Semigroup of Weakly Continuous Operators Associated to a Generalized Schrödinger Equation

In this work, we prove the existence and uniqueness of the solution of the generalized Schrödinger equation in the periodic distributional space P’. Furthermore, we prove that the solution depends continuously respect to the initial data in P’. Introducing a family of weakly continuous operators, we prove that this family is a semigroup of operators in P’. Then, with this family of operators, we get a fine version of the existence and dependency continuous theorem obtained. Finally, we provide some consequences of this study.

Group of Weakly Continuous Operators Associated to a Generalized Schrödinger Type Homogeneous Model

In this work, we prove the existence and uniqueness of the solution of the generalized Schrödinger type homogeneous model in the periodic distributional space P’. Furthermore, we prove that the solution depends continuously respect to the initial data in P’. Introducing a family of weakly continuous operators, we prove that this family is a group of operators in P’. Then, with this family of operators, we get a fine version of the existence and dependency continuous theorem obtained. Finally, we give some remarks derived from this study.

Fetkin-hydro,a new thermo-hydrological algorithm for low-temperature thermochronological modeling

Despite two decades of major advances in the field of thermochronological modeling,state-of-the-art numerical implementations still rely mostly on burial and exhumation processes to explain radiometric measurements.Even though such an approach has proved valuable,failing to account for other first-order geological variables has led to misinterpretations and therefore,calls for a refinement.In this study a new version of the Fetkin(finite element temperature kinematics,Ecopetrol)program is presented.Its new algorithm couples time-dependent hydrological and thermal calculations,thus rendering thermochronological ages that,instead of being solely dependent on the kinematical evolution of a system,conditioning by the fluid flow is also present.In contrast with previous thermochronological models,this work considers the influence of effective stress on rock properties(porosity and permeability)and therefore,in thermal conductivity.Sensitivity analyses addressing relevant geological questions show not only the versatility of the code but also,new perspectives on forward low-temperature thermochronological modeling.Groundwater circulation through pure-sandstone settings produce colder thermal architectures than those obtained in impermeable domains.Differences in cooling ages from models with and without fluid circulation are up to 5 Myr.A 4-fold variation in thrusting rates(0.5 km/Myr to 2 km/Myr)produces a 15-Myr difference in cooling ages in models with fluid flow,which contrasts to much lower differences,only 2 Myr,in domains without(or minimal)fluid circulation.2D thermal solutions in fold-bend-fold thrust belts composed of sandstones remain static despite substantial relief development by kinematic folding.A case-study from Western Argentina,in the Andean Precordillera,confirms the plausibility of the numerical algorithm here posed and raises new questions on the first-order thermal controls in settings under deformation.

An Inexact Restoration Package for Bilevel Programming Problems

Bilevel programming problems are a class of optimization problems with hierarchical structure where one of the con-straints is also an optimization problem. Inexact restoration methods were introduced for solving nonlinear programming problems a few years ago. They generate a sequence of, generally, infeasible iterates with intermediate iterations that consist of inexactly restored points. In this paper we present a software environment for solving bilevel program-ming problems using an inexact restoration technique without replacing the lower level problem by its KKT optimality conditions. With this strategy we maintain the minimization structure of the lower level problem and avoid spurious solutions. The environment is a user-friendly set of Fortran 90 modules which is easily and highly configurable. It is prepared to use two well-tested minimization solvers and different formulations in one of the minimization subproblems. We validate our implementation using a set of test problems from the literature, comparing different formulations and the use of the minimization solvers.

Boolean Automorphisms of a Hypercube Coincide with the Linear Isometries

Boolean homomorphisms of a hypercube, which correspond to the morphisms in the category of finite Boolean algebras, coincide with the linear isometries of the category of finite binary metric vector spaces.

Scholz’s Third Conjecture: A Demonstration for Star Addition Chains

This paper presents a brief demonstration of Scholz’s third conjecture [1] for n numbers such that their minimum chain addition is star type [2]. The demonstration is based on the proposal of an algorithm that takes as input the star-adding chain of a number n, and returns a string in addition to x = 2n - 1??of length equal to l (n) + n - 1. As for any type addition chain star of a number n, this chain is minimal demonstrates the Scholz’s third Conjecture for such numbers.

Thermal Conditions in Córdoba City, Argentina, during 1960-2010 Period

The present work analyzes daily minimum (Tmin) and maximum (Tmax) temperature series from Córdoba Observatory weather station, which is located near the center of the city of Córdoba, Argentina, and from the Pajas Blancas and Pilar observatories, in order to have a reference counterpart of regional climate. The air temperature in Córdoba city during 1960-2010 period shows lower/higher frequency of Tmin categories lower/higher than 15°C, with respect to rural thermal conditions. Tmax categories higher/lower than 30°C, in turn, presented higher/lower frequency in the city. While the mean annual Tmin showed a significant positive trend in the entire region in the study period, Tmax presented no significant changes over time. The difference between urban and rural thermal regimes remained uniform throughout the study period, so the process of urbanization does not seem to have changed the Urban heat island status measure from Córdoba Observatory, even though the population of the metropolis has doubled. Although nocturnal thermal conditions have changed over the period, particularly in urban areas, there has been no change in the regime of extreme daytime temperatures across the region. The annual mean Tmin increase is not monotonic, but presents a significant positive partial trend until a breakpoint around 1990, and then becomes neutral or negative and loses significance. For the annual mean Tmax, the partial trend slopes are not significant in any case, so the variation of annual mean thermal amplitude is due mainly to the increase of the Tmin, probably associated with increased rainfall in the region.

