Continuous-time formulation of reaction-diffusion processes on heterogeneous metapopulations

We present the derivation of the continuous-time equations governing the limit dynamics of discrete-time reaction-diffusion processes defined on heterogeneous metapopulations. We show that, when a rigorous time limit is performed, the lack of an epidemic threshold in the spread of infections is not limited to metapopulations with a scale-free architecture, as it has been predicted from dynamical equations in which reaction and diffusion occur sequentially in time

A new compact linear programming formulation for choice network revenue management

The choice network revenue management model incorporates customer purchase behavioras a function of the offered products, and is the appropriate model for airline and hotel networkrevenue management, dynamic sales of bundles, and dynamic assortment optimization.The optimization problem is a stochastic dynamic program and is intractable. A certainty-equivalencerelaxation of the dynamic program, called the choice deterministic linear program(CDLP) is usually used to generate dyamic controls. Recently, a compact linear programmingformulation of this linear program was given for the multi-segment multinomial-logit (MNL)model of customer choice with non-overlapping consideration sets. Our objective is to obtaina tighter bound than this formulation while retaining the appealing properties of a compactlinear programming representation. To this end, it is natural to consider the affine relaxationof the dynamic program. We first show that the affine relaxation is NP-complete even for asingle-segment MNL model. Nevertheless, by analyzing the affine relaxation we derive a newcompact linear program that approximates the dynamic programming value function betterthan CDLP, provably between the CDLP value and the affine relaxation, and often comingclose to the latter in our numerical experiments. When the segment consideration sets overlap,we show that some strong equalities called product cuts developed for the CDLP remain validfor our new formulation. Finally we perform extensive numerical comparisons on the variousbounds to evaluate their performance.

Dielectric formulation for Many-Particle Systems with General Interactions

An extension of the self-consistent field approach formulation by Cohen in the preceding paper is proposed in order to include the most general kind of two-body interactions, i.e., interactions depending on position, momenta, spin, isotopic spin, etc. The dielectric function is replaced by a dielectric matrix. The evaluation of the energies involves the computation of a matrix inversion and trace.

Gauge group and reality conditions in Ashtekar's complex formulation of canonical gravity

We discuss reality conditions and the relation between spacetime diffeomorphisms and gauge transformations in Ashtekars complex formulation of general relativity. We produce a general theoretical framework for the stabilization algorithm for the reality conditions, which is different from Diracs method of stabilization of constraints. We solve the problem of the projectability of the diffeomorphism transformations from configuration-velocity space to phase space, linking them to the reality conditions. We construct the complete set of canonical generators of the gauge group in the phase space which includes all the gauge variables. This result proves that the canonical formalism has all the gauge structure of the Lagrangian theory, including the time diffeomorphisms.

On the many-time formulation of classical particle dynamics

Starting from the standard one-time dynamics of n nonrelativistic particles, the n-time equations of motion are inferred, and a variational principle is formulated. A suitable generalization of the classical LieKnig theorem is demonstrated, which allows the determination of all the associated presymplectic structures. The conditions under which the action of an invariance group is canonical are studied, and a corresponding Noether theorem is deduced. A formulation of the theory in terms of n first-class constraints is recovered by means of coisotropic imbeddings. The proposed approach also provides for a better understanding of the relativistic particle dynamics, since it shows that the different roles of the physical positions and the canonical variables is not peculiar to special relativity, but rather to any n-time approach: indeed a nonrelativistic no-interaction theorem is deduced.

Front form and point form formulation in P.R.M. noninteractions theorems

The front form and the point form of dynamics are studied in the framework of predictive relativistic mechanics. The non-interaction theorem is proved when a Poincar-invariant Hamiltonian formulation with canonical position coordinates is required.

Synthesis of triheptanoin and formulation as a solid diet for rodents

Triheptanoin-enriched diets have been successfully used in the experimental treatment of various metabolic disorders. Maximal therapeutic effect is achieved in the context of a ketogenic diet where triheptanoin oil provides 3040% of the daily caloric intake. However, pre-clinical studies using triheptanoin-rich diets are hindered by the difficulty of administering to laboratory animals as a solid foodstuff. In the present study, we successfully synthesized triheptanoin to the highest standards of purity from glycerol and heptanoic acid, using sulfonated charcoal as a catalyst. Triheptanoin oil was then formulated as a solid, stable and palatable preparation using a ketogenic base and a combination of four commercially available formulation agents: hydrophilic fumed silica, hydrophobic fumed silica, microcrystalline cellulose, and talc. Diet compliance and safety was tested on C57Bl/6 mice over a 15-week period, comparing overall status and body weight change. Practical applications: This work provides a complete description of (i) an efficient and cost-effective synthesis of triheptanoin and (ii) its formulation as a solid, stable, and palatable ketogenic diet (triheptanoin-rich; 39% of the caloric intake) for rodents. Triheptanoin-rich diets will be helpful on pre-clinical experiments testing the therapeutic efficacy of triheptanoin in different rodent models of human diseases. In addition, using the same solidification procedure, other oils could be incorporated into rodent ketogenic diet to study their dosage and long-term effects on mammal health and development. This approach could be extremely valuable as ketogenic diet is widely used clinically for epilepsy treatment.

