An event occurring within a stationary environment, in the direction toward which an observer self-rotates, is perceived to precede a simultaneous event, in the direction away from which she moves. When self-rotation results from angular acceleration in the dark, perception of space is also distorted, such that the subjective straight-ahead shifts in the opposite direction to motion and temporal event promotion. A reference frameshift theory, based on the special theory of relativity, is proposed to explain these findings. Here, a hyperbolic tangent transformation of objective angular velocity constrains subjective self-rotation velocity within finite bounds, consistent with it being a limited perceptual resource. Identifying this subjective variable with vestibular nystagmus slow-phase angular velocity, the asymptotic perceived self-rotation velocity is estimated at ~200 °⁄s. When included in the Lorentz transformations of the new formalism, this value predicts experimental simultaneity distortion. Hypothetically, the hyperbolic tangent objective-to-subjective transfer function would maximize the differential entropy of the percept, and thereby also the stimulus/percept mutual information, if angular velocities of body rotation encountered in naturalistic environmental interaction have a logistic probability density distribution of scale 100 °⁄s, a proposed experimental test of the scheme.

In this paper we provide some important and significant observations on invo-regular rings appeared in Ann. Univ. Mariae Curie-Sklodowska Sect. A Mathematica (2018). In addition we exhibit that strongly invo-regular rings, invo-regular rings and quasi invo-regular rings all coincide with the well known and well characterized tripotent rings and all these rings further coincide with the well known unit regular rings.

Rubble stone masonry walls are widely diffused in most of the cultural and architectural heritage of historical cities. The mechanical response of such material is rather complicated to predict due to their composite nature. Vertical compression tests, diagonal compression tests, and shear-compression tests are usually adopted to experimentally investigate the mechanical properties of stone masonries. However, further tests are needed for the safety assessment of these ancient structures. Since the relation between normal and shear stresses plays a major role in the shear behavior of masonry joints, governing the failure mode, triplet test configuration was here investigated. First, the experimental tests carried out at the laboratory (LPMS) of the University of L'Aquila on stone masonry specimens were presented. Then, the triplet test was simulated by using the Total Strain Crack Model, which reflects all the ultimate states of quasi-brittle material such as cracking, crushing and shear failure. The goal of the numerical investigation was to evaluate the shear mechanical parameters of the masonry sample, including strength, dilatancy, normal and shear deformations. Furthermore, the effect of (i) confinement pressure and (ii) bond behavior at the sample-plates interfaces were investigated, showing that they can strongly influence the mechanical response of the walls.

Mereology stands for the philosophical concept of parthood and is based on a sound set of fundamental axioms and relations. One of these axioms relates to the existence of a universe as a thing having part all other things. The present article formulates this logical expression first as an algebraic inequality and eventually as an algebraic equation reading in words: The universe equals the sum of all things. “All things” here are quantified by a “number of things”. Eventually this algebraic equation is normalized leading to an expression The whole equals the sum of all fractions. This introduces “1” or “100%” as a quantitative – numerical - value describing the “whole”. The resulting “basic equation” can then be subjected to a number of algebraic operations. Especially squaring this equation leads to correlation terms between the things implying that the whole is more than just the sum of its parts. Multiplying the basic equation (or its square) by a scalar allows for the derivation of physics equations like the entropy equation, the ideal gas equation, an equation for the Lorentz-Factor, conservation laws for mass and energy, the energy-mass equivalence, the Boltzmann statistics, and the energy levels in a Hydrogen atom. It further allows deriving a “contrast equation” which may form the basis for the definition of a length and a time scale. Multiplying the basic equation with vectors, pseudovectors, pseudoscalars and eventually hypercomplex numbers opens up the realm of possibilities to generate many further equations.

Previous studies generally reckon that the full converter-base wind power generation (FCWG) is a ’decoupled’ power source from the grid, which hardly participates in electromechanical oscillations. However, it is found recently that strong interaction could be induced which might incur severe resonance incidents in electromechanical dynamic timescale. In this paper, the participation of FCWG in electromechanical dynamics is extensively investigated, and particularly, an unusual transition of electromechanical oscillation mode (EOM) is uncovered for the first time. The detailed mathematical models of open-loop and closed-loop power systems are firstly established, and modal analysis is employed to quantify the FCWG participation in electromechanical dynamics, with two new mode identification criteria, i.e., FCWG dynamics correlation ratio (FDCR) and quasi-electromechanical loop correlation ratio (QELCR). On this basis, the impact of different wind penetration levels and controller parameter settings on the participation of FCWG is investigated. It is revealed that if an FOM has a similar oscillation frequency to the system EOMs, there is a high possibility to induce strong interactions between FCWG dynamics and system electromechanical dynamics of the external power systems. In this circumstance, an interesting phenomenon may occur that an EOM may be dominated by FCWG dynamics, and hence is transformed into a quasi-EOM, which actively involves the participation of FCWG quasi-electromechanical state variables.

In this paper, quasi-static axial compression tests are performed on the nodal Moso bamboos to study the size effect on energy absorption of the bamboos and the damage pattern of the multiple bamboo columns. Experimental results show that under the same moisture content, growth age and growing environment, the specific energy absorption (SEA) of the test samples increases with the increase of the out-diameter and thickness of the bamboo columns, indicating that size effect exists for energy absorption of the Moso Bamboos. For the multiple bamboo columns, there are mainly three failure modes for the constituent single bamboo columns: splitting above the node, splitting below the node and splitting through the node. Also, the tensile tests are conducted on three kinds of dog-bone shaped bamboo samples to investigate the macroscopic tensile fracture mode in the longitudinal direction of Moso bamboos. Results show that there is no direct relationship between the fracture pattern and moisture content of the bamboos, as well as the growth age of the bamboos. However, the tensile loading rate and the shape of the dog-bone shaped bamboo sample could affect the macroscopic fracture pattern of the bamboos in some cases.

