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### Pluckings from the Tree of Smarandache Sequences and Functions

##### By: Charles Ashbacher

...also by Erhus Cniversity Press, dealt almost exclusively with some "basic" consequences of the Smarandache function. In this one, the universe of dis... ...y from the interest and excitement that can be generated by exploring the consequences of such a problem It is a well-known cliche among writers tha... ... some of these problems. In mathematics, one often does not know what the consequences of a statement are. Cnlike a novel however, there are no compl... ... n, where n is the smallest number such that m divides n'. and associated consequences has spawned many new branches of mathematics. A previous volu... ...t occur in n! 0 This function has many uses when dealing with some of the consequences of the Smarandache function Sen), most notably, the number of... ... prime, the Smarandache values would form the same 3 x 3 magic square. A logical extension of this problem places a restriction on the numbers. The...

### Noi Functii in Teoria Numerelor

##### By: Florentin Smarandache

...ant role in fuzzy relation equations. While the t-norm i may be interpreted as logical conjunction, the corresponding operation w i may be interpr... ... as logical conjunction, the corresponding operation w i may be interpreted as logical implication. The following basic properties 31 of w i ... ...practice. For example, in fuzzy reasoning [70], when the inference rule and the consequences are known, a problem to determine antecedents to be use... ...sible solutions according to some levels of plausibility is out of the scope of logical reasoning, strictly speaking. However one may for instance... ... 134 there are manifestations which are neither certain nor impossible and consequences of the presence of a given disorder d which are only po... ...n power of the model, we have to refine the non–fuzzy model in such a way that consequences (resp. manifestations) previously expressed as certain ... ...p. certainly absent) remain classified in the same way and where some possible consequences (resp. possibly present manifestations) are now allowed... ...ication, negation and a quantifier for generalization are used. As usual, those logical operators are characterized by the way they operate on the t... ... B ∧ t B ⊆ t A. (16) Introducing also the notation |= for (generalized) logical validity as in [28, 29] by |= A ≡ t A . ( 1 7 ) W...

### Basic Neutrosophic Algebraic Structures and Their Application to Fuzzy and Neutrosophic Models

##### By: W. B. Vasantha Kandasamy and Florentin Smarandache

...d terminal edges. For proof refer [11]. The following results are easy consequences of the above theorem. Result: [4]: Let G be any connecte... ... Machine Intelligence, 9 (1979) 149- 194. 75. Zhang, W.R., and S. Chen. A Logical Architecture for Cognitive Maps, Proceedings of the 2 nd IEEE ...

### G-Dimensional Theory & the Smarandache Quantum Paradoxes : Comparative Logic and Modern Quantum Theory

##### By: L. Stephen Young

... can be considered true physical paradoxes, G Dimensional Theory, a unique, logical and physically congruent system of physics, at significant varia... ...ason for this is that they are multi-disciplinary, having both physical and logical components. To consider these paradoxes, one needs be as much log... ...l prediction of events in physical systems. The recurring patterns indicate logical causality, i.e.: it is assumed there is a rational, causal, expla... ...onsiderations in a scientific value system ―the primary consideration being logical causality in predictive outcome of behavioral phenomena. Yet, reg... ...note however, that this is an apparent physical contradiction, as well as a logical one ―a characteristic absent from the general sorites paradox fo... ... definition of determinist: "..every event act or decision is the inevitable consequence of antecedents independent of the human will." [3] indicates... ...ve definition of 'determinist' as Every event in the subatomic world is the consequence of waves of probability collapsing into particles or waves ―...

### Fuzzy Relational Maps and Neutrosophic Relational Maps

##### By: W. B. Vasantha Kandasamy and Florentin Smarandache

...ant role in fuzzy relation equations. While the t-norm i may be interpreted as logical conjunction, the corresponding operation w i may be interpr... ... as logical conjunction, the corresponding operation w i may be interpreted as logical implication. The following basic properties 31 of w i ... ...practice. For example, in fuzzy reasoning [70], when the inference rule and the consequences are known, a problem to determine antecedents to be use... ...sible solutions according to some levels of plausibility is out of the scope of logical reasoning, strictly speaking. However one may for instance... ... 134 there are manifestations which are neither certain nor impossible and consequences of the presence of a given disorder d which are only po... ...n power of the model, we have to refine the non–fuzzy model in such a way that consequences (resp. manifestations) previously expressed as certain ... ...p. certainly absent) remain classified in the same way and where some possible consequences (resp. possibly present manifestations) are now allowed... ...ication, negation and a quantifier for generalization are used. As usual, those logical operators are characterized by the way they operate on the t... ... B ∧ t B ⊆ t A. (16) Introducing also the notation |= for (generalized) logical validity as in [28, 29] by |= A ≡ t A . ( 1 7 ) W...

