General one-loop formulas for $$H\rightarrow f\bar{f}\gamma $$ H → f f ¯ γ and its applications

The European Physical Journal C - Considering supergravity theory is a natural step in the development of gravity models. This paper follows the “algebraic“ path and constructs possible...     

On the derivation of the entropy of ideal quantum gases confined in a three-dimensional harmonic potential

In this work,the entropy functions of ideal quantum gases in a three-dimensional harmonic trap are analytically calculated using temperature as an explicit variable.Afterward,the applicability of the analytical formulas is validated by comparison with the numerical calculation.The results illustrate that the obtained functions could be applied for the whole temperature regime with a maximum relative deviation of less than 7.5%in the vicinity of the critical temperature Tcin the case of Bose gases.Meanwhile,for Fermi gases,although the analytical formula fits well at very low-and high-temperature regimes,it cannot be applied at temperature in the range[0.3-0.5]T_F,where T_F is the Fermi temperature.In addition,the consistency between our formulas and classical ones at significantly high temperatures is also discussed.     

Synthesis and Evaluation of Chalcone Derivatives as Novel Sunscreen Agent

Ultraviolet (UV) irradiation is a serious problem for skin health thus the interest in the research to develop sunscreen agent has been increasing. Chalcone is a promising compound to be developed as its chromophore absorbs in the UV region. Therefore, in the present work, we synthesized eight chalcone derivatives through Claisen–Schmidt condensation at room temperature. The evaluation of the optical properties of each chalcone derivatives in the UV region was conducted through spectroscopic and computational studies. The synthesized chalcones were obtained in good yields and they were active in the UV region. The results revealed that more methoxy substituents to chalcone leads toward red shift. All chalcone derivatives have high molar absorptivity value (21,000–56,000) demonstrating that they have the potential to be used as the sunscreen agent. The cytotoxicity assay showed that chalcone derivatives were demonstrating low toxicity toward normal human fibroblast cell, which is remarkable. Therefore, we concluded that the synthesized chalcones in this work were potential to be developed as novel sunscreen agents in real application.     

Generating Function of the Tilings of an Aztec Rectangle with Holes

We consider a generating function of the domino tilings of an Aztec rectangle with several unit squares removed from the boundary. Our generating function involves two statistics: the rank of the tiling and half number of vertical dominoes as in the Aztec diamond theorem by Elkies, Kuperberg, Larsen and Propp. In addition, our work deduces a combinatorial explanation for an interesting connection between the number of lozenge tilings of a semihexagon and the number of domino tilings of an Aztec rectangle.     

Fourier transform and smoothness of solutions of a class of semilinear elliptic degenerate equations with double characteristics

This paper is a continuation of our earlier note [V. T. T. Hien and N. M. Tri, “Analyticity of Solutions of Semililnear Equations with Double Characteristics,” J. Math. Anal. Appl. 337, 1249–1260 (2008)]. Here we prove the analyticity of solutions of a class of semilinear elliptic degenerate equations with double characteristics by using the Fourier transform.     

A Solution‐Processed Air‐Stable Perylene Diimide Derivative for N‐type Organic Thin Film Transistors

For future all‐soluble organic thin film transistor (OTFT) applications, a new soluble n‐type air‐stable perylene diimide derivative semiconductor material with (trifluoromethyl)benzyl groups (TC–PDI–F) is synthesized. The film is formed by spin‐coating in air and optimized for OTFT fabrications. The transistor characteristics and air‐stability of the TC–PDI–F OTFTs is measured to investigate the feasibility of using solution‐processed TC–PDI–F for future OTFT applications. For all‐solution OTFT process applications, the transistor characteristics are demonstrated by using TC–PDI–F as an n‐type semiconductor material and liquid‐phase‐deposited SiO₂ (LPD–SiO₂) as a gate dielectric material. All processes (except material synthesis and electrode deposition) and electrical measurements are conducted in air.     

Electronic structures of NbGen−/0/+ (n = 1–3) clusters from multiconfigurational CASPT2 and density matrix renormalization group-CASPT2 calculations

Density functional theory and multiconfigurational CASPT2 and density matrix renormalization group DMRG-CASPT2 have been employed to study the low-lying states of NbGe_n^−/0/+ (n = 1–3) clusters. With the DMRG-CASPT2 method, the active spaces are extended to a size of 20 orbitals. For most of the states, the CASPT2 relative energies are comparable with the DMRG-CASPT2 results. The leading configuration, bond distances, vibrational frequencies, and relative energies of the low-lying states of these clusters were calculated. The ground states of these clusters were computed to be ³Δ, ⁴Φ, and ⁵Φ of NbGe^−/0/+; ³A₂, ⁴B₁, and ³B₁ of cyclic-NbGe₂^−/0/+; and ¹A′, 1²A″ and 1²A′′ (²E), and ³A″ of tetrahedral-NbGe₃^−/0/+ isomers. For NbGe cluster, our calculations proposed that the ⁶∑ is almost degenerate with the ⁴Φ with the CASPT2 and DMRG-CASPT2 relative energies of 0.05 and 0.06 eV. The adiabatic detachment energies of NbGe_n⁻ (n = 1–3) clusters were estimated to be 1.46, 1.55, and 2.18 eV by the CASPT2 method. The relevant detachment energies of the anionic ground state and the ionization energies of the neutral ground states are evaluated at the CASPT2 level.     

Solvent Effects on the Structure-Activity Relationship of Phenytoin-like Anticonvulsant Drugs

The absorption spectra of nine compounds structurally related to phenytoin (5,5-diphenylhydantoin) were recorded in twelve solvents over the range of 200 to 400 nm. The effects of solvent dipolarity/polarizability and solvent/solute hydrogen bonding interactions were analyzed by means of the linear solvation energy relationship (LSER) concept proposed by Kamlet and Taft. The lipophilic activity of the investigated hydantoins was estimated by calculation of their log ₁₀ P values. The calculated values of log ₁₀ P were correlated with the ratio of the contributions of specific and non-specific solute/solvent interactions. The correlation equations were combined with the corresponding ED₅₀ values to generate new equations that demonstrate exact relationship between solute/solvent interactions and the structure-activity parameters.