Optimal time delays in a class of reaction-diffusion equations

ABSTRACT

A class of semilinear parabolic reaction diffusion equations with multiple time delays is considered. These time delays and corresponding weights are to be optimized such that the associated solution of the delay equation is the best approximation of a desired state function. The differentiability of the mapping is proved that associates the solution of the delay equation to the vector of weights and delays. Based on an adjoint calculus, first-order necessary optimality conditions are derived. Numerical test examples show the applicability of the concept of optimizing time delays.     

One‐pot green synthesis of Cu/bone nanocomposite and its catalytic activity in the synthesis of 1‐substituted 1H‐1,2,3,4‐tetrazoles and reduction of hazardous pollutants

In this work, a simple and green method is reported for the biosynthesis of Cu/bone nanocomposite using Cordyline fruticosa extract as a stabilizer and reductant. Animal bone was used as a natural support to prevent the accumulation of Cu nanoparticles. The catalytic activity of Cu/bone nanocomposite was assessed in the synthesis of 1‐substituted 1H‐1,2,3,4‐tetrazoles and reduction of various organic dyes, including 4‐nitrophenol (4‐NP), nigrosin (NS), congo red (CR) and methylene blue (MB). The best catalytic performance in the synthesis of 1‐substituted tetrazoles was achieved using 0.05 g of Cu/bone nanocomposite at 120°C. In addition, under optimal conditions, the absorption bands corresponding to 4‐NP, CR, NS and MB completely disappeared after about 6 min, 3 min, 50 s and 7 s, respectively. The biosynthesis protocol used in the preparation of Cu/bone nanocomposite offers a very attractive area for further research.     

The support designs of the triply even binary codes of length 48

In this paper, we present examples of codes all of whose weight classes support 1‐designs, with duals whose classes include two that support 2‐designs. We can find these examples in the triply even binary codes of length 48, which have been classified by Betsumiya and Munemasa.     

Stability of Antimicrobial Drug Molecules in Different Gravitational and Radiation Conditions in View of Applications during Outer Space Missions

The evolution of different antimicrobial drugs in terrestrial, microgravity and hypergravity conditions is presented within this review, in connection with their implementation during human space exploration. Drug stability is of utmost importance for applications in outer space. Instabilities may be radiation-induced or micro-/hypergravity produced. The antimicrobial agents used in space may have diminished effects not only due to the microgravity-induced weakened immune response of astronauts, but also due to the gravity and radiation-altered pathogens. In this context, the paper provides schemes and procedures to find reliable ways of fighting multiple drug resistance acquired by microorganisms. It shows that the role of multipurpose medicines modified at the molecular scale by optical methods in long-term space missions should be considered in more detail. Solutions to maintain drug stability, even in extreme environmental conditions, are also discussed, such as those that would be encountered during long-duration space exploratory missions. While the microgravity conditions may not be avoided in space, the suggested approaches deal with the radiation-induced modifications in humans, bacteria and medicines onboard, which may be fought by novel pharmaceutical formulation strategies along with radioprotective packaging and storage.     

含谐振单元和弹性支承谐振单元的声子晶体低频禁带特性研究

在结构中周期性地添加谐振单元可以构造局域共振声子晶体并产生低频禁带。本文提出了一种具有谐振单元和弹性支承谐振单元的声子晶体结构,通过声子晶体理论和振动理论对该结构的禁带特性和禁带调控特性进行了计算与分析。结果表明,该结构可在0 Hz处形成禁带;禁带内对振动的衰减强度由衰减因子和有限结构周期数共同决定;结构中存在1条可调控禁带和3条不可调禁带;可调控禁带可以通过改变谐振单元和弹性支承谐振单元的结构参数加以调控;不可调禁带包括第一禁带,它们能够较为稳定地对一定频率的弹性波产生衰减作用。该结构所具有的禁带特性在管路、桥梁和汽车减振领域具有潜在应用。     

The Synthesis of B2(SIDip)2 and its Reactivity Between the Diboracumulenic and Diborynic Extremes

A new compound with the formula L‐B₂‐L wherein the stabilizing ligand (L) is 1,3‐bis[diisopropylphenyl]‐4,5‐dihydroimidazol‐2‐ylidene (SIDip) has been synthesized, isolated, and characterized. The π‐acidity of the SIDip ligand, intermediate between the relatively non‐acidic IDip (1,3‐bis[diisopropylphenyl]imidazol‐2‐ylidene) ligand and the much more highly acidic CAAC (1‐[2,6‐diisopropylphenyl]‐3,3,5,5‐tetramethylpyrrolidin‐2‐ylidene) ligand, gives rise to a compound with spectroscopic, electrochemical, and structural properties between those of L‐B₂‐L compounds stabilized by CAAC and IDip. Reactions of all three L‐B₂‐L compounds with CO demonstrate the differences caused by their respective ligands, as the π‐acidities of the CAAC and SIDip carbenes enabled the isolation of bis(boraketene) compounds (L(OC)B‐B(CO)L), which could not be isolated from reactions with B₂(IDip)₂. However, only B₂(IDip)₂ and B₂(SIDip)₂ could be converted into bicyclic bis(boralactone) compounds.