Synthesis of triheptanoin and formulation as a solid diet for rodents

Triheptanoin-enriched diets have been successfully used in the experimental treatment of various metabolic disorders. Maximal therapeutic effect is achieved in the context of a ketogenic diet where triheptanoin oil provides 3040% of the daily caloric intake. However, pre-clinical studies using triheptanoin-rich diets are hindered by the difficulty of administering to laboratory animals as a solid foodstuff. In the present study, we successfully synthesized triheptanoin to the highest standards of purity from glycerol and heptanoic acid, using sulfonated charcoal as a catalyst. Triheptanoin oil was then formulated as a solid, stable and palatable preparation using a ketogenic base and a combination of four commercially available formulation agents: hydrophilic fumed silica, hydrophobic fumed silica, microcrystalline cellulose, and talc. Diet compliance and safety was tested on C57Bl/6 mice over a 15-week period, comparing overall status and body weight change. Practical applications: This work provides a complete description of (i) an efficient and cost-effective synthesis of triheptanoin and (ii) its formulation as a solid, stable, and palatable ketogenic diet (triheptanoin-rich; 39% of the caloric intake) for rodents. Triheptanoin-rich diets will be helpful on pre-clinical experiments testing the therapeutic efficacy of triheptanoin in different rodent models of human diseases. In addition, using the same solidification procedure, other oils could be incorporated into rodent ketogenic diet to study their dosage and long-term effects on mammal health and development. This approach could be extremely valuable as ketogenic diet is widely used clinically for epilepsy treatment.

Synthesis of triheptanoin and formulation as a solid diet for rodents

Triheptanoin-enriched diets have been successfully used in the experimental treatment of various metabolic disorders. Maximal therapeutic effect is achieved in the context of a ketogenic diet where triheptanoin oil provides 3040% of the daily caloric intake. However, pre-clinical studies using triheptanoin-rich diets are hindered by the difficulty of administering to laboratory animals as a solid foodstuff. In the present study, we successfully synthesized triheptanoin to the highest standards of purity from glycerol and heptanoic acid, using sulfonated charcoal as a catalyst. Triheptanoin oil was then formulated as a solid, stable and palatable preparation using a ketogenic base and a combination of four commercially available formulation agents: hydrophilic fumed silica, hydrophobic fumed silica, microcrystalline cellulose, and talc. Diet compliance and safety was tested on C57Bl/6 mice over a 15-week period, comparing overall status and body weight change. Practical applications: This work provides a complete description of (i) an efficient and cost-effective synthesis of triheptanoin and (ii) its formulation as a solid, stable, and palatable ketogenic diet (triheptanoin-rich; 39% of the caloric intake) for rodents. Triheptanoin-rich diets will be helpful on pre-clinical experiments testing the therapeutic efficacy of triheptanoin in different rodent models of human diseases. In addition, using the same solidification procedure, other oils could be incorporated into rodent ketogenic diet to study their dosage and long-term effects on mammal health and development. This approach could be extremely valuable as ketogenic diet is widely used clinically for epilepsy treatment.

The use of the SeDeM diagram expert system for the formulation of Captopril SR matrix tablets by direct compression

The SeDeM Diagram Expert System has been used to study excipients, Captopril and designed formulations for their galenic characterization and to ascertain the critical points of the formula affecting product quality to obtain suitable formulations of Captopril Direct Compression SR Matrix Tablets. The application of the Sedem Diagram Expert System enables selecting excipients with in order to optimize the formula in the preformulation and formulation studies. The methodology is based on the implementation of ICH Q8, establishing the design space of the formula with the use of experiment design, using the parameters of the SeDeM Diagram Expert System as system responses.

Synthesis of triheptanoin and formulation as a solid diet for rodents

Triheptanoin-enriched diets have been successfully used in the experimental treatment of various metabolic disorders. Maximal therapeutic effect is achieved in the context of a ketogenic diet where triheptanoin oil provides 30-40% of the daily caloric intake. However, pre-clinical studies using triheptanoin-rich diets are hindered by the difficulty of administering to laboratory animals as a solid foodstuff. In the present study, we successfully synthesized triheptanoin to the highest standards of purity from glycerol and heptanoic acid, using sulfonated charcoal as a catalyst. Triheptanoin oil was then formulated as a solid, stable and palatable preparation using a ketogenic base and a combination of four commercially available formulation agents: hydrophilic fumed silica, hydrophobic fumed silica, microcrystalline cellulose, and talc. Diet compliance and safety was tested on C57Bl/6 mice over a 15-week period, comparing overall status and body weight change. Practical applications: This work provides a complete description of (i) an efficient and cost-effective synthesis of triheptanoin and (ii) its formulation as a solid, stable, and palatable ketogenic diet (triheptanoin-rich; 39% of the caloric intake) for rodents. Triheptanoin-rich diets will be helpful on pre-clinical experiments testing the therapeutic efficacy of triheptanoin in different rodent models of human diseases. In addition, using the same solidification procedure, other oils could be incorporated into rodent ketogenic diet to study their dosage and long-term effects on mammal health and development. This approach could be extremely valuable as ketogenic diet is widely used clinically for epilepsy treatment.