### Fuzzy and Neutrosophic Analysis of Periyar's Views on Untouchability

##### By: W. B. Vasantha Kandasamy and Florentin Smarandache

... related to Untouchability 114 3.3 Some facts about Untouchability and its Consequences even after 57 years of Independence 334 Chapter F... ...in order to understand the multi-dimensional facets of untouchability and its consequences, we have given relevant excerpts from the translation of ... ...Smarandache [55-59]. 23 DEFINITION 1.4.1: In the neutrosophic logic every logical variable x is described by an ordered triple x = (T, I, F) wh... ...sistent logic, which means contradictory sources of information about a same logical variable, proposition or event one has T + I + F > 1. Thu... ...temporary casteist atrocities to analyze the evils of untouchability and its consequences using Fuzzy Cognitive Maps (FCMs) and Neutrosophic Cognit... ...everal cases, those who dare to love across caste lines have to face the dire consequence of death. R 10 – Varnashrama Dharma It was the earl... ... of the Brahmin society must only be Chandalas. So, in this 150 situation, logically you cannot be faulted since you have a place and plenty of e... ...eech of Periyar, 19-12-1973] 3.3 Some facts about Untouchability and its Consequences even after 57 years of Independence Here we give some ... ... Nadu 1920-1940, Koodal Pubishers, Madurai, (1980). 375 34. Periyar Dasan, Logical Analysis of Atheistic Principles of Periyar, unpublished Ph.D ...

### Smarandache Rings

##### By: W. B. Vasantha Kandasamy

...se to the reader as the proof requires vitally only the definitions and a logical use of them. A recent paper [27] which studies strictly wild al... ...utative ring II. Proof: Left for the reader to verify as it is an easy consequence of the definition. THEOREM 4.2.2: Let R be a ring. If R is ...

### Cyclopedia of Economics

##### By: Sam Vaknin

... is null and void. Any actions which are intended to terminate it and to annul its consequences should be legally and morally permissible. The sam... ...atements cannot be derived with certainty from any negative statement. This formal-logical trait reflects a deep psychological reality with unsettl... ...t. This formal-logical trait reflects a deep psychological reality with unsettling consequences. A positive statement about one's affiliation ("I ... ...nd self-aggrandizement, and the reification and embodiment of said subversion. The logical outcome is to call for the overthrow of all political sy... ...ute them. They dedicate all their attention to the immediate and ignore the future consequences of their actions. In other words, their attention a... ...g and, therefore, regards himself as omnipotent, omniscient and protected from the consequences of his own acts (immune) – the personality disorder... ...: a series of potentialities with attached probabilities, the potentials being the logically and physically possible products. What can we learn a... ...stitute a theory and produce falsifiable predictions. A metaphor is also subject to logical and aesthetic rules and to the rigors of the scientific ... ...its inclusion in the definer) is the very definition of a tautology, the gravest of logical fallacies. On the other hand: if such an external sour...

