In analogy to the class structureGL( IR)/O(1, 3) for general relativity with a local Lorentz group as stabilizer and a basic tetrad field for the parametrization, a corresponding class structure GL( I C)/U(2) is investigated for the standard model with a local hyperisospin group U(2). The lepton, quark, Higgs and gauge fields, used in the standard model, cannot be basic in a coset interpretatio...

The problem of analogy in theorem proving has been studied for several years now (see 5, 10, 12] for example). Those works restrict the use of analogy to proofs, disregarding the possibilities of using analogy also for counterexamples construction. Moreover, they deal with the problem of proving a new theorem once an appropriate source theorem has been provided as a guideline. We overcome these...

thinkers and philosophers have constantly benefited from different         approaches of reasoning to explore and justify their ideas. theses reasoning            approaches are considered as the principle instruments in speculative activities of the thinkers. to this end to achieve the procedure of thinking and the way philosophers achieve objectives, it is necessary to recognize their reasoni...

For an elliptic curve E defined over a fieldK, the Tate-Shafarevich group X(E/K) encodes important arithmetic and geometric information. An important conjecture of Tate and Shafarevich states X(E/K) is always finite. Supporting this conjecture is a cohomological analogy between Mordell-Weil groups of elliptic curves and unit groups of number fields. In this note, we follow the analogy to constr...