THE VANISHING DISCOUNT APPROACH FOR THE AVERAGE CONTINUOUS CONTROL OF PIECEWISE DETERMINISTIC MARKOV PROCESSES

This work is concerned with the existence of an optimal control strategy for the long-run average continuous control problem of piecewise-deterministic Markov processes (PDMPs). In Costa and Dufour (2008), sufficient conditions were derived to ensure the existence of an optimal control by using the vanishing discount approach. These conditions were mainly expressed in terms of the relative difference of the alpha-discount value functions. The main goal of this paper is to derive tractable conditions directly related to the primitive data of the PDMP to ensure the existence of an optimal control. The present work can be seen as a continuation of the results derived in Costa and Dufour (2008). Our main assumptions are written in terms of some integro-differential inequalities related to the so-called expected growth condition, and geometric convergence of the post-jump location kernel associated to the PDMP. An example based on the capacity expansion problem is presented, illustrating the possible applications of the results developed in the paper.

Extensions of discrete triangular distributions and boundary bias in kernel estimation for discrete functions

Asymmetric discrete triangular distributions are introduced in order to extend the symmetric ones serving for discrete associated kernels in the nonparametric estimation for discrete functions. The extension from one to two orders around the mode provides a large family of discrete distributions having a finite support. Establishing a bridge between Dirac and discrete uniform distributions, some different shapes are also obtained and their properties are investigated. In particular, the mean and variance are pointed out. Applications to discrete kernel estimators are given with a solution to a boundary bias problem. (C) 2010 Elsevier B.V. All rights reserved.

Meat Quality of Lambs Fed on Palm Kernel Meal, a By-product of Biodiesel Production

This study aimed to establish the optimum level of palm kernel meal in the diet of Santa Ines lambs based on the sensorial characteristics and fatty acid profile of the meat. We used 32 lambs with a starting age of 4 to 6 months and mean weight of 22 2.75 kg, kept in individual stalls. The animals were fed with Tifton-85 hay and a concentrate mixed with 0.0, 6.5, 13.0 or 19.5% of palm kernel meal based on the dry mass of the complete diet. These levels formed the treatments. Confinement lasted 80 days and on the last day the animals were fasted and slaughtered. After slaughter, carcasses were weighed and sectioned longitudinally, along the median line, into two antimeres. Half-carcasses were then sliced between the 12th and 13th ribs to collect the loin (longissimus dorsi), which was used to determine the sensorial characteristics and fatty acid profile of the meat. For sensorial evaluation, samples of meat were given to 54 judges who evaluated the tenderness, juiciness, appearance, aroma and flavor of the meat using a hedonic scale. Fatty acids were determined by gas chromatography. The addition of palm kernel meal to the diet had no effect on the sensorial characteristics of meat juiciness, appearance, aroma or flavor. However, tenderness showed a quadratic relationship with the addition of the meal to the diet. The concentration of fatty acids C12:0, C14:0 and C16:0 increased with the addition of palm kernel meal, as did the sum of medium-chain fatty acids and the atherogenicity index. Up to of 19.5% of the diet of Santa Ines lambs can be made up of palm kernel meal without causing significant changes in sensorial characteristics. However, the fatty acid profile of the meat was altered.

Hamiltonian mappings and circle packing phase spaces.

We introduce three area preserving maps with phase space structures which resemble circle packings. Each mapping is derived from a kicked Hamiltonian system with one of the three different phase space geometries (planar, hyperbolic or spherical) and exhibits an infinite number of coexisting stable periodic orbits which appear to ‘pack’ the phase space with circular resonances.

Quantum mechanics as an approximation to classical mechanics in Hilbert space

Classical mechanics is formulated in complex Hilbert space with the introduction of a commutative product of operators, an antisymmetric bracket and a quasidensity operator that is not positive definite. These are analogues of the star product, the Moyal bracket, and the Wigner function in the phase space formulation of quantum mechanics. Quantum mechanics is then viewed as a limiting form of classical mechanics, as Planck's constant approaches zero, rather than the other way around. The forms of semiquantum approximations to classical mechanics, analogous to semiclassical approximations to quantum mechanics, are indicated.

On S-asymptotically omega-periodic functions on Banach spaces and applications

This paper is devoted to the study of the class of continuous and bounded functions f : [0, infinity] -> X for which exists omega > 0 such that lim(t ->infinity) (f (t + omega) - f (t)) = 0 (in the sequel called S-asymptotically omega-periodic functions). We discuss qualitative properties and establish some relationships between this type of functions and the class of asymptotically omega-periodic functions. We also study the existence of S-asymptotically omega-periodic mild solutions of the first-order abstract Cauchy problem in Banach spaces. (C) 2008 Elsevier Inc. All rights reserved.

Existence Results for Second Order Differential Equations with Nonlocal Conditions in Banach Spaces

This work is concerned with implicit second order abstract differential equations with nonlocal conditions. Assuming that the involved operators satisfy sonic compactness properties, we establish the existence of local mild solutions, the existence of global mild solutions and the existence of asymptotically almost periodic solutions.

Controllability of Volterra-Fredholm type systems in Banach spaces

We show the results in Chalishajar [Controllability of mixed Volterra-Fredholm-type integro-differential systems in Banach space, J. Franklin Inst. 344(1) (2007) 12-21] and Chang and Chalishajar [Controllability of mixed Volterra-Fredholm type integro-differential systems in Banach space, J. Franklin Inst., doi:10.1016/j. jfranklin.2008.02.002] are only valid for ordinary differential control systems. As a result the examples provided cannot be recovered as applications of the abstract results. (C) 2008 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.