Exponentially supported polynomial basis set using fluctuation free integration in the Taylor expansion remainder term evaluation

2012 ◽  
Author(s):  
Meseret Tuba Gülpinar ◽  
Caner Gülpinar ◽  
Metin Demiralp
Keyword(s):  
Remainder Term ◽  
Taylor Expansion ◽  
Polynomial Basis ◽  
Basis Set ◽  
Term Evaluation

scholarly journals On the power series representation of smooth conformal martingales

1986 ◽  
Vol 103 ◽  
pp. 15-27
Author(s):  
Nguyen Xuan-loc
Keyword(s):  
Power Series ◽  
Remainder Term ◽  
Taylor Expansion ◽  
A Priori ◽  
Series Representation ◽  
A Priori Estimate ◽  
Process Definition ◽  
Priori Estimate ◽  
The Given ◽  
Power Series Representation

We introduce here the notion of (stochastically) differentiable process with respect to a fixed conformal martingale and compute the remainder term of the Taylor expansion of the given process (Definition 1 and Proposition 3). An a-priori estimate in the L2-norm of the above mentioned remainder term is given and consequently a power series representation of smooth conformal martingales is obtained (Theorem 4).

Respiratory rehabilitation with heat moisture exchanger after total laryngectomy: long-term evaluation

2019 ◽  
Vol 69 (2) ◽  
Author(s):  
Eugenia Allegra ◽  
Ignazio La Mantia ◽  
Maria R. Bianco ◽  
Nicolò Marino ◽  
Alessio Fallica ◽  
...  
Keyword(s):  
Total Laryngectomy ◽  
Moisture Exchanger ◽  
Term Evaluation ◽  
Respiratory Rehabilitation

Density functional theory, Comparative vibrational spectroscopic studies, HOMO-LUMO, and NBO analysis of Trichloro isocyanuric acid and Trithio cyanuric acid

2015 ◽  
Vol 8 (3) ◽  
pp. 2197-2221
Author(s):  
Theraviyum Chithambarathanu ◽  
M. Darathi ◽  
J. DaisyMagdaline ◽  
S. Gunasekaran
Keyword(s):  
Density Functional ◽  
Cyanuric Acid ◽  
Nbo Analysis ◽  
Basis Set ◽  
Potential Energy Distribution ◽  
Point Energy ◽  
Isocyanuric Acid ◽  
Ft Ir ◽  
Homo Lumo ◽  
Ft Raman

The molecular vibrations of Trichloro isocyanuric acid (C3Cl3N3O3) and Trithio cyanuric acid (C3H3N3S3) have been investigated in polycrystalline sample at room temperature by Fourier Transform Infrared (FT-IR) and FT-Raman spectroscopies in the region 4000-450 cm-1 and 4000-50 cm-1 respectively, which provide a wealth of structural information about the molecules. The spectra are interpreted with the aid of normal co-ordinate analysis following full structure optimization and force field calculations based on density functional theory   (DFT) using standard B3LYP / 6-311++ G (d, p) basis set for investigating the structural and spectroscopic properties. The vibrational frequencies are calculated and the scaled values are compared with experimental FT-IR and FT-Raman spectra. The scaled theoretical wave numbers shows very good agreement with experimental ones. The complete vibrational assignments are performed on the basis of potential energy distribution (PED) of vibrational modes, calculated with scaled quantum (SQM) method. Stability of the molecule arising from hyper conjugative interactions, charge delocalization has been analyzed using natural bond orbital (NBO) analysis. The results show that change in electron density (ED) in σ* and π* anti-bonding orbitals and second order delocalization   energy (E2) confirm the occurrence of Intra molecular Charge Transfer (ICT) within the molecule. The thermodynamic properties like heat capacity, entropy, enthalpy and zero point energy have been calculated for the molecule. The frontier molecular orbitals have been visualized and the HOMO-LUMO energy gap has been calculated. The Molecular Electrostatic Potential (MEP) analysis reveals the sites for electrophilic attack and nucleophilic reactions in the molecule.

Sign in / Sign up

Export Citation Format

Share Document