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...ke as p λ and x λ * (a set of λ is finite in engineering application, but this restriction is not needed in theoretical treatment). Since Eq. (4) c... ...here s 1 χS 1 }. Compared to Belnap’s quadruplet logic, NS and NL do not use restrictions among the components – and that’s why the NS/NL have a ... ...or relative indeterminant appurtenance are allowed in NS. b) In NS there is no restriction on T, I, F other than they are subsets of ] - 0, 1 + [, ... ...[, thus: - 0 [ inf T + inf I + inf F [ sup T + sup I + sup F [ 3 + . This non-restriction allows paraconsistent, dialetheist, and incomplete infor... ...s left from 1), while in NS they can be defined with respect to any of them (no restriction). g) Component “I”, indeterminacy, can be split into mor...

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... into the number 10 m :'v1odifications of this problem could include the restriction that there be no leading zeros in the result of the permutatio... ...s also easy to verifY that 10 also cannot terminate a cube. Relaxing the restriction that all of the digits be cubes leads to a similar problem that... ...the same 3 x 3 magic square. A logical extension of this problem places a restriction on the numbers. Theorem 26: It is possible to find a set of nu...

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...h H is called the subgraph of G if V(H) ⊆ V(G), E(H) ⊆ E(G) and I H is the restriction of I G to E(H). If H is a subgraph of G then G is said to b... ...a subdigraph of a digraph D if V(D') ⊂ V(D), A(D') ⊆ A(D) and I D' is the restriction of I D to A(D'). A directed walk joining the vertex u 0 to...

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...lattice L is called a sublattice of L if S is a lattice with respect to the restriction of ∩ and ∪ of L onto S. DEFINITION 1.2.10: Let L and M be ...

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... be a subring of R and let A be a fuzzy ideal of R. Let A' α denote the restriction of α δ R A of R α . Then A' α is a fuzzy ideal of R α . TH... ...fuzzy ring where µ = 2 1 N N µ µ ∪ = µ 1 ∪ µ 2 . Here 1 N µ denotes the restriction of µ to N 1 and 2 N µ denotes the restriction of µ to N 2 . ... ... X and defined by pointwise multiplication in the range space. A further restriction is placed on F by assuming that for each f ∈ F, X f = {w ∈ Ω |... ..., 1] i.e. if P 1 , …, P K are K subgroups in G and if µ is such that its restriction on each P i happens to be a S-fuzzy subsemigroup of G and if ... ...ubset of G which is a subgroup under the operation of G. µ E denotes the restriction map i.e. µ E : E → [0 1] such that µ E is fuzzy subgroup of ... ...ch t ∈ [0, 1] ; () t t t ˆ ˆ ˆ o ˆ µ η µ η = where µ η ˆ and ˆ denote the restriction of η and µ respectively over P ⊂ G i.e. ] 1 , 0 [ P : ˆ and ] ... ... ∈ G 1 and 2 2 x x ˆ ~ λ = λ for all x 2 ∈ P 2 ⊆ G 2 where λ is the restriction of P 2 in G 2 . DEFINITION 2.4.16: Let G be a S-bigroup. H ... ...to X with defined by point wise multiplication in range space. A further restriction in placed on V by assuming that for each f ∈ V; X f : {ω ∈ Ω |... ...X with defined by pointwise multiplication in the range space. A further restriction is placed on F by assuming that for each f ∈ F, X f = {ω ∈ Ω...

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... 2 , s s ' , A δ ) denoted by ' s Y ≤ s Y if Z 1 ⊂ Z 2 and s ' δ is the restriction of s δ on Z 1 × s A and ' s Y has a proper subset H ⊂ ... ...s s s s λ δ denoted by ' s K ≤ s K if Z 1 ⊆ Z 2 and s δ′ and s λ′ are the restriction of s s and λ δ respectively on Z 1 × s A and has a prope...

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...-associative algebra with a non-zero homomorphism w : A → F such that the restriction of w from B ⊂ A where B ≠ φ (B is a commutative algebra) say w...

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...ttice L is called a sublattice of L if S is a lattice with respect to the restriction of ∩ and ∪ of L onto S. Result 1.3.3: Every distributive la...

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... = {2 m+1 *3 k+1 } 4 which is a perfect fourth power. Since there are no restrictions on the values of m and k, this generates infinitely many term...

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...hmetic character of the series X a n b 1 b 2 :::b n , by admitting certain restrictions. Proposition 5. If a n 0, b n 1 are integers (n2N), and (i...

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... false, where t, i, and f are real values from the ranges T, I, F, with no restriction on T, I, F, or the sum n=t+i+f. Neutrosophic logic thus genera... ...here t, i, and f are real numbers taken from the sets T, I, and F with no restriction on T, I, F, nor on their sum n=t+i+f. The neutrosophic set ge... ...where t, i, f are real values from the ranges T, I, F in ]-0, 1+[, with no restriction on T, I, F or the sum n=t+i+f. Home. ["Neutrosophy / Neutros... ...solute or relative indeterminacy are allowed in NL. b) In NL there is no restriction on T, I, F other than they are subsets of ] - 0, 1 + [, thus: ... ...us: - 0 [ inf T + inf I + inf F [ sup T + sup I + sup F [ 3 + . This non-restriction allows paraconsistent, dialetheist, and incomplete information ... ...ent) = (T imp , I imp , F imp ), where sup T imp [ 0, inf F imp m 1; no restriction on I imp . NP(sure event) = (T sur , I sur , F sur ), wher... ...indeterminate event) = (T ind , I ind , F ind ); where inf I ind m 1; no restrictions on T ind or F ind . 2. NP(A) c {(T, I, F), where T, I, F are...

