Almost periodic skew-symmetric differential systems

We analyse solutions of almost periodic skew-symmetric homogeneous linear differential systems. We prove that in any neighbourhood of such a system there exists an almost periodic skew-symmetric system which does not possess any non-trivial almost periodic solution

Limit periodic linear difference systems with coefficient matrices from commutative groups

In this paper, limit periodic and almost periodic homogeneous linear difference systems are studied. The coefficient matrices of the considered systems belong to a given commutative group. We find a condition on the group under which the systems, whose fundamental matrices are not almost periodic, form an everywhere dense subset in the space of all considered systems. The treated problem is discussed for the elements of the coefficient matrices from an arbitrary infinite field with an absolute value. Nevertheless, the presented results are new even for the field of complex numbers

Non-oscillation of half-linear differential equations with periodic coefficients

We consider half-linear Euler type differential equations with general periodic coefficients. It is well-known that these equations are conditionally oscillatory, i.e., there exists a border value given by their coefficients which separates oscillatory equations from non-oscillatory ones. In this paper, we study oscillatory properties in the border case. More precisely, we prove that the considered equations are non-oscillatory in this case. Our results cover the situation when the periodic coefficients do not have any common period

Linear response strength functions with iterative Arnoldi diagonalization

We report on an implementation of a new method to calculate RPA strength functions with iterative non-hermitian Arnoldi diagonalization method, which does not explicitly calculate and store the RPA matrix. We discuss the treatment of spurious modes, numerical stability, and how the method scales as the used model space is enlarged. We perform the particle-hole RPA benchmark calculations for double magic nucleus 132Sn and compare the resulting electromagnetic strength functions against those obtained within the standard RPA.Comment: 9 RevTeX pages, 11 figures, submitted to Physical Review

Hierarchical MTW zeolites in tetrahydropyranylation of alcohols : comparison of bottom-up and top-down methods

Authors thank the Czech Science Foundation for financial support (17-06524Y). H.P. and J.Y. thank to the 111 project of the Ministry of Education of China (B17020). M.M. and S.M.V. acknowledge the support of EPSRC grant EP/K025112/1 and Capital for Great Technologies Grant EP/L017008/1.Despite a widespread application of zeolites in catalysis, these microporous materials still suffer from a low accessibility of active sites located deep in crystals due to limited size of channels (< 1 nm). Here, we prepared a series of micro-mesoporous zeolites with MTW topology and similar Si/Al molar ratio (50). Two topical approaches were applied here: i. bottom-up synthesis with a surfactant-SDA leading to so-called nanosponge material; ii. top-down desilication of bulk crystals by NaOH solution in the presence of tetraalkylammonium cations (TAA+). Prepared materials were characterized by powder X-ray diffraction, sorption of nitrogen, adsorption of pyridine and di-tert-butyl-pyridine followed by FTIR, solid state 27Al NMR, ICP-OES, SEM, TEM, and STEM-EDS. It was found that the desilication of MTW in the presence of TAA+ proceeds in different pathway compared to well-studied MFI. This variance was attributed to the different dimensionality of their channel systems (1D vs. 3D). Materials were tested in tetrahydropyranylation of alcohols differing in a chain length and degree of branching. The nanosponge MTW shows generally very good performance. Nevertheless, in cases of the branched alcohols MTW materials desilicated in the presence of TAA+ exhibited comparable or even higher activity than nanosponge based on TOF values. Therefore, desilicated MTW presents cheaper and equally or more effective catalyst compared to nanosponge material with the same topology.PostprintPeer reviewe