Solutions with concentration for conservation laws with discontinuous flux and its applications to numerical schemes for hyperbolic systems

Measure-valued weak solutions for conservation laws with discontinuous flux are proposed and explicit formulae have been derived. We propose convergent discontinuous flux-based numerical schemes for the class of hyperbolic systems that admit nonclassical -shocks, by extending the theory of discontinuous flux for nonlinear conservation laws to scalar transport equation with a discontinuous coefficient. The article also discusses the concentration phenomenon of solutions along the line of discontinuity, for scalar transport equations with a discontinuous coefficient. The existence of the solutions for transport equation is shown using the vanishing viscosity approach and the asymptotic behavior of the solutions is also established. The performance of the numerical schemes for both scalar conservation laws and systems to capture the -shocks effectively is displayed through various numerical experiments.     

Photoredox-Catalyzed Decarboxylative Bromination,Chlorination and Thiocyanation Using Inorganic Salts

Decarboxylative halogenation reactions of alkyl carboxylic acids are highly valuable reactions for the synthesis of structurally diverse alkyl halides. However, many reported protocols rely on stoichiometric strong oxidants or highly electrophilic halogenating agents. Herein, we describe visible-light photoredox-catalyzed decarboxylative halogenation reactions of N-hydroxyphthalimide-activated carboxylic acids that avoid stoichiometric oxidants and use inexpensive inorganic halide salts as the halogenating agents. Bromination with lithium bromide proceeds under simple, transition-metal-free conditions using an organic photoredox catalyst and no other additives, whereas dual photoredox-copper catalysis is required for chlorination with lithium chloride. The mild conditions display excellent functional-group tolerance, which is demonstrated through the transformation of a diverse range of structurally complex carboxylic acid containing natural products into the corresponding alkyl bromides and chlorides. In addition, we show the generality of the dual photoredox-copper-catalyzed decarboxylative functionalization with inorganic salts by extension to thiocyanation with potassium thiocyanide, which was applied to the synthesis of complex alkyl thiocyanates.     

Regio- and Z-Selective Alkyne Hydroamination and Hydrophenoxylation using Tetrafluoro-λ6-Sulfanyl Alkynes under Superbasic,Naked Anion Conditions

Alkyne hydroamination is an effective approach for the production of enamines and enamine-containing N-heterocycles. However, stereoselectivity control is a considerable challenge in this reaction because of the electronic repulsion between an incoming nitrogen lone pair and the alkyne π-system. Herein, we propose a methodology involving β-regio- and Z-selective alkyne hydroamination by using tetrafluoro-λ⁶-sulfanyl (SF₄) alkynes under superbasic, naked anion conditions. The reaction is compatible with a wide variety of N-heterocycles, including indoles, carbazoles, pyrazoles, and imidazoles, and selectively furnishes SF₄-linked Z-vinyl enamines with β-regioselectively. Moreover, the method can be extended to the β- and Z-controlled, base-mediated alkyne hydrophenoxylation with phenols to provide SF₄-linked Z-vinyl ethers in high yields. As the SF₄ unit has attracted attention as a bioisostere for alkynes, p-benzenes, bicyclo[1.1.1]pentyl (BCP) groups, and cubanes in medicinal chemistry, this chemistry represents an effective approach to creating novel drug candidates incorporating SF₄-containing molecules.     

Networks of periodic orbits in the circular restricted three-body problem with first order post-Newtonian terms

The motivation of this article is to numerically investigate the orbital dynamics of the planar post-Newtonian circular restricted problem of three bodies. By numerically integrating several large sets of initial conditions of orbits we obtain the basins of escape. Additionally, we determine the influence of the transition parameter on the orbital structure of the system, as well as on the families of simple symmetric periodic orbits. The networks and the stability of the symmetric periodic orbits are revealed, while the corresponding critical periodic solutions are also identified. The parametric evolution of the horizontal and the vertical stability of the periodic orbits are also monitored, as a function of the transition parameter.

     

Unusual synthesis of azines and their oxidative degradation to carboxylic acid using iodobenzene diacetate

Reaction of 3-hydrazonobutan-2-one oxime with aromatic aldehydes resulted in the formation of 1,2-bis(arylidene)hydrazine commonly referred as azine as an unexpected product, instead of expected product 3-(aryl)methylenehydrazonobutan-2-one oxime, which were subsequently oxidized to corresponding aromatic acids with an ecofriendly oxidizing agent iodobenzene diacetate. Azines and carboxylic acids were characterized by IR and NMR (¹H, ¹³C, HMBC, and HMQC) studies.     

A simple polymer electrolyte membrane system for enrichment of low-level tritium (3H) in environmental water samples

Tritium (³H) is an essential tracer of the Earth's water cycle; yet widespread adoption of tritium in hydrologic studies remains a challenge because of analytical barriers to quantification and detection of ³H by electrolytic pre-concentration. Here, we propose a simple tritium electrolytic enrichment system based on the use of solid polymer electrolyte membranes (PEMs) that can be used to enrich ³H in 250–3000?mL environmental water samples to a 10-mL final volume. The IAEA PEM-³H system reported here can produce high enrichment factors (>70-fold) and, importantly, removes some of the deterrents to conventional ³H enrichments methods, including the use of toxic electrolysis and neutralization chemicals, spike standards, a complex electrolysis apparatus that requires extensive cooling and temperature controls, and improves precision by eliminating the need for tracking recovery gravimetrics. Preliminary results with varying operating conditions show ³H enrichments to 70-fold and higher are feasible, spanning a wide range of tritium activities from 5 to 150 TU with a precision of ～4.5?%. Further work is needed to quantify inter-sample memory and to establish lower ³H detection limits. The IAEA PEM-³H system is open source, with 3-D CAD and design files made freely available for adoption and improvement by others.     

Base Catalysed Condensation of Acetone with Uracil Derivatives: One Step Synthesis of Pyranopyrimidines

Condensation of uracil derivatives (1,3,4) with acetone in the presence of triethylamine gave pyranopyrimidines (2,5,6).