Determination of long-chain branching in model polystyrene samples by the GPC-sedimentation method

The GPC–sedimentation velocity method proposed earlier for the determination of long-chain branches was examined quantitatively by using model star-shaped and comb-shaped polystyrene samples of known degree of branching. The results showed that separation by sedimentation velocity was more sensitive to branching variations than separation by GPC. The results showed also that at low and moderate levels of branching the GPC–sedimentation velocity method reflected accurately the amounts of branching in the model samples. At high levels of branching, the method underestimated the amount of branching. The discrepancy, however, appears to have been caused by the inadequacy of the theories used in the interpretation of the raw data and not by any inherent problem in the method itself. The relative sensitivities of the GPC-sedimentation, GPC-viscosity, and GPC–light scattering methods are discussed.     

The observation of abnormal signals in laser flash photolysis: a type of probable synchronized nuclear spin signals

In laser flash photolysis (LFP) work, noise-like signals were observed together with transient absorption decay spectra in time domain. Analyzed results show that it is a valuable resonance spectrum of excited state molecules, in which four molecular cases are given here. We proposed that this kind signal might originate from nuclear or nuclear and electron spin resonance features in the excited molecules based on radio wave frequency spectrum levels and the significant interaction with static magnetic field.     

Simulation of harmonic oscillators on the lattice

This work deals with the simulation of a two-dimensional ideal lattice having simple tetragonal geometry. The harmonic character of the oscillators give rise to a system of second-order linear differential equations, which can be recast into matrix form. The explicit solutions which govern the dynamics of this system can be expressed in terms of matrix trigonometric functions. For the derivation we employ the Lagrangian formalism to determine the correct solutions, which extremize the underlying action of the system. In the numerical evaluation we develop diverse state-of-the-art algorithms which efficiently tackle equations with matrix sine and cosine functions. For this purpose, we introduce two special series related to trigonometric functions. They provide approximate solutions of the system through a suitable combination. For the final computation an algorithm based on Taylor expansion with forward and backward error analysis for computing those series had to be devised. We also implement several MATLAB programs which simulate and visualize the two-dimensional lattice and check its energy conservation.     

Prescribed scalar curvature plus mean curvature flows in compact manifolds with boundary of negative conformal invariant

Using a geometric flow, we study the following prescribed scalar curvature plus mean curvature problem: Let \((M,g_0)\) be a smooth compact manifold of dimension \(n\ge 3\) with boundary. Given any smooth functions f in M and h on \(\partial M\), does there exist a conformal metric of \(g_0\) such that its scalar curvature equals f and boundary mean curvature equals h? Assume that f and h are negative and the conformal invariant \(Q(M,\partial M)\) is a negative real number, we prove the global existence and convergence of the so-called prescribed scalar curvature plus mean curvature flows. Via a family of such flows together with some additional variational arguments, we prove the existence and uniqueness of positive minimizers of the associated energy functional and give a confirmative answer to the above problem. The same result also can be obtained by sub–super-solution method and subcritical approximations.     

First eigenvalues of geometric operators under the Yamabe flow

Suppose \((M,g_0)\) is a compact Riemannian manifold without boundary of dimension \(n\ge 3\). Using the Yamabe flow, we obtain estimate for the first nonzero eigenvalue of the Laplacian of \(g_0\) with negative scalar curvature in terms of the Yamabe metric in its conformal class. On the other hand, we prove that the first eigenvalue of some geometric operators on a compact Riemannian manifold is nondecreasing along the unnormalized Yamabe flow under suitable curvature assumption. Similar results are obtained for manifolds with boundary and for CR manifold.     

Max-min of polynomials and exponential diophantine equations

In this paper we study the maximum-minimum value of polynomials over the integer ring Z. In particular, we prove the following: Let F(x,y) be a polynomial over Z. Then, maxx∈Z(T)miny∈Z|F(x,y)|=o(T1/2) as T→∞ if and only if there is a positive integer B such that maxx∈Zminy∈Z|F(x,y)|?B. We then apply these results to exponential diophantine equations and obtain that: Let f(x,y), g(x,y) and G(x,y) be polynomials over Q, G(x,y)∈(Q[x,y]−Q[x])∪Q, and b a positive integer. For every α in Z, there is a y in Z such that f(α,y)+g(α,y)bG(α,y)=0 if and only if for every integer α there exists an h(x)∈Q[x] such that f(x,h(x))+g(x,h(x))bG(x,h(x))≡0, and h(α)∈Z.     

