Exponential approximation in the norms and semi-norms

The deviations of some entire functions of exponential type from real-valued functions and their derivatives are estimated. As approximation metrics we use the Lp-norms and power variations on R. Theorems presented here correspond to the Ganelius and Popov results concerning the one-sided trigonometric approximation of periodic functions (see [4, 5 and 8]). Some related facts were announced in [2, 3, 6 and 7].

On the Approximation of the Generalized Cut Function of Degree p+1 By Smooth Sigmoid Functions

We introduce a modification of the familiar cut function by replacing the linear part in its definition by a polynomial of degree p + 1 obtaining thus a sigmoid function called generalized cut function of degree p + 1 (GCFP). We then study the uniform approximation of the (GCFP) by smooth sigmoid functions such as the logistic and the shifted logistic functions. The limiting case of the interval-valued Heaviside step function is also discussed which imposes the use of Hausdorff metric. Numerical examples are presented using CAS MATHEMATICA.

On the approximation by convolution operators in homogeneous Banach spaces on R^d

AMS Subject Classification 2010: 41A25, 41A35, 41A40, 41A63, 41A65, 42A38, 42A85, 42B10, 42B20

Approximation Properties of Schurer-Stancu Type Polynomials

MSC 2010: 41A25, 41A35

Approximation of Univariate Set-Valued Functions - an Overview

2000 Mathematics Subject Classification: 26E25, 41A35, 41A36, 47H04, 54C65.

Accurate WKB Approximation for a 1D Problem with Low Regularity

2000 Mathematics Subject Classification: 34L40, 65L10, 65Z05, 81Q20.

Weighted Approximation by a Class of Bernstein-Type Operators

AMS classification: 41A36, 41A10, 41A25, 41Al7.

On the Approximation by Convolution Operators in Homogeneous Banach Spaces of Periodic Functions

AMS Subject Classification 2010: 41A25, 41A27, 41A35, 41A36, 41A40, 42Al6, 42A85.

Organized crime legislation in the European Union. Harmonization and approximation of criminal law, national legislations and the EU framework decision on the fight against organised crime, by Francesco Calderoni

Book review: Heidelberg, Dordrecht, London, and New York, Springer, 2010, 189 pp., £93.55 (hardcover), ISBN 978-3-642-04330-7, e-ISBN 978-3-642-04331-4

A new SOS-DFPT approximation for NMR shielding calculations : the Loc.3 correction applied to the catalytic mechanism of Serine Proteases

Thèse numérisée par la Direction des bibliothèques de l'Université de Montréal.

Approximation de la distribution de la distance entre deux courbes empiriques

Mémoire numérisé par la Direction des bibliothèques de l'Université de Montréal.

Approximation uniforme par fonctions aléatoires

Mémoire numérisé par la Direction des bibliothèques de l'Université de Montréal.

Ground and Electronic Excited States from Pairing Matrix Fluctuation and Particle-Particle Random Phase Approximation

The accurate description of ground and electronic excited states is an important and challenging topic in quantum chemistry. The pairing matrix fluctuation, as a counterpart of the density fluctuation, is applied to this topic. From the pairing matrix fluctuation, the exact electron correlation energy as well as two electron addition/removal energies can be extracted. Therefore, both ground state and excited states energies can be obtained and they are in principle exact with a complete knowledge of the pairing matrix fluctuation. In practice, considering the exact pairing matrix fluctuation is unknown, we adopt its simple approximation --- the particle-particle random phase approximation (pp-RPA) --- for ground and excited states calculations. The algorithms for accelerating the pp-RPA calculation, including spin separation, spin adaptation, as well as an iterative Davidson method, are developed. For ground states correlation descriptions, the results obtained from pp-RPA are usually comparable to and can be more accurate than those from traditional particle-hole random phase approximation (ph-RPA). For excited states, the pp-RPA is able to describe double, Rydberg, and charge transfer excitations, which are challenging for conventional time-dependent density functional theory (TDDFT). Although the pp-RPA intrinsically cannot describe those excitations excited from the orbitals below the highest occupied molecular orbital (HOMO), its performances on those single excitations that can be captured are comparable to TDDFT. The pp-RPA for excitation calculation is further applied to challenging diradical problems and is used to unveil the nature of the ground and electronic excited states of higher acenes. The pp-RPA and the corresponding Tamm-Dancoff approximation (pp-TDA) are also applied to conical intersections, an important concept in nonadiabatic dynamics. Their good description of the double-cone feature of conical intersections is in sharp contrast to the failure of TDDFT. All in all, the pairing matrix fluctuation opens up new channel of thinking for quantum chemistry, and the pp-RPA is a promising method in describing ground and electronic excited states.

A new SOS-DFPT approximation for NMR shielding calculations : the Loc.3 correction applied to the catalytic mechanism of Serine Proteases

Thèse numérisée par la Direction des bibliothèques de l'Université de Montréal.