Every Boolean algebra ( A, ∧, ∨) gives rise to a ring ( A, +, ·) by defining a + b := ( a ∧ ¬ b ) ∨ ( b ∧ ¬ a ) = ( a ∨ b ) ∧ ¬( a ∧ b ) ( this operation is called symmetric difference in the case of sets and XOR in the case of logic ) and a · b := a ∧ b. The zero element of this ring coincides with the 0 of the Boolean algebra ; the multiplicative identity element of the ring is the 1 of the Boolean algebra.

Bézout's lemma is a consequence of the Euclidean division defining property, namely that the division by a nonzero integer b has a remainder strictly less than | b |.

United States federal courts only act as interpreters of statutes and the constitution by elaborating and precisely defining the broad language ( connotation 1 ( b ) above ), but, unlike state courts, do not act as an independent source of common law ( connotation 1 ( a ) above ).

The most common way to formalize this is by defining a field as a set together with two operations, usually called addition and multiplication, and denoted by + and ·, respectively, such that the following axioms hold ; subtraction and division are defined implicitly in terms of the inverse operations of addition and multiplication :< ref group =" note "> That is, the axiom for addition only assumes a binary operation The axiom of inverse allows one to define a unary operation that sends an element to its negative ( its additive inverse ); this is not taken as given, but is implicitly defined in terms of addition as " is the unique b such that ", " implicitly " because it is defined in terms of solving an equation — and one then defines the binary operation of subtraction, also denoted by "−", as in terms of addition and additive inverse.

The critical first steps in change management are ( a ) defining change ( and communicating that definition ) and ( b ) defining the scope of the change system.

* Define a b as " not b < a " ( i. e., take the inverse complement of the relation ), which corresponds to defining a ~ b as " neither a < b nor b < a "; these relations and ~ are in general not transitive ; however, if they are, ~ is an equivalence ; in that case "<" is a strict weak order.

By defining appropriate constants a and b, this can be rewritten as

b ) how " sentimentality " or " pathos ", which are the defining traits of kitsch, do not find room within Kant's " aesthetical indifference ".

By defining this relation as valid for all integer n and nonzero b, it follows that

In a similar manner to rational numbers, we can extend the natural numbers N to the integers Z by defining integers as an ordered pair of natural numbers ( a, b ).

The greatest common divisor is often written as GCD ( a, b ) or, more simply, as ( a, b ), although the latter notation is also used for other mathematical concepts, such as two-dimensional vectors.

In modern mathematical language, the ideal generated by a and b is the ideal generated by g alone ( an ideal generated by a single element is called a principal ideal, and all ideals of the integers are principal ideals ).

* 1998 – José Enrique Moyal, Israeli mathematical physicist and engineer ( b. 1910 )

In mathematics, an ordered pair ( a, b ) is a pair of mathematical objects.

* September 5 – Richard C. Tolman, American mathematical physicist ( b. 1881 )

** José Enrique Moyal, mathematical physicist ( b. 1910 )

* March 17 – Daniel Bernoulli, Dutch-born mathematical physicist ( b. 1700 )

A finite difference is a mathematical expression of the form f ( x + b ) − f ( x + a ).

Fortunately it is possible to alter the equation by substituting || w || with ( the factor of 1 / 2 being used for mathematical convenience ) without changing the solution ( the minimum of the original and the modified equation have the same w and b ).

Exponentiation is a mathematical operation, written as b < sup > n </ sup >, involving two numbers, the base b and the exponent ( or index or power ) n. When n is a positive integer, exponentiation corresponds to repeated multiplication ; in other words, a product of n factors, each of which is equal to b ( the product itself can also be called power ):

: b ) He received a doctorate in sociology, mathematical statistics and philosophy from the Univ.

Ibn al-Shatir ( b. 1304 ) developed a geocentric system that employed mathematical techniques, such as the Tusi-couple and Urdi lemma, that were almost identical to those Nicolaus Copernicus later employed in his heliocentric system, implying that its mathematical model was influenced by the Maragha school.

:* Level b: the underlying mathematical relations ;

MBBK's refutation was not strictly mathematical in nature, rather it asserted that the WRR authors and contributors had intentionally or unintentionally ( a ) selected the names and / or dates in advance and ( b ) designed their experiments to match their selection and thereby achieved their " desired " result.

The mathematical operation digital sum in base b can also be called the digital sum.

* Cancellation property, the mathematical property that if a * b

When describing base in mathematical notation, the letter b is generally used as a symbol for this concept, so, for a binary system, b equals 2.

Some graphemes may not represent any sound at all ( like the b in English debt ), and often the rules of correspondence between graphemes and phonemes become complex or irregular, particularly as a result of historical sound changes that are not necessarily reflected in spelling.

Pāṇini's systematic approach to analysis includes components for: ( a ) forming grammatical rules, ( b ) an inventory of sounds, ( c ) a list of verbal roots organized into sublists, and ( d ) a list of classes of morphs.

