Liouville–Green (WKB) asymptotics for almost-diagonal linear second-order matrix difference equations

A Liouville–Green (or WKB) asymptotic approximation theory is developed for a class of almost-diagonal (‘asymptotically diagonal’) linear second-order matrix difference equations. Rigorous and explicitly computable bounds for the error terms are obtained, the asymptotics being made with respect to both, the index and some parameter affecting the equation. The case of the associated inhomogeneous equations is also considered in detail. Some examples and a number of applications are presented for the purpose of illustration.     

Online induction heating for determination of isotope composition of woody stem water with laser spectrometry: a methods assessment

Application of stable isotopes of water to studies of plant–soil interactions often requires a substantial preparatory step of extracting water from samples without fractionating isotopes. Online heating is an emerging approach for this need, but is relatively untested and major questions of how to best deliver standards and assess interference by organics have not been evaluated. We examined these issues in our application of measuring woody stem xylem of sagebrush using a Picarro laser spectrometer with online induction heating. We determined (1) effects of cryogenic compared to induction-heating extraction, (2) effects of delivery of standards on filter media compared to on woody stem sections, and (3) spectral interference from organic compounds for these approaches (and developed a technique to do so). Our results suggest that matching sample and standard media improves accuracy, but that isotopic values differ with the extraction method in ways that are not due to spectral interference from organics.     

Mechanistic aspects on molecular structure formation of polymeric networks from diisocyanates with amidine compounds

Polymeric networks are produced by step‐growth polyaddition and co‐polyaddition reactions of 1‐ethylimidazoline in combination with various diisocyanates. Five aromatic, two aliphatic diisocyanates and a polyurethane prepolymer are used as particular reactant in N,N‐dimethylformamide as solvent at room temperature. Obviously, 1‐ethylimidazoline can serve as trifunctional monomer, which enables a crosslinking reaction with diisocyanates. Molecular structure elements of the polymeric networks were studied by solid state 13C‐NMR spectroscopy revealing that detailed molecular structure formations are determined whether aromatic or aliphatic diisocyanates are used. Quantum chemical calculations were used as supporting method to elucidate the complex reaction cascades. Hence, it can be shown that beside 3:1 stoichiometric structures 2:1 based structures are formed as well. These structures are observed as kinetically controlled products only when aromatic diisocyanate monomers are used. © 2018 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2018 , 56, 977–985     

Double Aztec diamonds and the tacnode process

Discrete and continuous non-intersecting random processes have given rise to critical “infinite-dimensional diffusions”, like the Airy process, the Pearcey process and variations thereof. It has been known that domino tilings of very large Aztec diamonds lead macroscopically to a disordered region within an inscribed ellipse (arctic circle in the homogeneous case), and a regular brick-like region outside the ellipse. The fluctuations near the ellipse, appropriately magnified and away from the boundary of the Aztec diamond, form an Airy process, run with time tangential to the boundary.     

Quantum Pfaffians and hyper-Pfaffians

The concept of the quantum Pfaffian is rigorously examined and refurbished using the new method of quantum exterior algebras. We derive a complete family of Plücker relations for the quantum linear transformations, and then use them to give an optimal set of relations required for the quantum Pfaffian. We then give the formula between the quantum determinant and the quantum Pfaffian and prove that any quantum determinant can be expressed as a quantum Pfaffian. Finally the quantum hyper-Pfaffian is introduced, and we prove a similar result of expressing quantum determinants in terms of quantum hyper-Pfaffians at modular cases.     

Review of wavelet methods for the solution of reaction–diffusion problems in science and engineering

Wavelet method is a recently developed tool in applied mathematics. Investigation of various wavelet methods, for its capability of analyzing various dynamic phenomena through waves gained more and more attention in engineering research. Starting from ‘offering good solution to differential equations’ to capturing the nonlinearity in the data distribution, wavelets are used as appropriate tools at various places to provide good mathematical model for scientific phenomena, which are usually modeled through linear or nonlinear differential equations. Review shows that the wavelet method is efficient and powerful in solving wide class of linear and nonlinear reaction–diffusion equations. This review intends to provide the great utility of wavelets to science and engineering problems which owes its origin to 1919. Also, future scope and directions involved in developing wavelet algorithm for solving reaction–diffusion equations are addressed.     

Intermolecular Stetter reaction of aromatic aldehydes with (E)-(2-nitrovinyl)cyclohexane induced by N-heterocyclic carbene and thiourea

Intermolecular Stetter reaction of aromatic aldehydes with (E)-(2-nitrovinyl)cyclohexane catalyzed by thiazolium A has been developed. The reaction rate and efficiency are profoundly impacted by the presence of thiourea B. The reaction affords moderate to good yields of the Stetter product. Some factors influencing yield were discussed.     

The derivation of the conservation law for defocusing nonlinear Schrödinger equations with non-vanishing initial data at infinity

For nonlinear Schrödinger equations in less than or equal to four dimension, with non-vanishing initial data at infinity, a new approach to derive the conservation law is obtained. Since this approach does not contain approximating procedure, the argument is simplified and some of technical assumption of the nonlinearity to derive the conservation law and time global solutions, is removed.     

Robust multilevel methods for quadratic finite element anisotropic elliptic problems

This paper discusses a class of multilevel preconditioners based on approximate block factorization for conforming finite element methods employing quadratic trial and test functions. The main focus is on diffusion problems governed by a scalar elliptic partial differential equation with a strongly anisotropic coefficient tensor. The proposed method provides a high robustness with respect to non‐grid‐aligned anisotropy, which is achieved by the interaction of the following components: (i) an additive Schur complement approximation to construct the coarse‐grid operator; (ii) a global block (Jacobi or Gauss–Seidel) smoother complementing the coarse‐grid correction based on (i); and (iii) utilization of an augmented coarse grid, which enhances the efficiency of the interplay between (i) and (ii). The performed analysis indicates the high robustness of the resulting two‐level method. Moreover, numerical tests with a nonlinear algebraic multilevel iteration method demonstrate that the presented two‐level method can be applied successfully in the recursive construction of uniform multilevel preconditioners of optimal or nearly optimal order of computational complexity. Copyright © 2013 John Wiley & Sons, Ltd.