Inverse problem with a time‐integral condition for a fractional diffusion equation

We find the conditions for the unique solvability of the inverse problem for a time‐fractional diffusion equation with Schwarz‐type distributions in the right‐hand sides. This problem is to find a generalized solution of the Cauchy problem and an unknown space‐dependent part of an equation's right‐hand side under a time‐integral overdetermination condition.     

TheNulstellensatz on infinite-dimensional complex spaces

We prove an analog of Hilbert's Nullstellensatz for ideals generated by a finite number of polynomial functionals on infinite-dimensional complex vector spaces.Translated fromMatematichni Metodi ta Fiziko-Mekhanichni Polya, Vol. 40, No. 4, 1997, pp. 13–20.     

Some properties of electrolyte solutions in nanoconfinement revealed by the measurement of transient filtration potential after pressure switch off

We have demonstrated that with a composite nanoporous ceramic membrane in a batch membrane cell it is technically feasible to switch off the trans-membrane hydrostatic pressure difference within tens of milliseconds. That enabled us to resolve practically the whole time evolution of transient filtration potential. Measurements of the latter have been complemented by measurements of steady-state salt rejection by the composite membrane and by measurements of the streaming potential and hydraulic permeability of membrane supports available separately. A theory has been developed in terms of network thermodynamics for the electrical response of a bilayer membrane to a pressure perturbation. In combination with the results of salt rejection measurements, from the time transients of filtration potential we could determine the ion transport numbers within the nanoporous layer. Besides that, from the dependence of steady-state salt rejection on the trans-membrane volume flow, we have determined the diffusion permeability of and the salt reflection coefficient in the nanoporous layer. This has enabled us to estimate the contributions of Donnan and non-Donnan mechanisms to the rejection of ions by the nanoporous membrane used in this study. It has been unexpectedly found that the Donnan exclusion played only a secondary role. Our hypothesis is that the non-Donnan exclusion of ions from the nanopores might be caused by changes in water properties in nanoconfinement. Proceeding from the results of steady-state filtration experiments with the membrane and the support, we also concluded that the nanoporous layer was imperfection-free and had a quite narrow pore size distribution, which made it a suitable object for fundamental studies of ion transfer mechanisms in nanopores.     

Collision-energy-resolved penning ionization electron spectroscopy of HCOOH, CH3COOH, and HCOOCH3 by collision with He*(2(3)S) metastable atoms

Penning ionization of formic acid (HCOOH), acetic acid (CH3COOH), and methyl formate (HCOOCH3) upon collision with metastable He*(2(3)S) atoms was studied by collision-energy/electron-energy-resolved two-dimensional Penning ionization electron spectroscopy (2D-PIES). Anisotropy of interaction between the target molecule and He*(2(3)S) was investigated based on the collision energy dependence of partial ionization cross sections (CEDPICS) obtained from 2D-PIES as well as ab initio molecular orbital calculations for the access of a metastable atom to the target molecule. For the interaction potential calculations, a Li atom was used in place of He*(2(3)S) metastable atom because of its well-known similarity in interaction with targets. The results indicate that in the studied collision energy range the attractive potential localizes around the oxygen atoms and that the potential well at the carbonyl oxygen atom is at least twice as much as that at the hydroxyl oxygen. Moreover we can notice that attractive potential is highly anisotropic. Repulsive interactions can be found around carbon atoms and the methyl group.     

Flux-driven cellular precipitation in open system to form porous Cu3Sn

Recently, a new morphology of porous Cu₃Sn with lamellar structure is observed. Several possible explanations of the formation are proposed and compared. The most reasonable one seems to be the one based on a theory of flux-driven cellular precipitation in open system. Outflux of Sn from Cu₆Sn₅ generates simultaneously supersaturation with vacancies and with copper leading to the eutectoid-like transformation β → α + γ (where γ is void). The transformation is complete due to a complete outflux of Sn from the Cu₆Sn₅ phase. Simple formulae for prediction of the lamellar structure parameters and the propagation velocity are obtained and compared reasonably with experimental data. The suggested model can be interpreted as one more case of the flux-driven phase transformations in open systems.     

Truncated matrix trigonometric problem of moments: operator approach

We study the truncated matrix trigonometric problem of moments. A parametrization of all solutions of this problem (both in the nondegenerate and degenerate cases) is obtained by using the operator approach. This parametrization establishes the one-to-one correspondence between a certain class of analytic functions and all solutions of the problem. We use the important Chumakin results on the generalized resolvents of isometric operators.     

Thermoelectric energy conversion in layered structures with strained Ge quantum dots grown on Si surfaces

The efficiency of the energy conversion devices depends in many ways on the materials used and various emerging cost-effective nanomaterials have promised huge potentials in highly efficient energy conversion. Here we show that thermoelectric voltage can be enhanced by a factor of 3 using layer-cake growth of Ge quantum dots through thermal oxidation of SiGe layers stacked in SiO₂/Si₃N₄ multilayer structure. The key to achieving this behavior has been to strain the Ge/Si interface by Ge dots migrating to Si substrate. Calculations taking into account the carrier trapping in the dot with a quantum transmission into the neighboring dot show satisfactory agreement with experiments above ≈200 K. The results may be of interest for improving the functionality of thermoelectric devices based on Ge/Si.