### Fuzzy Cognitive Maps and Neutrosophic Cognitive Maps

##### By: W. B. Vasantha Kandasamy and Florentin Smarandache

...trongly resemble neural networks, and they have powerful and far-reaching consequences as a mathematical tool for modeling complex systems. Prof. Ba... ... this stimulus input vector with FCM matrix, K.C. Lee et al [65] obtain a consequence vector as follows: (0, 0, 0, 0, 0.3, 0, – 0.3, 0.5) × FCM ma... ...3, 0, – 0.3, 0.5) × FCM matrix = (– 0.5, 0, 0.24, 0, – 0.08, 0, 0). The consequence vector may be interpreted such that changes in those three fact... ... vector can be organized into (0, 0, 0, – 0.1, 0.3, 0, – 0.3, .2). Then a consequence vector may be obtained as (– 0.15, .02, 0, – 0.24, 0, –0.12, 0... ...∩ M j ) ⊂ ( ~ Q j ∩ M j ). Here “⊂” stands for fuzzy set inclusion (logical implication). For brevity, fuzzy causal relationship is abbreviate... ...ity, fuzzy causal relationship is abbreviated as FCR in the following. Logical implication has an antecedent (or premise) and a consequent (or con... ...t (or premise) and a consequent (or conclusion). A typical example of the logical implication is “If A, then B”. In the logical implication, there a... ...quence: negation of A (or ¬ A). The FCR is more complicated than the logical implication. 1. Modus tollens does not hold in the FCR. “When mi... ...ble for relations between several concepts are indeterminate). 2. In a logical implication “If A, Then B”, we cannot draw inference in case when ...

### Capitalistic Musings

##### By: Sam Vaknin

...y captured by econometric models. These either lack predictive powers or lapse into logical fallacies, such as the "omitted variable bias" or "rever... ... behaviour. It must adequately cope with irrationality and cognitive deficits. d. Logical compatibility – It must not violate the laws of its inte... ...s new position and will be interpreted as immunity, conferred from above, from the consequences of illegal activities. The very allocation of opt... ...ce resources in order to attain their utility functions, to secure the outcomes and consequences (the value, the preference, that the player attache... ...that at least one of them is forced to alter at least one vector (Strategy). The Consequence to the agent is the value of a function that assigns... ... is the value of a function that assigns real numbers to each of the outcomes. The consequence represents a list of outcomes, prioritized, ranked. ... ...to cooperate and to cooperate in the formation of an outside agency. There is no logical or mathematical reason to exclude the latter possibility... ...ose related to the subject and those pertaining to the rest of the universe). d. Logically compatible – It must not violate the laws of logic bot... ...t of seeing a pattern emerging out of a big body of data. The insights must be the logical conclusion of the logic, the language and of the develop...

### Utility, Rationality and Beyond – from Behavioral Finance to Informational Finance

##### By: Sukanto Bhattacharya

...could still possibly be explained away as “infinite loss” but there is no logically acceptable way to explain the log of a negative number if f(X) > ... ...e theory was originally stated in much generalized, abstract terms. As a consequence, it presented possible areas of application covering a number ... ...while dynamically they may be viewed as set-valued vector functions. If a logical proposition is said to be t% true in T, i% indeterminate in I and ... ...f p t at every t so as to minimize the total error. It is quite logical to assume that the p t values will have to be related in some way... ...oduct of the relative reward r (c n ) that the individual attaches to the consequences resulting from the choice c n , the likelihood that the choice... ... arbitrage opportunities over any significant length of time. By logical extension, considering a structured portfolio with n assets, the be... ...ow, Peterson, U.S.A., 1957. Festinger, L., J. M. Carlsmith. Cognitive consequences of forced compliance. Journal of Abnormal and Social Psycho... ...ooper. Motivational basis of dissonance: The singular role of behavioral consequences. Journal of Personality and Social Psychology 56, 1989: 899-9...

### Progress in Physics : The Journal on Advanced Studies in Theoretical and Experimental Physics, Including Related Themes from Mathematics, Volume 2

##### By: Florentin Smarandache

... its geometrical analysis and identifcation of the invariants, as a direct consequence of its initial invalidated assum- ptions about ther-parameter, ... .../9906004). 21. Abrams L. S. The total space-time of a point charge and its consequences for black holes. Int. J. Theor. Phys., 1996, v. 35, 2661 (see ... ...of observable time around rotating bulky bodies like stars or planets. The consequences should be more pronounced in the interaction of the components... ... principle is valid for time density felds in atoms. Postulate III has two consequences: CONSEQUENCE I An atom undergoing excitation radiates the mome... ...effcient) for quantum numbers n 1, we obtain F N =(1+ )q cos 2 θ. (109) CONSEQUENCE II An atom undergoing relaxation absorbs the momentum fux of a ... ... resonance effect in a quadrupole mass-detector. However, it would be more logical way, making no as- sumptions or propositions, to solve the Synge-We...

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