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 Book Id: WPLBN0002097645 Subjects: Non-Fiction, Education, Smarandache Collections Collections: Literature, Education, Authors Community, Mathematics ► Abstract Full Text Search Details...just give the basic concepts or notion like equivalence relation greatest common divisor etc. Second section is devoted to giving the definition of ... ...nd b are integers both not zero, then an integer d is called the greatest common divisor of a and b if i. d > 0 ii. d is a common divisor of a a... ... > 0 ii. d is a common divisor of a and b and iii. if any integer f is a common divisor of both a and b then f is also a divisor of d. The grea... ...n divisor of both a and b then f is also a divisor of d. The greatest common divisor of a and b is denoted by g.c.d (a, b) or simply (g.c.d). If... ...and b are relatively prime then (a, b) = 1. DEFINITION 1.1.2: The least common multiple of two positive integers a and b is defined to be the smal... ... property). 2. a, b, c ∈ G implies a • (b • c) = (a • b) • c (associative law). 3. There exist an element e ∈ G such that a • e = e • a = a for all ... ...tional condition (L 4 ) x ∩ x = x, x ∪ x = x. (L 1 ) is the commutative law (L 2 ) is the associative law (L 3 ) is the absorption law and (L 4... ...sociative law (L 3 ) is the absorption law and (L 4 ) is the idempotent law. DEFINITION 1.3.7: A partial order relation ≤ on A is called a total... ...Orin Chein et al [11]). DEFINITION [41]: Let L be a loop. The flexible law FLEX: x • yx = xy • x for all x, y ∈ L. If a loop L satisfies left alt...
 Book Id: WPLBN0002097100 ► Abstract Full Text Search Details...t countries are those having a boundary line (not merely a single point) in common. The conjecture has acted as a catalyst in the branch of mathem... ...he edges or lines of G. If two distinct lines x and y are incident with a common point, then they are adjacent lines. A graph with p points and q ... ...rails is C ∏ = − p i i d 1 ) 1 ( ! where d i = id (v i ) and C is the common value of all the cofactors. Several interesting properties i... ...sider any two binary neutrosophic relation P N (X, Y) and Q N (Y, Z) with a common set Y. The standard composition of these relations which is denot... ...communication even though e-mail guarantees a lot of privacy it is a highly common practice to hack e-mail. Hacking is legally a cyber crime but is ... ...ism Debate: Expert Reasoning, Fuzzy Logic and Complex Statutes, Vanderbilt Law Review, 52 (1999), 1243-1340. http://law.vanderbilt.edu/lawreview/vo...
 Book Id: WPLBN0002097650 Subjects: Non-Fiction, Education, Smarandache Collections Collections: Technology, Literature, Education, Logic, Authors Community, Mathematics ► Abstract Full Text Search Details...3 ∈ N; (n 1 + n 2 ) n 3 = n 1 n 3 + n 2 n 3 (right distributive law). This near-ring will be termed as right near-ring. If n 1 (n 2 ... ...ents of N are left cancelable we say that N fulfils the left cancellation law. Similarly one defines right cancelable. N is an integral domain if N ... ... a S-seminear-ring. We call a non empty subset I of R to be a Smarandache common ideal related to A (S-common ideal related to A) (A ⊂ R) and A a ne... ...quipped with associative binary operations + and ' '. Bisemigroups with a common neutral element for the two associative binary operations are calle... ...enerated by A 1 and A 2 so A denotes the free bimonoid as both have the common identity, Λ the empty sequence . . z ) , z ( = Λ δ ) a , z ( ) a... ...L 1 ∪ L 2 where each L i is an even order loop should we paste or have common paths between the two K 2n graphs. This question is an interesting ... ...tive biring. We say the biring R has a monounit if a unit exists which is common to both R 1 and R 2 we call the common unit as the 138 monouni... ...t) cancellable we say that N fulfils the left (right) 196 cancellation law. N is a bi-integral domain if both N 1 and N 1 has no zero-divisors. ...
