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)....     

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 \(n=\dim M>4/\phi +1\).

     

Framework functionalisation triggers metal complex binding

Post-synthetic derivatisation of a porous material produces a functionalized material that binds the metal complex V(O)acac2, in contrast to the unfunctionalized precursor, which is inactive for complex binding.     

Structure-activity relationships in cholapod anion carriers: enhanced transmembrane chloride transport through substituent tuning

Chloride transport by a series of steroid-based "cholapod" receptors/carriers was studied in vesicles. The principal method involved preincorporation of the cholapods in the vesicle membranes, and the use of lucigenin fluorescence quenching to detect inward-transported Cl-. The results showed a partial correlation between anion affinity and transport activity, in that changes at the steroidal 7 and 12 positions affected both properties in concert. However, changes at the steroidal 3-position yielded irregular effects. Among the new steroids investigated the bis-p-nitrophenylthiourea 3 showed unprecedented activity, giving measurable transport through membranes with a transporter/lipid ratio of 1:250 000 (an average of <2 transporter molecules per vesicle). Increasing transporter lipophilicity had no effect, and positively charged steroids had low activity. The p-nitrophenyl monourea 25 showed modest but significant activity. Measurements using a second method, requiring the addition of transporters to preformed vesicle suspensions, implied that transporter delivery was problematic in some cases. A series of measurements employing membranes of different thicknesses provided further evidence that the cholapods act as mobile anion carriers.     

Nonribosomal peptide synthesis in animals: the cyclodipeptide synthase of Nematostella

Cyclodipeptide synthases (CDPSs) are small enzymes structurally related to class-I aminoacyl-tRNA synthetases (aaRSs). They divert aminoacylated tRNAs from their canonical role in ribosomal protein synthesis, for cyclodipeptide formation. All the CDPSs experimentally characterized to date are?bacterial. We show here that a predicted CDPS from the sea anemone Nematostella vectensis is an active CDPS catalyzing the formation of various cyclodipeptides, preferentially containing tryptophan. Our findings demonstrate that eukaryotes encode active CDPSs and suggest that all CDPSs have?a similar aminoacyl-tRNA synthetase-like architecture and ping-pong mechanism. They also raise questions about the biological roles of the cyclodipeptides produced in bacteria and eukaryotes.