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...e event) = (T imp , I imp , F imp ), where sup T imp [ 0, inf F imp m 1; no restriction on I imp . NP(sure event) = (T sur , I sur , F sur ), ... ...ally indeterminate event) = (T ind , I ind , F ind ); where inf I ind m 1; no restrictions on T ind or F ind . 2. NP(A) c {(T, I, F), where T, I, ...

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... antianlytic on A if ∂f ∂z =0. A mapping f is said to be dianalytic if its restriction to every connected com- ponent of A is analytic or antianalytic... ...s of orbits of ξ acting on v(Γ) and E(Γ) ,re- spectively and ξ N Γ (x) the restriction of ξ to N Γ (x). According to the Corollary 1.3.1, we get the f...

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... relative indeterminacy are allowed in NL. 454 b) In NL there is no restriction on T, I, F other than they are subsets of ] - 0, 1 + [, thus: ... ...s: - 0 ≤ inf T + inf I + inf F ≤ sup T + sup I + sup F ≤ 3 + . This non-restriction allows paraconsistent, dialetheist, and incomplete information... ...ive indeterminant appurtenance are allowed in NS. b) In NS there is no restriction on T, I, F other than they are subsets of ] - 0, 1 + [, thus: ... ... + . The inequalities (2.1) and (2.4) of IFS are relaxed. 455 This non-restriction allows paraconsistent, dialetheist, and incomplete information... ... from 1), while in NS they can be defined with respect to any of them (no restriction). g) Component “I”, indeterminacy, can be split into more s...

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...e two possible states given the market vector in time t. However, if this restriction {m 11 = m 22 , m 12 = m 21 } is removed, we arrive at ineffi...

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...S 4 . However, this is not true globally. On the Shilov boundary Q 5 , the restriction of the Fiber bundle E to the Shilov boundary Q 5 is written by ... ...he Fiber bundle E locally can be written as D 2 ×S 1 but not globally. The restriction of the Fiber bundleE to the Shilov boundaryQ 2 =S 1 ×S 1 /Z 2 =...

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...) and the assumptions (i), (ii) bellow those equations. By releasing those restrictions we would have arrived at an even more involved situation which...

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...ted as “yes”, “no”, and “something else” it is then possible to avoid the restrictions forced on us by the law of the excluded middle. Chapter three... ...efinition 1.8.1: Words such as all, any, every, and some are used to place restrictions on the use of a variable. The formal term for this is quantif... ...ical operators with 1.0 equivalent to T and 0.0 equivalent to F. If the restrictions are to the three possibilities 1,.0, 0.0 and 0.5, then the be... ...alued logic. Example: If i is always zero and t and f have only the restrictions of being between zero and one, then the ¬, /\ and \/ connect... ..., i 2 }, f 1 ≥ f 3 and f 1 ≤ 1 – max { i 1 , i 2 , i 3 }. With these restrictions, f 1 is greater than or equal to whatever value emerges from ... ... i 2 }, f 2 ≥ f 3 and f 2 ≤ 1 – max { i 1 , i 2 , i 3 }. With these restrictions f 2 = min{ 1 – max{i 2 , i 3 }, max { f 2 , f 3... ... – max {i,i }, max {f, f}} ). The middle term is clearly i and with the restriction that t + f + i = 1.0, it follows that max {f, f } = f, max { ... ...max { i, i }, max { t, t }}). The middle term is clearly i and with the restriction that t + f + i = 1.0, it follows that max {t, t } = t, max { ... ...ed conclusion. The theorem for NL2 is similar, but has an additional restriction. Theorem 4.3.41: i) If a well-formed expression A in NL2 is...

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...other. NASA wanted to oversee, but Congress insisted on placing too many restrictions. Then when top-notch NASA engineers began defecting to TheCo...

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...owed to alter anything in it, and must either pass or throw it out without restriction. When the Bill has passed the Lords and is signed by the king, ...

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...rranean, and to conduct those operations without regard to the established restrictions of international practice, without regard to any consideration... ...int was observed. GERMANY’S RUTHLESS POLICY The new policy has swept every restriction aside. Vessels of every kind, whatever their flag, their charac... ...onsideration due to all peaceful and law-abiding persons, except so far as restrictions may be necessary for their own protection and for the safety o... ...s except by permit from the President and except under such limitations or restrictions as the President may prescribe. Eighth. An alien enemy whom th... ... No alien enemy shall land in or enter the United States except under such restrictions and at such places as the President may pre- scribe. Eleventh....

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...ut pay dearer for our imports. Notwithstanding what has now been observed, restrictions on the exportation of machinery are not, in our opinion, justi... ...the principle of reciprocity. Until, by the common consent of nations, all restrictions upon trade are done away, a nation cannot be required to aboli... ... to themselves. Thirdly, because the indirect mode of taxing a country, by restrictions on its commerce, disturbs the distribution of industry most ad... ... country would have traded, than gain to the coun- try in whose favour the restrictions are imposed. And lastly, because a country never could obtain ... ...r as to demand them even from its colonies, with- out subjecting itself to restrictions in some degree equiva- lent, for the benefit of those whom it ... ...r, that it requires a species of bounty on the article to create a demand. Restrictions on importation do, however, tend to keep down the value and pr... ...an would otherwise be there. From this it obvi- ously follows, that if the restrictions were removed, we should have to pay rather more for some of th... ..., the case of France and England. Those two nations, in consequence of the restrictions with which they have loaded their commer- cial intercourse, ca... ...but differing in this only, that one of them adopts a system of commercial restrictions, and the other adopts free trade. This would be a decisive exp...

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...ctly forbad the selling any liquor to them; and when they complain’d of this restriction, we told them that if they would continue sober during the tr...

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...mances, that impresses itself on the most indifferent reader; and the very restrictions and weaknesses of the man served perhaps to strengthen the viv...