In the previous paper 1 , the second and the third authors introduced a simple construction of a Siegel cusp form of degree 2. This construction has an advantage because the Fourier coefficients are explicitly computable. After this work was completed, Kikuta and Mizuno proved that the p-adic limit of a sequence of the aforementioned cusp forms becomes a Siegel cusp form of degree 2 with level ...

Chemical Reactivity Theory (CRT) contains reactivity indices defined as first and second derivatives of ground-state properties with respect to electron number such as the electronegativity and the hardness. This necessitates use of the Perdew, Parr, Levy, and Balduz (PPLB) version of noninteger density-functional theory (NIDFT) to provide a basis for CRT in DFT. However, the PPLB NIDFT yields ...

In the present investigation, the results of extensive benchmarking study of density functional theory (DFT) methods on some catalytically important metal dimers have been reported. The calculations were carried out on Al2, Ti2, V2, Cr2, Mn2, Fe2, Co2, Ni2, Cu2, and Zn2 using DFT functionals such as GGA, meta GGA, hybrid meta GGA along with recently developed Minnesota functionals. The bond len...

The structures and interaction energies of guanine and uracil quartets have been determined by B3LYP hybrid density functional calculations. The total interaction energy ∆E T of the C 4h-symmetric guanine quartet consisting of Hoogsteen type base pairs with two hydrogen bonds between two neighbor bases is-66.07 kcal/mol at the highest level. The uracil quartet with C6-H6...O4 interactions betwe...

In the current investigation, the molecular structure of the anticonvulsant agent (2E)-2-[3-(1H-imidazol-1-yl)-1-phenylpropylidene]-N-phenylhydrazinecarboxamide ((2E)-HIPC) was theoretically modelled using ab initio Hartree-Fock (HF) and density functional theory (DFT/B3LYP) calculations. The Fourier transform (FT) infrared and FT-Raman spectra of (2E)-HIPC were also recorded, and the observed ...

As well known, spacelike proton form factors expressed in the Breit frame may be interpreted as the Fourier transform of static space distributions of electric charge and current. In particular, the electric form factor is simply the Fourier transform of the charge distribution F (q) = ∫ e ρ(r)dr. We don’t have an intuitive interpretation of the same level of simplicity for the proton timelike ...

The goal of this paper is to provide a complete and refined study the standard L-functions $$L(\pi ,{\text {Std}},s)$$ for certain non-generic cuspidal automorphic representations $$\pi $$ $$G_2({\mathbb {A}})$$ . For representation that corresponds modular form $$\varphi level one even weight on $$G_2$$ , we explicitly define completed L-function, $$\Lambda (\pi Assuming Fourier coefficient no...

For an arbitrary number field K with ring of integers OK , we prove an analogue over finite rings of the form OK/p of the Fundamental Theorem on the Fourier transform of a relative invariant of prehomogeneous vector spaces, where p is a big enough prime ideal of OK and m > 1. In the appendix, F. Sato gives an application of the Theorems 1.2 and 1.5 (and Theorems A, B, C in [4]) to the functiona...

Feedforward networks have powerful approximation capabilities without the “explosion of parameters” problem faced by Fourier and polynomial expansions. This paper first introduces feedforward networks and describes their approximation capabilities, then we address several practical issues faced by applications of feedforward networks. First, we demonstrate networks can provide a reasonable esti...

In this paper, we study ergodic properties of α-stable autoregressive fractionally integrated moving average (ARFIMA) processes which form a large class of anomalous diffusions. A crucial practical question is how long trajectories one needs to observe in an experiment in order to claim that the analyzed data are ergodic or not. This will be solved by checking the asymptotic convergence to 0 of...