Computation rules for a GPDA are the same as a PDA except that the a < sub > i + 1 </ sub >' s and b < sub > i + 1 </ sub >' s are now strings instead of symbols.

Note that the rules to move-up or pull-down the a, b, or c indexes are trivial, (+......+), so that f < sup > abc </ sup >

The basic rules of probabilities that will be used are that a ) if an event can happen in a variety of different ways then its probability is the sum of the probabilities of the possible ways and b ) if a process involves a number of independent subprocesses then its probability is the product of the component probabilities.

Xeer is defined by a few fundamental tenets that are immutable and which closely approximate the principle of jus cogens in international law: These precepts include: a ) payment of blood money ( locally referred to as diya ) for libel, theft, physical harm, rape and death, as well as supplying assistance to relatives ; b ) assuring good inter-clan relations by treating women justly, negotiating with " peace emissaries " in good faith, and sparing the lives of socially protected groups " Birr Magaydo ," ( e. g. children, women, the pious, poets, messengers, sheikhs, and guests ); c ) family obligations such as the payment of dowry, and sanctions for eloping ; d ) rules pertaining to the management of resources such as the use of pasture land, water, and other natural resources ; e ) providing financial support to married female relatives and newlyweds ; f ) donating livestock and other assets to the poor.

* November 7 – Gordon Coventry, Australian rules footballer ( b. 1901 )

In telecommunication, a n-entity is an active element in the n-th layer of the Open Systems Interconnection -- Reference Model ( OSI-RM ) that ( a ) interacts directly with elements, i. e., entities, of the layer immediately above or below the n-th layer, ( b ) is defined by a unique set of rules, i. e., syntax, and information formats, including data and control formats, and ( c ) performs a defined set of functions.

* Leigh Colbert ( b. 1975 ), Australian rules footballer

These rules lead to another ( equivalent ) rule — the sign of any product a × b depends on the sign of a as follows:

For either one of these rules, we can make a more accurate approximation by breaking up the interval b into some number n of subintervals, computing an approximation for each subinterval, then adding up all the results.

" Principles, values, standards, or rules of behavior that guide the decisions, procedures and systems of an organization in a way that ( a ) contributes to the welfare of its key stakeholders, and ( b ) respects the rights of all constituents affected by its operations.

* Stan Rule ( b. 1924 ), Australian rules footballer

Orthographies with a high grapheme-to-phoneme correspondence ( excluding exceptions due to loan words and assimilation ) include those of Finnish, Albanian, Georgian, Turkish ( apart from ğ and various palatal and vowel allophones ), Serbo-Croatian ( Serbian, Croatian and Bosnian ), Bulgarian, Macedonian ( if the apostrophe is counted, though slight inconsistencies may be found ), Eastern Armenian ( apart from o, v ), Basque ( apart from palatalized l, n ), Haitian Creole, Castilian Spanish ( apart from h, x, b / v, and sometimes k, c, g, j, z ), Czech ( apart from ě, ů, y, ý ), Polish ( apart from ó, h, rz ), Romanian ( apart from distinguishing semivowels from vowels ), Ukrainian ( mainly phonemic with some other historical / morphological rules, as well as palatalization ), Swahili ( missing aspirated consonants, which do not occur in all varieties and are sparsely used anyways ), Mongolian ( apart from letters representing multiple sounds depending on front or back vowels, the soft and hard sign, silent letters to indicate / ŋ / from / n / and voiced versus voiceless consonants ) Azerbaijani ( apart from k ), and Kazakh ( apart from и, у, х, щ, ю ).

* Jack Conley ( Australian rules footballer ) ( b. 1923 ), an Australian rules footballer

:( b ) Nothing in these Rules shall interfere with the operation of special rules made by an appropriate authority for roadsteads, harbours, rivers, lakes, or inland waterways connected with the high seas and navigable by seagoing vessels.

:( b ) In construing and complying with these rules due regard shall be had to all dangers of navigation and collision and to any special circumstances, including the limitations of the vessels involved, which may make a departure from these rules necessary to avoid immediate danger

Neofunctionalism describes and explains the process of regional integration with reference to how three causal factors interact with one another: ( a ) growing economic interdependence between nations, ( b ) organizational capacity to resolve disputes and build international legal regimes, and ( c ) supranational market rules that replace national regulatory regimes.

::( b ) To use or employ, in connection with the purchase or sale of any security registered on a national securities exchange or any security not so registered, or any securities-based swap agreement ( as defined in section 206B of the Gramm-Leach-Bliley Act ), any manipulative or deceptive device or contrivance in contravention of such rules and regulations as the Commission may prescribe as necessary or appropriate in the public interest or for the protection of investors.

In general, the act lowered tax rates and simplified retirement and qualified plan rules such as for Individual retirement accounts, 401 ( k ) plans, 403 ( b ), and pension plans.