Avila and Molina [1] introduced the notion of generalized weak structures which naturally generalize minimal structures, generalized topologies and weak structures and the structures α(g),π(g),σ(g) and β(g). This work is a further investigation of generalized weak structures due to Avila and Molina. Further we introduce the structures ro(g) and rc(g) and study the properties of the structures r...

We investigate valued fields which admit a valuation basis. Given a countable ordered abelian group G and a real closed, or algebraically closed field F , we give a sufficient condition for a valued subfield of the field of generalized power series F ((G)) to admit a K-valuation basis. We show that the field of rational functions F (G) and the field F (G) of power series in F ((G)) algebraic ov...

We investigate valued fields which admit a valuation basis. Given a countable ordered abelian group G and a real closed or algebraically closed field F with subfield K, we give a sufficient condition for a valued subfield of the field of generalized power series F ((G)) to admit aK-valuation basis. We show that the field of rational functions F (G) and the field F (G) of power series in F ((G))...

Let G be a finite abelian group G with N elements. In this paper we give a O(N) time algorithm for computing a basis of G. Furthermore, we obtain an algorithm for computing a basis from a generating system of G with M elements having time complexity O(M ∑ p|N e(p)⌈p 1/2⌉μ(p)), where p runs over all the prime divisors of N , and pe(p), μ(p) are the exponent and the number of cyclic groups which ...

We prove some general results on the T -equivariant K-theory KT (G/P ) of the flag variety G/P , where G is a semisimple complex algebraic group, P is a parabolic subgroup and T is a maximal torus contained in P . In particular, we make a conjecture about a positivity phenomenon in KT (G/P ) for the product of two basis elements written in terms of the basis of KT (G/P ) given by the dual of th...

A theoretical study of the kinetic and mechanism of intramoleccha cychcation of (1)-undeca-7,8-dien-2-yne was performed using MT methods at B3LYP and B3PW91 levels of theory using 6-311g, 6-311C.6-31 IGs*, 6-31I+G, 6-31 I4-SG and 6-3114H-Gs* basis seo. Equilibrium molecular geometries andharmonic vibrational frequencies of the reaccint, transition state and product wens calculated. Theconsidere...

keto-enol tautomerism was investigated for ionized pyruvic acid using the dft(b3lyp) method and the larger basis sets [6-31++g(d,p), 6-311++g(3df, 3pd) and aug-cc-pvdz]. change of the tautomeric preference was observed when going from the neutral to ionized tautomeric mixture. ionization favors the enolization process (ketoenol) of pyruvic acid, whereas the ketonization (ketoenol) is preferred ...