The intermediate disorder regime for a directed polymer model on a hierarchical lattice

We study a directed polymer model defined on a hierarchical diamond lattice, where the lattice is constructed recursively through a recipe depending on a branching number $b\in \mathbb{N}$ and a segment number $s\in \mathbb{N}$. When $b\le s$ it is known that the model exhibits strong disorder for all positive values of the inverse temperature $\beta$, and thus weak disorder reigns only for $\beta =0$ (infinite temperature). Our focus is on the so-called intermediate disorder regime in which the inverse temperature $\beta \equiv {\beta }_n$ vanishes at an appropriate rate as the size $n$ of the system grows. Our analysis requires separate treatment for the cases $b<s$ and $b=s$. In the case $b<s$ we prove that when the inverse temperature is taken to be of the form ${\beta }_n=\stackrel{?}{\beta }{(b/s)}^{n/2}$ for $\stackrel{?}{\beta }>0$, the normalized partition function of the system converges weakly as $n\to \infty$ to a distribution $L\left(\stackrel{?}{\beta }\right)$ and does so universally with respect to the initial weight distribution. We prove the convergence using renormalization group type ideas rather than the standard Wiener chaos analysis. In the case $b=s$ we find a critical point in the behavior of the model when the inverse temperature is scaled as ${\beta }_n=\stackrel{?}{\beta }/n$; for an explicitly computable critical value ${\kappa }_b>0$ the variance of the normalized partition function converges to zero with large $n$ when $\stackrel{?}{\beta }\le {\kappa }_b$ and grows without bound when $\stackrel{?}{\beta }>{\kappa }_b$. Finally, we prove a central limit theorem for the normalized partition function when $\stackrel{?}{\beta }\le {\kappa }_b$.     

Spatially Directed Pyrolysis via Thermally Morphing Surface Adducts

Combustion is often difficult to spatially direct or tune associated kinetics—hence a run-away reaction. Coupling pyrolytic chemical transformation to mass transport and reaction rates (Damköhler number), however, we spatially directed ignition with concomitant switch from combustion to pyrolysis (low oxidant). A ‘surface-then-core’ order in ignition, with concomitant change in burning rate,is therefore established. Herein, alkysilanes grafted onto cellulose fibers are pyrolyzed into non-flammable SiO₂ terminating surface ignition propagation, hence stalling flame propagating. Sustaining high temperatures, however, triggers ignition in the bulk of the fibers but under restricted gas flow (oxidant and/or waste) hence significantly low rate of ignition propagation and pyrolysis compared to open flame (Liñán's equation). This leads to inside-out thermal degradation and, with felicitous choice of conditions, formation of graphitic tubes. Given the temperature dependence, imbibing fibers with an exothermically oxidizing synthon (MnCl₂) or a heat sink (KCl) abets or inhibits pyrolysis leading to tuneable wall thickness. We apply this approach to create magnetic, paramagnetic, or oxide containing carbon fibers. Given the surface sensitivity, we illustrate fabrication of nm- and μm-diameter tubes from appropriately sized fibers.     

Engineered Biocatalytic Synthesis of β-N-Substituted-α-Amino Acids

Non-canonical amino acids (ncAAs) are useful synthons for the development of new medicines, materials, and probes for bioactivity. Recently, enzyme engineering has been leveraged to produce a suite of highly active enzymes for the synthesis of β-substituted amino acids. However, there are few examples of biocatalytic N-substitution reactions to make α,β-diamino acids. In this study, we used directed evolution to engineer the β-subunit of tryptophan synthase, TrpB, for improved activity with diverse amine nucleophiles. Mechanistic analysis shows that high yields are hindered by product re-entry into the catalytic cycle and subsequent decomposition. Additional equivalents of l -serine can inhibit product reentry through kinetic competition, facilitating preparative scale synthesis. We show β-substitution with a dozen aryl amine nucleophiles, including demonstration on a gram scale. These transformations yield an underexplored class of amino acids that can serve as unique building blocks for chemical biology and medicinal chemistry.     

Enantioselective Hydrosilylation of β,β-Disubstituted Enamides to Construct α-Aminosilanes with Vicinal Stereocenters

Despite the advances in the area of catalytic alkene hydrosilylation, the enantioselective hydrosilylation of alkenes bearing a heteroatom substituent is scarce. Here we report a rhodium-catalyzed hydrosilylation of β,β-disubstituted enamides to directly afford valuable α-aminosilanes in a highly regio-, diastereo-, and enantioselective manner. Stereodivergent synthesis could be achieved by regulating substrate geometry and ligand configuration to generate all the possible stereoisomers in high enantio-purity.     

Two improved formulations for the minimum latency problem

In network problems, latency is associated with the metric used to evaluate the length of the path from a root vertex to each vertex in the network. In this work we are dealing with two applications or variations of the minimum latency problem known as the repairman problem and the deliveryman problem. We have developed two integer formulations for the minimum latency problem and compared them with other two formulations from the literature for the time-dependent traveling salesman problem. The present work highlights the similarities and differences between the different formulations. In addition, we discuss the convenience of including a set of constraints in order to reduce the computation time needed to reach the optimal solution. We have carried out extensive computational experimentation on asymmetrical instances, since they provide the characteristics of the deliveryman and repairman problems in a better way.     

First total synthesis of two new heterocyclic compounds:Bretschneiderazines A and B

Facile synthesis of the two new natural heterocyclic compounds bretschneiderazines A（2） and B（3）,isolated from an extract of the stems of Bretschneidera sinensis,is reported.We employed the cyclization reaction of benzamide by directed lithiation and sequential treatment with sulfur and phosgene as key steps.All new compounds have been fully characterized by means of IR,¹H NMR,¹³C NMR,and HRMS.     

Estimates for eigenvalues of stochastic matrices

It is well-known that the eigenvalues of stochastic matrices lie in the unit circle and at least one of them has the value one. Let {1, r 2 , ··· , r N } be the eigenvalues of stochastic matrix X of size N × N . We will present in this paper a simple necessary and sufficient condition for X such that |r j | < 1, j = 2, ··· , N . Moreover, such condition can be very quickly examined by using some search algorithms from graph theory.