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The classical lambda calculus may be regarded both as a programming language and as a formal algebraic system for reasoning about computation. It provides a computational model equivalent to the Turing machine, and continues to be of…
This paper summarizes theoretical definitions of the relativistic coordinate time scales introduced by the IAU 2000 framework as well as practical aspects of their use. It is argued that the IAU framework already defines relativistic local…
This paper gives a personal assessment of Epoch making advances in Matrix Computations from antiquity and with an eye towards tomorrow. We trace the development of number systems and elementary algebra, and the uses of Gaussian Elimination…
Recently, the non-linear Changhee differential equations were introduced in [5] and these differential equations turned out to be very useful for studying special polynomials and mathematical physics. Some interesting identities and…
In this paper, we propose a new approach to Cwikel estimates both for the Euclidean space and for the noncommutative Euclidean space.
Alternative approaches to Lebesgue integration are considered.
Computations, where the number of results is much smaller than the input data and are produced through some sort of accumulation, are called Reductions. Reductions appear in many scientific applications. Usually, reductions admit an…
In recent literature there are an increasing number of papers where the forbidden sets of difference equations are computed. We review and complete different attempts to describe the forbidden set and propose new perspectives for further…
This is a survey note of the author's observations on the discrete-time analogues of It\^o formulas.
In this paper, some new integral inequalities on time scales are presented by using elementarily analytic methods in calculus of time scales.
For certain tropical quartic curves the existing techniques could not predict the lifting behavior of their bitangents over the real numbers. We close this gap by using patchworking techniques. Further, this paper provides an analysis of…
In this note we present a survey on some classical and modern approaches on Pythagorean triples. Some questions are also posed in direction of some materials under review. In particular some non commutative and operator theoretical…
The paper reviews various arithmetic analogues of Hamiltonian systems and presents some new facts suggesting ways to relate/unify these examples.
Throughout more than two millennia many formulas have been obtained, some of them beautiful, to calculate the number pi. Among them, we can find series, infinite products, expansions as continued fractions and expansions using radicals.…
In systems with few degrees of freedom modern quantum calculations are, in general, numerically more efficient than semiclassical methods. However, this situation can be reversed with increasing dimension of the problem. For a…
The regain of interest in Moon exploration has substantially grown in the last years. For this reason, the space agencies consider the development of a precise navigation and positioning service similar to the Earth GNSS. Aiming at some…
Classical tensors, the familiar mathematical objects denoted by symbols such as $t_{i}$, $t^{ij}$ and $t_{k}^{ij}$, are usually interpreted either as 'coordinatizable objects' with coordinates changing in a specific way under a change of…
This note modifies the reference encoding of Turing machines in the $\lambda$-calculus by Dal Lago and Accattoli, which is tuned for time efficiency, as to accommodate logarithmic space. There are two main changes: Turing machines now have…
The possibility of detecting the gravitomagnetic clock effect using artificial Earth satellites provides the incentive to develop a more intuitive approach to its derivation. We first consider two test electric charges moving on the same…
For relativistic modelling of high-accuracy astronomical data several time scales are used: barycentric and geocentric coordinate times, TCB and TCG, as well as two additional time scales, TDB and TT, that are defined as linear functions of…