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Complete lattice (X)

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 Book Id: WPLBN0002097645 Subjects: Non-Fiction, Education, Smarandache Collections Collections: Literature, Education, Authors Community, Mathematics ► Abstract Full Text Search Details...A 1 A 2 A 3 A 4 A 5 2 The picture on the cover represents the lattice of subgroups of the Smarandache loop L 15 (8). The lattice of subg... ...The lattice of subgroups of the commutative loop L 15 (8) is a non-modular lattice with 22 elements. This is a Smarandache loop which satisfies the S... ...sic Concepts 7 1.2 A few properties of groups and graphs 8 1.3 Lattices and its properties 11 2. Loops and its properties 2... ...: Theory and Applications, Heldermann Verlag, 1990. But none of them are completely devoted for the study of loops. The author of this book has ... ...ch is introductory in nature covers some notions about groups, graphs and lattices. Chapter two gives some basic properties of loops. The importance... ... is equal to the number of distinct proper (2n – 1) edge colourings of the complete graph K 2n . In chapter three we introduce Smarandache loops ... ...e reader is expected to have a good knowledge in algebra we have not done complete justice in recollecting all notions. This chapter has three sectio... ...me basic ideas about conjugates. Further in this section one example of a complete graph is described as we obtain an application of loops to the ed... ...in which each pair of disjoint vertices are joined by an edge is called a complete graph. Upto isomorphism, there is just one complete graph on n ...
 Book Id: WPLBN0002097085 ► Abstract Full Text Search Details... in the physical projection of subatomic particles into macro-group systems. Complete absence of structural projection in a physical system is non-ra... ... motive force -ϒ, acting upon its mass in that quanta. This definition is in complete accord with Newton's first law of motion and moreover provides ... ...-nucleon nucleus together ―this in response to question: "How do protons on lattice corners maintain their equilibrium and not Coulomb explode?" [51]... ...ternal to the nucleus, stored in curvature in the surrounding spatial field lattice ―a geometric solution rather than the MT virtual particle premise... ...ossess perfect nuclear cubic symmetry, i.e. have a common characteristic of completely filled η potential shells. Analysis of the noble group Z prog... ... energy stored? Modern theory, in terms of potential energy, does not offer completely satisfactory answers to these questions. However, from the pr... ...articles. [5] Except for theoretical aspects then, the two systems are not completely incompatible. In this sense the particle-field identities rel... ... weakly refracted, or diffracted, depending on angle relative to the crystal lattice, (i.e. path intersection with nuclear g fields.) The above func...
 Book Id: WPLBN0001235285 Subjects: Non Fiction, Education, Morals Collections: Literature, Education, Philosophy, Authors Community ► Abstract Full Text Search Details...es and their negation are unprovable. The system is consistent and true - but not "complete" because not all its sentences can be decided as true o... ... consistent formal logical system can prove its own consistency. The system may be complete - but then we are unable to show, using its axioms and ... ... consistent In other words, a computational system, like the Matrix, can either be complete and inconsistent - or consistent and incomplete. By try... ...d inconsistent - or consistent and incomplete. By trying to construct a system both complete and consistent, God has run afoul of Gödel's theorem an... ...one basis for discrimination preferable to another? Can we eliminate discrimination completely and if it were possible, would it have been desirable... ...not imagine beings whose complexity does not spring from some material (or energy) lattice. But our inability to imagine something, even in princip...
 Book Id: WPLBN0001235239 Subjects: Fiction, Drama and Literature, Poetry ► Abstract Full Text Search Details...ubicle. Some women mesh their hands, trapping her flapping arms, flailing about, her cheeks lattices of translucent rivulets. Her fear is audible in... ...undated. I heave myself onto a leathery love seat and crumble, am embryo ensconced. I must completely reconsider I know not what, till when, what p... ...grounds, each day discovering new installations. Our brains fused and rarely did I have to complete my sentences. Or hers. We strolled, hands clasp... ... listen to the Program for the Mother and Child, Listen now you lovely kids, our program is complete and she brings me a big bowl of fruits and I ea... ...s and fixes everything at home. But I keep reading, sometimes five whole books a day. I am completely uninterested in their content. I don't read ev...
