Studying dispersoid systems

Summary Measurements of energy transformation in mitochondria are done on a capillary differential titration calorimeter CTD2156. It is important to mention that a sediment is quickly formed by the mitochondria suspension without mixing by means of a vibrating needle. During the measurements, the vibrating needle is located inside the working volume of the chamber. The design of the calorimeter is substantiated theoretically. It provides a new mode of a reagent input in the measuring volume of the calorimetric chambers. It expands the spectrum of tasks that can be solved using this instrument. In the capillary calorimeter the calorimetric chambers unit is simple and small in size. These advantages of capillary chambers provide an opportunity to unite 20 capillary calorimetric chambers in one calorimetric block. It allows designing a multi-channel titration calorimeter. There are obvious advantages of such a calorimeter over other instruments in screening researches and in researches of objects maintaining stability only for a short time.     

Hydrogen transport through Pd-Ni alloy electrodeposited on Pd substrate

Hydrogen transport through a Pd-Ni alloy electrodeposited on a Pd substrate (Pd-Ni/Pd bilayer symmetric electrode) has been investigated using cyclic voltammetry and a.c. impedance spectroscopy combined with the electrochemical hydrogen permeation method. The permeation build-up current transients and the measured impedance spectra were analyzed using the time-lag method for the bilayer electrode and a complex non-linear least squares data-fitting method based upon the derived Faradaic admittance for the hydrogen absorption into and diffusion through the bilayer electrode under the permeable boundary condition, respectively. The value of the hydrogen diffusivity in the Pd-Ni layer was lower than that in the Pd layer. Furthermore, the values of the charge transfer resistance and equilibrium absorption constant for the Pd-Ni/Pd bilayer electrode were higher than those for the Pd single layer electrode. From the experimental results, the role of the thin Ni(OH)₂ film formed on the Pd-Ni layer surface in the hydrogen transport through the Pd-Ni/Pd bilayer electrode is discussed in terms of its passivating effect and extremely large hydrogen solubility. Received: 22 January 1997 / Accepted: 15 April 1997     

Oxidative Coupling in a Series of Derivatives of 4a,9-Diaza-1,2,4a,9a-tetrahydrofluorene. 6. Reactions with Substituted 2-Aminoethanols

Oxidative coupling of derivatives of 4a,9-diaza-1,2,4a,9a-tetrahydro-9H-fluorene with 2-ethyl-, 2,2-dimethyl-, and 2-hydroxymethyl-2-methylaminoethanol in the presence of MnO₂ led to the selective formation of the corresponding mono- and di(hydroxymethyl)quinonediimines, subsequent cyclization of which gave the products of 6,7-annelation. Coupling with 2,2-di(hydroxymethyl)aminoethanol gave the annelation products directly.     

Global Existence of Solutions and Lower Bound Estimate of Blow-Up Time for the Keller-Segel Chemotaxis Model北大核心CSCD

A macroscopic nonlinear Keller-Segel model for chemotactic cell migration was considered, where the existence region of the model is a bounded convex one on Ω ⊂ RN(N≥2). The global existence of the solution on Ω ⊂ R3 was obtained by means of the energy estimate method. The lower bound of the blow-up time was proved for N = 3 and N = 2. © 2022 Editorial Office of Applied Mathematics and Mechanics. All rights reserved.     

Schrödinger方程的连续时空有限元方法

本文讨论Schr?dinger方程的连续时空有限元方法,通过引入相应的时空投影算子,利用实部虚部分离技巧,得到了变量u在时间节点处的L²范数,以及u和u_t的全局L²(H¹)和L²(L²)范数意义下的最优误差估计结果.该文的结论对进一步探索和设计Schr?dinger方程的数值算法是有益的.     

On bandwidth sums of graphs

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Two new bounds on the size of binary codes with a minimum distance of three

We prove two new upper bounds on the size of binary codes with a minimum distance of three, namelyA(10, 3)76 andA(11, 3)152.     

Energy relaxation in aϕ 4 with long range interactions

We investigate the influence of long range interactions on the relaxation behaviour of a lattice model with an on-site potential of ⁴-type and infinite range harmonic interactions. For finite number of particlesN, it is shown that the autocorrelation functions <E _n(t)E _n > of the fluctuations of the one-particle energiesE _n(t) decays exponentially. The corresponding relaxation time is proportional toN and is given by (T, N) =N₀(T). The temperature dependent time scale ₀ can explicitly be related to the dynamics of a one-particle correlator of the noninteracting system. The results are derived using Mori-Zwanzig projection formalism. The corresponding memory kernel is calculated within a mode coupling approximation and by a perturbative approach. Both results agree in leading order in 1/N. It is speculated that any interaction of range generates a timescale .     

An improved Menshov-Rademacher theorem

We study the a.e. convergence of orthogonal series defined over a general measure space. We give sufficient conditions which contain the Menshov-Rademacher theorem as an endpoint case. These conditions turn out to be necessary in the particular case where the measure space is the unit interval and the moduli of the coefficients form a nonincreasing sequence. We also prove a new version of the Menshov-Rademacher inequality.

     

Turán's Pure Power Sum Problem

Let be complex numbers, and consider the power sums , . Put , where the minimum is over all possible complex numbers satisfying the above. Turán conjectured that , for some positive absolute constant. Atkinson proved this conjecture by showing . It is now known that , for . Determining whether or approaches some other limiting value as is still an open problem. Our calculations show that an upper bound for decreases for , suggesting that decreases to a limiting value less than as .