Two 1,3‐Diazabicyclo[3.1.0]hex‐3‐enes with a ‘Tripod’ Core

The photochromic 1,3‐diazabiclyclo[3.1.0]hex‐3‐enes 5 and 6 were synthesized from two premade tris‐aldehydes and two premade aziridinyl ketones and characterized (Scheme 1). Their spectra showed structure? photochromic behavior relationships (SPBR), which were analyzed.     

Synthesis of certain 2-substituted-1H-benzimidazole derivatives as antimicrobial and cytotoxic agents

A series of 2-substituted-1H-benzimidazole derivatives were synthesized and evaluated for antimicrobial, antifungal and cytotoxic activities. The results showed that all tested compounds showed potent antimicrobial activity against some species of Gram-negative bacteria (Pseudomonas aeruginosa, Escherichia coli, Salmonella typhi) and fungi (Candida albicans) with minimum inhibitory concentrations (MICs) lower than 0.016 μg/mL. In contrast, all tested compounds were inactive against Staphylococcus aureus (Gram-positive bacterium). The final targets were also tested for their antitumor activity in vitro on cervical carcinoma (HeLa) cell line. Eight of the test compounds displayed more potent cytotoxic effect than doxorubicin at nanomolar concentrations. Compounds 2c and 3c exerted the strongest cytoyoxic effect with IC(50) 15 and 13 nM, respectively.     

Benzimidazole Annulated New Heterocyclic Compounds: Synthesis of New Polycyclic Pyrazole Derivatives

Several ( 3 ) new benzimidazole based polycyclic compounds of potential pharmaceutical interest have been prepared starting from 2‐benzimidazolelyl (1,3‐dioxo‐2‐indenylidene) acetonitrile. Unhypothesized, the C≡N function of the plausible intermediates was released as HCN rather than a classical nucleophilic addition when treated with bidentate reagents such as hydrazines, 5‐amino‐1H‐1,2,4‐triazole, 5‐amino‐4‐cyano‐1H‐pyrazole and 2‐aminobenzimidazole. When compound 3 reacted with active acetonitrile derivatives it afforded new polyfunctional pyridines via elimination of HCN in addition to, new pyrimidine, pyrazine and azepine derivatives.     

Two coupled oscillators in the form of a frequency converter in interaction with a single atom via two-photon processes

We consider the problem of a two-level atom with degenerate two-photon transitions interacting with a single-mode radiation field in the presence of a parametric frequency-converter term. A Hamiltonian representing such a system contains three time-dependent coupling parameters. We obtain an exact solution of the wave function in the Schr?dinger picture, using the canonical transform and under a certain choice of the coupling parameters. We use the results obtained to discuss the atomic inversion as well as the linear entropy in addition to both the variance and entropy squeezing. We show that the system at a certain time is sensitive to variations in both the detuning parameter ?? and the ratio of the coupling parameter g.     

New features of a single-mode nonlinear Stark shift in the presence of phase damping

The influence of the nonlinear Stark shift, for the multi-quanta JCM in the presence of phase damping is studied. In particular the temporal evolution of the atomic inversion, the linear entropy and the entropy squeezing are investigated. The linear entropy is used as an indicator of the degree of entanglement between the atom and the field. The results indicate the sensitivity of these aspects to changes either in the decay parameter or the Stark shift parameter.     

A new existence theory for periodic solutions to evolution equations

ABSTRACT

This paper deals with a new existence theory for periodic solutions to a broad class of evolution equations. We first establish new fixed point theorems for affine maps in locally convex spaces and ordered Banach spaces. Our new fixed point results extend, encompass and complement a number of well-known theorems in the literature, including the famous Chow and Hale fixed point theorem. With these obtained fixed point results, we investigate the existence of periodic solutions for some class of nonhomogeneous linear systems in Banach spaces with lack of compactness. Some illustrative examples are also given.     

Noise-Based Damping of Chaotic Entanglement in Pulsed Driven Two-Qubit System

This paper investigates the entanglement dynamics of a two-qubit system in the presence of n-sequential ${\sin }^2$-pulse shape. The study explores entanglement under two scenarios: when the system is completely isolated from the environment and when it interacts with one of the surrounding environments, namely the thermal environment and the common dephasing environment. The authors quantify entanglement through concurrence while systematically examining the effects of initial state preparation, qubit coupling strength, laser-qubit interaction intensity, pulse sequences, and decohering environments. The results highlight that the entanglement of the two-qubit system strongly depends on the initial state. Increasing the coupling strength between the qubits and the n-sequential pulse enhances the maximum values of entanglement. Conversely, augmenting the laser-qubits coupling or introducing the influence of the environment diminishes the entanglement.     

Turbulent flow around single concentric long capsule in a pipe

A numerical solution was developed for the equations governing the turbulent flow around single concentric long capsule in a pipe. First, a turbulence model was established for the concentric annulus between the capsule and the pipe to simulate the flow as axi-symmetric, two dimensional, steady flow without edge effect. Second, the same case was considered taking into account the edge effect. Finally, turbulence modelling was established to simulate the case as a three dimensional steady flow, with a view of investigating the validity of axi-symmetric flow assumption. Three different turbulence models were used: an algebraic model (Baldwin–Lomax model) and two types of two-equation models (k–ε and k–ω). Obtained results of pressure gradient along the capsule were compared with available experimental data to verify the used models. In addition, experimental data of the velocity profiles of other investigators were also used in this concern. The results predicted by the three different turbulence models were shown to agree well with the experimental data, though precision differed from one to another.     

Comparison of human skull and spherical shell vibrations—implications for head injury modeling

Spherical shell models have been formulated as geometric approximations of the human head. By insuring geometrical and material similarity between the model and human head, impact response and skull fracture studies were expected to yield results in close agreement with model predictions. This, however, was not the case. Model predictions of skull fracture loads were typically twice the observed level. A comparison was made between the resonant frequencies of two dry human skulls and corresponding spherical shell models. Poor agreement was observed. A vibrational analysis of the model revealed that the uniformity of the spherical shell approximmately doubles the effective stiffness and resonant frequencies as compared with the dry human skull. The elastic modulus of the model was adjusted to bring its resonances into closer agreement with those of the skull. The synthesized“effective” modulus was 50% lower than the material property of human cranial bone. Interestingly, this adjustment also brought model predictions of skull fracture into closer agreement with available human cadaver data.