Potential of antioxidant extracts produced by aqueous processing ofrenewable resources for the formulation of cosmetics

The performance of natural extracts obtained from underutilized and residual vegetal and macroalgal biomass processed with food-grade green solvents was compared with that of commercial antioxidants. Selected extracts were obtained from two terrestrial sources: winery byproducts concentrate (WBC) and chestnut burs hydrothermally fractionated extract (CBAE), and from two underutilized seaweeds: Sargassum muticum extracts, either extracted with ethanol (SmEE) or after alginate extraction and hydrothermal fractionation (SmAE) and from Ulva lactuca processed by mild acid extraction and membrane concentration (UlAE). These extracts showed in vitro antioxidant properties comparable to commercial antioxidants and were safe for topical use based on the absence of skin-irritant effects at 0.1% on reconstructed human tissues. The stability of several cosmetic model emulsions was assessed during accelerated oxidation assays. The incorporation of natural extracts produced from renewable underutilized resources at 0.4-0.5% in an oil-in-water emulsions reduced lipid oxidation during storage.

Synthesis of triheptanoin and formulation as a solid diet for rodents

Triheptanoin-enriched diets have been successfully used in the experimental treatment of various metabolic disorders. Maximal therapeutic effect is achieved in the context of a ketogenic diet where triheptanoin oil provides 30-40% of the daily caloric intake. However, pre-clinical studies using triheptanoin-rich diets are hindered by the difficulty of administering to laboratory animals as a solid foodstuff. In the present study, we successfully synthesized triheptanoin to the highest standards of purity from glycerol and heptanoic acid, using sulfonated charcoal as a catalyst. Triheptanoin oil was then formulated as a solid, stable and palatable preparation using a ketogenic base and a combination of four commercially available formulation agents: hydrophilic fumed silica, hydrophobic fumed silica, microcrystalline cellulose, and talc. Diet compliance and safety was tested on C57Bl/6 mice over a 15-week period, comparing overall status and body weight change. Practical applications: This work provides a complete description of (i) an efficient and cost-effective synthesis of triheptanoin and (ii) its formulation as a solid, stable, and palatable ketogenic diet (triheptanoin-rich; 39% of the caloric intake) for rodents. Triheptanoin-rich diets will be helpful on pre-clinical experiments testing the therapeutic efficacy of triheptanoin in different rodent models of human diseases. In addition, using the same solidification procedure, other oils could be incorporated into rodent ketogenic diet to study their dosage and long-term effects on mammal health and development. This approach could be extremely valuable as ketogenic diet is widely used clinically for epilepsy treatment.

Weak systems of Gandy, Jensen and Devlin

In Part I, we formulate and examine some systems that have arisen in the study of the constructible hierarchy; we find numerous transitive models for them, among which are supertransitive models containing all ordinals that show that Devlin's system BS lies strictly between Gandy's systems PZ and BST'; and we use our models to show that BS fails to handle even the simplest rudimentary functions, and is thus inadequate for the use intended for it in Devlin's treatise. In Part II we propose and study an enhancement of the underlying logic of these systems, build further models to show where the previous hierarchy of systems is preserved by our enhancement; and consider three systems that might serve for Devlin's purposes: one the enhancement of a version of BS, one a formulation of Gandy-Jensen set theory, and the third a subsystem common to those two. In Part III we give new proofs of results of Boffa by constructing three models in which, respectively, TCo, AxPair and AxSing fail; we give some sufficient conditions for a set not to belong to the rudimentary closure of another set, and thus answer a question of McAloon; and we comment on Gandy's numerals and correct and sharpen other of his observations.

Economic impacts of alternative water policy scenarios in the Spanish production system: an input-output analysis

The objective of this paper is to analyse the economic impacts of alternative water policies implemented in the Spanish production system. The methodology uses two versions of the input-output price model: a competitive formulation and a mark-up formulation. The input-output framework evaluates the impact of water policy measures on production prices, consumption prices, intermediate water demand and private welfare. Our results show that a tax on the water used by sectors considerably reduces the intermediate water demand, and increases the production and consumption prices. On the other hand, according to Jevons' paradox, an improvement in technical efficiency, which leads to a reduction in the water requirements of all sectors and an increase in water production, increases the amount of water consumed. The combination of a tax on water and improved technical efficiency takes the pressure off prices and significantly reduces intermediate water demand. JEL Classification: C67 ; D57 ; Q25. Keywords: Production prices; Consumption prices; Water uses; Water policy; Water taxation.