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.     

The effect of cationic groups on the stability of 19F MRI contrast agents in nanoparticles

Fluorine‐19 (¹⁹F)‐based contrast agents are increasingly used for magnetic resonance imaging. Conjugated to polymers, they provide an excellent quantitative imaging tool to detect the movement of the polymeric nanoparticles in vivo as there is no background signal in tissue. One of the challenges is the decline in signal intensity when the conjugated hydrophobic fluorinated functionalities aggregate. Therefore, a new fluorinated monomer was prepared from l ‐arginine that carries a 2,2,2‐trifluoroethyl functional group for imaging. The resulting monomer, 2,2,2‐trifluoroethylamide l ‐arginine methacrylamide (3FArgMA), was copolymerized with poly(ethylene glycol) methyl ether methacrylate (PEGMEMA), [2‐(2,3,4,6‐tetra‐O‐acetyl‐α‐d ‐mannopyranosyloxy)ethyl methacrylate or 1‐O‐methacryloyl‐2,3:4,5‐di‐O‐isopropylidene‐β‐d ‐fructopyranose, respectively, using poly(methyl methacrylate) macro‐reversible addition–fragmentation chain transfer polymerization agent. The resulting block copolymers, which varied in 3FArgMA content, were self‐assembled into micelles of hydrodynamic diameters from 25 to 60 nm. The permanently positively charged arginine functionality on the 3FArgMA displayed repulsive forces against aggregation enabling high spin–spin relaxation times (T₂) in acidic as well as alkaline solutions. However, the longer poly(ethylene glycol) side functionality in PEGMEMA enabled better steric stabilization (T₂~30 ms) while the short fructose side chain was not enough to maintain high T₂ values, in particular when a higher 3FArgMA content was used. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2019, 57, 1994–2001     

Synthesis and Self-Assembly of Mixed-Graft Block Copolymers

Mixed-graft block copolymers (mGBCPs) consist of two or more types of polymeric side chains grafted on a linear backbone in a random, alternating, or pseudo-alternating sequence. They can phase-separate with the backbone serving as the interface of the blocks, and the side chains dominate their self-assembly behavior. mGBCPs are an accessible polymer architecture for exploring the idea of encoding polymer properties through the macromolecular architecture, as there are two distinct structural components that can be tuned: the backbone and the side chains. In this Concept article, the current literature on the synthesis of mGBCPs is reviewed, and the advantages and disadvantages of each synthetic method are noted. The self-assembly of mGBCPs is also discussed where possible. Finally, directions for future research on mGBCP synthesis and self-assembly are suggested.     

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.     

A model for crack formation during active solid pyrolysis of a char-forming solid: crack patterns; surface area generation; volatile mass efflux

A model is developed for the formation and propagation of cracks in a material sample that is heated at its top surface, pyrolyses, and then thermally degrades to form char. In this work the sample is heated uniformly over its entire top surface by a hypothetical flame (a heat source). The pyrolysis mechanism is described by a one-step overall reaction that is dependent nonlinearly on the temperature (Arrhenius form). Stresses develop in response to the thermal degradation of the material by means of a shrinkage strain caused by local mass loss during pyrolysis. When the principal stress exceeds a prescribed threshold value, the material forms a local crack. Cracks are found to generally originate at the surface in response to heating, but occasionally they form in the bulk, away from ever-changing material boundaries. The resulting cracks evolve and form patterns whose characteristics are described. Quantities examined in detail are: the crack spacing in the pyrolysis zone; the crack length evolution; the formation and nature of crack loops which are defined as individual cracks that have joined to form loops that are disconnected from the remaining material; the formation of enhanced pyrolysis area; and the impact of all of the former quantities on mass flux. It is determined that the mass flux from the sample can be greatly enhanced over its nominal (non-cracking) counterpart. The mass efflux profile qualitatively resembles those observed in Cone Calorimeter tests.     

“Brown-Ring”-Related Coordination Polymers of the Quartet-{FeNO}7 Chromophore

A conspicuous detail of the so-called brown-ring test (the analytical test on nitrate) is the reddish color of the bottom layer of concentrated sulfuric acid, which develops upon the bleeding of the brown layer into the acid. Crystals of the same color form from a solution of ferrous sulfate in concentrated sulfuric acid on saturation with gaseous nitric oxide. The structure of this H₃O[{Fe(NO)(μ₄-SO₄)(μ₂-SO₄)_0.5}_n/n] ( 1a ) is made up from infinite chessboard-type layers with sulfur on the field junctions and Fe(NO) moieties below the black and above the white fields. An Fe–N–O angle of about 160° causes disorder in the tetragonal space group I4/mmm. A similar crystal pathology was found in the related [{Fe(MeOH)(NO)(μ₄-SO₄)}_n/n] ( 1b ) in the same crystal class. A one-dimensional coordination polymer is formed in crystals of a third compound that comprises the Fe(NO)O₅ coordination pattern, namely the brown oxalato species [{Fe(H₂O)(NO)(μ₂-ox)}_n/n · H₂O] ( 2 ). A still larger NO tilt of about 156° is not obscured by disorder in the triclinic crystals of 2 .     

小直径棒材超声横波检测仿真分析

采用超声水浸聚焦斜入射方式进行小棒材表面、近表缺陷检测时,声波在水/棒和棒/缺陷界面会发生反射、折射、散射、衍射及波形转换等一系列物理变换。此时缺陷可检性对声波入射条件十分敏感,常出现由于检测条件设置不当而导致缺陷漏检、误检的情况。为解决这一问题,本文针对小棒材超声斜入射检测中的主要参数——入射角和水距,开展声场及缺陷声响应仿真,研究检测参数对不同部位缺陷检测能力的影响,并对仿真结果进行试验验证。通过研究得到了检测水距、入射角度对缺陷检测能力的影响,并得到最优检测条件。试验验证结果表明研究制定的检测方案可有效检测出表面、近表面裂纹缺陷。