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Unitary Operators (X)

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 Book Id: WPLBN0002097044 Collections: Math, Literature, Algebra, Authors Community, Mathematics ► Abstract Description Details...one of the most utilised concepts in fuzzy models and neutrosophic models. From solving equations to characterising linear transformations or linear operators, matrices are used. Matrices find their applications in several real models. In fact it is not an exaggeration if one says that matrix theory and linear algebra (i.e. vector spaces) form an inseparable component ... Full Text Search Details... From solving equations to characterising linear transformations or linear operators, matrices are used. Matrices find their applications in severa... ...oint of T 1 and * 2 T is the adjoint of T 2 . The notion of normal and unitary operators on the bivector spaces are defined in an analogous way... ...T 1 and * 2 T is the adjoint of T 2 . The notion of normal and unitary operators on the bivector spaces are defined in an analogous way. T is a... ...ry operators on the bivector spaces are defined in an analogous way. T is a unitary operator on the bivector space V = V 1 ∪ V 2 if and only if T ... ...ator on the bivector space V = V 1 ∪ V 2 if and only if T 1 and T 2 are unitary operators on the vector space V 1 and V 2 . Similarly T is a n... ...the bivector space V = V 1 ∪ V 2 if and only if T 1 and T 2 are unitary operators on the vector space V 1 and V 2 . Similarly T is a normal op... ...rmal operator on the bivector space if and only if T 1 and T 2 are normal operators on V 1 and V 2 respectively. We can extend all the notions o... ...T = T 1 ∪ T 2 is a linear bioperator such that only one of the component operators has characteristic values and the other has no characteristic ...
 Date: 2013, Volume 1 Book Id: WPLBN0002828224 ► Abstract Table of Contents Details...al DSm rule of combination . . . 124 6.2.2 Examples . . . . . 126 6.3 Operations on sets . . . . . 127 6.4 Fusion of beliefs defined on single sub-unitary intervals . . . 130 6.4.1 DSm rules of combination . . . . 130 6.4.2 Example with the DSm classic rule . . . 132 6.4.3 Example with the hybrid DSm rule . . . 134 6.5 Generalization of DSm rules for sets . . . . 13...
 Book Id: WPLBN0002097060 Subjects: Non Fiction, Philosophy, Art ► Abstract Full Text Search Details.... The sets T, I, F are not necessarily intervals, but may be any real sub-unitary subsets: discrete or continuous; single-element, finite, or (count... ...s, but dynamically the components T, I, F are set-valued vector functions/operators depending on many parameters, such as: time, space, etc. (some o... ...spect to the observer (subjectivity is another parameter of the functions/operators T, I, F). For example: “John is smart” can be (.35, .67, .60) a... ...Derida's ideology: the death of all ideologies! Philosophy is not a unitary theoretical generalized representation of the world (just to inter... ...). All is based and raised on contradictions and neutralities. World is unitary in its variations and differentiations (Lossky, "World as an organi... ...lly referring to the analytic philosophy). Neutrosophy is not only "unitary and fight of contradictions" (V. I. Lenin), but their transcendenc... ... b) there is a proper subset P (different from the empty set —, from the unitary element and from the idempotent element if any with respect to S 2... ...logic. Statically T, I, F are subsets, but dynamically they are functions/operators depending on many known or unknown parameters. Constants: (T, I... ... + . Statically T, I, F are subsets, but dynamically T, I, F are functions/operators depending on many known or unknown parameters. Atomic formulas:...
 Book Id: WPLBN0002097043 Subjects: Non Fiction, Algebra, Smarandache Collections ► Abstract Full Text Search Details...omplex fields. Here we recall the concepts of linear functionals, adjoint, unitary operators and normal operators. DEFINITION 1.1.2: Let F be a f... ...ields. Here we recall the concepts of linear functionals, adjoint, unitary operators and normal operators. DEFINITION 1.1.2: Let F be a field of ... ... finite dimensional inner product real vector space. If T and U are linear operators on V and c is a scalar i. (T + U) ∗ = T ∗ + U ∗ . ... ...ations and another ‘ ×’ operation internal on A), where R is a commutative unitary Smarandache ring (S-ring) and S its proper subset that is a field... ...] is called S-multi vector space. Now we have to define Smarandache linear operators and Smarandache linear transformations. We also define for the... ..., β ∈ V and c ∈ P. Let SL P (V, V) denote the collections of all S- linear operators from V to V. DEFINITION 1.2.20: Let V be a S-vector space ove... ...int of T 1 and * 2 T is the adjoint of T 2 . The notion of normal and unitary operators on the bivector spaces are defined in an analogous way.... ...y operators on the bivector spaces are defined in an analogous way. T is a unitary operator on the bivector space V = V 1 ∪ V 2 if and only if T 1... ...tor on the bivector space V = V 1 ∪ V 2 if and only if T 1 and T 2 are unitary operators on the vector space V 1 and V 2 . Similarly T is a no...
