Stability analysis of Crank-Nicolson and Euler schemes for time-dependent diffusion equations

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Massive spin-2 particles via embedment of the Fierz-Pauli equations of motion

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Ordinary fractional differential equations are in fact usual entire ordinary differential equations on time scales

Despite the huge number of works considering fractional derivatives or derivatives on time scales some basic facts remain to be evaluated. Here we will be showing that the fractional derivative of monomials is in fact an entire derivative considered on an appropriate time scale.

Allometric equations for estimating tree biomass in restored mixed-species Atlantic Forest stands

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

A squeezed state holomorphic phase space representation of equations of motion

A mapping scheme is presented which takes quantum operators associated to bosonic degrees of freedom into complex phase space integral kernel representatives. The procedure consists of using the Schrödinger squeezed state as the starting point for the construction of the integral mapping kernel which, due to its inherent structure, is suited for the description of second quantized operators. Products and commutators of operators have their representatives explicitly written which reveal new details when compared to the usual q-p phase space description. The classical limit of the equations of motion for the canonical pair q-p is discussed in connection with the effect of squeezing the quantum phase space cellular structure. © 1993.

Comparison of predictive equations for resting energy expenditure in overweight and obese adults

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Use of autogenous bone and beta-tricalcium phosphate in maxillary sinus lifting: a prospective, randomized, volumetric computed tomography study

The correction of bone defects can be performed using autogenous or alloplastic materials, such as beta-tricalcium phosphate (β-TCP). This study compared the changes in bone volume (CBV) after maxillary sinus lifting using autogenous bone (n=12), autogenous bone associated with β-TCP 1:1 (ChronOS; DePuy Synthes, Paoli, CA, USA) (n=9), and β-TCP alone (n=11) as grafting material, by means of cone beam computed tomography (CBCT). CBV was evaluated by comparing CBCT scans obtained in the immediate postoperative period (5-7 days) and at 6 months postoperative in each group using OsiriX software (OsiriX Foundation, Geneva, Switzerland). The results showed an average resorption of 45.7±18.6% for the autogenous bone group, 43.8±18.4% for the autogenous bone+β-TCP group, and 38.3±16.6% for the β-TCP group. All bone substitute materials tested in this study presented satisfactory results for maxillary sinus lifting procedures regarding the maintenance of graft volume during the healing phase before the insertion of implants, as assessed by means of CBCT.

Scalar-bipolar asymptotic modules for solving (2+1)-dimensional nonlinear evolution equations with constraints

An infinite hierarchy of solvable systems of purely differential nonlinear equations is introduced within the framework of asymptotic modules. Eacy system consists of (2+1)-dimensional evolution equations for two complex functions and of quite strong differential constraints. It may be interpreted formally as an integro-differential equation in (1+1) dimensions. © 1988.