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[en] An attempt has been made to replace the principle of relativity with the principle of covariance. This amounts to modification of the theory of relativity based on the two postulates (i) the principle of covariance and (ii) the light principle. Some of the fundamental results and the laws of relativistic mechanics, electromagnetodynamics and quantum mechanics are re-examined. The principle of invariance is questioned. (A.K.)
[en] The structure constants of an algebra determine a cube called the cubical array associated with the algebra. The permuted indices of the cubical array associated with a finite semifield generate new division algebras. We do not not require that the algebra be finite and ask 'Is it possible to choose a basis for the algebra such any permutation of the indices of the structure constants leaves the algebra unchanged?' What are the associated algebras? Author shows that the property 'weakly quadratic' is invariant under all permutations of the indices of the corresponding cubical array and presents two algebras for which the cubical array is invariant under all permutations of the indices.
[en] Theorems are discussed which indicate that while convergence in measure is the best that can be proved for the sequence as a whole, there is much more to be said about subsequences. It is concluded that the Pade conjecture remains today unproved and uncontradicted. (U.S.)
[en] Using the recently obtained supersymmetric Becchi-Rouet-Stora-Tyutin transformations, the authors derive BRST- and supersymmetry-invariant equations which consist of the usual first- or second-class constraints plus ghost contributions. The ghost additions to the second-class constraints make them first-class
[en] Physicists and philosophers have long claimed that the symmetries of our physical theories - roughly speaking, those transformations which map solutions of the theory into solutions - can provide us with genuine insight into what the world is really like. According to this 'Invariance Principle', only those quantities which are invariant under a theory's symmetries should be taken to be physically real, while those quantities which vary under its symmetries should not. Physicists and philosophers, however, are generally divided (or, indeed, silent) when it comes to explaining how such a principle is to be justified. In this paper, I spell out some of the problems inherent in other theorists' attempts to justify this principle, and sketch my own proposed general schema for explaining how - and when - the Invariance Principle can indeed be used as a legitimate tool of metaphysical inference.
[en] We present our first investigations into the notational invariance of the standard model, including: an introduction to the principles of notational invariance, algorithms for implementing changes of notation, and examples demonstrating the invariance.
[en] A generalization of the conformal Galilei algebra with Levi subalgebra isomorphic to is introduced and a virtual copy of the latter in the enveloping algebra of the extension is constructed. Explicit expressions for the Casimir operators are obtained from the determinant of polynomial matrices. For the central factor algebra , an exact formula giving the number of invariants is obtained and a procedure to compute invariant functions that do not depend on the variables of the Levi subalgebra is developed. It is further shown that such solutions determine complete sets of invariants provided that the relation is satisfied. (paper)