 Book Id: WPLBN0002097647 Subjects: Non-Fiction, Education, Smarandache Collections ► Abstract Full Text Search Details...case both rings have identity. In case f(1 R )=1 S ; we say the map f is unitary. DEFINITION 2.4.2: Let f: R→ S be a ring homomorphism, the kern... ...he requirement r(x + y) = rx + ry. (r ∈ R, x, y ∈ M); for all groups with operators, we also have (a+b) x = ax + by, (ab) x = a(bx), I R x = x for a... ... and another ‘×’ operation internal on A) 64 where R is a commutative unitary Smarandache ring and S its proper subset which is a field. Exa... ...s direction. DEFINITION [63]: Let R be a ring, R is said to be locally unitary if for each x ∈ R there exists an idempotent e ∈ R for which ex = ... ...mpotent s ∈ R such that xs = sx = x. THEOREM [152]: Let R be a locally unitary ring then R is a locally semiunitary ring. Proof: By the very ... ... a locally semiunitary ring. Proof: By the very definition of locally unitary ring and locally semiunitary ring the result follows. THEOREM ... ...Univ. of Chicago Press, (1969). 32. Higman.D.G, Modules with a group of operators, Duke Math. J., Vol. 21, 369- 376, (1954). 33. Higman.G, The u...
 Book Id: WPLBN0002097103 Subjects: Non Fiction, Education, Smarandache Collections ► Abstract Full Text Search Details...inf. The sets T, I, F are not necessarily intervals, but may be any real sub-unitary subsets: discrete or continuous; single-element, finite, or ... ...ters, and therefore they can be considered set-valued vector functions or even operators. The parameters can be: time, space, etc. (some of them ar... ...th respect to the observer (subjectivity is another parameter of the functions/operators T, I, F). For example: “John is smart” can be (.35, .67, .... ...n of Neutrosophic Logical Connectives: The connectives (rules of inference, or operators), in any non-bivalent logic, can be defined in various ways... ...s studied are: genetic algorithm (a model of machine learning based on genetic operators), evolutionary programming (a stochastic optimization strat... ...zy Set Theory, the difference between these two theories is the way the fusion operators are defined. One uses the definitions of neutrosophic pro... ...osed by Florentin Smarandache tries to bring all the logics together towards a unitary, formally analyzable, general model of reality [5]. A part of...
 Book Id: WPLBN0002097108 Subjects: Non Fiction, Education, Smarandache Collections ► Abstract Full Text Search Details...Infinite FRE to a complete browerian lattices 162 1.28 Semantics of implication operators and fuzzy relational products 164 Chapter Two SO... ...orithm to problems in chemical industries 199 2.11 Semantics of implication operators and fuzzy relational products applied to HIV/AIDS pat... ... , , , , 0 b a b a b a t Max-SO and min-SO are extensions of the α and the σ operators defined by Sanchez [84] for the min t-norm. The max-SO ex... ...andomly generated population and progress to improve solutions by using genetic operators such as crossover and mutation operators. In each interact... ...the penalty or barrier method [38, 41]. [64-66] introduced some special genetic operators to handle the constrained optimization problem, but those ... ...nt)=1. This has application in philosophy (see the neutrosophy). That’s why the unitary standard interval [0, 1] used in IFS has been extended to th... ...) In NS the components T, I, F can also be non-standard subsets included in the unitary non-standard interval ] - 0, 1 + [, not only standard subset... ...y non-standard interval ] - 0, 1 + [, not only standard subsets included in the unitary standard interval [0, 1] as in IFS. e) NS, like dialetheism...
