The main objective consists in endowing the elementary particles with an algebraic space-time structure in the perspective of unifying quantum field theory and general relativity: this is realized in the frame of the Langlands global program based on the infinite dimensional representations of algebraic groups over adele rings. In this context, algebraic quanta, strings and fields of particles ...

1. Introduction. Although the theory of the abstract Lebesgue integral has strong intrinsic architectural articulation, the very importance of the theory for a variety of mathematical applications has tended to cloud its basic simplicity and elegance. The large number of approaches and formalisms, each justified by its appropriate-ness in connection with particular applications, has given the t...

Let V be a vector space over a fully ordered field F. In Sec. 2 we characterize cones K with ascending chain condition (ACC) on faces of Ii. In Sec. 3 we show that if K has ACC on faces, then an operator A is strongly irreducible if and only if A is irreducible. In Sec. 4 we prove theorems of Perron-Frobenius type for a strongly irreducible operator A in the case that FR, the real field, and K ...

1. Unique Prime Factorization of Ideals: 21 September 2010 2 2. Minkowski Theory: 28 September 2010 5 October 2010 4 3. Cyclotomic Fields and Fermat: 6 13 October 2010 9 4. Multiplicative Minkowski and Dirichlet’s Unit Theorem: 19 26 October 2010 10 5. Factoring Rational Primes in Algebraic Number Fields: 26 October 2010 14 6. Application to Zeta Functions: 3 9 November 2010 18 7. Hilbert’s Ram...

Galois group, 222adeles, 149Artin’s conjecture, 293automorphic form, 292bar resolution, 172biquadratic reciprocity, 271Brauer group, 205Brauer-Hasse-Noether theorem, 252central simple algebra, 206centralizer, 206chain map, 163change of group, 184Chebotarev density theorem, 282class formation, 222class group, 33cohomological functor, 16...

The nonlinear bending behavior of sector graphene sheets is studied subjected to uniform transverse loads resting on a Winkler-Pasternak elastic foundation using the nonlocal elasticity theory. Considering the nonlocal differential constitutive relations of Eringen theory based on first order shear deformation theory and using the von-Karman strain field, the equilibrium partial differential eq...

Abstract We study the algebraic $$K\!$$ K -theory and Grothendieck–Witt theory of proto-exact categories vector bundles over monoid schemes. Our main results are complete description space an integral scheme X in terms its Picard group $${{\,\mathrm{Pic}\,}}(X)$$ ...

In this paper we develop a natural generalization of Schauder basis theory, we term operator-valued basis or simply ov-basis theory, using operator-algebraic methods. We prove several results for ov-basis concerning duality, orthogonality, biorthogonality and minimality. We prove that the operators of a dual ov-basis are continuous. We also dene the concepts of Bessel, Hilbert ov-basis and obta...