Spectroscopy is the study of the interaction between radiation and matter as a function of wavelength. Theoretical vibrational spectroscopy has been discussed in this paper. In this paper, various approximations for solving Schrödinger Equation have been discussed. Ab-initio methods and DFT methods, various basis set have been discussed in details.

We present a finite-size scaling approach for the calculations of the critical parameters for binding an electron to an electric dipole field. This approach gives very accurate results for the critical parameters by using a systematic expansion in a finite basis set. The approach is general and could be used to obtain the critical conditions for stable dipole-bound dianions. 2003 Published by E...

King and Korf [9] introduced, in the framework of a discrete-time dynamic market model on a general probability space, a new concept of arbitrage called free lunch in the limit which is slightly weaker than the common free lunch. The definition was motivated by the attempt at proposing the pricing theory based on the theory of conjugate duality in optimization. We show that this concept of arbi...

This work analyses a case where.Murrell's proposal, stating that a second-order point must lie above a first-order one, is apparently violated. Study at the SCF-UMP2 level within the D95 + + basis set, of one critical point of the O2HFanion, previously proposed to be of order two by Lopez, shows the importance of the electronic correlation. The critical point associated with the 21-1 state shou...

For given quasi-continuous functions g, h with g ≤ h and diffusion process M determined by stochastic differential equations or symmetric Dirichlet forms, characterizations of the value functions eg(s, x) = sup σ J (s,x) (σ) and ¯ w(s, x) = infτ sup σ J (s,x) (σ, τ) are well studied so far. In this paper, by using the time dependent Dirichlet forms, we generalize these results to time inhomogen...

For two high-quality piecewise polynomial geometrically smooth (G) surface constructions, explicit G functions are derived that form the basis of a functions space on the G surfaces. The spaces are refinable and nested, i.e. the functions can be rerepresented at a finer level. By choosing all basis functions to be first order smooth a maximal set of degrees of freedom is obtained that have smal...

We present the newest results for the determination of heavy-quark masses from low-energy moments of the vacuum polarization function. The results presented here update an earlier determination of the quark masses and incorporate new theoretical calculations of the low-energy moments of the vacuum polarization and new experimental data at the bottom threshold.

and Applied Analysis 3 where Hα is a Γ-open set, Gγ is a Σ-open set, and Mγ is a Γ-compact set. It is easy to see that {Gγ ×{0}}γ∈Ω is an open cover ofK×{0}, thus there is a finite subcoverGγ1 ×{0}, . . . , Gγn ×{0}. Then, Gγ1 × {0, 1} \Mγ1 × {1} ∪ · · · ∪Gγn × {0, 1} \Mγn × {1} 1.6 misses only finitely many Γ-compact sets Mγ1 × {1}, . . . ,Mγn × {1}. AsMγj j 1, 2, . . . , n is compact, we have...

We present a finite-size scaling approach for the calculations of the critical parameters of the few-body Schrödinger equation. This approach gives very accurate results for the critical parameters by using a systematic expansion in a finite basis set. To illustrate this approach we added detailed calculations for the critical screening length and the critical exponents for the Yukawa potential...

Nadykto, Yu, Jakovleva, Herb and Xu have recently reported a DFT study on the structure and formation thermodynamics of sulfuric acid-base-water clusters, with ammonia and a handful of amines as bases [1]. This study partially overlaps with our previous work [2], and a significant part of the discussion in their manuscript concerns differences between their results and ours. This comment is int...