Nonlinear stochastic differential equations containing generalized delta processes

In this paper, some classes of nonlinear stochastic differential equations involving the generalized delta process and its derivatives are considered in the framework of the Colombeau generalized stochastic process theory. All initial problems considered are proven to have a unique unbiased solution. Several examples are exposed that provide more insight into the assumptions made in the theorems.     

A LFER Kinetic Study of The Reaction of 5‐Substituted Orotic Acids with Diazodiphenylmethane

Linear free energy relationships (LFER) were applied to the kinetic data for the reaction of 5‐substituted orotic acids, series 1 , with diazodiphenylmethane (DDM) in N,N–dimethylformamide and compared with results obtained for 2‐substituted benzoic acids, series 2 . The correlation analysis of the kinetic data with σ substituent parameters was carried out using SSP (single substituent parameter) methods. From the sign and value of proportinality constant ρ, lower sensitivity to the substituent effect was obtained in series 1 , 0.876, than in the series 2 , 1.877. Evaluation of substituent “ortho‐effect” was performed using the Charton model, which includes the steric substituent parameter, and Fujita and Nishioka's model, which describes the total ortho‐effect as contribution of ordinary polar effect, the ortho‐steric and ortho‐polar effects. Results of correlations, obtained by using the Charton model, showed highest contribution of the polar effect, 0.861 vs. 2.101, whereas the steric effect is of lowest significance, 0.117 vs. 0.055, for series 1 and 2 , respectively. Also, a low negative value of coefficient with the steric effect, –0.08, obtained from the Fujita–Nishioka model indicated low steric effect, influencing a decrease of the reaction rate in series 1 . The structural and substituent effects were also studied by using the density functional theory method, and together with kinetic data, it gave a better insight into the influence of the effect of both geometry and substituent on the π?electron density shift induced reactivity of investigated acids.     

Cavity cooling of atoms: within and without a cavity

We compare the efficiencies of two optical cooling schemes, where a single particle is either inside or outside an optical cavity, under experimentally-realisable conditions. We evaluate the cooling forces using the general solution of a transfer matrix method for a moving scatterer inside a general one-dimensional system composed of immobile optical elements. Assuming the same atomic saturation parameter, we find that the two cooling schemes provide cooling forces and equilibrium temperatures of comparable magnitude.     

Stress clamp experiments on multicellular tumor spheroids

The precise role of the microenvironment on tumor growth is poorly understood. Whereas the tumor is in constant competition with the surrounding tissue, little is known about the mechanics of this interaction. Using a novel experimental procedure, we study quantitatively the effect of an applied mechanical stress on the long-term growth of a spheroid cell aggregate. We observe that a stress of 10 kPa is sufficient to drastically reduce growth by inhibition of cell proliferation mainly in the core of the spheroid. We compare the results to a simple numerical model developed to describe the role of mechanics in cancer progression.     

Partitioning infinite trees

A graph G is bisectable if its edges can be colored by two colors so that the resulting monochromatic subgraphs are isomorphic. We show that any infinite tree of maximum degree Δ with infinitely many vertices of degree at least Δ −1 is bisectable as is any infinite tree of maximum degree Δ ≤ 4. Further, it is proved that every infinite tree T of finite maximum degree contains a finite subset E of its edges so that the graph T − E is bisectable. To measure how “far” a graph G is from being bisectable, we define c(G) to be the smallest number k > 1 so that there is a coloring of the edges of G by k colors with the property that any two monochromatic subgraphs are isomorphic. An upper bound on c(G), which is in a sense best possible, is presented. © 2000 John Wiley & Sons, Inc. J Graph Theory 34: 113–127, 2000     

A combinatorial problem related to sparse systems of equations

Nowadays sparse systems of equations occur frequently in science and engineering. In this contribution we deal with sparse systems common in cryptanalysis. Given a cipher system, one converts it into a system of sparse equations, and then the system is solved to retrieve either a key or a plaintext. Raddum and Semaev proposed new methods for solving such sparse systems common in modern ciphers which are combinations of linear layers and small S-boxes. It turns out that the solution of a combinatorial MaxMinMax problem provides an upper bound on the average computational complexity of those methods. In this paper we initiate the study of a linear algebra variation of the MaxMinMax problem. The complexity bound proved in this paper significantly overcomes conjectured complexity bounds for Gröbner basis type algorithms.     

A new approach to live reaction monitoring using active flow technology in ultra‐high‐speed HPLC with mass spectral detection

A new type of chromatography column referred to as a parallel segmented flow (PSF) column enables ultra‐high‐speed high‐performance liquid chromatography‐MS to be undertaken. This occurs because the separation efficiency obtained on PSF columns has been shown in prior studies to be superior to conventional columns, and the flow stream is split radially inside the outlet end fitting of the column, rather than in an axial post‐column flow stream split. As a result, the flow through the column can be five times higher than the flow through the MS. In this work, the degradation of amino acids in dilute nitric acid was used to illustrate the process. Separations were obtained in less than 12 s, although the reinjection process was initiated 6 s after the previous injection. The degradation rate constant of tryptophan, in the presence of tyrosine and phenylalanine, was determined. Copyright © 2015 John Wiley & Sons, Ltd.