 Book Id: WPLBN0002097644 Subjects: Non-Fiction, Education, Smarandache Collections Collections: Math, Literature, Education, Algebra, Authors Community, Mathematics ► Abstract Full Text Search Details...minary notions 1.1 Semigroups, groups and Smarandache semigroups 7 1.2 Lattices 11 1.3 Rings and fields 19 1.4 Vector spaces 22 1.5 Group r... ...s 29 2.2 Semirings and its properties 33 2.3 Semirings using distributive lattices 38 2.4 Polynomial semirings 44 2.5 Group semirings and semigr... ...ackground in algebra that will enable one to follow and understand the book completely. This book consists of seven chapters. The first chapter i... ...pter. Chapter four, which is one of the major parts of this book contains a complete systematic introduction of all concepts together with a sequent... .... In this chapter we recall some basic properties of semigroups, groups, lattices, Smarandache semigroups, fields, vector spaces, group rings and... ...1. Can Z 121 have subgroups of even order? If so find all of them. 1.2 Lattices In this section we just recall the basic results about lattic... ...is very meagre. In my opinion I have not come across a textbook that covers completely all the properties of semirings. Hence this complete chapter ... ...rties about it, analogous to rings. This chapter also gives for the sake of completeness the definition of several types of special semirings like ∗-... ...miring. 2.5 Group Semirings and Semigroup Semirings This section is completely devoted to the introduction and study of group semirings and ...
 Book Id: WPLBN0002097108 Subjects: Non Fiction, Education, Smarandache Collections ► Abstract Full Text Search Details...E constraints 48 1.7 Method of solution to fuzzy relation equations in a complete Brouwerian lattice 55 1.8 Multi-objective optimization pr... ....7 Method of solution to fuzzy relation equations in a complete Brouwerian lattice 55 1.8 Multi-objective optimization problems with fuzz... ...ts 146 1.26 Solvability criteria for systems of FRE 156 1.27 Infinite FRE to a complete browerian lattices 162 1.28 Semantics of implication operat... ...ility criteria for systems of FRE 156 1.27 Infinite FRE to a complete browerian lattices 162 1.28 Semantics of implication operators and fuzzy ... ...trosophic logic 222 3.2 Fuzzy neutrosophic sets 230 5 3.3 On neutrosophic lattices 235 3.4 Neutrosophic notions: Basic concepts 239 3.5 Neutr... ...n of NRE with max product Composition 259 4.3 Method of solution to NRE in a complete Browerian lattice 260 4.4 Multi-objective optimisation p... ...uct Composition 259 4.3 Method of solution to NRE in a complete Browerian lattice 260 4.4 Multi-objective optimisation problem with NRE con... ...ic notions and definitions about the NREs and introduces NREs. Section 4.11 is completely devoted to suggest how one can apply NREs in the study of... ...methods of neural networks and genetic algorithm is used in solving problems. A complete set of references is given in the end of the book citing th...
 Book Id: WPLBN0002097105 ► Abstract Full Text Search Details...E constraints 48 1.7 Method of solution to fuzzy relation equations in a complete Brouwerian lattice 55 1.8 Multi-objective optimization pr... ....7 Method of solution to fuzzy relation equations in a complete Brouwerian lattice 55 1.8 Multi-objective optimization problems with fuzz... ...ts 146 1.26 Solvability criteria for systems of FRE 156 1.27 Infinite FRE to a complete browerian lattices 162 1.28 Semantics of implication operat... ...ility criteria for systems of FRE 156 1.27 Infinite FRE to a complete browerian lattices 162 1.28 Semantics of implication operators and fuzzy ... ...trosophic logic 222 3.2 Fuzzy neutrosophic sets 230 5 3.3 On neutrosophic lattices 235 3.4 Neutrosophic notions: Basic concepts 239 3.5 Neutr... ...n of NRE with max product Composition 259 4.3 Method of solution to NRE in a complete Browerian lattice 260 4.4 Multi-objective optimisation p... ...uct Composition 259 4.3 Method of solution to NRE in a complete Browerian lattice 260 4.4 Multi-objective optimisation problem with NRE con... ...ic notions and definitions about the NREs and introduces NREs. Section 4.11 is completely devoted to suggest how one can apply NREs in the study of... ...methods of neural networks and genetic algorithm is used in solving problems. A complete set of references is given in the end of the book citing th...
 Book Id: WPLBN0002097647 Subjects: Non-Fiction, Education, Smarandache Collections ► Abstract Full Text Search Details...esearch Press Rehoboth, NM 2002 2 The picture on the cover is the lattice representation of the S-ideals of the Smarandache mixed direct pro... ...ajor difference between a ring and a Smarandache ring. For, in a ring the lattice representation of ideals is always a modular lattice but we see in... ...n of ideals is always a modular lattice but we see in case of S-rings the lattice representation of S-ideal need not in general be modular. This ... ...reliminary notions 1.1 Groups 7 1.2 Semigroups 11 1.3 Lattices 14 1.4 Smarandache semigroups 19 2. Rings and i... ...g around 243 Smarandache concepts. As it is well known, studying any complete structure is an exercise in unwieldiness. On the other hand, stud... ... recollected for ready reference only the basic results. Chapter three is completely devoted to the introduction, description and analysis of the Sm... ... in section five. Section six introduces modules and the final section is completely devoted to the recollection of the rings which satisfy chain co... ... 4.3 Some New Smarandache elements and their properties This section is completely devoted to the study of properties of elements in rings and the... ...itor group. Proof: Follows by the definition. Just for the sake of completeness we give the definition of semiring as it used to define semio...
