Nonexistence results for higher order pseudo‐parabolic equations in the Heisenberg group

Sufficient conditions are obtained for the nonexistence of solutions to the nonlinear higher order pseudo‐parabolic equation where is the Kohn‐Laplace operator on the (2N + 1)‐dimensional Heisenberg group , m≥1,p > 1. Then, this result is extended to the case of a 2 × 2‐system of the same type. Our technique of proof is based on judicious choices of the test functions in the weak formulation of the sought solutions. Copyright © 2016 John Wiley & Sons, Ltd.     

Some approximation results involving the q‐Szász–Mirakjan–Kantorovich type operators via Dunkl's generalization

The purpose of this paper is to introduce a family of q‐Szász–Mirakjan–Kantorovich type positive linear operators that are generated by Dunkl's generalization of the exponential function. We present approximation properties with the help of well‐known Korovkin's theorem and determine the rate of convergence in terms of classical modulus of continuity, the class of Lipschitz functions, Peetre's K‐functional, and the second‐order modulus of continuity. Furthermore, we obtain the approximation results for bivariate q‐Szász–Mirakjan–Kantorovich type operators that are also generated by the aforementioned Dunkl generalization of the exponential function. Copyright © 2017 John Wiley & Sons, Ltd.     

On Inclusion Properties of Two Versions of Orlicz–Morrey Spaces

There are two versions of Orlicz–Morrey spaces (on \({\mathbb {R}}^n\)), defined by Nakai in 2004 and by Sawano, Sugano, and Tanaka in 2012. In this paper, we discuss the inclusion properties of these two spaces and compare the results. Computing the norms of the characteristic functions of balls in \({\mathbb {R}}^n\) is one of the keys to our results. Similar results for weak Orlicz–Morrey spaces of both versions are also obtained.     

A computational mechanistic study of the deamination reaction of melamine

A detailed computational study of the deamination reaction of melamine by OH^–, n H₂O/OH^–, n H₂O (where n = 1, 2, 3), and protonated melamine with H₂O, has been carried out using density functional theory and ab initio calculations. All structures were optimized at M06/6‐31G(d) level of theory, as well as with the B3LYP functional with each of the basis sets: 6‐31G(d), 6‐31 + G(d), 6‐31G(2df,p), and 6‐311++G(3df,3pd). B3LYP, M06, and ω B97XD calculations with 6‐31 + G(d,p) have also been performed. All structures were optimized at B3LYP/6‐31 + G(d,p) level of theory for deamination simulations in an aqueous medium, using both the polarizable continuum solvation model and the solvation model based on solute electron density. Composite method calculations have been conducted at G4MP2 and CBS‐QB3. Fifteen different mechanistic pathways were explored. Most pathways consisted of two key steps: formation of a tetrahedral intermediate and in the final step, an intermediate that dissociates to products via a 1,3‐proton shift. The lowest overall activation energy, 111 kJ mol^?1 at G4MP2, was obtained for the deamination of melamine with 3H₂O/OH^?.     

A Simple Post-Polymerization Modification Method for Controlling Side-Chain Information in Digital Polymers

A three-step post-polymerization modification method was developed for the design of digitally encoded poly(phosphodiester)s with controllable side groups. Sequence-defined precursors were synthesized, either manually on polystyrene resins or automatically on controlled pore glass supports, using two phosphoramidite monomers containing either terminal alkynes or triisopropylsilyl (TIPS) protected alkyne side groups. Afterwards, these polymers were modified by stepwise copper-catalyzed azide–alkyne cycloaddition (CuAAC). The terminal alkynes were first reacted with a model azide compound, and after removal of the TIPS groups, the remaining alkynes were reacted with another organic azide. This simple method allows for quantitative side-chain modification, thus opening up interesting avenues for the preparation of a wide variety of digital polymers.     

Bootstrap in supersymmetric Liouville field theory. I. NS sector

A four point function of basic Neveu–Schwarz exponential fields is constructed in the N=1$N=1$ supersymmetric Liouville field theory. Although the basic NS structure constants were known previously, we present a new derivation, based on a singular vector decoupling in the NS sector. This allows to stay completely inside the NS sector of the space of states, without referencing to the Ramond fields. The four-point construction involves also the NS blocks, for which we suggest a new recursion representation, the so-called elliptic one. The bootstrap conditions for this four point correlation function are verified numerically for different values of the parameters.     

Quantum Bohmian model for financial market

We apply methods of quantum mechanics for mathematical modeling of price dynamics at the financial market. The Hamiltonian formalism on the price/price-change phase space describes the classical-like evolution of prices. This classical dynamics of prices is determined by “hard” conditions (natural resources, industrial production, services and so on). These conditions are mathematically described by the classical financial potential V(q),$V(q),$ where q=(_q1,…,_qn)$q=(q_1,\dots ,q_n)$ is the vector of prices of various shares. But the information exchange and market psychology play important (and sometimes determining) role in price dynamics. We propose to describe such behavioral financial factors by using the pilot wave (Bohmian) model of quantum mechanics. The theory of financial behavioral waves takes into account the market psychology. The real trajectories of prices are determined (through the financial analogue of the second Newton law) by two financial potentials: classical-like V(q)$V(q)$ (“hard” market conditions) and quantum-like U(q)$U(q)$ (behavioral market conditions).     

Precursor-directed biosynthesis of nonribosomal lipopeptides with modified glutamate residues

Precursor-directed biosynthesis of calcium dependent antibiotics (CDAs) with modified 3-trifluoromethyl and 3-ethyl glutamate residues was achieved by feeding synthetic glutamate analogues to a mutant strain of Streptomyces coelicolor impaired in the biosynthesis of the natural precursor (2S,3R)-3-methyl glutamic acid.     

Estimation of the Polymerization Rate of Liquid Propylene Using Adiabatic Reaction Calorimetry and Reaction Dilatometry

The use of pressure‐drop and constant‐pressure dilatometry for obtaining rate data for liquid propylene polymerization in filled batch reactors was examined. The first method uses reaction temperature and pressure as well as the compressibility of the reactor contents to calculate the polymerization rate; in the second, the polymerization rate is calculated from the monomer feed rate to the reactor. Estimated polymerization rates compare well to those obtained using the well‐developed isoperibolic calorimetry technique, besides pressure‐drop dilatometry provides more kinetic information during the initial stages of the polymerization than the other methods.

     

Single‐Walled TiO2 Nanotubes: Enhanced Carrier‐Transport Properties by TiCl4 Treatment

In the present work we report significant enhancement of the photoelectrochemical properties of self‐ organized TiO₂ nanotubes by a combined “de‐coring” of classic nanotubes followed by an appropiate TiCl4 treatment. We show that, except for the expected particle decoration, a key effect of the TiCl4 treatment is that the electron transport characteristics in TiO₂ nanotubes can be drastically improved, for example, we observe an enhancement of up to 70 % in electron‐transport times.