Characterization of measures by potentials

Let μ be a measure in a Banach spaceE, f be an even function onR. We consider the potentialg(a)=f _E f(‖x?a‖)dμ(x). The question is as follows: For whichf does the potentialg determine μ uniquely? In this article we give answers in the cases whereE=l _∞ ⁿ and wheref(t)=|t| ^p andE is a finite dimensional Banach space with symmetric analytic norm. Calculating the Fourier transform of the functionf(‖x‖ _∞) we give a new proof of the J. Misiewicz's result that the functionf(‖x‖ _∞) is positive definite only iff is a constant function.     

A Procedure for Transforming Impedance Spectra for the Determination of Mechanism of Electrochemical Reactions

Transformation of impedance spectra into relaxation time spectra (RTS) is used for determining contributions of individual processes of the oxygen electroreduction reaction (OER) to the polarization resistance of the electrochemical cell. The transformation technique involves the solution of the convolution equation found with the aid of a modified Van Cittert iteration algorithm checked on model impedance spectra. The technique, when used to analyze impedance spectra of electrochemical cells air|Pt|YSZ|YSZ + Pt|air, shows that the conversion of a globular structure of the YSZ + Pt cermet layer to a columnar one is accompanied by a change of peak amplitudes in RTS. The revealed RTS dynamics when heated to 750°C is compared with peculiarities of individual processes in OER.     

用重复卷积法求解物理宽化函数

用重复卷积法求解物理宽化函数吴万国,林嘉　（福州大学中心实验室,福州３５０００２）（中国（福建）对外贸易中心集团,福州３５０００１）关键词Ｘ射线衍射,晶粒度,晶格畸变,重复卷积粉末试样的Ｘ射线衍射谱线一般具有一定的宽度,引起话线宽化的主要原因有仪器致...     

光周期敏感不育水稻中激素的二阶导数卷积伏安法研究

二阶导数卷积伏安法应用于水稻中痛量雌雄激素的检测，具有快速，灵敏，干扰少的特点。本文以光周期敏感核不育水稻农垦５８Ｓ为材料，以农垦５８作对照，了叶焉和穗中雌，雄性激素的含量，研究了不同光周期条件下两类激素的变化。     

Accuracy and CPU time of JE-TLM,PLRC-TLM and CRC-TLM methods for plasma medium

The current density (JE), the piecewise linear recursive convolution (PLRC) and the constant convolution recursive (CRC) techniques are developed and integrated into the transmission line matrix (TLM) algorithm. A comparison of these three schemes according to the criteria of accuracy and CPU time is presented. Numerical experiments show that JE provides the most accurate solution and requires the least CPU time; PLRC is nearly as accurate but consumes more CPU time than CRC.     

How good is CuAAC “click” chemistry for polymer coupling reactions?

¹H NMR and SEC analyses are used to investigate the overall efficiency of Copper Catalyzed Azide Alkyne Cycloaddition (CuAAC) “click” coupling reactions between alkyne‐ and azide‐terminated polymers using polystyrene as a model. Quantitative convolution modeling of the entire molecular weight distribution is applied to characterize the outcomes of the functional polymer synthesis reactions (i.e., by atom transfer radical polymerization), as well as the CuAAC coupling reaction. Incomplete functionality of the azide‐terminated polystyrene (∼92%) proves to be the largest factor compromising the efficacy of the CuAAC coupling reaction and is attributed primarily to the loss of terminal bromide functionality during its synthesis. The efficiency of the S_N2 reaction converting bromide to azide was found to be about 99%. After taking into account the influence of non‐functional polymer, we find that, under the reaction conditions used, the efficiency of the CuAAC coupling reaction determined from both techniques is about 94%. These inefficiencies compromise the fidelity and potential utility of CuAAC coupling reactions for the synthesis of hierarchically structured polymers. While CuAAC efficiency is expected to depend on the specific reaction conditions used, the framework described for determining reaction efficiency does provide a means for ultimately optimizing the reaction conditions for CuAAC coupling reactions. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2018 , 56, 75–84     

Finite tchebycheff transformations of generalized functions

By using Hilbert space techniques, the finite Tchebycheff transformations of the first and the second kind are defined on appropriate spaces of generalized functions. The inversion theorems are established and some operation transform formulas are obtained. These results are applied in solving certain distributional differential equations.     

Stable blow-up dynamics in the -critical and -supercritical generalized Hartree equation

We study stable blow-up dynamics in the generalized Hartree equation with radial symmetry, which is a Schrödinger-type equation with a nonlocal, convolution-type nonlinearity: First, we consider the -critical case in dimensions and obtain that a generic blow-up has a self-similar structure and exhibits not only the square root blowup rate , but also the log-log correction (via asymptotic analysis and functional fitting), thus, behaving similarly to the stable blow-up regime in the -critical nonlinear Schrödinger equation. In this setting, we also study blow-up profiles and show that generic blow-up solutions converge to the rescaled , a ground state solution of the elliptic equation . We also consider the -supercritical case in dimensions . We derive the profile equation for the self-similar blow-up and establish the existence and local uniqueness of its solutions. As in the NLS -supercritical regime, the profile equation exhibits branches of nonoscillating, polynomially decaying (multi-bump) solutions. A numerical scheme of putting constraints into solving the corresponding ordinary differential equation is applied during the process of finding the multi-bump solutions. Direct numerical simulation of solutions to the generalized Hartree equation by the dynamic rescaling method indicates that the is the profile for the stable blow-up. In this supercritical case, we obtain the blow-up rate without any correction. This blow-up happens at the focusing level , and thus, numerically observable (unlike the -critical case). In summary, we find that the results are similar to the behavior of stable self-similar blowup solutions in the corresponding settings for the nonlinear Schrödinger equation. Consequently, one may expect that the form of the nonlinearity in the Schrödinger-type equations is not essential in the stable formation of singularities.     

On log-normal convolutions: An analytical–numerical method with applications to economic capital determination

We put forward an efficient algorithm for approximating the sums of independent and log-normally distributed random variables. Namely, by combining tools from probability theory and numerical analysis, we are able to compute the cumulative distribution functions of the just-mentioned sums to a high precision and in a relatively short computing time. We illustrate the effectiveness of the new method in the contexts of the individual and collective risk models, aggregate economic capital determination, and economic capital allocation.     

ON CERTAIN CLASS OF MEROMORPHIC FUNCTIONS WITH POSITIVE COEFFICIENTS

In the present investigation we define a new class of meromorphic functions on the punctured unit disk △*:= {z ∈ C : 0 < |z| < 1} by making use of the generalized Dziok-Srivastava operator H l m [α1 ]. Coefficient inequalities, growth and distortion inequalities, as well as closure results are obtained. We also establish some results concerning the partial sums of meromorphic functions and neighborhood results for functions in new class.