Remote Fluorination and Fluoroalkyl(thiol)ation Reactions

Remote functionalization reactions have the power to transform a C−H (or C−C) bond at a distant position from a functional group. This Review summarizes recent advances and key breakthroughs in remote fluorination, trifluoromethylation, difluoromethylation, trifluoromethylthiolation, and fluoroalkenylation reactions. Several powerful strategies have emerged to control the reactivity and distal selectivity such as the undirected radical approach, the 1,5-hydrogen atom transfer, the metal migration, the use of distant directing groups, and the ring-opening reactions. These unconventional and predictable C−H (and C−C) functionalization transformations should allow for the preparation of a wide range of otherwise-difficult-to-access alkyl, aromatic, heteroaromatic, and structurally complex fluorides.     

Flow auctions

Flow goods (like electricity) are sold through auctions in a dynamic framework. An important design question is the frequency of such auctions. We use a simple dynamic auction model in continuous time to answer this question. We focus on the relationship between the persistency of bidders’ valuations and the optimal choice of frequency. If the seller focuses on the equilibrium in which bidders follow a repeated static Nash strategy, then the frequency of auctions should typically increase when persistency declines. However, accounting for the fact that bidders can follow different equilibria that are collusive in nature, the comparative statics are reversed, forcing the seller to reduce the frequency when bidders’ valuations are less persistent. The argument builds on the fact that high frequency auctions are more conducive to collusion among bidders.     

From crack deflection to lattice vibrations—macro to atomistic examination of dynamic cleavage fracture

A set of cleavage experiments with strip-shaped single-crystal silicon specimens subjected to three-point bending is reported. The experiments enabled examination of the relationships between the dynamic energy release rate, the velocity, the orientation-dependent cleavage energy, and the cleavage plane of propagation.Dynamic crack propagation experiments show that when a [0 0 1] silicon single crystal is fractured under three-point bending at ‘parallel’ velocity (directly measured at the bottom surface of the specimen) of up to , it prefers to cleave along the vertical (1 1 0) plane, while when the specimen is fractured under the same conditions but at a velocity higher than , it cleaves along the inclined (1 1 1) plane. At intermediate velocities, the crack will deflect from the (1 1 0) plane to the (1 1 1) plane. Crack velocity was determined by the initial notch length. The local (calculated) velocity of deflection between the cleavage planes ranges from , for a crack propagating on the (1 1 0) plane in the direction, to about , for a crack on the (1 1 0) plane, but in the [0 0 1] direction.It is suggested that the cause of the deflection phenomenon is the anisotropic, velocity-dependent cleavage energy, resulted phonon radiation caused by anisotropic, velocity-dependent lattice vibrations. We have studied the effect of material properties and propose selection criteria to explain the deflection phenomenon: the crack will deflect to the plane of least-energy, for which G−Γ_i(V)=max, or to the plane with maximum crack tip velocity, V_i(Γ)=max.     

Measurements of anisotropic elastic constants of type 308 stainless-steel electroslag welds

In austenitic-stainless-steel weld metal, mechanical anisotropy is caused by preferred local orientation of elongated subgrains and preferred crystallographic orientation. Ultrasonic and static tensile-test methods used to determine elastic stiffness and compliance matrices, respectively, demonstrated that orthotropic symmetry exists. Inversion of this compliance matrix gave a stiffness matrix which showed general agreement between the two methods. It is suggested that the data can be used directly in finite-element analyses of weldments containing Type 308 stainless steel.     

Fractal porous media II: Geometry of porous geological structures

Some geological structures are analysed and found to be fractal. An interesting feature is the very large range of scales involved; the spreading dimension is also measured for some of them. The consequences of these measurements on the analysis of transport processes in porous media are presented - the existence of fractal structures multiplies the variety of actual porous media.     

Some limit theorems for negatively associated random variables

Let {X _n , n ≥ 1} be a sequence of negatively associated random variables. The aim of this paper is to establish some limit theorems of negatively associated sequence, which include the L ^p -convergence theorem and Marcinkiewicz–Zygmund strong law of large numbers. Furthermore, we consider the strong law of sums of order statistics, which are sampled from negatively associated random variables.