The paper examines common elements between Lévai’s and Milson’s potentials obtained by Liouville transformations of two rational canonical Sturm-Liouville equations (RCSLEs) with even density functions which are exactly solvable via Jacobi polynomials in a real or accordingly imaginary argument. We refer to the polynomial numerators of the given rational density function as ‘tangent polynomial’ (TP) and thereby term the aforementioned potentials as ‘e-TP’ A special attention is given to the overlap between the two potentials along symmetric curves which represent two different forms of the Ginocchio potential exactly quantized via Gegenbauer and Masjed-Jamei polynomials respectively. Our analysis reveals that the actual interconnection between Lévai’s parameters for these two rational realizations of the Ginocchio potential is much more complicated than one could expect based on the striking resemblance between two quartic equations derived by Lévai for ‘averaged’ Jacobi indexes.

Keywords: liquid alloys, microstratification, dispersed particles, spontaneous dispersion, criteria for true (entropic) spontaneous dispersion, mechanisms of quasi-spontaneous dispersion, methods and results for assessing size of dispersed particles.

In this study, we present the concept of interval-valued fuzzy soft point and then introduce the notions of neighborhood and quasi-neighbourhood of it in interval-valued fuzzy soft topological spaces. Separation axioms in interval-valued fuzzy soft topology, so-called $q$-$T_{i}$ for $ i=0,1,2,3,4 ,$ is introduced and some of its basic properties are also studied.

Creating self-learning algorithms, developing deep neural networks and improving other methods that "learn" for various areas of human activity is the main goal of the theory of machine learning. It helps to replace the human with a machine, aiming to increase the quality of production. The theory of artificial neural networks, which already have replaced the humans in problems of detection of moving objects, recognition of images or sounds, time series prediction, big data analysis and numerical methods remains the most dispersed branch of the theory of machine learning. Certainly, for each area of human activity it is necessary to select appropriate neural network architectures, methods of data processing and some novel tools from applied mathematics. But the universal problem for all these neural networks with specific data is the achieving the highest accuracy in short time. Such problem can be resolved by increasing sizes of architectures and improving data preprocessing, where the accuracy rises with the training time. But there is a possibility to increase the accuracy without time growing, applying optimization methods. In this survey we demonstrate existing optimization algorithms of all types, which can be used in neural networks. There are presented modifications of basic optimization algorithms, such as stochastic gradient descent, adaptive moment estimation, Newton and quasi-Newton optimization methods. But the most recent optimization algorithms are related to information geometry, for Fisher-Rao and Bregman metrics. This approach in optimization extended the theory of classic neural networks to quantum and complex-valued neural networks, due to geometric and probabilistic tools. There are provided applications of all introduced optimization algorithms, what delighted many kinds of neural networks, which can be improved by including any advanced approaches in minimization of the loss function. Afterwards, we demonstrated ways of developing optimization algorithms in further researches, engaging neural networks with progressive architectures. Classical gradient based optimizers can be replaced by fractional order, bilevel and, even, gradient free optimization methods. There is a possibility to add such analogues in graph, spiking, complex-valued, quantum and wavelet neural networks. Besides the usual problems of image recognition, time series prediction, object detection, there are many are other tasks for modern theory of machine learning, such as solving problem of quantum computations, partial differential and integro-differential equations, stochastic processes and Brownian motion, making decisions and computer algebra.

This article is some review of results that were obtained at 2007-2021 years development of “The Information as Absolute” concept and the informational physical model, which is based on the concept; including a number of fundamental physical problems are briefly considered in framework of the conception and the model. Recently in physics there are several publications, that present lists of the problems. However, those lists are essentially incomplete, for at least two reasons. Firsts of all, a number of phenomena are studied traditionally by philosophy, and so corresponding problems are usually considered to be “metaphysical”. However, they relate also to some concrete physical phenomena. For example, physics evidently studies Matter, and so the metaphysical problems “what is ontology of Matter”, “what is “Space”, “Time” and a few other physical phenomena and notions as well, are really a Meta-physical problems “what does physics study?” There are other fundamental physical problems, which are not considered as such in physics, and are absent in the “fundamental problems lists”. Those include the problems, which really exist, yet are incorporated into standard physical theories, and so are fundamental “implicitly”, which in physics are “solved by default” ‒ and mostly erroneously. Note, though, that a number of “Meta-physical”, and concrete fundamental, problems more in detail are considered in the paper “The Informational Conception and Basic Physics”, https://arxiv.org/abs/0707.4657, v5 (2021), so this paper is, in certain sense, an expanded conclusion of this paper, which includes, correspondingly, more in detail consideration of some more general physical problems; and, besides, in this article, the problem “what are Gravity and Electric Forces” is essentially clarified comparing with the arXiv 2021 paper version above. Besides, the concrete problem “What is Life”, and the rational cosmological model, where a few vague points in standard cosmology rather probably are rationally clarified, while the fundamental problem “matter – antimatter asymmetry” in Matter is solved practically for sure, are considered, and one of recently published rather complete “lists of fundamental problems” is commented in Appendix.