 Book Id: WPLBN0002097105 ► Abstract Full Text Search Details...Infinite FRE to a complete browerian lattices 162 1.28 Semantics of implication operators and fuzzy relational products 164 Chapter Two SO... ...orithm to problems in chemical industries 199 2.11 Semantics of implication operators and fuzzy relational products applied to HIV/AIDS pat... ... , , , , 0 b a b a b a t Max-SO and min-SO are extensions of the α and the σ operators defined by Sanchez [84] for the min t-norm. The max-SO ex... ...andomly generated population and progress to improve solutions by using genetic operators such as crossover and mutation operators. In each interact... ...the penalty or barrier method [38, 41]. [64-66] introduced some special genetic operators to handle the constrained optimization problem, but those ... ...nt)=1. This has application in philosophy (see the neutrosophy). That’s why the unitary standard interval [0, 1] used in IFS has been extended to th... ...) In NS the components T, I, F can also be non-standard subsets included in the unitary non-standard interval ] - 0, 1 + [, not only standard subset... ...y non-standard interval ] - 0, 1 + [, not only standard subsets included in the unitary standard interval [0, 1] as in IFS. e) NS, like dialetheism...
 Book Id: WPLBN0002097090 Subjects: Non Fiction, Philosophy, Smarandache Collections ► Abstract Full Text Search Details...e set CS = { /\, \/, ¬ } all of them can be constructed using these three operators. Therefore, each of these additional connectives will be consider... ...nnectives will be considered an abbreviation for an expression built from operators in CS. Other complete sets of connectives also exist. Provin... ...h table as ¬ p /\ ¬q and p ‌ q the same truth table as ¬p \/ ¬q, these operators can also be considered abbreviations for more complex expressions... ...t of computer programming. Languages such as C++ and Java contain logical operators corresponding to the conjunction, disjunction and negation. They... ...), double vertical bar (||) and exclamation point (!) respectively. These operators accept values that are Boolean and return a Boolean. The behavio... ... The sets T, I, F are not necessarily intervals, but may be any real sub-unitary subsets: discrete or continuous; single-element, finite, or (coun... ... The sets T, I, F are not necessarily intervals, but may be any real sub-unitary subsets: discrete or continuous; single-element, finite, or (coun...
 Book Id: WPLBN0002097118 Subjects: Non Fiction, Education, Smarandache Collection ► Abstract Full Text Search Details...al quantities on his time line and the spatial section, made by projecting operators b α = dx α ds andh αβ =−g αβ +b α b β , which fully defne his rea... ...ies of the space are derived from the fact that the chr. inv.-differential operators ∂ ∂t = 1 √ g 00 ∂ ∂t and ∂ ∂x i = ∂ ∂x i + + 1 c 2 v i ∂ ∂t... ...ubling” version of the Lorentz groupSO(1,3). Low discussed the irreducible unitary representations of such U(1,3) group and the relevance for the stro... ...ure. The Yang’s algebra can be written in terms of the 6D angular momentum operators and a 6D pseudo-Euclidean metricη MN : ˆ M μν = Σ μν , ˆ M 56 = ... ...A E A =X A E A +iY A E A and the boosts/rotation parameters θ allowing the unitary condition ˉU † =U −1 to hold in the generalized Clifford unit- ary ... ...μνρ dz μνρ +... remains invariant (upon setting the Planck scale Λ=1). The unitary condition ˉU † =U −1 under the combined reversal and complex-conjug... ...=U −1 holds and the norm < ˉZ † Z> s remains invariant under the analog of unitary transformations in complexifed C-spaces. These techniques are not v... ...lus and re- solution of the ordering ambiguity for the product of momentum operators Clifford algebra is a very useful tool for description of ge- ome... ...pe q ∙ e p =q−ip=z , (126) which reminds us of the creation/annihilation operators used in the harmonic oscillator. We shall now review the steps in...
 Book Id: WPLBN0002097119 ► Abstract Full Text Search Details...tial section — chrono- metrically invariant quantities, made by projecting operators b α = dx α ds and h αβ =−g αβ +b α b β which fully defne his real... ...operties of the space are derived from the fact that chr.inv.-differential operators ∂ ∂t = 1 √ g 00 ∂ ∂t and ∂ ∂x i = ∂ ∂x i + 1 c 2 v i ∂ ∂t a... ... section — chronometrically invar- iant quantities, made by the projecting operators b α = dx α ds andh αβ =−g αβ +b α b β which fully defne his real ... ...ies of the space are derived from the fact that the chr. inv.-differential operators ∂ ∂t = 1 √ g 00 ∂ ∂t and ∂ ∂x i = ∂ ∂x i + + 1 c 2 v i ∂ ∂t... ...e made independent of the reference frame if we defne a suitable system of unitary vec- tors by which we can pass from holonomic to anholonomic descri... ...e at each point and e (k) e (l) =δ (k) (l) . (88) If these vectors are unitary, in a Riemannian 4-spacetime are the standard vierbiens [5]. If we ... ...from the initial pure disentangled states of a composed system simply by a unitary transformation. Motivated by Eintein-Podolsky-Rosen paper, in 1935 ...
