Amide-Directed C−H Sodiation by a Sodium Hydride/Iodide Composite

A new protocol for amide-directed ortho and lateral C−H sodiation is enabled by sodium hydride (NaH) in the presence of either sodium iodide (NaI) or lithium iodide (LiI). The transient organosodium intermediates could be transformed into functionalized aromatic compounds.     

pH-Sensitive Oscillatory Motion of a Urease Motor on the Urea Aqueous Phase

A self-propelled object coupled with an enzyme reaction between urease and urea was investigated at the air/aqueous interface. A plastic object that was fixed to a urease-immobilized filter paper was used as a self-propelled object, termed a urease motor, placed on an aqueous urea solution. The driving force of the urease motor is the difference in the surface tension around the object. Oscillatory motion or no motion was triggered depending on the initial pH of the urea solution. Both the frequency and maximum speed of the oscillatory motion varied depending on the initial pH of the water phase. The mechanisms underlying the oscillatory motion and no motion were discussed in relation to the bell-shaped enzyme activity of urease in the enzyme reaction and the surface tension around the urease motor.     

Normalizing and variance stabilizing transformations for intraclass correlations

Summary A concept of normalizing transformations of statistics is constructed on the basis of the rate of convergence to normality. The concept is applied to derive a normalizing transformation of a maximum likelihood estimate of intraclass correlation coefficient in ap-variate normal sample. Numerical comparisons are made to examine whether the proposed transformation is efficient to achieve normality. The relationship between normalization and variance stabilization is also considered. The Institute of Statistical Mathematics     

Numerical simulation of free surface flows with the level set method using an extremely high-order accuracy WENO advection scheme

Three-dimensional dynamic gas–liquid flow simulations that accurately track the phase interface are numerically challenging. This article presents a numerical study of the performance of the level-set phase–interface tracking method when combined with extremely high order (7th to 11th) weighted essentially non-oscillatory (WENO) advection schemes for gas–liquid free surface flows. Comparisons between simulation results and prior benchmark results suggest that such a combination of methods can be satisfactorily applied to the level-set and Navier-Stokes equations for free surface flow simulations when volume conservation is enforced at every time step, and minor numerical oscillations are suppressed through use of an artificial viscosity term. In particular, simulations of solid body rotation, the unsteady flow following an ideal dam break, tank sloshing, and the rise of a single bubble all agree with analytical or experimental results to within ± 3.12% when the level-set method is combined with an 11th order WENO scheme. Furthermore, use of an 11th order WENO advection scheme actually has a computational cost advantage because, for the same accuracy, it can be used on a coarser grid when compared with a more-common second-order advection scheme; computational savings of up to 87% are possible.     

Discreteness and rationality of F-jumping numbers on singular varieties

We prove that the F-jumping numbers of the test ideal t(X; D, \mathfraka^t){\tau(X; \Delta, \mathfrak{a}^t)} are discrete and rational under the assumptions that X is a normal and F-finite scheme over a field of positive characteristic p, K _X  + Δ is \mathbb Q{\mathbb {Q}}-Cartier of index not divisible p, and either X is essentially of finite type over a field or the sheaf of ideals \mathfraka{\mathfrak{a}} is locally principal. This is the largest generality for which discreteness and rationality are known for the jumping numbers of multiplier ideals in characteristic zero.     

Compact directed acyclic word graphs for a sliding window

Suffix trees are a well-known and widely-studied data structure highly useful for string matching. The suffix tree of a string w can be constructed in O(n) time and space, where n denotes the length of w. Larsson achieved an efficient algorithm to maintain suffix trees for a sliding window. It contributes to prediction by partial matching (PPM) style statistical data compression scheme. Compact directed acyclic word graphs (CDAWGs) are a more space-economical data structure for indexing strings. In this paper we propose a linear-time algorithm to maintain CDAWGs for a sliding window.     

When does the subadditivity theorem for multiplier ideals hold?

Demailly, Ein and Lazarsfeld proved the subadditivity theorem for multiplier ideals on nonsingular varieties, which states the multiplier ideal of the product of ideals is contained in the product of the individual multiplier ideals. We prove that, in the two-dimensional case, the subadditivity theorem holds on log terminal singularities. However, in the higher dimensional case, we have several counterexamples. We consider the subadditivity theorem for monomial ideals on toric rings and construct a counterexample on a three-dimensional toric ring.

     

Stochastic phase lockings in a relaxation oscillator forced by a periodic input with additive noise: A first-passage-time approach

Noise effects on phase lockings in a system consisting of a piecewise-linear van der Pol relaxation oscillator driven by a periodic input are studied. The problem of finding the period of the oscillator is reduced to the first-passage-time problem of the Ornstein-Uhlenbeck process with time-varying boundary. The probability density functions of the first-passage time are used to define the operator which governs a transition of an input phase density after one cycle of the oscillator. Phase lockings in a stochastic sense are investigated on the basis of the density evolution by the operator.