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Abstract In [4] we have introduced Smarandache quasigroups which are Smarandache non-associative structures. A quasigroup is a groupoid whose composition table is a Latin square. There are squares in the [...]

Abstract Shyam Sunder Gupta [3] has defined Smarandache consecutive and reversed Smarandache sequences of triangular numbers. Delfim F.M. Torres and Viorica Teca [1] have further investigated these sequences and defined [...]

Abstract In this paper, we have introduced Smarandache quasigroups which are Smarandache non-associative structures. W.B.Kandasamy [2] has studied Smarandache groupoids and Smarandache semigroups etc. Substructure of Smarandache quasigroups are also [...]

Abstract In this paper, we have introduced Smarandache quasigroups which are Smarandache non-associative structures. W.B.Kandasamy [2] has studied groupoid ring and loop ring. We have defined Smarandache quasigroup rings which [...]

Abstract G. Pilz [1] has defined near-rings and semi-near-rings. In this paper we introduce the concepts of quasi-near ring and semiquasi-near ring. We have also defined Smarandache semiquasi-near-ring. Some examples [...]

Since the discovery of antimatter it has only been- treated at the level of second quantization, where as, matter is treated at all levels of study, from Newtonian mechanics to quantum field theory. To resolve this scientific imbalance of 20th century, Santilli in 1993 [1],[2],[3] took up to study antimatter at all levels. In this paper we present the classical representation of antimatter at Newtonian level and emerging images at subsequent levels. The most appropriate theory of antimatter as proposed by Santilli [4] is based on a new map called isoduality which is applicable at the Newtonian level and all the subsequent levels of study of antimatter. Santilli also formulated the new anti-isomorphic isodual images of the Galilean, special and general relativities compatible with the experimental knowledge on electromagnetic interactions. Antigravity for antimatter [6] (and vice versa) is a natural consequence of this study and awaits validity due to lack of sufficient experimental evidence. [ABSTRACT FROM AUTHOR]

In 1935, A. Einstein stated, in a historical paper with-B. Podolsky and N. Rosen [1] that " quantum mechanics is not a complete theory" and that determinism could be recovered at least under limit conditions (EPR argument). In 1964, J. S. Bell [2] proved a theorem according to which a system of quantum mechanical particles with spin 1/2 with SU(2) Lie algebra [σi, σj] = 2ϵi,j,kσk, where the σs are the Pauli matrices, cannot admit a classical counterpart, thus appearing to disprove the EPR argument. In 1978, R. M. Santilli [3] discovered the axiom-preserving generalization-" completion" of the various branches of Lie's theory (universal enveloping algebras, Lie algebras, and Lie groups) based on the isoassociative product Xi*Xj = Xi...Xj,... > 0, with Lie-Santilli isoalgebras [XiXj]* = Xi*Xj - Xj*Xi = Ci,j,k,Xk classified into regular (irregular) when the C-quantities are constant (functions). In 1998 [4] Santilli proved that Bell's theorem is valid for point-particles, but it is inapplicable for systems of extended particles with spin 1/2 under deep mutual entanglement, and that said systems do admit classical counterparts when represented with the isotopic SU(2) Lie-Santilli isoalgebars [Σi, Σj]* = 2ϵi,j,kΣk, where Σk are the new Pauli-Santilli isomatrices, with realization of the isotopic element ... = Diag. (1/λ, λ), det ... = 1 providing a concrete and explicit realization of "hidden variables" under the full validity of quantum axioms. Subsequently, Santilli [5] proved that Einstein's determinism is progressively approached in the structure of hadrons, nuclei and stars and it is fully recovered at the limit of gravitational collapse (see Refs. [6] for a detailed presentation). In this lecture, by following our recent paper [7], we outline the aspects of the Lie-Santilli isotheory which are essential for Santilli's proofs of the EPR argument. [ABSTRACT FROM AUTHOR]

The study of antimatter was initiated by Paul Dirac in 1920 but solely continued in the 20th century at the level of second quantization. In this paper, we outline and update the studies of antimatter at all possible classical and particle levels by R. M. Santilli , which studies have been motivated by evidence that Earth has been devastated in the past by antimatter asteroids. The studies were conducted following the prior construction of an anti-Hermitean image of the mathematics used for matter, including an anti-Hermitean image of Lie's theory. The ensuing isodual theory of antimatter predicts that: all characteristics of antimatter are opposite those of matter as a necessary condition to represent matter-antimatter annihilation; charge conjugation can be generalized into anti-Hermitean isodual map applicable for all classical and operators quantities; and predicts that antimatter emits a new light, known as Santilli isoduallight, whose characteristics are all opposite to those of light emitted by matter. We review the basic mathematical and physical formalism of the isodual theory of antimatter; we show that it verifies available experimental data on antimatter; and we identify predictions suitable for experimental verifications. In a second paper, we plan to review the status of the ongoing efforts to detect antimatter galaxies, antimatter asteroids, antimatter cosmic rays, and antimatter light coronas. [ABSTRACT FROM AUTHOR]

In this paper, we define Smarandache seminormal subgroupoids. We have proved some results for finding the Smarandache seminormal subgroupoids in Z(n) when n is even and n is odd. [ABSTRACT FROM AUTHOR]

In this paper we present some new results on Camina groups. Infinite generalizations of Camina groups and generalized Camina groups are also discussed. We further define and study some new group structures which arise out of inter-relations between conjugacy classes, order classes, and cosets with respect to a normal subgroup. [ABSTRACT FROM AUTHOR]

In this paper we define two kinds of pseudo-Smarandache functions. We have investigated more than fifty terms of each pseudo-Smarandache function. We have proved some interesting results and properties of these functions. [ABSTRACT FROM AUTHOR]