Hyperbolic conservation laws with vanishing nonlinear diffusion and linear dispersion in heterogeneous media

We analyze family of solutions to multidimensional scalar conservation law, with flux depending on the time and space explicitly, regularized with vanishing diffusion and dispersion terms. Under a condition on the balance between diffusion and dispersion parameters, we prove that the family of solutions is precompact in L¹_loc{L^1_{\rm loc}}. Our proof is based on the methodology developed in Sazhenkov (Sibirsk Math Zh 47(2):431–454, 2006), which is in turn based on Panov’s extension (Panov and Yu in Mat Sb 185(2):87–106, 1994) of Tartar’s H-measures (Tartar in Proc R Soc Edinb Sect A 115(3–4):193–230, 1990), or Gerard’s micro-local defect measures (Gerard Commun Partial Differ Equ 16(11):1761–1794, 1991). This is new approach for the diffusion–dispersion limit problems. Previous results were restricted to scalar conservation laws with flux depending only on the state variable.     

Cooperative Ligands in Dissolution of Gold

Development of new, environmentally benign dissolution methods for metallic gold is driven by needs in the circular economy. Gold is widely used in consumer electronics, but sustainable and selective dissolution methods for Au are scarce. Herein, we describe a quantitative dissolution of gold in organic solution under mild conditions by using hydrogen peroxide as an oxidant. In the dissolution reaction, two thiol ligands, pyridine-4-thiol and 2-mercaptobenzimidazole, work in a cooperative manner. The mechanistic investigations suggest that two pyridine-4-thiol molecules form a complex with Au⁰ that can be oxidized, whereas the role of inexpensive 2-mercaptobenzimidazole is to stabilize the formed Au^I species through a ligand exchange process. Under optimized conditions, the reaction proceeds vigorously and gold dissolves quantitatively in two hours. The demonstrated ligand-exchange mechanism with two thiols allows to drastically reduce the thiol consumption and may lead to even more effective gold dissolution methods in the future.     

More on “Connected (n, m)-graphs with minimum and maximum zeroth-order general Randi? index”

Let G be a graph and d(u) denote the degree of a vertex u in G. The zeroth-order general Randi? index ⁰R_α(G) of the graph G is defined as ∑_u∈V(G)d(u)^α, where the summation goes over all vertices of G and α is an arbitrary real number. In this paper we correct the proof of the main Theorem 3.5 of the paper by Hu et al. [Y. Hu, X. Li, Y. Shi, T. Xu, Connected (n,m)-graphs with minimum and maximum zeroth-order general Randi? index, Discrete Appl. Math. 155 (8) (2007) 1044-1054] and give a more general Theorem. We finally characterize ¹ for α<0 the connected G(n,m)-graphs with maximum value ⁰R_α(G(n,m)), where G(n,m) is a simple connected graph with n vertices and m edges.     

Defect Distributions Related to Weakly Convergent Sequences in Bessel-Type Spaces $${H_{\Lambda }^{-s,p}}$$

We consider microlocal defect distributions associated to a weakly convergent sequences \(u_n\) in \(H^{-s,p}_{\Lambda }\) and \(v_n\) in \(H^{s+m,q}_{\Lambda }\) through the space of pseudo-differential operators with the symbols in \((s^{m,N+1}_\Lambda )_0\). Symbols correspond to a weight function \(\Lambda \) determining a quasi-elliptic symbol. Results are applied to partial differential equations with symbols related to weights of the type \(\Lambda \).     

Silica Gel as a Promoter of Sequential Aza‐Michael/Michael Reactions of Amines and Propiolic Esters: Solvent‐ and Metal‐Free Synthesis of Polyfunctionalized Conjugated Dienes

We present an efficient, simple, metal‐ and solvent‐free silica‐gel‐promoted synthesis of functionalized conjugated dienes by sequential aza‐Michael/Michael reactions by starting from commercially available primary amines and propiolic esters. The scope and usefulness of the method is demonstrated for 31 examples, including a range of propiolic esters, aliphatic amines, and differently substituted aromatic amines. For aliphatic amines, the products were obtained within 0.5 to 4 h in 52 to 85 % yield, compared with 3.5 to 22 h under classical solution‐phase synthesis, which proceeds with similar or lower yields. The method was found to be particularly useful for weakly nucleophilic aromatic amines, which provided products in 21 to 73 % yield over 2.5 to 9.5 h compared with yields of 0 to 49 % over 1 to 6 d under standard solution‐phase conditions, and for more hydrophobic esters that gave products in yields of 47 to 79 % over 1 to 3 h compared with 0 to 45 % over 4 to 114 h in solvent.     

Study of heterogeneous equilibria in saturated solutions of some sparingly soluble 8-hydroxyquinolines

Heterogeneous equilibria in saturated aqueous solutions of 8-hydroxyquinoline (A), 2-methyl-8-hydroxyquinoline (B) and 5-chloro-8-hydroxyquinoline (C) were investigated at constant ionic strength (1M sodium chloride), at 25.0 +/- 0.1 degrees , by the application of the following methods: the formation function method, the method of bound protons, the method of free proton sites and the solubility method. The following equilibrium constants were determined: K(s1)=[H(2)A(+)]/[H(3)O(+)], K(s2)=[HA] and K(s3)=[H(3)O(+)] [A(-)]. Their mean pK values are: -2.88, 2.42 and 12.09 for A, -3.27, 2.71 and 12.73 for B, and -0.34, 3.88 and 12.75 for C. In addition, the acidity constants of investigated 8-hydroxyquinolines were determined by pH-metric titrations. The values obtained for these constants were consistent with those calculated on the basis of corresponding equilibrium constants determined in heterogeneous systems.     

Radiation effects in nanoclusters embedded in solids

Nanoclusters embedded in hard solid materials such as silica show great promise forincreased practical applications, as they combine the exciting nanosize effects with veryhigh structural stability. Ion irradiation can be used to tailor the properties of theseclusters, the perhaps most dramatic example being the use of swift heavy ions to reshapespherical metal nanoparticles to have antennas or become rods. In this article we reviewexperimental and simulation studies of ion beam processing of nanoclusters embedded insolids.     

Dirichlet Problem at Infinity for $\mathcal A$-Harmonic Functions

We study the Dirichlet problem at infinity for -harmonic functions on a Cartan–Hadamard manifold M and give a sufficient condition for a point at infinity x ₀∈M(∞) to be -regular. This condition is local in the sense that it only involves sectional curvatures of M in a set U∩M, where U is an arbitrary neighborhood of x ₀ in the cone topology. The results apply to the Laplacian and p-Laplacian, 1<p<∞, as special cases.