Control aspects in nonlinear Hill's equation

The Hill's equations-even in the linear original version are a describer of phenomenon having chaotic flavor, giving sometimes very unusual situations. The theory of the so called intervals of instability in the equation provides the precise description for most of these phenomena. Considerations on nonlinearities into the Hill's equation is a quite recent task. The linearized version for almost of these systems it reduces to the Hill's classical linear one. In this paper, some indicative facts are pointed out on the possibility of having the linear system stabilizable and/or exactly controllable. As consequence of such an approach we get results having strong classical aspects, like the one talking about location of parameters in intervals of stability. A result for nonlinear proper periodic controls, is considered too. (C) 2010 Elsevier B.V. All rights reserved.

The generator coordinate method in the unrestricted Hartree-Fock formalism

The generator coordinate method was implemented in the unrestricted Hartree-Fock formalism. Weight functions were built from Gaussian generator functions for 1s, 2s, and 2p orbitals of carbon and oxygen atoms. These weight functions show a similar behavior to those found in the generator coordinate restricted Hartree-Fock method, i.e., they are smooth, continuous, and tend to zero in the limits of integration. Moreover, the weight functions obtained are different for spin-up and spin-down electrons what is a result from spin polarization. (C) 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012

NONLOCAL EFFECTS IN THE NUCLEUS-NUCLEUS FUSION CROSS-SECTION

Effects of the nonlocality of factorizable potentials are taken into account in the calculation of nucleus-nucleus fusion cross section through an effective mass approach. This cross section makes use of the tunneling factor calculated for the nonlocal barrier, without the explicit introduction of any result coming from coupled channel calculation, besides the approximations of Hill-Wheeler and Wong. Its new expression embodies the nonlocal effects in a factor which redefines the local potential barrier curvature. Applications to different systems, namely O-16 + Co-59, O-16,O-18 + Ni-58,Ni-60,Ni-64, and O-16,O-18 + Cu-63,Cu-65 are presented, where the nonlocal range is treated as a free parameter.

Hill Instability Analysis Of Tlp Tether Subjected To Combined Platform Surge And Heave Motions

This paper presents the Hill instability analysis of Tension Leg Platform (TLP) tether it, deep sea. The 2-D nonlinear beam model which is Undergoing Coupled axial and transverse vibrations, is applied. The governing equations are reduced to nonlinear Hill equation by use of the Galerkin's method and the modes superposition principle. The Hill instability charted Lip to large parameters is obtained. An important parameter M is defined and can he expressed as the functions of tether length, the platform surge and heave motion amplitudes. Some example studies are performed for various environmental conditions. The results demonstrate that the nonlinear coupling between the axial and transverse vibrations has a significant effect on the response of structure.. It needs to be considered for the accurate dynamic analysis of long TLP tether subjected to the combined platform surge and heave motions.

Qualidade fisiológica de sementes, crescimento e eficiência do uso do fósforo de Corymbia citriodora Hill & Johnson

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Adsorption from a one-dimensional lattice gas and the Brunauer–Emmett–Teller equation

An exact treatment of adsorption from a one-dimensional lattice gas is used to eliminate and correct a well-known inconsistency in the Brunauer–Emmett–Teller (B.E.T.) equation—namely, Gibbs excess adsorption is not taken into account and the Gibbs integral diverges at the transition point. However, neither model should be considered realistic for experimental adsorption systems.

Student mathematical notebook of Ebenezer Hill, 1785

This mathematical notebook of Ebenezer Hill was kept in 1795 while he was a student at Harvard College. The volume contains rules, definitions, problems, drawings, and tables on arithmetic, geometry, trigonometry, surveying, calculating distances, and dialing. Some of the exercises are illustrated by hand-drawn diagrams, including some of buildings and trees.

Enteric methane emissions and nitrogen utilisation efficiency for two genotype of hill hoggets offered fresh, ensiled and pelleted ryegrass

Thirty-six 12-month-old hill hoggets were used in a 2 genotype (18 Scottish Blackface vs. 18 Swaledale×Scottish Blackface)×3 diet (fresh vs. ensiled vs. pelleted ryegrass) factorial design experiment to evaluate the effects of hogget genotype and forage type on enteric methane (CH4) emissions and nitrogen (N) utilisation. The hoggets were offered 3 diets ad libitum with no concentrate supplementation in a single period study with 6 hoggets for each of the 6 genotype×diet combinations (n=6). Fresh ryegrass was harvested daily in the morning. Pelleted ryegrass was sourced from a commercial supplier (Aylescott Driers & Feeds, Burrington, UK) and the ryegrass silage was ensiled with Ecosyl (Lactobacillus plantarum, Volac International Limited, Hertfordshire, UK) as an additive. The hoggets were housed in individual pens for at least 14 d before being transferred to individual respiration chambers for a further 4 d with feed intake, faeces and urine outputs and CH4 emissions measured. There was no significant interaction between genotype and forage type on any parameter evaluated. Sheep offered pelleted grass had greater feed intake (e.g. DM, energy and N) but less energy and nutrient apparent digestibility (e.g. DM, N and neutral detergent fibre (NDF)) than those given fresh grass or grass silage (P<0.001). Feeding pelleted grass, rather than fresh grass or grass silage, reduced enteric CH4 emissions as a proportion of DM intake and gross energy (GE) intake (P<0.01). Sheep offered fresh grass had a significantly lower acid detergent fibre (ADF) apparent digestibility, and CH4 energy output (CH4-E) as a proportion of GE intake than those offered grass silage (P<0.001). There was no significant difference, in CH4 emission rate or N utilisation efficiency when compared between Scottish Blackface and Swaledale × Scottish Blackface. Linear and multiple regression techniques were used to develop relationships between CH4 emissions or N excretion and dietary and animal variables using data from sheep offered fresh ryegrass and grass silage. The equation relating CH4-E (MJ/d) to GE intake (GEI, MJ/d), energy apparent digestibility (DE/GE) and metabolisability (ME/GE) resulted in a high r2 (CH4-E=0.074 GEI+9.2 DE/GE−10.2 ME/GE−0.37, r2=0.93). N intake (NI) was the best predictor for manure N excretion (Manure N=0.66 NI+0.96, r2=0.85). The use of these relationships can potentially improve the precision and decrease the uncertainty in predicting CH4 emissions and N excretion for sheep production systems managed under the current feeding conditions.

Detailed analysis of a conservative difference approximation for the time fractional diffusion equation

Diffusion equations that use time fractional derivatives are attractive because they describe a wealth of problems involving non-Markovian Random walks. The time fractional diffusion equation (TFDE) is obtained from the standard diffusion equation by replacing the first-order time derivative with a fractional derivative of order α ∈ (0, 1). Developing numerical methods for solving fractional partial differential equations is a new research field and the theoretical analysis of the numerical methods associated with them is not fully developed. In this paper an explicit conservative difference approximation (ECDA) for TFDE is proposed. We give a detailed analysis for this ECDA and generate discrete models of random walk suitable for simulating random variables whose spatial probability density evolves in time according to this fractional diffusion equation. The stability and convergence of the ECDA for TFDE in a bounded domain are discussed. Finally, some numerical examples are presented to show the application of the present technique.