This paper is focused on equational theories and equationally defined varieties of lattices which are not assumed to be modular. It contains both an elementary introduction to the subject and a survey of open problems and recent work. The concept of a "splitting" of the lattice of lattice theories is defined here for the first time in print. These splittings are shown to correspond bi-uniquely ...

In this note we study two questions regarding linear time-invariant distributed systems, namely: (1) When can the given system be approximated by a lumped system? (2) When can the given system be stabilized by a lumped system? In each case we obtain a complete answer to the question in terms of the behaviour of the purely atomic parts of the stable numerator and denominator of the plant.

We demonstrate the variations of single harmonic resonance enhancement during high-order harmonics generation in zinc-containing atomic and molecular species at conditions single-color two-color pumps laser-induced plasmas by applying different laser sources. show how selenides this metal notably modify (9th, 15th or 16th) compared with purely zinc plasmas. The are demonstrated using fixed (806...

Given a complete separable nite measure space (X; ; ) and nested partitions of X, we construct unbalanced Haar-like wavelets on X that form an unconditional basis for Lp(X; ; ) where 1 < p <1. Our construction and proofs build upon ideas of Burkholder and Mitrea. We show that if (X; ; ) is not purely atomic, then the unconditional basis constant of our basis is (max(p; q) 1). We derive a fast a...

The interfacial impedance of polycrystalline solid electrodes in the absence of Faradaic reactions is never purely capacitive; the deviation from ideal capacitive behaviour is usually larger on rough electrodes than on smooth ones. We present qualitative experiments to demonstrate that the frequency dependence of capacitance on solid electrodes is due to the atomic scale inhomogeneities rather ...

Volumetric strain can be divided into two parts: strain due to bond distance change and strain due to vacancy sources and sinks. In this paper, efforts are focused on studying the atomic lattice strain due to a vacancy in an FCC metal lattice with molecular dynamics simulation (MDS). The result has been compared with that from a continuum mechanics method. It is shown that using a continuum mec...

We have successfully grown ultrathin continuous aluminum film by molecular beam epitaxy. This percolative aluminum film is single crystalline and strain free as characterized by transmission electron microscopy and atomic force microscopy. The weak anti-localization effect is observed in the temperature range of 1.4 to 10 K with this sample, and it reveals that, for the first time, the dephasin...

Chemical reactions are manifestations of the dynamics of molecular valence electrons and their couplings to atomic motions. Emerging methods in attosecond science can probe purely electronic dynamics in atomic and molecular systems1–6. By contrast, time-resolved structural-dynamics methods such as electron7–10 or X-ray diffraction11 and X-ray absorption12 yield complementary information about t...

A purely inseparable field extension $K$ of a $k$ characteristic $p\not=0$ is said to be $\omega_0$-generated over if $K/k$ not finitely generated, but $L/k$ generated for each proper intermediate $L$. In 1986, Deveney solved the question posed by R. Gilmer and W. Heinzer, which consists in knowing lattice fields an necessarily linearly ordered under inclusion, constructing example where $[k^{p...