3 </ sup > more complicated than this, the latter statement might be false ( see Poincaré lemma ).

For example, if u < sub > 1 </ sub > is an eigenvector of A, with a real eigenvalue smaller than one, then the straight lines given by the points along α u < sub > 1 </ sub >, with α ∈ R, is an invariant curve of the map.

For any positive integer n, the set of all n-tuples of real numbers forms an n-dimensional vector space over R, which is denoted R < sup > n </ sup > and sometimes called real coordinate space.

*( EF2 ) For all nonzero a and b in R,.

For example, an ester ( RCOOR ') has an ester functional group ( COOR ) and is composed of an alkoxy moiety (- OR ') and an acyl moiety ( RCO -), or, equivalently, it may be divided into carboxylate ( RCOO -) and alkyl (- R ') moieties.

For materials that absorb light, like metals and semiconductors, n is complex, and R < sub > p </ sub > does not generally go to zero.

For example, Latin P came to be written like Greek rho ( written Ρ but pronounced ), so the Roman letter equivalent to rho was modified to R to keep it distinct.

( For example, in spherical coordinates, let radius r go to R² / r where R is the Earth's radius.

For any information rate R < C and coding error ε > 0, for large enough N, there exists a code of length N and rate ≥ R and a decoding algorithm, such that the maximal probability of block error is ≤ ε ; that is, it is always possible to transmit with arbitrarily small block error.

For example, a " 512 megabyte " RAM module is 512 × 1024 < sup > 2 </ sup > bytes ( 512 ×, or ), rather than.

For instance, since a function is bijective if and only if it is both injective and surjective, a module homomorphism is an isomorphism if and only if it is both a monomorphism and an epimorphism.

For example, the Fitting lemma shows that the endomorphism ring of a finite length indecomposable module is a local ring, so that the strong Krull-Schmidt theorem holds and the category of finite length modules is a Krull-Schmidt category.

* For a semisimple module, the endomorphism ring is a von Neumann regular ring.

For example, one could have an exact sequence of vector spaces and linear maps, or of modules and module homomorphisms.

For "× 8 "- registered DIMMs, each side is 72 bits wide, so the memory controller only addresses one side at a time ( the two-sided module is dual-ranked ).

For many mechanical data processing machines, such as the IBM punched card accounting machines, their calculating operations were directed by the use of a quick-swap control panel wired to route signals between module sockets.

For example, the SA Arch module contains tools for doing live SANS 204 Energy efficiency calculations now required when submitting building plans in South Africa.

For an abstract vector space V ( rather than the concrete vector space ), or more generally a module M over a ring R, with the endomorphism algebra End ( M ) ( algebra of linear operators on M ) replacing the algebra of matrices, the analog of scalar matrices are scalar transformations.

For example the space stations Salyut 7 and Mir, and the ISS module Zarya were capable of unmanned remote guided station keeping, and docking maneuvers with both resupply craft and new modules.

For example, the module multimethods. py provides CLOS-style multimethods for Python without changing the underlying syntax or keywords of the language.

For example, projects can have bug tracking issues assigned to each project, the list of project customers becomes a customer relationship management module, and each person on the project plan has their own task lists, calendars, and messaging functionality associated with their projects.

For Apache's httpd, the mod_rewrite module is often used to reject or redirect attempted hotlinks to images and media.

For cycloidal gears ( as used in BS978-2 Specification for fine pitch gears ) and cycloidal-type gears each module, ratio and number of teeth in the pinion requires a different hobbing cutter so the technique is only suitable for large volume production.

For example, the first cohomology group of a complex elliptic curve is a free module of rank 2 over the integers, while the first ℓ-adic cohomology group of an elliptic curve over a finite field is a free module of rank 2 over the ℓ-adic integers, provided l is not the characteristic of the field concerned, and is dual to its Tate module.

For abelian varieties the first ℓ-adic cohomology group is the dual of the Tate module, and the higher cohomology groups are given by its exterior powers.

