..., λ) , x λ + y ν = (x + y) min (λ, v) , d µ o x λ + c K o y v = (dx + cy) min{µ , λ, k, v}. Proof: Left for the reader to refer [75]. The... ...y for all x ∈ V, (K o A)(x) = sup{min {K(c), A(y)}c ∈ P ⊂ R , y ∈ V, x = cy P is a subfield in R relative to which V is defined}. DEFINITION 4.... .... x λ + y ν = (x + y) min (λ, ν) , d µ o x λ + c κ o y ν = (dx + cy) min{µ , λ, κ, ν}. Problem 4.5.59: Show if M is a δ-Noetherian module... ...r all x ∈ H ⊂ G (K o A)(x) = sup{min {K(c), A(y)}  c ∈ S, y ∈ H ⊂ G, x = cy}. Fuzzy singletons are defined as in case of any other fuzzy subset. ... ...,λ} , x λ + y ν = (x + y) min (λ ,ν) , dµ o x λ + c R o y ν = (dx + cy) min (µ, λ, k, ν} . Problem 5.5.39: Prove the fuzzy subset ν of SF (... ...49. JACOBSON, Nathan, Basic Algebra I, Freeman, New York, 1974. 50. JUN, Young Bae, NEGGERS, J. and KIM, Hee Sik, Normal L-fuzzy ideals in semiring... ...c groups, J. Fuzzy Math., 3, 465-470 (1995). 56. KIM, Kyung Ho, and JUN, Young Bae, Normal fuzzy R-subgroups in near- rings, Fuzzy Sets and Systems,... ...ximations in a fuzzy group, Inform. Sci., 90, 203-220 (1991). 71. KWON, Young-In, Fuzzy Near-ring modules over fuzzy near-rings, Pusan Kyongnam Ma...

...lessly. There is no quantitative law of conservation of mental states. We teach our youngsters – thereby replicating our knowledge and giving them c... ...n architecture, etc. This preference of the Elders (a term of veneration) over the Youngsters (a denigrating term) typifies them strongly. These cu... ...os just to survive). They are also more likely to have a youth cult: to prefer the young, the new, the revolutionary, the fresh – to the old, the h... ...es. The Encyclopaedia Britannica: "... Others have argued that because even rather young children are capable of showing empathy with the pain of ... ...nd, therefore, some children are more sensitive to moral prohibitions than others. Young children's growing awareness of their own emotional states... ...rder to preserve a minimum of supersymmetry in our 4-d universe, we use Calabi-Yau (CY) manifolds (on which the extra dimensions are compactified) f... ...folds (on which the extra dimensions are compactified) for low energies. A certain CY manifold even yields the transition from the big bang (10 or ...

... PHYSICS Volume 2 Acknowledgements I began this research in 1984 when I, a young scientist in those years, started my scientifc studies under the dire... ... )= 1 m 0 c 2 Φ α η α . In a gravitational wave detector like Weber’s, the cy- lindrical pig is isolated as much as possible from external infuences o...