Convex underestimators of polynomials

Convex underestimators of a polynomial on a box. Given a non convex polynomial ${f\in \mathbb{R}[{\rm x}]}$ and a box ${{\rm B}\subset \mathbb{R}^n}$ , we construct a sequence of convex polynomials ${(f_{dk})\subset \mathbb{R}[{\rm x}]}$ , which converges in a strong sense to the “best” (convex and degree-d) polynomial underestimator ${f^{*}_{d}}$ of f. Indeed, ${f^{*}_{d}}$ minimizes the L ₁-norm ${\Vert f-g\Vert_1}$ on B, over all convex degree-d polynomial underestimators g of f. On a sample of problems with non convex f, we then compare the lower bounds obtained by minimizing the convex underestimator of f computed as above and computed via the popular α BB method and some of its other refinements. In most of all examples we obtain significantly better results even with the smallest value of k.     

Crosslinkable high dielectric constant polymer dielectrics for low voltage organic field‐effect transistor memory devices

I n this study, we successfully synthesized water/methanol soluble random copolymers with a high dielectric constant, poly(n‐(hydroxymethyl) acrylamide‐co‐5‐(9‐(5‐(diethylamino)pentyl)?2‐(4‐vinylphenyl)?9H‐fluorene(P(NMA‐co‐F6NSt)), which contained chemical crosslinkable segment (NMA) and hole trapping building block (F6NSt). The feeding molar ratios of two monomers (NMA:F6NSt) were set as 100:0, 95:5, 80:20, and 67:33 for the copolymers of P1 , P2 , P3, and P4 , respectively. The crosslinked P(NMA‐co‐F6NSt) thin film could serve as both dielectric and charge storage layers in organic field‐effect transistor (OFET) memory device and exhibited high k (i.e., 4.91–6.47) characteristics, leading to a low voltage operation and a small power consumption. Devices based on the P1 ‐ P4 dielectrics showed excellent insulating properties and good charge storage performance under a low operating voltage in a range of ±5V because of tightly network structures and well‐dispersed trapping cites. In particular, P3 ‐based memory device exhibited a large memory window of 4.13 V with stable data retention stability over 10⁴ s, a large on/off ratio of 10⁴, and good endurance characteristics as high as 200 cycles. The above results suggested that a high‐performance OFET memory device could be facilely achieved using the novel crosslinkable high‐k copolymers. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2016 , 54, 3224–3236     

One‐Step Pyro‐Synthesis of a Nanostructured Mn3O4/C Electrode with Long Cycle Stability for Rechargeable Lithium‐Ion Batteries

A nanostructured Mn₃O₄/C electrode was prepared by a one‐step polyol‐assisted pyro‐synthesis without any post‐heat treatments. The as‐prepared Mn₃O₄/C revealed nanostructured morphology comprised of secondary aggregates formed from carbon‐coated primary particles of average diameters ranging between 20 and 40 nm, as evidenced from the electron microscopy studies. The N₂ adsorption studies reveal a hierarchical porous feature in the nanostructured electrode. The nanostructured morphology appears to be related to the present rapid combustion strategy. The nanostructured porous Mn₃O₄/C electrode demonstrated impressive electrode properties with reversible capacities of 666 mAh g^?1 at a current density of 33 mA g^?1, good capacity retentions (1141 mAh g^?1 with 100 % Coulombic efficiencies at the 100^th cycle), and rate capabilities (307 and 202 mAh g^?1 at 528 and 1056 mA g^?1, respectively) when tested as an anode for lithium‐ion battery applications.     

A Bio‐inspired Cu4O4 Cubane: Effective Molecular Catalysts for Electrocatalytic Water Oxidation in Aqueous Solution

Inspired by the cubic Mn₄CaO₅ cluster of natural oxygen‐evolving complex in Photosystem II, tetrametallic molecular water oxidation catalysts, especially M₄O₄ cubane‐like clusters (M=transition metals), have aroused great interest in developing highly active and robust catalysts for water oxidation. Among these M₄O₄ clusters, however, copper‐based molecular catalysts are poorly understood. Now, bio‐inspired Cu₄O₄ cubanes are presented as effective molecular catalysts for electrocatalytic water oxidation in aqueous solution (pH 12). The exceptional catalytic activity is manifested with a turnover frequency (TOF) of 267 s^?1 for [(L_Gly‐Cu)₄] at 1.70 V and 105 s^?1 for [(L_Glu‐Cu)₄] at 1.56 V. Electrochemical and spectroscopic study revealed a successive two‐electron transfer process in the Cu₄O₄ cubanes to form high‐valent Cu^III and Cu^IIIO^. intermediates during the catalysis.