For scripting languages, FreeTDS is used in conjunction with a module for that language such as DBD :: Sybase in Perl, Python-Sybase for Python, or Ruby DBI for Ruby

For now, the GSAPI GNOME Speech module is being

* For every index set I, the addition map M < sup >( I )</ sup > → M can be extended to a module homomorphism M < sup > I </ sup > → M ( here M < sup >( I )</ sup > denotes the direct sum of copies of M, one for each element of I ; M < sup > I </ sup > denotes the product of copies of M, one for each element of I ).

For example, if M is a left module, we can define multiplication on the right to be the same as multiplication on the left.

For the density of the observable universe of about 4. 6 × 10 < sup >− 28 </ sup > kg / m < sup > 3 </ sup > and given the known abundance of the chemical elements, the corresponding maximal radiation energy density of 9. 2 × 10 < sup >− 31 </ sup > kg / m < sup > 3 </ sup >, i. e. temperature 3. 2K.

For example, the direct sum of the R < sub > i </ sub > form an ideal not contained in any such A, but the axiom of choice gives that it is contained in some maximal ideal which is a fortiori prime.

For example, for maximal use of distribution, a computer running on a different hardware architecture should be able to reliably reconstruct a serialized data stream, regardless of endianness.

For general groups, Cauchy's theorem guarantees the existence of an element, and hence of a cyclic subgroup, of order any prime dividing the group order ; Sylow's theorem extends this to the existence of a subgroup of order equal to the maximal power of any prime dividing the group order.

For any normal modal logic L, a Kripke model ( called the canonical model ) can be constructed, which validates precisely the theorems of L, by an adaptation of the standard technique of using maximal consistent sets as models.

For a right ideal A of a ring R, the following conditions are equivalent to A being a maximal right ideal of R:

For example, is a maximal ideal in, but is not a field.

For instance, the third proof uses that every filter is contained in an ultrafilter ( i. e., a maximal filter ), and this is seen by invoking Zorn's lemma.

For example, the Hilbert class field, which is the maximal unramified abelian extension of a number field, corresponds to a very special class of ideals.

For example, the abelianized absolute Galois group G of is ( naturally isomorphic to ) an infinite product of the group of units of the p-adic integers taken over all prime numbers p, and the corresponding maximal abelian extension of the rationals is the field generated by all roots of unity.

He measures the quality of fit to Cramér's conjecture by measuring the ratio R of the logarithm of a prime to the square root of the gap ; he writes, “ For the largest known maximal gaps, R has remained near 1. 13 .” is still less than 1, and it does not provide support to Granville's refinement that c should be greater than 1.

For totally ordered sets, the notions of maximal element and maximum on one hand and minimal element and minimum on the other hand coincide.

For maximal function, each catalytic subunit must also be phosphorylated, which occurs on Thr 197 and helps orientate catalytic residues in the active site.

Therefore, both SO ( 2n ) and SO ( 2n + 1 ) have rank n. For example, in the rotation group SO ( 3 ) the maximal tori are given by rotations about a fixed axis.

For an arbitrary group scheme G, the ring of global sections also has a commutative Hopf algebra structure, and by taking its spectrum, one obtains the maximal affine quotient group.

For, on their account, omnipotence is a matter of " maximal power ", not an ability to bring about all possible states of affairs.

In mathematics, the Frattini subgroup Φ ( G ) of a group G is the intersection of all maximal subgroups of G. For the case that G has no maximal subgroups, for example the trivial group e or the Prüfer group, it is defined by Φ ( G ) = G. It is analogous to the Jacobson radical in the theory of rings, and intuitively can be thought of as the subgroup of " small elements " ( see the " non-generator " characterization below ).

:: Kakeya maximal function conjecture: For all, there exists a constant such that for any function f and all,

For instance, a minimal element of P will be a maximal element of P < sup > d </ sup >: minimality and maximality are dual concepts in order theory.

For simplification of language, without any loss of precision, one might just call a maximal C < sup > k </ sup >− atlas on a given set a C < sup > k </ sup >− manifold.

For 0 < k < ∞ and any n − dimensional C < sup > k </ sup >− manifold, the maximal atlas contains a C < sup >∞</ sup >− atlas on the same underlying set by a theorem due to Whitney.

For, let be the maximal element in that belongs to an antichain of size in, and set.