On the area of constant mean curvature discs and annuli with circular boundaries

It is still an open question whether a constant mean curvature (CMC) disc which is bounded by a circle is necessarily a spherical cap or a flat disc. The authors together with López [1] recently showed that the only stable CMC discs which are bounded by a circle are spherical caps. In this paper we derive lower bounds for the area of constant mean curvature discs and annuli with circular boundaries in 3-dimensional space forms. Received November 8, 1999; in final form January 18, 2000 / Published online March 12, 2001     

Thienopyrazine‐Based Low‐Bandgap Poly(heteroaryleneethynylene)s for Photovoltaic Devices

Summary: Low‐bandgap π‐conjugated polymers that consist of alkyl thiophene/alkoxy phenylene and 2,3‐diphenylthieno[3,4‐b]pyrazine units have been prepared in high yields by a Sonogashira polycondensation. The copolymers are characterized by NMR, IR, UV, GPC, and elemental analysis. Thin films of the polymers P1 , P2 , and P3 exhibit an optical bandgap of ≈1.57–1.60 eV. Under simulated AM 1.5 conditions P2/PCBM devices on polyester foil provide a short circuit current of I_SC = 10.72 mA · cm⁻², an open circuit voltage of V_oc = 0.67 V, and a power conversion efficiency of 2.37%.

Schematic of the photovoltaic device made from the polymers synthesized here.     

Opening or Closing the Lock? When Reactivity Is the Key to Biological Activity

Thiol‐mediated processes play a key role to induce or inhibit inflammation proteins. Tailoring the reactivity of electrophiles can enhance the selectivity to address only certain surface cysteines. Fourteen 2′,3,4,4′‐tetramethoxychalcones with different α‐X substituents (X=H, F, Cl, Br, I, CN, Me, p‐NO₂‐C₆H₄, Ph, p‐OMe‐C₆H₄, NO₂, CF₃, COOEt, COOH) were synthesized, containing the potentially electrophilic α,β‐unsaturated carbonyl unit. The assessment of their reactivity as electrophiles in thia‐Michael additions with cysteamine shows a change in the reactivity of more than six orders of magnitude. Moreover, a clear correlation between their reactivity and an influence on the inflammation proteins heme oxygenase‐1 (HO‐1) and the inducible NO synthase (iNOS) is demonstrated. As the biologically most active compound, the α‐CF₃‐chalcone is shown to inhibit the NO production in RAW264.7 mouse macrophages in the nanomolar range.     

Application of homotopy-perturbation method to fractional IVPs

Fractional initial-value problems (fIVPs) arise from many fields of physics and play a very important role in various branches of science and engineering. Finding accurate and efficient methods for solving fIVPs has become an active research undertaking. In this paper, both linear and nonlinear fIVPs are considered. Exact and/or approximate analytical solutions of the fIVPs are obtained by the analytic homotopy-perturbation method (HPM). The results of applying this procedure to the studied cases show the high accuracy, simplicity and efficiency of the approach.     

Optimal placement of stereo sensors

Autonomous wireless devices such as sensor nodes and stereo cameras, due to their low cost of operation coupled with the potential for remote deployment, have found a plethora of applications ranging from monitoring air, soil and water to seismic detection and military surveillance. Typically, such a network spans a region of interest with the individual nodes cooperating to detect events and disseminate information. Given a deployment of sensors and targets over a region, a sensor pairing is desired for each target that optimizes the coverage under certain constraints. This problem can be modeled as an integer programming problem and solved using branch-and-cut. For larger problems, it is necessary to limit the number of variables, and a GRASP routine was developed for this purpose. Valid cutting planes are developed and computational results presented. Research supported in part by NSF grant numbers DMS–0317323 and CMS–0301661.     

In silico fight against novel coronavirus by finding chromone derivatives as inhibitor of coronavirus main proteases enzyme

Structural Chemistry - Novel coronavirus, 2019-nCoV is a danger to the world and is spreading rapidly. Very little structural information about 2019-nCoV make this situation more difficult for drug...