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Surface Nanophysics: Macro-, Meso-, Micro- and Nano-approaches

2017

The surface factor is very important for manipulating objects at a nanoscale. Thermodynamic behaviour is observed from the classical point of view, and conditional division into macro-, meso-, micro- and nano-approaches is presented. Processes of physical and chemical adsorption on the surface are presented from the energy and structure aspects. The occurrence of electronic states of the surface is presented from the classical point of view in comparison with molecular electronic states. One of the most important non-invasive optical methods to investigate nanoparticles is the surface plasmon resonance (SPR), which is quite useful for practical detection of nanoparticles in the surrounding …

Constant inner potential DFT for modelling electrochemical systems under constant potential and bias

2021

Electrochemical interfaces and reactions play a decisive role in e.g. clean energy conversion but understanding their complex chemistry remains an outstanding challenge. Constant potential or grand canonical ensemble (GCE) simulations are indispensable for unraveling the properties of electrochemical processes as a function of the electrode potential. Currently, constant electrode potential calculations at the density functional theory (DFT) level are carried out by fixing the Fermi level of the simulation cell. However, the Fermi level from DFT calculations does does not always reflect the experimentally controlled electrode potential or describe the thermodynamic independent variable in G…

Gaussian plane and spherical means in separable Hilbert spaces

1982

AsYouLikeHim: Images ofGalileoSince the17thCentury

2003

On the Background to Hilbert’s Paris Lecture “Mathematical Problems”

2018

Much has been written about the famous lecture on “Mathematical Problems” (Hilbert 1901) that David Hilbert delivered at the Second International Congress of Mathematicians, which took place in Paris during the summer of 1900 (Alexandrov 1979; Browder 1976). Not that the event itself evoked such great interest, nor have many writers paid particularly close attention to what Hilbert had to say on that occasion. What mattered – both for the text and the larger context – came afterward. Mathematicians remember ICM II and Hilbert’s role in it for just one reason: this was the occasion when he unveiled a famous list of 23 problems, a challenge to those who wished to make names for themselves in …

Remembering an Era: Roger Penrose’s Paper on “Gravitational Collapse: The Role of General Relativity”

2018

Back in the 1960s, Einstein’s theory of general relativity re-emerged as a field of important research activity. Much of the impetus behind this resurgence came from powerful new mathematical ideas that Roger Penrose and Stephen Hawking applied to prove general singularity theorems for global space-time structures. Their results stirred the imaginations of astrophysicists and gave relativistic cosmology an entirely new research agenda. A decade later, black holes and the big hang model were on the tongues of nearly everyone who followed recent trends in science. As popular expositions dealing with quasars, pulsars, and the geometry of black holes began to appear in magazines and textbooks, …

Operator (Quasi-)Similarity, Quasi-Hermitian Operators and All that

2016

Motivated by the recent developments of pseudo-Hermitian quantum mechanics, we analyze the structure generated by unbounded metric operators in a Hilbert space. To that effect, we consider the notions of similarity and quasi-similarity between operators and explore to what extent they preserve spectral properties. Then we study quasi-Hermitian operators, bounded or not, that is, operators that are quasi-similar to their adjoint and we discuss their application in pseudo-Hermitian quantum mechanics. Finally, we extend the analysis to operators in a partial inner product space (pip-space), in particular the scale of Hilbert space s generated by a single unbounded metric operator.

On Taylor coefficients of entire functions integrable against exponential weights

2001

A New Family of Deformations of Darboux-Pöschl-Teller Potentials

2004

The aim of this Letter is to present a new family of integrable functional-difference deformations of the Schrodinger equation with Darboux–Poschl–Teller potentials. The related potentials are labeled by two integers m and n, and also depend on a deformation parameter h. When h→ 0 the classical Darboux–Poschl–Teller model is recovered.

A Method of Conversion of some Coefficient Inverse Parabolic Problems to a Unified Type of Integral-Differential Equation

2011

Coefficient inverse problems are reformulated to a unified integral differential equation. The presented method of conversion of the considered inverse problems to a unified Volterra integral-differential equation gives an opportunity to distribute the acquired results also to analogous inverse problems for non-linear parabolic equations of different types.