in this paper, we introduce $p$-semilinear transformations for linear algebras over a field ${bf f}$ of positive characteristic $p$, discuss initially the elementary properties of $p$-semilinear transformations, make use of it to give some characterizations of linear algebras over a field ${bf f}$ of positive characteristic $p$. moreover, we find a one-to-one correspondence between $p$-semiline...

in this article we introduce the notion of textit{fractal $omega$-operad} emerging from  a natural $omega$-operad associated to any coglobular object in the category of higher operads in batanin's sense, which in fact is a coendomorphism $omega$-operads. we have in mind coglobular object of higher operads which algebras are kind of higher transformations. it follows that this natural $omega$-op...

Among the symmetries in physics, the rotation symmetry is most familiar to us. It is known that the spherical harmonics serve useful purposes when the world is rotated. Squeeze transformations are also becoming more prominent in physics, particularly in optical sciences and in high-energy physics. As can be seen from Dirac’s light-cone coordinate system, Lorentz boosts are squeeze transformatio...

Among the symmetries in physics, the rotation symmetry is most familiar to us. It is known that the spherical harmonics serve useful purposes when the world is rotated. Squeeze transformations are also becoming more prominent in physics, particularly in optical sciences and in high-energy physics. As can be seen from Dirac’s light-cone coordinate system, Lorentz boosts are squeeze transformatio...

The migration of a legacy system is one of the most challenging tasks in the area of software evolution. There are existing several different approaches to migrate a legacy system with different advantages and disadvantages. One solution is to translate the software into an intermediate language which spans from the low abstraction level to the very high abstraction level. Once the software has...

Spatial coordinate transformations have helped simplifying mathematical issues and solving complex boundary-value problems in physics for decades already. More recently, material-parameter transformations have also become an intuitive and powerful engineering tool for designing inhomogeneous and anisotropic material distributions that perform wanted functions, e.g., invisibility cloaking. A nec...

The semantics of a programming language are often described in a natural language. Such descriptions are often ambiguous and hard (or even impossible) to construct in a precise way. To tackle these problems one could specify a formal description of the semantics by using a mathematical model. In this report such a mathematical model is presented for the .NET Intermediate Language (IL) in the fo...

The capability of acquiring accurate and dense three-dimensional geospatial information that covers large survey areas rapidly enables airborne light detection and ranging (LiDAR) has become a powerful technology in numerous fields of geospatial applications and analysis. LiDAR data filtering is the first and essential step for digital elevation model generation, land cover classification, and ...

Introduction and summary. Symmetry and invariance considerations have long played important roles in physics. The 32 crystal classes—that is, groups of rotations in three-dimensional space all the elements of which are of the order 2, 3, 4 or 6—were determined 137 years ago, in the same year in which group theory was born. The determination of the 230 space groups, by Schönflies and by Fedorov ...

A mathematical framework that unifies the standard formalisms of special relativity and quantum mechanics is proposed. For this a Hilbert space H of functions of four variables x, t furnished with an additional indefinite inner product invariant under Poincaré transformations is introduced. For a class of functions in H that are well localized in the time variable the usual formalism of nonrela...