Mathematical Models for Unstable Quantum Systems and Gamow States

We review some results in the theory of non-relativistic quantum unstable systems. We account for the most important definitions of quantum resonances that we identify with unstable quantum systems. Then, we recall the properties and construction of Gamow states as vectors in some extensions of Hilbert spaces, called Rigged Hilbert Spaces. Gamow states account for the purely exponential decaying part of a resonance; the experimental exponential decay for long periods of time physically characterizes a resonance. We briefly discuss one of the most usual models for resonances: the Friedrichs model. Using an algebraic formalism for states and observables, we show that Gamow states cannot be pure states or mixtures from a standard view point. We discuss some additional properties of Gamow states, such as the possibility of obtaining mean values of certain observables on Gamow states. A modification of the time evolution law for the linear space spanned by Gamow shows that some non-commuting observables on this space become commuting for large values of time. We apply Gamow states for a possible explanation of the Loschmidt echo.     

Lossless Medical Image Compression by Using Difference Transform

This paper introduces a new method of compressing digital images by using the Difference Transform applied in medical imaging. The Difference Transform algorithm performs the decorrelation process of image data, and in this way improves the encoding process, achieving a file with a smaller size than the original. The proposed method proves to be competitive and in many cases better than the standards used for medical images such as TIFF or PNG. In addition, the Difference Transform can replace other transforms like Cosine or Wavelet.     

Green Extraction Techniques as Advanced Sample Preparation Approaches in Biological,Food, and Environmental Matrices: A Review

Green extraction techniques (GreETs) emerged in the last decade as greener and sustainable alternatives to classical sample preparation procedures aiming to improve the selectivity and sensitivity of analytical methods, simultaneously reducing the deleterious side effects of classical extraction techniques (CETs) for both the operator and the environment. The implementation of improved processes that overcome the main constraints of classical methods in terms of efficiency and ability to minimize or eliminate the use and generation of harmful substances will promote more efficient use of energy and resources in close association with the principles supporting the concept of green chemistry. The current review aims to update the state of the art of some cutting-edge GreETs developed and implemented in recent years focusing on the improvement of the main analytical features, practical aspects, and relevant applications in the biological, food, and environmental fields. Approaches to improve and accelerate the extraction efficiency and to lower solvent consumption, including sorbent-based techniques, such as solid-phase microextraction (SPME) and fabric-phase sorbent extraction (FPSE), and solvent-based techniques (μQuEChERS; micro quick, easy, cheap, effective, rugged, and safe), ultrasound-assisted extraction (UAE), and microwave-assisted extraction (MAE), in addition to supercritical fluid extraction (SFE) and pressurized solvent extraction (PSE), are highlighted.     

Analysis of Plant–Plant Interactions Reveals the Presence of Potent Antileukemic Compounds

A method to identify anticancer compounds in plants was proposed based on the hypothesis that these compounds are primarily present in plants to provide them with an ecological advantage over neighboring plants and other competitors. According to this view, identifying plants that contain compounds that inhibit or interfere with the development of other plant species may facilitate the discovery of novel anticancer agents. The method was developed and tested using Magnolia grandiflora, Gynoxys verrucosa, Picradeniopsis oppositifolia, and Hedyosmum racemosum, which are plant species known to possess compounds with cytotoxic activities. Plant extracts were screened for growth inhibitory activity, and then a thin-layer chromatography bioautography assay was conducted. This located the major antileukemic compounds 1, 2, 4, and 5 in the extracts. Once the active compounds were located, they were extracted and purified, and their structures were determined. The growth inhibitory activity of the purified compounds showed a significant correlation with their antileukemic activity. The proposed approach is rapid, inexpensive, and can easily be implemented in areas of the world with high biodiversity but with less access to advanced facilities and biological assays.     

Synthesis of pentabromopseudilin and other arylpyrrole derivatives via Heck arylations

Pentrabromopseudilin and other 2 and 3-arylpyrrole derivatives were synthesized through the Heck–Matsuda reaction involving endocyclic enecarbamates and N-protected 3-pyrrolines, respectively. The overall processes permitted an easy and efficient access to these structural motifs present in several bioactive compounds. Attempts to synthesize the compound isopentabromopseudilin led to a tribromo aryl maleimide. We hypothesize that this latter compound is the putative product arising from the unusual thermal instability of isopentabromopseudilin.     

Production of metakaolin from industrial cellulose waste

Research focused on the transformation and utilization of industrial wastes into products of commercial interest plays an increasingly important role. Residual pulp can become useful in the manufacture of different materials, providing high value to this waste and reducing its environmental impact when disposed of improperly in the environment. The main constituents of this waste are kaolin and calcium carbonate (CaCO₃). Starting from kaolin, metakaolin can be produced by calcination of the residue at 630?°C for 2?h in a rotary reactor with air flow, followed by solubilization with hydrochloric acid to remove the CaCO₃. The development of technological alternatives aimed at the reuse of certain wastes can result in applications of real economic interest to the chemical industry and ceramics and glass, which is the case in this study. The raw material and metakaolin obtained were analyzed by thermogravimetric analysis and derivative thermogravimetric analysis, X-ray diffraction, and X-ray fluorescence spectroscopy with promising results. This is because metakaolin was obtained free of contamination by other materials.     

Simplified model for mass diffusivity estimation based on dynamic pendant drop volume analysis

We present a simplified correlation for calculating the dissolved gas moles in a pendant drop during the diffusion time, for several drop shapes. After this correlation is determined, the Yang and Gu (Ind Eng Chem Res 44:4474–4483, 2005) dynamic pendant drop volume analysis (DPDVA) method for calculation of mass diffusivity from the pendant drop volume variation against time can be used. We solved the differential equation in cylindrical coordinates for the mass transfer model of the gas diffusion into the liquid inside the pendant drop, using a different characteristic length (L_C), instead of the outer radius of the syringe needle (r_n) used in Yang and Gu (Ind Eng Chem Res 44:4474–4483, 2005) for defining the dimensionless variables. L_C is the relationship between the pendant drop volume and its mass transfer surface area at the initial conditions. The generalized correlation saves time, simplifies the method application and the deviations in the diffusion coefficient calculation respect to the complete Yang and Gu model are below 6%.     

Kinematical and gravitational analysis of the rocket-borne clock experiment by Vessot and Levine using the revised Robertson's test theory of special relativity

The kinematic aspects of the rocket-borne clock experiment by Vessot and Levine are analyzed with the revised Robertson's test theory of special relativity (Found. Phys. 14, 625 (1984)). Besides the expected time-dilation, it is found that the intermediate steps of this experiment yield in principle Michelson-Morley type information (a relation between longitudinal and transverse length contractions) in the third order of the velocities involved, but no relativity-of-simultaneity related effects.The flat space-time test theory induces a family of spherically symmetric line elements that become the Schwarzschild line element in the relativistic case and also in theabinito rest frame of the theory. These line elements represent the same space-time manifold, but pertain in a one-to-one correspondence to the different flat space-time coordinate transformations of the test theory. The conserved energy is related to the family of local energies in the tangent plane. No deviations from the orthodoxy appear at the pertinent levels of approximation. Hence the unexplained residuals of the Vessot-Levine experiment are not due in obvious ways to kinematic and gravitational frequency shifts caused by deviations of the real coordinate transformations from the Lorentz transformations.This work was started while the author was at Departamento de Fisica, Facultad Experimental de Ciencias, Universidad del Zulia, Maracaibo, Venezuela. It was completed at the Department of Physics, Utah State University, Logan, Utah 83422.