On the position of the upper limit temperature of homogeneous nucleation of precipitates in low concentrated Al?Zn alloys

The upper limit temperature T_hn of the onset of homogeneous nucleation of Guinier-Preston (GP) zones was determined for three Al Zn alloys with xZn = 4.5, 6.0 and 8.0 at.% by SAXS investigations (cooling from the range of homogeneity to various temperatures T_a and ageing at T_a). The results are T_hn = (95 ± 3) °C for xZn = 4.5 at.%, (118 ± 3) °C (6.0 at.%) and (154 ± 3) °C (8.0 at.%), respectively. The obtained results fit well the data known for the alloys with higher contents of Zn. It is stressed that one has to distinguish between T_hn, determined by isothermal measurements after a direct quench or cooling to the respective T_a, and the upper limit temperature T_rhn of the onset of the rapid homogeneous nucleation of GP zones (continuous cooling).     

Chain transfer reactions in emulsion polymerization of butadiene/styrene

Calculation of regulating index r from M̄_W values determined by experiments is proposed. The calculation is based on the assumption that the M̄_W values only depend on the conversion and the regulating index in emulsion polymerization. On this basis the calculation of regulator concentration in the latex particles was also possible. M̄_W values calculated in this way and experimental M̄_W values show good agreement.     

Magnetic nanotips: the realisation of an atomic-scale beam-splitter

We present the first realisation of ferromagnetic Fe nanotips. Studies of the field emitted beams of electrons and metallic ions above and under the Curie temperature T_c were made. We have observed a reversible splitting of the electron beams when the temperature crossed through T_c and multiple spot patterns for the emitted metallic ion beams. These phenomena were not observed with Fe microtips or non-magnetic nanotips and thus were correlated to a strong magnetic interaction at the atomic scale apex of the nanotips. The Fe nanotips constitute an atomic scale beam-splitter.     

A generalized distance and enhanced Ekeland’s variational principle for vector functions

We propose a definition of lower closed transitive relations and prove the existence of minimal elements for such a relation. This result is shown to contain probably a large part of existing versions of Ekeland’s variational principle (EVP). We introduce the notion of a weak τ-function p as a generalized distance and use it together with the above result on minimal elements to establish enhanced EVP for various settings, under relaxed lower semicontinuity assumptions. These principles conclude the existence not only of p-strict minimizers of p-perturbations of the considered vector function, but also p-sharp and p-strong minimizers. Our results are proved to be stronger than the classical EVP and many generalizations in the literature, even in the usual one-dimensional case, by numerous corollaries and examples. We include equivalent formulations of our enhanced EVP as well.     

Localization algebras and deformations of Koszul algebras

We show that the center of a flat graded deformation of a standard Koszul algebra A behaves in many ways like the torus-equivariant cohomology ring of an algebraic variety with finite fixed point set. In particular, the center of A acts by characters on the deformed standard modules, providing a “localization map”. We construct a universal graded deformation of A and show that the spectrum of its center is supported on a certain arrangement of hyperplanes which is orthogonal to the arrangement coming from the algebra Koszul dual to A. This is an algebraic version of a duality discovered by Goresky and MacPherson between the equivariant cohomology rings of partial flag varieties and Springer fibers; we recover and generalize their result by showing that the center of the universal deformation for the ring governing a block of parabolic category O{\mathcal{O}} for \mathfrakgl_n{\mathfrak{gl}_n} is isomorphic to the equivariant cohomology of a Spaltenstein variety. We also identify the center of the deformed version of the “category O{\mathcal{O}}” of a hyperplane arrangement (defined by the authors in a previous paper) with the equivariant cohomology of a hypertoric variety.     

Fixed Points,Continuous Selections,and Existence of Solution of Optimization-Related Problems

We propose a definition of a generalized type of Knaster–Kuratowski–Mazurkiewicz (KKM) mappings, called a weak T-KKM mapping, and a corresponding weak KKM property. A new extension of the Fan–Glicksberg fixed-point theorem is established. Sufficient conditions for the existence of a continuous selection, a fixed point of a composition, and a coincidence point are also provided. Then, we use the obtained results to study the existence of solutions to various optimization-related problems. Discussions and detailed examples are included as well to compare our results with existing ones and to explain their advantages in many situations.     

Photoluminescence properties of various CVD-grown ZnO nanostructures

We have studied systematically room-temperature photoluminescence (PL) properties of many nanostructured ZnO samples grown by chemical vapour deposition (CVD). Their PL spectra consist of two emissions peaked in the ultraviolet (UV) and green regions. The relative intensity of these emissions depends on the excitation energy density, size and morphology of ZnO nanostructures. Based on the excitation-density dependence of the integrated intensity ratio of UV-to-green emission, we could classify PL spectra of ZnO nanostructures into three groups characteristic of size and morphology. Our study also reveals that with increasing excitation density, the UV-peak position shifts slightly towards longer wavelengths while the green emission around 514-520 nm is almost unchanged. This green-luminescence emission is dominant when the nanostructure sizes range from 20 to 200 nm, which is related to a large surface-to-volume ratio.     

On a backward problem for fractional diffusion equation with Riemann-Liouville derivative

In the present paper, we study the initial inverse problem (backward problem) for a two-dimensional fractional differential equation with Riemann-Liouville derivative. Our model is considered in the random noise of the given data. We show that our problem is not well-posed in the sense of Hadamard. A truncated method is used to construct an approximate function for the solution (called the regularized solution). Furthermore, the error estimate of the regularized solution in L² and H^τ norms is considered and illustrated by numerical example.