 Book Id: WPLBN0002097038 Subjects: Non Fiction, Education, Smarandache Collections Collections: Math, Literature, Education, Authors Community, Mathematics ► Abstract Full Text Search Details...d in the array 16 3 2 13 5 10 II 8 9 6 7 12 ,4 15 14 I such that the common sum is 34. It is well-known that magic squares can be constructed u...
 Book Id: WPLBN0002097044 Collections: Math, Literature, Algebra, Authors Community, Mathematics ► Abstract Full Text Search Details...logic, it is more appropriate to accept the notion of indeterminacy. It is common for any one to say that a particular thing is indeterminate than ... ...more so in mathematics. Because when one says something is imaginary, to a common mind it means that the thing does 6 not exist, but indetermina... ... B C B . 2. Further bimatrix multiplication satisfies the distributive law for if A B = A 1 ∪ A 2 , B B = B 1 ∪ B 2 and C B = C 1 ∪ C 2 ... .... 78 The bimatrix A B has ( 6 3 6 3 6 3) and (0 1 0 1 0 1) as common rows and 05 63 and 01 01 ⎡⎤⎡ ⎤ ⎢⎥⎢ ⎥ ⎢⎥⎢ ⎥ ⎢⎥⎢ ⎥ ⎢⎥⎢ ⎥ ⎣⎦⎣ ⎦ ... ...mon rows and 05 63 and 01 01 ⎡⎤⎡ ⎤ ⎢⎥⎢ ⎥ ⎢⎥⎢ ⎥ ⎢⎥⎢ ⎥ ⎢⎥⎢ ⎥ ⎣⎦⎣ ⎦ are common columns. Thus A B is a row-column overlap bimatrix. Thus the co...
 Book Id: WPLBN0002097105 ► Abstract Full Text Search Details...res [1, 4, 10-12, 18, 34, 52, 75-80, 82, 108, 111]. The max-min composition is commonly used when a system requires conservative solutions in the s... ... .6 12 Consider now two binary fuzzy relations P(X, Y) and Q(Y, Z) with a common set Y. The standard composition of these relations, which is ... ...t is reflexive, anti symmetric and transitive is called a partial ordering. The common symbol ≤ is suggestive of the properties of this class of rel... ... procedures [1, 11, 16, 24, 30, 82]. 33 The “max-min” composition [117] is commonly used when a system requires conservative solutions in the s... ... 2 ) In this way, Ω 1 contains sets of I j ’s which have some element(s) in common and we can decompose the original problem into k sub-problems... ... 2 ) given in Figure 2.1.3. 173 The linear equation is based on Ohm’s law, the drop in voltage V across a resistor R is given by the linea... ...in voltage V across a resistor R is given by the linear relation V = iR (Ohm’s law). The hydrodynamic analogue to the mean velocity v for laminar f... ...ting), from accepted / rejected / pending, etc. and guided by the fact that the law of excluded middle did not work any longer in the modern logics,...
 Book Id: WPLBN0002097085 ► Abstract Full Text Search Details...adox, specifically defines the statement as being false. Nevertheless it is common practice in both scientific and pure logic systems to measure the ... ... as beta ( β), by Einstein, i.e., β = (1-(v/c) 2 ) -1/2 , [14] γ is now the common symbol for this factor.] With (3.1), we see that the secant of an... ...d thus has conjunctive motion with the body. We now suspend Newton's first law of motion, Principia, (1687), as a given principle and treat it inst... ... o = 0: - ϒ = mvsec(θ) /t 2 . (15) From Newton's second law of motion, the resultant acceleration (A), of the body is then, A ... ...s in that quanta. This definition is in complete accord with Newton's first law of motion and moreover provides a causal definition for inertial moti... ... expansion in the motion vector body. In accordance with the inverse square law then, longitudinal length in the gravity vector S' body is defined by... ...Periodic Table), should possess perfect nuclear cubic symmetry, i.e. have a common characteristic of completely filled η potential shells. Analysis ... ...nts should be available as well ―as deduced from the physical properties of common isotopes and their tendencies for noble-like structures ―within t... ...rine, we find exact n-p pairing with 6 C-12, 7 N-14, and 8 O-16, but the common isotopes of boron, 5 B-11 and fluorine, 9 F-19 have an addition...
