Strictly finite range forces from the signum-Gordon field: exact results in two spatial dimensions

Exact formula for the force between two identical static point charges coupled to the nonlinear scalar field of two-dimensional signum-Gordon model is obtained. Pertinent solution of the field equation is found in the form of one-dimensional integral. The force exactly vanishes when the distance between the charges exceeds certain critical value.Comment: published versio

The impact of the application of chilled air flow as an additional coolant on surface quality obtained after grinding process.

Praca obejmuje, badania zastosowania dodatkowego sprężonego i schłodzonego powietrza, jako dodatkowego czynnika chłodzącego do metody smarowania za pomocą mgły olejowej. Dzięki takiemu sposobowi chłodzenia i smarowania strefy szlifowania, uzyskać można poprawę jakości powierzchni po procesie obróbczym. Uzyskane przy tym sposobie smarowania parametry chropowatości okazały się niższe niż w przypadku zastosowania smarowania strefy szlifowania tylko za pomocą metody MQL. Jest to nowa proekologiczna - hybrydowa metoda chłodząco-smarująca łącząca zalety metody MQL i sprężonego schłodzonego powietrza.This thesis concerns testing the application of additional compressed and chilled air as an additional coolant to a method of lubrication with the oil mist. This way of cooling and lubrication of the grinding zone can lead to improving the quality of a surface of the grinding process. The surface roughness parameters and the forces during the grinding obtained through that way lubrication turned out to be lower than in case of spreading the grinding zone by using MQL method. This is a new, environment-friendly, hybrid method combining the advantages of MQL method and of com-pressed cooled air

On relativistic quantum mechanics of the Majorana particle : quaternions, paired plane waves, and orthogonal representations of the Poincaré group

The standard momentum operator −i∇ has the trivial domain (the null vector) if the L2 Hilbert space consists of only real-valued functions. In consequence, it is useless in quantum mechanics of the relativistic Majorana particle which is formulated in such a Hilbert space. Instead, one can consider the axial momentum operator introduced in (2019) Phys. Lett. A 383 1242. In the present paper we report several new results which elucidate usability of the axial momentum observable. First, a new motivation for the axial momentum is given, and the Heisenberg uncertainty relation checked. Next, we show that the general solution of time evolution equation written in the axial momentum basis has a connection with quaternions. Furthermore, it turns out that in the case of massive Majorana particles, single traveling monochromatic plane waves are not possible, but there exist solutions which have the form of two plane waves traveling in opposite directions. Another issue discussed here in detail is relativistic invariance. A single real, orthogonal and irreducible representation of the Poincaré group—consistent with the lack of antiparticle—is unveiled

Spinning Q-balls in the complex signum-Gordon model

Rotational excitations of compact Q-balls in the complex signum-Gordon model in 2+1 dimensions are investigated. We find that almost all such spinning Q-balls have the form of a ring of strictly finite width. In the limit of large angular momentum M_z their energy is proportional to |M_z|^(1/5).Comment: 10 page

Electronic Evidence in the Light of the Council of Europe’s New Guidelines

This paper aims to analyse the significance of the “Guidelines of the Committee of Ministers of the Council of Europe on electronic evidence in civil and administrative proceedings” adopted by the Council of Europe on January 30, 2019. The authors examine the practical aspects of the specific guidelines following from this soft law instrument. They make an in-depth analysis of metadata as an essential element of electronic evidence. The authors also present the fundamental principles of electronic evidence, as presented in the Guidelines, along with an explanation of their meaning, including the principle on the protection of human rights and rule of law. The paper ends with the authors’ conclusions regarding treatment of electronic evidence in the courts, the practical significance of the Guidelines and the importance of IT law in legal education

Note on scale invariance and self-similar evolution in (3+1)-dimensional signum-gordon model

Several classes of self-similar, spherically symmetric solutions of relativistic wave equation with a nonlinear term of the form sign($\varphi$) are presented. They are constructed from cubic polynomials in the scale invariant variable t/r. One class of solutions describes the process of wiping out the initial field, another an accumulation of field energy in a finite and growing region of space

Budowa systemu do jednoczesnego podawania kilku mediów chłodząco-smarujących w strefę szlifowania.

W opracowaniu przedstawiono budowę systemu samoczynnego podawania w strefę skrawania medium chłodzącego oraz smarującego w zależności od kinematycznej odmiany szlifowania. System ten pozwala na sterowanie wypływu sprężonego schłodzonego powietrza oraz mgły olejowej (MQL). Oba czynniki wykorzystywać można do chłodzenia jak i smarowania strefy obróbki oraz do kondycjonowania ściernicy.The paper presents the development of the system self-administration in the cutting zone cooling and lubricating fluid based on kinematic variety of grinding. This system allows you to control the flow of cooled compressed air and oil mist (MQL). Both elements can be used to cool and lubricate the cutting zone and to condition the wheel