 Book Id: WPLBN0002097649 Subjects: Non-Fiction, Education, Smarandache Collections ► Abstract Full Text Search Details... 2 L 5 (3). a. Do the two sided ideals of Z 2 L 5 (3) form a modular lattice? b. Find only the right ideals of Z 2 L 5 (3). What is its lattic... ... Z 4 L 9 (2) and Z 4 L 9 (8) find a. The set of right ideals and its lattice structure. b. The set of left ideals and their lattice structure.... ...f left ideals and their lattice structure. c. Two sided ideals and their lattice structure. 11. Find for the loop rings Z 4 L 9 (2) and Z 4 L 9... ... ring, inner commutative loop ring, pseudo commutative loop rings and the lattice of substructures of loop rings like ideals, subrings, and their Sm... ...roved that every representation of a semi simple analytic Moufang loop is completely reducible. Here we derive the Smarandache analogue of all these ... ...rime but t ≠ u, t, u ∈ Z n \ {0}. Clearly the class of groupoids Z(n) is completely contained in Z ∗ (n). Similarly we define Z ∗∗ (n) to be the cla... ... a S-groupoid ring. Thus we see the class of S-groupoid rings contains completely the class of groupoid rings which are SNA-rings. THEOREM 3.2... .... 3.4. Smarandache substructures in Groupoid rings This section is completely devoted to the introduction of Smarandache substructures in gro... ...∈ I or y ∈ I. The study of groupoid rings in mathematical literature is completely absent so the study of these ideals S-ideals, pseudo ideals and...
 Book Id: WPLBN0002097651 Subjects: Non-Fiction, Education, Smarandache Collections ► Abstract Full Text Search Details...0 > t 1 > … > t n . Suppose further that (R, M) and (A t , M ∩ A t ) are complete local rings for all t ∈ Im (A) such that R P ⊂ 0 t A . Then R h... ...Ω α A A ) ( × × ∈ ∈ = . 54 Now we proceed on to define the concept of complete fuzzy direct sum. DEFINITION 1.4.6: Let {R α | α ∈ Ω } be a co... ... all α ∈ Ω . Then the Cartesian cross product α Ω α A × ∈ is called the complete fuzzy direct sum of the A α . We proceed on to recall the wea... ... is requested to refer [80]. We replace the interval [0, 1] by a finite lattice L which has 0 to be the least element and 1 to be the largest elem... ...e, fuzzy ideals have been defined over [0, 1] when we define it over a lattice L we call them L-fuzzy ideal. DEFINITION [61-64]: An L-fuzzy ide... ... function J : R → L (R is a commutative ring with identity L stands for a lattice with 0 and 1) satisfying the following axioms i. J (x + y) ≥ J ... ...field is defined for the first time in this book. We just for the sake of completeness recall the definition of bifields. DEFINITION 1.6.2: A bir... ...y absent. This concept is defined only in this book. Just for the sake of completeness we start to give the definition of fuzzy semirings and proceed... ... 2 2 M × is a semidivision ring. Example 1.7.4: Let C 11 be the chain lattice with 11 elements, C 11 is a finite semiring in fact a finite semi...
 Book Id: WPLBN0002097118 Subjects: Non Fiction, Education, Smarandache Collection ► Abstract Full Text Search Details... self-contradictory support or an explicit contradiction, but which is not completely proven as a paradox. We present herein four elementary quantum q... ... self-contradictory support or an explicit contradiction, but which is not completely proven as a paradox. A quasi- paradox is an informal contradicto... ...tude of the fractal fuc- tuations. Note that it is possible to have a more complete construction in which the full velocity feld V+W intervenes in the... .... Fur- thermore, discrete Clifford-algebraic methods based on hyperdiamond-lattices have been instrumental in construct- ingE 8 lattices and deriving ... ...na of Nature. This thesis will be- come clearer if we consider the “number lattice” introduced by Minkowski (Fig. 1). Therein are given all points of ... ...nd denomina- tors, respectively. If we exclude all points of the Minkowski lattice with coordinates have a common divisor different from unity, this p... ...less thanm and relatively prime with m. Therefore, if we expand the number lattice infnitely, the average density of rational numbers in the plane (th... ...e point-mass and briefy discuss its geometry. Although I have obtained the complete solution up to the rotating point-charge I reserve its derivation ... ... that all geodesics that do not run into the Hilbert boundary atr 0 =α are complete. His result is easily extended to any r 0 0 in (17). The correct...
