New lower bounds on the radius of spatial analyticity for the KdV equation

The radius of spatial analyticity for solutions of the KdV equation is studied. It is shown that the analyticity radius does not decay faster than $t^{?1/4}$ as time t goes to infinity. This improves the works of Selberg and da Silva (2017) [30] and Tesfahun (2017) [34]. Our strategy mainly relies on a higher order almost conservation law in Gevrey spaces, which is inspired by the I-method.     

Synthesis of Highly Functionalized N,N-Diarylamides by an Anodic C,N-Coupling Reaction

We report an innovative, sustainable and straightforward protocol for the synthesis of N,N-diarylamides equipped with nonprotected hydroxyl groups by using electrosynthesis. The concept allows the application of various substrates furnishing diarylamides with yields up to 57 % within a single and direct electrolytic protocol. The method is thereby easy to conduct in an undivided cell with constant current conditions offering a versatile and short-cut alternative to conventional pathways.     

Kinetics and mechanism of trichloroisocyanuric acid/NaNO2-triggered nitration of aromatic compounds under acid-free and Vilsmeier-Haack conditions

Kinetics and mechanism of nitration of aromatic compounds using trichloroisocyanuric acid (TCCA)/NaNO₂, TCCA-N,N-dimethyl formamide (TCCA-DMF)/NaNO₂, and TCCA-N,N-dimethyl acetamide (TCCA-DMA)/NaNO₂ under acid-free and Vilsmeier-Haack conditions. Reactions followed second-order kinetics with a first-order dependence on [Phenol] and [Nitrating agent] ([TCCA], [(TCCA-DMF)], or [(TCCA-DMA)] >> [NaNO₂]). Reaction rates accelerated with the introduction of electron-donating groups and retarded with electron-withdrawing groups, but did not fit well into the Hammett's theory of linear free energy relationship or its modified forms like Brown-Okamoto or Yukawa-Tsuno equations. Rate data were analyzed by Charton's multiple linear regression analysis. Isokinetic temperature (β) values, obtained from Exner's theory for different protocols, are 403.7 K (TCCA-NaNO₂), 365.8 K (TCCA-DMF)/NaNO₂, and 358 K (TCCA-DMA)/NaNO₂. These values are far above the experimental temperature range (303-323 K), indicating that the enthalpy factors are probably more important in controlling the reaction.     

Homogenization of Periodically Heterogeneous Thin Beams

Consider an elastic thin three-dimensional body made of a periodic distribution of elastic inclusions. When both the thickness of the beam and the size of the heterogeneities tend simultaneously to zero the authors obtain three different one-dimensional models of beam depending upon the limit of the ratio of these two small parameters.     

Order-Stability in Complex Biological,Social, and AI-Systems from Quantum Information Theory

This paper is our attempt, on the basis of physical theory, to bring more clarification on the question “What is life?” formulated in the well-known book of Schrödinger in 1944. According to Schrödinger, the main distinguishing feature of a biosystem’s functioning is the ability to preserve its order structure or, in mathematical terms, to prevent increasing of entropy. However, Schrödinger’s analysis shows that the classical theory is not able to adequately describe the order-stability in a biosystem. Schrödinger also appealed to the ambiguous notion of negative entropy. We apply quantum theory. As is well-known, behaviour of the quantum von Neumann entropy crucially differs from behaviour of classical entropy. We consider a complex biosystem S composed of many subsystems, say proteins, cells, or neural networks in the brain, that is, S=(Si). We study the following problem: whether the compound system S can maintain “global order” in the situation of an increase of local disorder and if S can preserve the low entropy while other Si increase their entropies (may be essentially). We show that the entropy of a system as a whole can be constant, while the entropies of its parts rising. For classical systems, this is impossible, because the entropy of S cannot be less than the entropy of its subsystem Si. And if a subsystems’s entropy increases, then a system’s entropy should also increase, by at least the same amount. However, within the quantum information theory, the answer is positive. The significant role is played by the entanglement of a subsystems’ states. In the absence of entanglement, the increasing of local disorder implies an increasing disorder in the compound system S (as in the classical regime). In this note, we proceed within a quantum-like approach to mathematical modeling of information processing by biosystems—respecting the quantum laws need not be based on genuine quantum physical processes in biosystems. Recently, such modeling found numerous applications in molecular biology, genetics, evolution theory, cognition, psychology and decision making. The quantum-like model of order stability can be applied not only in biology, but also in social science and artificial intelligence.     

Novel local smoothness indicators for improving the third‐order WENO scheme

The local smoothness indicators play an important role in the performance of a weighted essentially nonoscillatory (WENO) scheme. Due to having only 2 points available on each substencil, the local smoothness indicators calculated by conventional methods make the third‐order WENO scheme too dissipative. In this paper, we propose a different method to calculate the indicators by using all the 3 points on the global stencil of the third‐order WENO scheme. The numerical results demonstrate that the WENO scheme with the new indicators has less dissipation and better resolution than the conventional third‐order WENO scheme of Jiang and Shu for both smooth and discontinuous solutions.     

Domain decomposition methods in a geometrical multiscale domain using finite volume schemes

The heat equation is solved by using a finite volume discretization in a domain that consists of a two-dimensional central node and several one-dimensional outgoing branches. Several interface connection options to match the submodels set on the node and on the branches, with or without continuity, are looked at. For each of them, a monolithic scheme is defined, and existence and uniqueness of the solution is proved. New schemes are deduced, which are obtained through domain decomposition methods in the form of interface systems, with one or two unknowns per interface. A comparative systematic study is carried out from an algebraic and numerical point of view according to the interface conditions: Dirichlet, Neumann, or Robin. An efficient diagonal preconditioning is proposed.     

The self-assemblies of a newly designed star-shaped molecule end-capped with bromine atoms studied by scanning tunneling microscopy

A new star-shaped molecule StOF-Br_3 containing oligofluorenes and halogen atoms(Bromine) has been synthesized and studied by Scanning Tunneling Microscopy(STM) at the highly oriented pyrolytic graphite(HOPG) surface.We have obtained the high-resolution self-assembled STM images,from which the highly ordered and closely packed non-porous arrangements of the StOF-Br_3 molecular selfassemblies at the heptanoic acid/HOPG surface could be observed.The molecular models and selfassembled StOF-Br_3 architectures have been given in the following text.Besides,we have also figured out the surface free energy by the density functional theory(DFT) calculation,which proved that the halogen...halogen interaction was strong enough to stabilize the ordered molecular self-assemblies.This work verifies the existence of bromine...bromine interactions,and meanwhile provides a kind of effective approach for quickly building ordered molecular nanoarchitectures with large areas and different geometries.