 Book Id: WPLBN0002097117 Subjects: Non Fiction, Education, Smarandache Collections ► Abstract Full Text Search Details.... Combined conflicting opinions tend to cancel out and assisted by the strong law of large numbers, a consensus emerges as the sample opinion appro... ...s, in case of a model, add two or more FCMs to produce a new FCM. The strong law of large numbers ensures in some sense that, knowledge reliability... ...Combined conflicting opinions tend to cancel out and assisted with the strong law of large numbers, a consensus emerges as the sample opinion approx... ...s to construct FCMs with iterative interviews or questionnaire mailings. The law of large numbers require that the random samples be independent, i... ...otion of untouchability from the time of the ancient lawgiver Manu (approx. 1 Common Era) 1 . So, we specifically study the social effects of untouc... ..., ride bicycles or wear new clothes. They are not allowed to draw water from common ponds, or graze their cattle on public grounds. In teashops in ... ...terminate in his opinion. Now we proceed on to take a few of the attributes, common in the study of all the five aspects of untouchability viz., re... ... and investigate the effect. Thus we take these five as major nodes and their common attributes of as the other nodes: N 1 - Religious untoucha... ... use all public roads by Dalits R 10 - Fight against denial of right to use common wells and lakes by Dalits R 11 - Rights denied to Dalits to ...
 Book Id: WPLBN0002097045 ► Abstract Full Text Search Details...attributes overlap i.e. in the study or analysis of a model when we have some common attributes given by experts i.e. the concepts / attributes are ... ...ributes are not totally disjoint but have certain concepts / attributes to be common. Such study has already been analyzed. Here we wish to describ... ...s / attributes only when a point or a edge or some points and some edges are common in the directed graphs obtained between those pairs of models. ... ...that this bigraph is very special in its own way for it has only one point in common, viz. v 2 = v' 1 . Example 2.1.3: Let G = G 1 ∪ G 2 be a b... ...ure. It is interesting to observe that the graphs have only two points in common viz. v 1 = v' 1 and v 2 and v' 2 . Thus G = {v 1 , v 2 ,... ... Combined conflicting opinions tend to cancel out and assisted by the strong law of large numbers, a consensus emerges as the sample opinion approx... ...alism Debate: Expert Reasoning, Fuzzy Logic and Complex Statutes, Vanderbilt Law Review, 52, 1243-1340, 1999. http://law.vanderbilt.edu/lawreview/v... ...le physics, information fusion, neutrosophy (a generalization of dialectics), law of sensations and stimuli, etc. He can be contacted at smarand@...
 Book Id: WPLBN0002097651 Subjects: Non-Fiction, Education, Smarandache Collections ► Abstract Full Text Search Details...tive biring. We say the biring R has a monounit if a unit exists which is common to both R 1 and R 2 . If R 1 and R 2 are rings which has separat... ...t (right) cancelable we say that N fulfills the left (right) cancellation law. N is a bi-integral domain if both N 1 and N 2 has no zero divisors. ... ... for all i, j. Proof: Let q i = Π{n j ; i ≠ j }> 1 since the greatest common divisor of q 1 , q 2 , …, q r is 1 then there exists a i ∈ Z suc... ...t A be a S-T-fuzzy subsemigroup of P ⊂ G, G a S-semigroup. Then the least common multiple of the fuzzy order of the elements of P in G with respect ... ...: Let A be a S-T-fuzzy sub-bisemigroup of the S-bigroup G. Then the least common multiple of the S-fuzzy order of the elements of G with respect to A... ...erly contained in 〈S 〉; as in 〈S 〉 we may or may not have the associative law to be true. Remark: Even (ab)c ≠ a(bc) in general for all a, b, c ∈ ... ...comparison of one BIBD with the another and also give the analysis of the common features. Thus the S-planar near-ring has more advantages than t...