 Book Id: WPLBN0002097119 ► Abstract Full Text Search Details...arge requires the determination of the mappingψ. The orthodox analysis has completely failed to understand this and has consequently failed to solve t... ...d from it and re- presents a distinct manifold.” His claims about (13) are completely false. He has made an incorrect assumption about the origin. His... ...t all those geodesics which do not run into the boundary atr=α on (18) are complete. Now (18) with α
 Book Id: WPLBN0001235286 Subjects: Non Fiction, Philosophy, Science ► Abstract Full Text Search Details... century to demonstrate the problematic nature of some of Cantor's thinking (Cohen completed Godel's work in 1963). But continuity can be finite an... ...larities imply a tear in the fabric of spacetime and the ubiquity of these creature completely annuls its continuous character. Modern superstrings ... ...s no less excruciating than solving a classic PT diagram. But if we want to obtain complete knowledge about a quantum system, we need a non-perturb... ...re-Conscious (Threshold of Consciousness) are but Fields of Potentials organized in Lattices. Potentials of what? To represent realities (internal ... ...ns (hyperstructures) and memory (the stamping process). Minsky (1980) Memory is a complete conscious state and it is reconstructed as such. In ou... ... Conversely, in a process known as redintegration, mental and emotional states are completely invoked and restored when only a single element is en... ...rain) with its product (mind). Some of these scholars postulate the existence of a lattice of preconceived, born, categorical knowledge about the u...
 Book Id: WPLBN0002097103 Subjects: Non Fiction, Education, Smarandache Collections ► Abstract Full Text Search Details...) A single change in one of any connective’s truth table is enough to form a (completely) different logic. The rules are hypothetical or factual.... ... generalizes: - the intuitionistic probability, which supports incomplete (not completely known/determined) probability spaces (for 0 < n < 1 and i ... ...easing Boolean functions of variables, and also the number of free distributive lattices with generators [18, 20, 28, 29, 38, 54]. Determining these n... ...evaluated from and operators on since we include the possibility to deal with a complete paradoxical source of information such that . These deﬁnition... ...ys negative and therefore reaches its maximal value when (66) (67) (68) This completes the deﬁnition of our new transformation model. Note that can... ... because whenever we imagine it, our imagination can never be it (we can never completely describe it: more we describe it, more wrong we are). It i...
 Book Id: WPLBN0001235224 Subjects: Non Fiction, Education, Economics ► Abstract Full Text Search Details...rst, the English speaker inside the room himself is a conscious entity, replete and complete with mental states, cognition, awareness and emotional ... ...n legitimately- marked trademarked goods; f. Unjustifiably - whether partially or completely - refusing to deal on an enterprise's customary comme... ... century to demonstrate the problematic nature of some of Cantor's thinking (Cohen completed Godel's work in 1963). But continuity can be finite an... ...larities imply a tear in the fabric of spacetime and the ubiquity of these creature completely annuls its continuous character. Modern superstrings ... ...e transition to a different cultural model, replete with different morals, will be completed with success. But it will not eliminate all pervious m... ...rain) with its product (mind). Some of these scholars postulate the existence of a lattice of preconceived, born, categorical knowledge about the u... ...re-Conscious (Threshold of Consciousness) are but Fields of Potentials organized in Lattices. Potentials of what? To represent realities (internal ... ... origin (brain) with its product (mind). Some of them postulated the existence of a lattice of preconceived, born categorical knowledge about the u...
 Book Id: WPLBN0001235225 Subjects: Non Fiction, Religion, Philosophy ► Abstract Full Text Search Details...rst, the English speaker inside the room himself is a conscious entity, replete and complete with mental states, cognition, awareness and emotional ... ...n legitimately- marked trademarked goods; f. Unjustifiably - whether partially or completely - refusing to deal on an enterprise's customary comme... ... century to demonstrate the problematic nature of some of Cantor's thinking (Cohen completed Godel's work in 1963). But continuity can be finite an... ...larities imply a tear in the fabric of spacetime and the ubiquity of these creature completely annuls its continuous character. Modern superstrings ... ...e transition to a different cultural model, replete with different morals, will be completed with success. But it will not eliminate all pervious m... ...rain) with its product (mind). Some of these scholars postulate the existence of a lattice of preconceived, born, categorical knowledge about the u... ...re-Conscious (Threshold of Consciousness) are but Fields of Potentials organized in Lattices. Potentials of what? To represent realities (internal ... ... origin (brain) with its product (mind). Some of them postulated the existence of a lattice of preconceived, born categorical knowledge about the u...
