Mechanism of the acid-catalyzed hydrolysis of N-acylsulfamates

The kinetics of hydrolysis of a series of N-acylsulfamate esters p-XC₆H₄OSO₂NHCOR as models for more complex, biologically important compounds has been examined. Structure-reactivity, solvent-reactivity, thermodynamic data, etc. support a bimolecular mechanism involving water in the transition state (TS).     

Encapsulation of Indomethacin in PVP: Solid-State NMR Studies

Summary: ¹³C solid-state NMR and ¹H relaxation time measurements have been used to determine the structure of the crystalline and amorphous forms of the pharmaceutical drug indomethacin. Cross-polarization dynamics parameters were calculated for individual NMR resonances providing an insight into the mobility of functional groups in two forms of indomethacin. The changes of mobility in indomethacin/polyvinylpyrrolidone (PVP) formulation have been investigated via¹H-¹³C solid-state NMR methods. Differences between the amorphous material and its crystalline counterpart have been observed. The γ-amorphous indomethacin rapidly crystallizes with time. It has been shown that encapsulation in the PVP stabilizes the amorphous form of the drug by preventing crystallization due to reduced mobility of the guest in the formulation.     

Hydrosilylation Reactions Catalyzed by Rhenium

Hydrosilylation is an important process, not only in the silicon industry to produce silicon polymers, but also in fine chemistry. In this review, the development of rhenium-based catalysts for the hydrosilylation of unsaturated bonds in carbonyl-, cyano-, nitro-, carboxylic acid derivatives and alkenes is summarized. Mechanisms of rhenium-catalyzed hydrosilylation are discussed.     

Action de O- et N-nucléophiles sur les sels de phényl-3 benzopyrylium-1

3-Phenyl-1-benzopyrylium percholorates 1a, 1i react exculusively at C-2 with ethanol and isopropyl alcohol, affording mixed acetals 2a, 3a, 3i . Aqueous ammonia gives symmetrical secondary amines 4a, 4b or bis(3-phenyl-2H-1-benzopyran-2-yl)amines, while with aqueous aliphatic amines (40%) bis-acetals 5a, 5b or 2,2′-oxy-bis(3-phenyl-2H-1-benzopyrans) are characterized. In some other acidic conditions, 5a and 5b are also obtained.     

A Fresh Variational-Analysis Look at the Positive Semidefinite Matrices World

Engineering sciences and applications of mathematics show unambiguously that positive semidefiniteness of matrices is the most important generalization of non-negative real numbers. This notion of non-negativity for matrices has been well-studied in the literature; it has been the subject of review papers and entire chapters of books.     

Conjugate and cut loci of a two-sphere of revolution with application to optimal control

The objective of this article is to present a sharp result to determine when the cut locus for a class of metrics on a two-sphere of revolution is reduced to a single branch. This work is motivated by optimal control problems in space and quantum dynamics and gives global optimal results in orbital transfer and for Lindblad equations in quantum control.     

Solvability of Minimal Graph Equation Under Pointwise Pinching Condition for Sectional Curvatures

We study the asymptotic Dirichlet problem for the minimal graph equation on a Cartan–Hadamard manifold M whose radial sectional curvatures outside a compact set satisfy an upper bound

$$\begin{aligned} K(P)\le - \frac{\phi (\phi -1)}{r(x)^2} \end{aligned}$$

and a pointwise pinching condition

$$\begin{aligned} |K(P) |\le C_K|K(P') | \end{aligned}$$

for some constants \(\phi >1\) and \(C_K\ge 1\), where P and \(P'\) are any 2-dimensional subspaces of \(T_xM\) containing the (radial) vector \(\nabla r(x)\) and \(r(x)=d(o,x)\) is the distance to a fixed point \(o\in M\). We solve the asymptotic Dirichlet problem with any continuous boundary data for dimensions \(n=\dim M>4/\phi +1\).

     

Global Optimality Conditions in Maximizing a Convex Quadratic Function under Convex Quadratic Constraints

For the problem of maximizing a convex quadratic function under convex quadratic constraints, we derive conditions characterizing a globally optimal solution. The method consists in exploiting the global optimality conditions, expressed in terms of -subdifferentials of convex functions and -normal directions, to convex sets. By specializing the problem of maximizing a convex function over a convex set, we find explicit conditions for optimality.     

Turnpike Property in Optimal Microbial Metabolite Production

Journal of Optimization Theory and Applications - We consider the problem of maximization of metabolite production in bacterial cells formulated as a dynamical optimal control problem (DOCP)....