Embedding of Dynamical Symmetry Groups U(1, 1) and U(2) of a Free Particle on AdS 2 and S 2 into Parasupersymmetry Algebra

Using two different types of the laddering equations realized simultaneously by the associated Gegenbauer functions, we show that all quantum states corresponding to the motion of a free particle on AdS ₂ and S ² are splitted into infinite direct sums of infinite-and finite-dimensional Hilbert subspaces which represent Lie algebras u(1, 1) and u(2) with infinite- and finite-fold degeneracies, respectively. In addition, it is shown that the representation bases of Lie algebras with rank 1, i.e., gl(2, C), realize the representation of nonunitary parasupersymmetry algebra of arbitrary order. The realization of the representation of parasupersymmetry algebra by the Hilbert subspaces which describe the motion of a free particle on AdS ₂ and S ² with the dynamical symmetry groups U(1, 1) and U(2) are concluded as well.     

The role of hydrogen bonds in thermodynamic and structural properties in binary mixtures of morpholine + 2-methylcyclohexanol: a combined experimental and computational study

Structural Chemistry - Thermodynamic properties of binary mixtures of 2-methylcyclohexanol with morpholine are measured as a function of composition and temperature. The excess molar volumes were...     

A combined experimental and computational investigation of the binary mixtures of 2-methylcyclohexanol and isobutanol

Structural Chemistry - The measured densities and viscosities of the binary mixtures of the isobutanol and 2-methylcyclohexanol were reported experimentally in a certain range of concentrations at...     

Boron nitride nanotube (BNNT) as a sensor of hydroperoxyl radical (HO<Subscript>2</Subscript>): A DFT study

In this present study, the adsorption behavior of HO₂ radical on the exterior surface of (5, 0) zigzag boron nitride nanotube (BNNT) has been investigated. The electronic structures and geometries of studied complexes were calculated at B3LYP-D3/6-31++G (d, p) computational level. The value of adsorption energy for the most stable configuration (A) is obtained ?0.68 eV, indicating physisorption process. Meaningful change of HOMO–LUMO gap after adsorption confirming BNNT can be introduced as a promising sensor for sensing of HO₂ radical.     

Solution of preemptive multi-objective network design problems applying Benders decomposition method

This paper deals with preemptive priority based multi-objective network design problems in which construction times together with travel costs are taken into account. These cost and time objective functions are ordered lexicographically with respect to manager’s strategies in order to decrease total cost and total construction time of the network. To solve this preemptive problem, instead of the standard sequential approach, a modified Benders decomposition algorithm is developed. It is proved that this algorithm decreases the (expected) number of computations and so this algorithm is efficient for large-scale network design problems.     

Spectrum-Generating Symmetries for the Superpotentials Acot θ and Btanh y

The hierarchy of supersymmetric partner Schrödinger equations for the superpotentials Acot?θ and Btanh?y with A and B as half-integer and negative integer numbers are solved. The number of bound states for given trigonometric and hyperbolic potentials are infinite and finite, respectively. In addition to the spectrum-generating corresponding to the standard supersymmetry which is based on shifting potential parameter, there exist three other different methods for generating the spectrum. The first method is based on supersymmetrizing two given models via infinite and finite number of their bound states. This is realized by the ladder operators which shift only quantum numbers. The second and third methods are based on supersymmetrizing any of the models via all bound states corresponding to hierarchy of their partner potentials. They are respectively realized via simultaneous increasing or decreasing of quantum number and the potential parameter, and also, increasing one of them while decreasing the other. Any of the second and third methods leads to introducing two different classes of the algebraic solutions for both models.     

Discovery of a Highly Selective Glycogen Synthase Kinase‐3 Inhibitor (PF‐04802367) That Modulates Tau Phosphorylation in the Brain: Translation for PET Neuroimaging

Glycogen synthase kinase‐3 (GSK‐3) regulates multiple cellular processes in diabetes, oncology, and neurology. N‐(3‐(1H‐1,2,4‐triazol‐1‐yl)propyl)‐5‐(3‐chloro‐4‐methoxyphenyl)oxazole‐4‐carboxamide (PF‐04802367 or PF‐367) has been identified as a highly potent inhibitor, which is among the most selective antagonists of GSK‐3 to date. Its efficacy was demonstrated in modulation of tau phosphorylation in vitro and in vivo. Whereas the kinetics of PF‐367 binding in brain tissues are too fast for an effective therapeutic agent, the pharmacokinetic profile of PF‐367 is ideal for discovery of radiopharmaceuticals for GSK‐3 in the central nervous system. A ¹¹C‐isotopologue of PF‐367 was synthesized and preliminary PET imaging studies in non‐human primates confirmed that we have overcome the two major obstacles for imaging GSK‐3, namely, reasonable brain permeability and displaceable binding.     

Comments on “Barut-Girardello Coherent States for the Parabolic Cylinder Functions”

In Chenaghlou and Faizy (Int. J. Theor. Phys. 2008), the authors claim that they have constructed the Barut-Girardello coherent states for the parabolic cylinder functions. However, we point out here that by introducing these coherent states, Schrödinger was able to put forth the idea of “coherent states of the quantum harmonic oscillator” over eighty years ago. These coherent states are derived not only from the Barut-Girardello eigenvalue equation, but also from the Schrödinger and the Klauder-Perelomov approaches. Thus, contrary to their claim, the authors have not introduced new coherent states. In particular, a wide range of the parabolic cylinder functions do not form an orthonormal basis.