Synthesis of Amides and Esters by Palladium(0)-Catalyzed Carbonylative C(sp3)−H Activation

The 1,4-palladium shift strategy allows the functionalization of remote C−H bonds that are difficult to reach directly. Reported here is a domino reaction proceeding by C(sp³)−H activation, 1,4-palladium shift, and amino- or alkoxycarbonylation, which generates a variety of amides and esters bearing a quaternary β-carbon atom. Mechanistic studies showed that the aminocarbonylation of the σ-alkylpalladium intermediate arising from the palladium shift is fast using PPh₃ as the ligand, and leads to the amide rather than the previously reported indanone product.     

Abnormal blueshift of UV emission in single-crystalline ZnO nanowires

Single-crystalline ZnO nanowires (NWs) were synthesized by a facile vapor transport method. The good orientation and high crystal quality were characterized by X-ray diffraction (XRD), scanning electron microscope (SEM) and high-resolution transmission electron microscope (HRTEM) measurements. Excitation-power-dependence photoluminescence spectra of ZnO NWs show that the UV emission displayed an evident blueshift with increasing excitation power and the corresponding energy shift might be as large as 10 meV. This anomalous phenomenon correlates to the band bending level caused by the surface built-in electric field due to the existence of substantial oxygen vacancies. By increasing the excitation power, the enhanced neutralization effect near the surface will reduce the built-in electric field and lead to a reduction of band bending which triggers the blueshift of the UV emission.     

Sequential location-allocation problems on chains and trees with probabilistic link demands

In this paper, we consider multiperiod minisum location problems on networks in which demands can occur continuously on links according to a uniform probability density function. In addition, demands may change dynamically over time periods and at most one facility can be located per time period. Two types of networks are considered in conjunction with three behavioral strategies. The first type of network discussed is a chain graph. A myopic strategy and long-range strategy for locatingp-facilities are considered, as is a discounted present worth strategy for locating two facilities. Although these problems are generally nonconvex, effective methods are developed to readily identify all local and global minima. This analysis forms the basis for similar problems on tree graphs. In particular, we construct algorithms for the 3-facility myopic problem and the 2-facility long-range and discounted cost problems on a tree graph. Extensions and suggestions for further research on problems involving more general networks are provided.     

A Necessary and Sufficient Proximity Condition for Smoothness Equivalence of Nonlinear Subdivision Schemes

In the recent literature on subdivision methods for approximation of manifold-valued data, a certain “proximity condition” comparing a nonlinear subdivision scheme to a linear subdivision scheme has proved to be a key analytic tool for analyzing regularity properties of the scheme. This proximity condition is now well known to be a sufficient condition for the nonlinear scheme to inherit the regularity of the corresponding linear scheme (this is called smoothness equivalence). Necessity, however, has remained an open problem. This paper introduces a smooth compatibility condition together with a new proximity condition (the differential proximity condition). The smooth compatibility condition makes precise the relation between nonlinear and linear subdivision schemes. It is shown that under the smooth compatibility condition, the differential proximity condition is both necessary and sufficient for smoothness equivalence. It is shown that the failure of the proximity condition corresponds to the presence of resonance terms in a certain discrete dynamical system derived from the nonlinear scheme. Such resonance terms are then shown to slow down the convergence rate relative to the convergence rate of the corresponding linear scheme. Finally, a super-convergence property of nonlinear subdivision schemes is used to conclude that the slowed decay causes a breakdown of smoothness. The proof of sufficiency relies on certain properties of the Taylor expansion of nonlinear subdivision schemes, which, in addition, explain why the differential proximity condition implies the proximity conditions that appear in previous work.     

On the optimization of two-class work-conserving parameterized scheduling policies

Numerous scheduling policies are designed to differentiate quality of service for different applications. Service differentiation can in fact be formulated as a generalized resource allocation optimization towards the minimization of some important system characteristics. For complex scheduling policies, however, optimization can be a demanding task, due to the difficult analytical analysis of the system at hand. In this paper, we study the optimization problem in a queueing system with two traffic classes, a work-conserving parameterized scheduling policy, and an objective function that is a convex combination of either linear, convex or concave increasing functions of given performance measures of both classes. In case of linear and concave functions, we show that the optimum is always in an extreme value of the parameter. Furthermore, we prove that this is not necessarily the case for convex functions; in this case, a unique local minimum exists. This information greatly simplifies the optimization problem. We apply the framework to some interesting scheduling policies, such as Generalized Processor Sharing and semi-preemptive priority scheduling. We also show that the well-documented \(c\mu \)-rule is a special case of our framework.     

The diameter of a random subgraph of the hypercube

In this paper we present an estimation for the diameter of random subgraph of a hypercube. In the article by A. V. Kostochka (Random Struct Algorithms 4 (1993) 215–229) the authors obtained lower and upper bound for the diameter. According to their work, the inequalities n + m_p ≤ D(G_n) ≤ n + m_p + 8 almost surely hold as n → ∞, where n is dimension of the hypercube and m_p depends only on sampling probabilities. It is not clear from their work, whether the values of the diameter are really distributed on these 9 values, or whether the inequality can be sharpened. In this paper we introduce several new ideas, using which we are able to obtain an exact result: D(G_n) = n + m_p (almost surely). © 2012 Wiley Periodicals, Inc. Random Struct. Alg., 2012     

Direct Likelihood Evaluation for the Renewal Hawkes Process

An interesting extension of the widely applied Hawkes self-exiting point process, the renewal Hawkes (RHawkes) process, was recently proposed by Wheatley, Filimonov, and Sornette, which has the potential to significantly widen the application domains of the self-exciting point processes. However, they claimed that computation of the likelihood of the RHawkes process requires exponential time and therefore is practically impossible. They proposed two expectation–maximization (EM) type algorithms to compute the maximum likelihood estimator (MLE) of the model parameters. Because of the fundamental role of likelihood in statistical inference, a practically feasible method for likelihood evaluation is highly desirable. In this article, we provide an algorithm that evaluates the likelihood of the RHawkes process in quadratic time, a drastic improvement from the exponential time claimed by Wheatley, Filimonov, and Sornette. We demonstrate the superior performance of the resulting MLEs of the model relative to the EM estimators through simulations. We also present a computationally efficient procedure to calculate the Rosenblatt residuals of the process for goodness-of-fit assessment, and a simple yet efficient procedure for future event prediction. The proposed methodologies were applied on real data from seismology and finance. An R package implementing the proposed methodologies is included in the supplementary materials.     

Moufang sets of mixed type F4

Moufang sets were introduced by Jacques Tits in order to understand isotropic linear algebraic groups of relative rank one, but the notion is more general. We describe a new class of Moufang sets, arising from so‐called mixed groups of type ${\mathsf{F}}_4$ in characteristic 2, obtained as the fixed point set under a suitable involution.     

The Farrell–Jones Conjecture for the solvable Baumslag–Solitar groups

In this paper, we prove the Farrell–Jones Conjecture for the solvable Baumslag–Solitar groups with coefficients in an additive category. We also extend our results to groups of the form, Z[1/p] semidirect product with any virtually cyclic group, where p is a prime number.