 Book Id: WPLBN0002097650 Subjects: Non-Fiction, Education, Smarandache Collections Collections: Technology, Literature, Education, Logic, Authors Community, Mathematics ► Abstract Full Text Search Details...ations and another ‘ ×’ operation internal on A) where R is a commutative unitary S-ring and X its proper subset which is a field. Notions of S-ri... ... V; where T is a linear transformation from V to V. The set of all linear operators from V to V is denoted by L F (V, V). L F (V, V) is also a vecto... ... X two separate distinct binary operations ∗ and ∗' (such that the binary operators ∗ and ∗' are closed with respect to X i.e. for every pair of ele... ...int of T 1 and * 2 T is the adjoint of T 2 . The notion of normal and unitary operators on the bivector spaces are defined in an analogous way. ... ... 1 and * 2 T is the adjoint of T 2 . The notion of normal and unitary operators on the bivector spaces are defined in an analogous way. T is a u... ... operators on the bivector spaces are defined in an analogous way. T is a unitary operator on the bivector space V = V 1 ∪ V 2 if and only if T 1 ... ...or on the bivector space V = V 1 ∪ V 2 if and only if T 1 and T 2 are unitary operators on the vector space V 1 and V 2 . Similarly T is a n... ...e bivector space V = V 1 ∪ V 2 if and only if T 1 and T 2 are unitary operators on the vector space V 1 and V 2 . Similarly T is a normal op... ...al operator on the bivector space if and only if T 1 and T 2 are normal operators on V 1 and V 2 respectively. We can extend all the notions on b...
 Book Id: WPLBN0001235244 Subjects: Non Fiction, Education, Internet ► Abstract Full Text Search Details...bscriber loyalty, such as their topical bulletin boards run by hired systems operators (called “sysops”) and boasting content provided by subscribers ... ...F .3d 1132, 1133 (9th Cir. 2003) (establishing that eavesdropping on vehicle operators could not be allowed, primarily because it dis- abled the prope... ... 212, 213 two-factor authentication, 53 typewriters, “smart,” 15, 19, 20, 34 unitary rights holder, 189 United States v. Am. Library Ass ’n, 282– 83n6...
 Book Id: WPLBN0001235224 Subjects: Non Fiction, Education, Economics ► Abstract Full Text Search Details... Predictably, failure ensued - from electricity utilities in California to railway operators in Britain. The simultaneous crumbling of these urban ... ...zation of resources grow. The sale of radio frequencies to the first cellular phone operators in the West - a situation which repeats itself in East... ... to the German-speaking parts of the dying Habsburg Empire). He dispensed with the unitary nature of the psyche and proposed instead a trichotomy, ... ...structed and expected to do one, and only one, thing. It has a single purpose and a unitary function. We, humans, are more like computers than like ... ...e private sector takes over the medium from "below" (makes offers to the owners or operators of the medium that they cannot possibly refuse) - or f... ...ommunications Act of 1996 envisaged a form of "organized anarchy". It allowed media operators to invade each other's turf. Phone companies were all...
 Book Id: WPLBN0001235225 Subjects: Non Fiction, Religion, Philosophy ► Abstract Full Text Search Details... Predictably, failure ensued - from electricity utilities in California to railway operators in Britain. The simultaneous crumbling of these urban ... ...zation of resources grow. The sale of radio frequencies to the first cellular phone operators in the West - a situation which repeats itself in East... ... to the German-speaking parts of the dying Habsburg Empire). He dispensed with the unitary nature of the psyche and proposed instead a trichotomy, ... ...structed and expected to do one, and only one, thing. It has a single purpose and a unitary function. We, humans, are more like computers than like ... ...e private sector takes over the medium from "below" (makes offers to the owners or operators of the medium that they cannot possibly refuse) - or f... ...ommunications Act of 1996 envisaged a form of "organized anarchy". It allowed media operators to invade each other's turf. Phone companies were all...
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