 Book Id: WPLBN0002097093 Subjects: Non Fiction, Education, Smarandache Collections ► Abstract Full Text Search Details...d to prime numbers . . . . . . . . . . . . . . . . . . 247 11 On the least common multiple of the rst n positive integers . . . . . . . . 255 Chapter... ...lt a +b +c 3 p 3R is another source for inequalities. For example, by the law of sinus, a = 2R sinA, etc., we get the classical trigonometric inequal... ...) d (24) where d;m;n;k are positive integers; m > n; and d is an arbitrary common divisor of (m n)(k 2 +mn), m(k 2 +n 2 ), n(k 2 +m 2 ). For a comple... ...iangles, and where r is integer are given by formulae (24), where d is any common divisor of the following expressions: (m n)(k 2 +mn); m(k 2 +n 2 );... ...s of (28) can be obtained from (30), by multiplying each term of (30) by a common factor d. These give all H-triangles with the required conditions. R... ...::b x i :::x n jx 1 x 2 :::x n (3) Let d = (x 1 ;x 2 ;:::;x n ) = greatest common divisor of x 1 ;:::;x n . Then x =dy 1 ;:::x n =dy n ; where (y 1 ;:...
 Book Id: WPLBN0002097108 Subjects: Non Fiction, Education, Smarandache Collections ► Abstract Full Text Search Details...res [1, 4, 10-12, 18, 34, 52, 75-80, 82, 108, 111]. The max-min composition is commonly used when a system requires conservative solutions in the s... ... .6 12 Consider now two binary fuzzy relations P(X, Y) and Q(Y, Z) with a common set Y. The standard composition of these relations, which is ... ...t is reflexive, anti symmetric and transitive is called a partial ordering. The common symbol ≤ is suggestive of the properties of this class of rel... ... procedures [1, 11, 16, 24, 30, 82]. 33 The “max-min” composition [117] is commonly used when a system requires conservative solutions in the s... ... 2 ) In this way, Ω 1 contains sets of I j ’s which have some element(s) in common and we can decompose the original problem into k sub-problems... ... 2 ) given in Figure 2.1.3. 173 The linear equation is based on Ohm’s law, the drop in voltage V across a resistor R is given by the linea... ...in voltage V across a resistor R is given by the linear relation V = iR (Ohm’s law). The hydrodynamic analogue to the mean velocity v for laminar f... ...ting), from accepted / rejected / pending, etc. and guided by the fact that the law of excluded middle did not work any longer in the modern logics,...
 Book Id: WPLBN0002097643 Subjects: Non-Fiction, Education, Smarandache Collections ► Abstract Full Text Search Details...p > 1 is a prime if its only divisor are ± 1 and ± p. DEFINITION: The least common multiple of two positive integers a and b is defined to be the ... ...osure). 2. For all a, b, c ∈ S we have a  (b  c) = (a  b)  c (associative law). (S, ) is a semigroup. DEFINITION: If in a semigroup (S, ) w... ...s properly contained in ; as in we may or may not have the associative law to be true. Remark: Even (ab) c ≠ a (bc) in general for all a, b... ... Alternative, 17, 20, 40-44, 56, 62, 65, 91, 92, 106-108 Associative Law, 11, 93 Automaton, 88, 93-96 Binary operation, 8, 11, 16, 25, 3...
 Book Id: WPLBN0002097649 Subjects: Non-Fiction, Education, Smarandache Collections ► Abstract Full Text Search Details... (closure axiom) 2. a. (b.c) = (a.b).c for all a, b, c ∈ L. (associative law) (S, .) is called the semigroup. The semigroup in general may not ha... ...b) . c for some a, b, c ∈ R. 3. a. (b + c) = a.b + a.c (The distributive law are true) for all a, b, c, ∈ R. Let R be a non-assoiciative ring. R ... ...is said to be associative if its multiplication satisfies the associative law that is (xy) z = x (yz). 92 A non-associative algebra L is a Lie ... ...ne all non- isomorphic Lie algebras. The following is a very important and commonly used example. Example. 4.1.3: Let gl (n, C) be the set of all ... ...t we are happy to state that we have introduced several notions which are common to associative algebras and analysed it in the case of Jordan algeb...