Virtual screening of flavonoids from Jatropha gossypiifolia L.as potential drugs for diabetic complications

Background:Diabetes mellitus is a chronic metabolic disease that is a risk factor for epidemic pathologies.Under hyperglycemic conditions,the enzyme aldose reductase catalyzes the formation of sorbitol in the metabolism of glucose via polyols,leading to the development of diabetic complications.Therefore,inhibitors of this enzyme are therapeutic targets for the prophylaxis and treatment of these conditions.Methods:In this study,a generalized linear regression model was developed to analyze flavonoids-obtained from a database-that have been tested as inhibitors of aldose reductase.In this sense,the molecular descriptors implemented in DRAGON and MATLAB software were used to determine the correlation between the chemical structure of the inhibitors and their pharmacological activity.The model was validated according to the Organisation for Economic Co-operation and Development Standards and subsequently used for the virtual screening of the flavonoids identified in Jatropha gossypiifolia L.Results:The proposed model showed a good fit for its statistical parameters(R2=0.95).In addition,it showed good predictive power(R2 ext=0.94)and robustness(Q2 LOO=0.92).The experimental chemical space wherein the predictions were reliable(domain of application)was also defined.Finally,the model was used to identify 10 flavonoids from Jatropha gossypiifolia L.as candidates for natural drugs.Compounds with a low probability of oral absorption were identified,among which the elagic acid biflavonoid showed the greatest promise(pIC50 predicted=9.75).Conclusion:The Jatropha gossypiifolia L.species harbors flavonoids with high potential as inhibitors of the aldose reductase enzyme,in which the biflavonoid ellagic acid was shown to be the most promising inhibitor of the aldose reductase enzyme,suggesting its possible use in the treatment of the late complications of diabetes mellitus.

Evaluation of Two Highly Porous Microcrystalline Biphasic Calcium Phosphate-Based Bone Grafts for Bone Regeneration: An Experimental Study in Rabbits

A biphasic bone grafting biomaterial based on a mixture of calcium phosphates and beta-tricalcium phosphate (β-TCP) phases with high nanoporosity was synthesized. The synthesis route was based on calcium phosphate composition and the incorporation of glycolic acid as a pore former, giving a material composed of 97% β-TCP and 3% calcium orthophosphates (CaPO4). An in vitro study of the purity, microstructure, crystalline domain, and pores size for the material obtained was performed by SEM analysis as well as full structural characterization. The region of interest related to the surface was determined by the specific surface area measured with the BET method. In vivo evaluation of bone response was performed by implanting the new low-cost biphasic manufacturing material synthesized in this work, which was compared with a biphasic material of similar chemical and microstructural composition existing in the commercial market and with higher cost called Synergy Odontit® β-TCP. The materials were implanted separately into 5 mm diameter defects in the tibias of New Zealand White rabbits at 30, 60, and 90 days. The results obtained showed that the host tissue well accepted the new biphasic material;the presence of new bone formation was observed. A more complete resorption was observed for the new microcrystalline biphasic material compared to for a commercial β-TCP material.

The Universe as a Graviton Condensate: The “Dark-Bright Conjecture”

The idea of a homogeneous, isotropic and spatially flat universe brings with it some unresolved issues, such as the nature of dark matter and the “coincidence problem”, i.e. the same order of magnitude between matter and vacuum density at the present time. In order to better understand these problems, it has been recently presented a physical interpretation based on quantum corrections within the second order Friedmann equation, which assumes a quantum condensate composed of gravitons filling the universe. In this article we show that the above supposition is consistent with the picture of a holographic universe created from vacuum fluctuations. From five postulates based on principles of modern quantum cosmology, we propose a very simple conjecture that, while shedding light on the properties of dark matter and dark energy, is able to predict values for the cosmological parameters which are in great agreement with the most accurate data gathered in recent astronomical observations.

Development of a Low Cost Pulsed Laser Deposition System for Thin Films Growth

.Pulsed Laser Deposition (PLD) is a powerful technique to grow thin films. Oxides, Magnetics and superconducting materials have been obtained by PLD and theirs properties are strongly dependent of deposition parameters. The construction of a simple and cheap PLD system that is suitable for growing various thin films, including magnetic materials, controlling some deposition parameters is presented. The design characteristics and construction are presented for each one of the devices that compose this PLD system. The equipment has the possibility of carrying out films deposition using up to five targets under controlled atmosphere and substrate temperature. The system also allows controlling the cool off sample time after growing up films at high temperatures. A wide range of relative speeds between target and substrate axial rotation can be externally controlled. With the configuration and the dimensions adopted in their construction, a PLD system of great experimental flexibility is achieved, at a very low cost regarding the commercial systems. To evaluate their performance and effectiveness, the deposition characteristics of a BaFe12O19 film on (0001) sapphire substrate is presented.

Complementarity between quantum coherence and mixedness:a majorization approach

Quantum coherence is a relevant resource for various quantum information processing tasks,but it is fragile since it is generally affected by environmental noise.This is reflected in the loss of purity of the system,which in turn limits the amount of quantum coherence of it.As a consequence,a complementarity relation between coherence and mixedness arises.Previous works characterize this complementarity through inequalities between theℓ1-norm of coherence and linear entropy,and between the relative entropy of coherence and von Neumann entropy.However,coherence-mixedness complementarity is expected to be a general feature of quantum systems,regardless of the measures used.Here,an alternative approach to coherence-mixedness complementarity,based on majorization theory,is proposed.Vectorial quantifiers of coherence and mixedness,namely the coherence vector and the spectrum,respectively,are used,instead of scalar measures.A majorization relation for the tensor product of both vectorial quantifiers is obtained,capturing general aspects of the trade-off between coherence and mixedness.The optimal bound for qubit systems and numerical bounds for qutrit systems are analyzed.Finally,coherence-mixedness complementarity relations are derived for a family of symmetric,concave and additive functions.These results provide a deeper insight into the relation between quantum coherence and mixedness.