 Book Id: WPLBN0002097036 Subjects: Non Fiction, Education, Mathematics ► Abstract Full Text Search Details...be congruent to 0 modulo 4 and n+4 would be congruent to 1 modulo 4. This completes the cycle. Case 2: The base B is even. Basis step For B = 4, the ... ...er, which is even for n+1, odd for n+2, even for n+3 and odd for n+4. This completes the cycle and the inductive condition is verified. 2) Symmetric S... ...000000000000000000000000000000000000000000000000000000... Figure 19 Finite Lattice ...0000000000000000000000000000000000000000000000000000000000000... ...000000000000000000000000000000000000000000000000... 92 Figure 20 Infinite Lattice ...1111111111111111111111111111111111111111111111111111111111111...
 Book Id: WPLBN0002097650 Subjects: Non-Fiction, Education, Smarandache Collections Collections: Technology, Literature, Education, Logic, Authors Community, Mathematics ► Abstract Full Text Search Details...having my family working along with me late hours every night in order to complete this – but then, I have had a rare kind of intellectual satisfact... ...initions of groups, loops and Smarandache loops (S-loops) for the sake of completeness and also for our notational convenience, as we would be using... ...note by Z ∗∗ (n) thus Z ∗∗ (n) = {Z n , ∗, (t, u)} This class of groupoids completely contains the class of groupoids Z ∗ (n) and Z(n). Thus Z(n) ⊂ Z... ... is an important one. We know the set of ideals of a ring forms a modular lattice. The study in this direction is an interesting and an innovativ... ...y the semiring is of infinite order. Example 1.5.2: Let L be the chain lattice given by the following diagram: L is s... ...cteristic associated with it. Example 1.5.3: The following distributive lattice S is also a semiring of order 8. S i... ...ifield. Example 1.5.4: Z o is a semifield. Example 1.5.5: Any chain lattice L is a semifield. In example 1.5.4, the semifield is of characte... ... about them. 3.1 Bisemigroups and its applications This section is completely devoted to the recollection of bisemigroup and give some exampl... ... α t does not belong to R. 152 The interested reader can develop a complete notion of polynomial quad rings and polynomial quad birings. The ...
 Book Id: WPLBN0001235233 Subjects: Non Fiction, Psychology, Education ► Abstract Full Text Search Details... origin (brain) with its product (mind). Some of them postulated the existence of a lattice of preconceived, born categorical knowledge about the ... ...es, and will put their lives in danger – just to reach this bliss of wholeness and completeness. There is, in other words, a preference of inner eq... ...rain) with its product (mind). Some of these scholars postulate the existence of a lattice of preconceived, born, categorical knowledge about the u... ...ychoanalysis was, when elaborated, a Kuhnian paradigm shift. It broke with the past completely and dramatically. It generated an inordinate amount o... ...ten tend to fuse the two (dream and reality) into a whole and act upon it. e. To complete their mission successfully (adaptation to the world usi... ... does not react to external sensory stimuli while in operation. It takes an almost complete suspension of judgement in order to influence the conte... ...ubstrate (brain) with its product (mind). Some of them postulate the existence of a lattice of preconceived, inborn categorical knowledge about the ... ...frameworks), universally accessible, atemporal and non-spatial. This third text is COMPLETE in the sense that it includes both the manifest and the...
 Book Id: WPLBN0002097122 ► Abstract Full Text Search Details...antum Mechanics. At some future time relativity will be replaced by a more complete theory, just as Newtonian mechanics was replaced by relativity,... ...erved, the language of the description must be continually altered. Godel's completeness theorem plainly states that a fixed language can only descr... ...-forms. Space-forms come from moding out (identifying opposite sides of the lattice's fundamental domain) discrete isometry (metric preserving trans... ...al domain) discrete isometry (metric preserving transformations) subgroup's lattice structure. (Mathematically, space-forms are defined on spaces of... ...The idea being used to find the period of one spin rotation, is that in one complete period of a spin rotation of states on a space-form, light shou... ...lar state, this state is called a metric state. Godel's consistency and completeness theorems - A mathematical theory which says that there are ... ...e of real promise; a time of bold exploration to be made possible by a more complete understanding of relativity. And relativity, far from sufferin...
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