 Book Id: WPLBN0002097101 Subjects: Non Fiction, Education, Smarandache Collections ► Abstract Full Text Search Details...ombined conflicting opinions tend to cancel out and assisted by the strong law of large numbers, a consensus emerges as the sample opinion approximat... ...in case of a model, add two or more FCMs to produce a new FCM. The strong law of large numbers ensures in some sense that knowledge reliability incr... ... Combined conflicting opinions tend to cancel out and assisted the strong law of large numbers a consensus emerges as the sample opinion approximate... ...bined (and normalized) FCM entry f ij tends to be in {–1, 1}. The strong law of large numbers ensures that f ij provides a rational approximation ... ...ts (Levels and Variations), several kinds of Relations (Causal, Inference Common, similarity, ill-defined, Crisp, Level-Variation, and other common r... ... effect during a single iteration, but an event which has a real delay. A common example of this kind of timing events is the effect of oil-price var... ... might result in assigning grades of membership in a way unsupportable by common sense reasoning. In order to facilitate a more reasonable represe... ...firm to issue guarantees. The nested FCMs are shown below linked to their common nodes, N3, “Insiders Waive Claim to Firm’s Assets” and N4, “Firm Is... ...on, I translate these variables into singleton values. This approach is a common practice. The resulting FCM is still fuzzy, because both edge and c...
 Book Id: WPLBN0001235223 Subjects: Non Fiction, Education, Economics ► Abstract Full Text Search Details...nce XXXVII. The Lessons of Transition XXXVIII. The Morality of Child Labor XXXIX. Law and Technology XL. The Author Economics - Psychology's Neg... ...t to disguise its nature as a social science by applying complex mathematics where common sense and direct experimentation would have yielded far b... ...dministered by some supreme, transcendental principle is restored. This sense of "law and order" is further enhanced when the theory yields predic... ...ons which come true, either because they are self-fulfilling or because some real "law", or pattern, has emerged. Alas, this happens rarely. As "Th... ...wer. Influential antitrust thinkers, such as Robert Bork, recommended to revise the law to focus solely on consumer welfare. These - and other ins... ...ofit and loss centers. Competition used to be extraneous to the firm - now it is commonly an internal affair among autonomous units within a loos... ...r assets as well. They end up charging borrowers the wrong interest rates or, more common, financing risky projects. Badly managed banks pay highe... ... Governments would like to maintain the stability of their financial systems. The common interest is overwhelming - and moral hazard seems to be a... ...cording to an August 2000 article written by Albert Beer of America Re. ART is also common in the public and not for profit sectors. Captive.com co...
 Book Id: WPLBN0001235224 Subjects: Non Fiction, Education, Economics ► Abstract Full Text Search Details... In some countries, the obligation to save life is legally codified. But while the law of the land may create a LEGAL right and corresponding LEGAL... ...d, if so (b) in which circumstances – can be easily settled using modern contract law. Yes, a contract can be annulled and voided if signed under ... ...s to provide goods and services (always at a personal cost to the provider) are the commonest of contracts. We open a business. We sell a software ... ...poses numerous and insurmountable philosophical problems. No one disputes the now common view that the main crime committed in aborting a pregnanc... ... Why is there a debate regarding this question? "Thou shalt not kill" is a natural law, it appears in virtually every legal system. It is easily an... ..., the quantity, quality, or functions are wrong, lacking, altogether missing". The common error - that we criticize the absent - is the outcome of ... ...ive self-definitions I share with someone (i.e., the more affiliations we have in common) , the larger and more overriding is my moral obligation ... ...y do shareholders cooperate with such corporate brigandage? In an important Chicago Law Review article whose preprint was posted to the Web a few we... ...akunin), trade unions (anarcho- syndicalists), ideal communism (Kropotkin). What is common to this smorgasbord is the affirmation of freedom as the ...
