Invariant discrete flows

In this paper, we investigate the evolution of joint invariants under invariant geometric flows using the theory of equivariant moving frames and the induced invariant discrete variational complex. For certain arc length preserving planar curve flows invariant under the special Euclidean group , the special linear group , and the semidirect group , we find that the induced evolution of the discrete curvature satisfies the differential‐difference mKdV, KdV, and Burgers' equations, respectively. These three equations are completely integrable, and we show that a recursion operator can be constructed by precomposing the characteristic operator of the curvature by a certain invariant difference operator. Finally, we derive the constraint for the integrability of the discrete curvature evolution to lift to the evolution of the discrete curve itself.     

Molecular dynamics of the intramolecular 1, 3-dipolar ene reaction of a nitrile oxide and an alkene: non-statistical behavior of a reaction involving a diradical intermediate*

ABSTRACT

Potential energy surfaces and molecular dynamics of the intramolecular 1, 3-dipolar cycloaddition and ene reaction of a nitrile oxide with an alkene were performed in the gas phase and in dichloromethane with density functional theory. One hundred trajectories were propagated in the gas phase and in dichloromethane, respectively. Twenty percent of the trajectories in the gas phase involve bicyclic intermediate and the mean time gap is 472fs. A dynamically stepwise reaction is observed. In dichloromethane, more reactive trajectories were obtained and the time gap is larger than that in the gas phase.     

The maximum multiplicity of the largest k-th eigenvalue in a matrix whose graph is acyclic or unicyclic

Given a graph $G$ we are interested in studying the symmetric matrices associated to $G$ with a fixed number of negative eigenvalues. For this class of matrices we focus on the maximum possible nullity. For trees this parameter has already been studied and plenty of applications are known. In this work we derive a formula for the maximum nullity and completely describe its behavior as a function of the number of negative eigenvalues. In addition, we also carefully describe the matrices associated with trees that attain this maximum nullity. The analysis is then extended to the more general class of unicyclic graphs. Further our work is applied to re-describing all possible partial inertias associated with trees, and is employed to study an instance of the inverse eigenvalue problem for certain trees.     

Oxidative dehydrogenation of n-octane over a vanadium–magnesium oxide catalyst: Influence of the gas hourly space velocity

Oxidative dehydrogenation (ODH) of n-octane was carried out over a vanadium–magnesium oxide catalyst in a continuous flow fixed bed reactor. The catalyst was characterized by ICP–OES, powder XRD and SEM. The catalytic tests were carried out at different gas hourly space velocities (GHSVs), viz. 4000, 6000, 8000, and 10,000 h^?1. The best selectivity for octenes was obtained at the GHSV of 8000 h^?1, while that for C8 aromatics was attained at the GHSV of 6000 h^?1 at high temperatures (500 and 550 °C). The catalytic testing at the GHSV of 10,000 h^?1 showed the lowest activity, while that at the GHSV of 4000 h^?1 consistently showed the lowest ODH selectivity. Generally, the best ODH performance was obtained by the catalytic testing at the GHSVs of 6000 and 8000 h^?1. No phasic changes were observed after the catalytic testing.     

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.     

Preparation,structure elucidation,and antioxidant activity of new bis(thiosemicarbazone) derivatives

Schiff-base–bearing new bis(thiosemicarbazone) derivatives were prepared from terephthalaldehyde and various thiosemicarbazides. FT–IR, ¹H NMR, ¹³C NMR, and UV–Vis spectroscopic methods and elemental analysis were used to elucidate the identification of the synthesized molecules. The in vitro antioxidant activity of the synthesized compounds was analysed with the 1,1-diphenyl-2-picryl hydrazyl free-radical–trapping process. The synthesized compounds exhibited lower antioxidant activity than the standard ascorbic acid. IC₅₀ values of the synthesized molecules measured from 3.81 ± 0.01 to 29.05 ± 0.11 μM. Among the synthesized compounds, compound 3 had the best antioxidant activity. Moreover, this study explained the structure–activity relationship of the synthesized molecules with different substituents in radical trapping reactions.     

Distinguishability and Disturbance in the Quantum Key Distribution Protocol Using the Mean Multi-Kings’ Problem

We introduce a quantum key distribution protocol using mean multi-kings’ problem. Using this protocol, a sender can share a bit sequence as a secret key with receivers. We consider a relation between information gain by an eavesdropper and disturbance contained in legitimate users’ information. In BB84 protocol, such relation is known as the so-called information disturbance theorem. We focus on a setting that the sender and two receivers try to share bit sequences and the eavesdropper tries to extract information by interacting legitimate users’ systems and an ancilla system. We derive trade-off inequalities between distinguishability of quantum states corresponding to the bit sequence for the eavesdropper and error probability of the bit sequence shared with the legitimate users. Our inequalities show that eavesdropper’s extracting information regarding the secret keys inevitably induces disturbing the states and increasing the error probability.