In this paper we show that every g-frame for a Hilbert space H can be represented as a linear combination of two g-orthonormal bases if and only if it is a g-Riesz basis. We also show that every g-frame can be written as a sum of two tight g-frames with g-frame bounds one or a sum of a g-orthonormal basis and a g-Riesz basis for H . We further give necessary and sufficient conditions on g-Besse...

The hydrogen abstraction reaction of OH radical with CH3CH2OCF2CHF2 (HFE-374pc2) is investigated theoretically by semi-classical transition state theory. The stationary points on the potential energy surface of the reaction are located by using KMLYP density functional method along with 6-311++G(d,p) basis set. Vibrational anharmonicity coefficients, ...

The adaptive responses of crop genotypes and patterns of genotype x location (G x L) interaction are important to crop improvement as they are the basis for selection for specific adaptation and for elucidation of the causes of G x L interaction. Their legitimate assessment, however, requires yield data for the test genotypes for a large number of sites and over multiple years. Such data are se...

The basis number b(G) of a graphG is defined to be the least integer k such thatG has a kfold basis for its cycle space. In this note, we determine the basis number of the corona of graphs, in fact we prove that b(v ◦T)= 2 for any tree and any vertex v not inT , b(v ◦H)≤ b(H) + 2, where H is any graph and v is not a vertex of H , also we prove that if G= G1 ◦ G2 is the corona of two graphs G1 a...

In this research, this possibility was investigated the relative stablilty geometry and bindingenergies of the hydrogen bonds of Molybdate-Phosphonic Acid (MPA) complex in gas phase onthe basis of result of ab initio and DFT calculations. Three DFT methods have been applied forcalculations are B3LYP, BP86 and B3PW91 that have been studied in two series of basis sets:D95** and 6-31+G(d,p) for hy...

The Shortest Maximal Cycle Basis (SMCB) problem is that of finding a cycle basis B of a given graph G such that the length of the longest cycle included in B is the smallest among all bases of G. We show that any cycle basis B’ of G such that the sum of the lengths of the cycles included in B’ is the smallest among all cycle bases of G constitutes a solution to the SMCB problem. Finding a basis...

We discuss molecular orbital basis sets that contain both Gaussian and polynomial (ramp) functions. We show that, by modeling ramp-Gaussian products as sums of ramps, all of the required one- and two-electron integrals can be computed quickly and accurately. To illustrate our approach, we construct R-31+G, a mixed ramp-Gaussian basis in which the core basis functions of the 6-31+G basis are rep...

The main question of this paper is: When does Groebner basis computation (Buchberger, 1965, 1985) commute with composition? More precisely, let F be a finite set of polynomials in the variables x1, . . . , xn, and let G be a Groebner basis of the ideal generated by F under some term ordering. Let Θ = (θ1, . . . , θn) be a list of n polynomials in the variables x1, . . . , xn. Let F ∗ be the set...