 Book Id: WPLBN0002097119 ► Abstract Full Text Search Details... . . . . . . . . . 63 S. J. Crothers On the Generalisation of Kepler’s 3rd Law for the Vacuum Field of the Point-Mass. . . . . . . . . . . . . . . . .... ...arity at r=α, and appears to be valid only for r>α. This limitation is not commonly regarded as serious, and certainly is not so if the general theory... ...riance, at r=r 0 , of the circumference of a great circle, of Kepler’s 3rd Law [1, 2], of the Kretschmann scalar, of the radius of curvature C(r 0 )=α... ...curvature will necessarily manifest in the associated form of Kepler’s 3rd Law, and the Kretschmann scalar [22]. I fnally remark that the fact that a ... ...: gr-qc/0102054). 22. Crothers S. J. On the Generalisation of Kepler’s 3rd Law for the Vacuum Field of the Point-Mass. Progress in Physics, 2005, v. 2... ...tory. The principal objective of this research is to extract that which is common to every one of the theoretical approaches. We will see further that... ...ea to consider those characteristics of gravitational wave felds which are common to most of the criteria. Such an integrating factor is Petrov’s clas... ...ocal bivector set. Every anti- symmetric pair of indicesαβ is denoted by a common index a, and the number of the common indices isN= n(n−1) 2 . It is ... ...al method that we propose to apply to this problem joins both felds into a common feld. The method itself does not differ for each feld: to set an inv...
 Book Id: WPLBN0002097084 Subjects: Non Fiction, Mathematics, Finances ► Abstract Full Text Search Details... cash flows in the future according to some prearranged formula. The most common type of swap is the "plain 40 vanilla" interest rate swap, in whi... ...cipal. Both payment streams are denominated in the same currency. Another common type of swap is the currency swap. This contract calls for the count... ...ore the day of maturity, it is termed an American option. A third, not-so-common category is one where the holder can exercise the option only on sp... ... option pricing using the numerical method of trinomial trees, which is a common 42 numerical algorithm used in the pricing of the non-European op... ...ff between information usage and information acquisition (Berry, 1985). A common solution method would be to allocate an equal number of trials betw... ...ce curves are always convex to the origin because of the operation of the law of substitution. This law states that the scarcer a commodity becomes,... ...ates. To prevent this from happening one needs to strictly adhere to the law of substitution under all circumstances. This however, at times, could ... ...n would be quite substantial, thereby validating an extended substitution law based on an expected information measure of utility. The 68 specifi... ... afforded by its mere availability can nevertheless suffice to uphold the law of substitution. 70 4.2 Utility and Thermodynamics I...
 Book Id: WPLBN0001235284 Subjects: Non Fiction, Education, Global Finance ► Abstract Full Text Search Details... Credit Default Swap CECA Comprehensive Economic Cooperation Agreement CIS Commonwealth of Independent States CRAs Credit Rating Agencies ECA Europe a... ... Actis (which was spun off as a management buyout from the UK government’s Commonwealth Development Corporation [CDC] in 2004, with CDC remaining its ... ...eform the present financial system. If there is a strong political will, a common international framework could be evolved which national regulatory a... ...r called the European System of Financial Supervision, which could enforce common standards among European regulators. While supporting the need for n... ...n update on the Basel Accords. The new rules propose strict definitions of common equity held by banks, introduction of a leverage ratio and provision... ...nstraints Imposed by the EEA Agreement,” Society of International Economic Law (SIEL), Second Biennial Global Conference, University of Barcelona, Jul... ...ding Crisis: Causes and Effects of the Mort- gage Meltdown, Wolters Kluwer Law & Business, 2008. Kavaljit Singh, Globalization of Finance: A Citizen’s...
 Book Id: WPLBN0002828534 Subjects: Non Fiction, Science, Neutrosophic Physics ► Abstract Description Details...Neutrosophic Physics. Let be a physical entity (i.e. concept, notion, object, space, field, idea, law, property, state, attribute, theorem, theory, etc.), be the opposite of , and be their neutral (i.e. neither nor but in between). Neutrosophic Physics is a mixture of two or three of these entities , , and that hold...
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