Inverse Loops Research Articles

On the universality and isotopy-isomorphy of (r,s,t)-inverse quasigroups and loops with applications to cryptography

This paper introduced a condition called $\mathcal{R}$-condition under which $(r,s,t)$-inverse quasigroups are universal. Middle isotopic $(r,s,t)$-inverse loops, satisfying the $\mathcal{R}$-condition and possessing a trivial set of $r$-weak inverse permutations were shown to be isomorphic; isotopy-isomorphy for $(r,s,t)$-inverse loops. Isotopy-isomorphy for $(r,s,t)$-inverse loops was generally characterized. With the $\mathcal{R}$-condition, it was shown that for positive integers $r$, $s$ and $t$, if there is a $(r,s,t)$-inverse quasigroup of order $3k$ with an inverse-cycle of length $gcd(k,r+s+t)>1$, then there exists an $(r,s,t)$-inverse quasigroup of order $3k$ with an inverse-cycle of length $gcd\big(k(r+s+t), (r+s+t)^2\big)$. The procedure of application of such $(r,s,t)$-inverse quasigroups to cryptography was described and explained, while the feasibility of such $(r,s,t)$-inverse quasigroups was illustrated with sample values of $k,r,s$ and $t$.

On Characterization of Graphs Structures Connected with Some Algebraic Properties

In this paper, we have characterized graph structures connected with some algebraic properties. Also, this paper is actually the concatenation of graph theory and algebra. We have introduced left and right inverse graphs of antiautomorphic inverse property loops. Also, there is a connection between bipartite graphs and mathematical structures, commutator subloop, associator subloop, and associative part, the nucleus of the loop, through edge labeling.

A study of the holomorphy of (r, s, t)-inverse loops

In this paper, the holomorphic study of inverse properties in loops is put in a more general setting. For various combinations of r, s, t ∈ ℤ in parities, it was established that: (i) the A(Q)-holomorph H(Q) of a loop Q is an (r, s, t)-inverse loop if and only if Q is an (r, s, t) -inverse loop; (ii) the A(Q) -holomorph H(Q) of a loop Q is an (r, s, t)-inverse loop if and only if Q is an (r, s, t)-inverse loop, A(Q) is a particular kind of group (e.g abelian, Boolean) and any two elements of A(Q) satisfies some autotopic conditions. Specifically, m-inverse loop (when m is odd), double weak inverse property loop (WWIPL) and weak inverse property loop were found to satisfy the case (i) while m-inverse loop (when m is even) and weak inverse property loop were found to satisfy case (ii). For a Buchsteiner loop (which is a special kind of WWIPL) Q, it was shown that the A(Q)-holomorph H(Q) is a Buchsteiner loop if and only if A(Q) is a nuclear automorphism group. The left (right) inner automorphism group of a Buchsteiner loop Q was shown to be a normal subgroup of the automorphism group of Q. Existing examples of loops which are relevant to this study were cited.

An improved parametric model for hysteresis loop approximation.

A number of improvements have been added to the existing analytical model of hysteresis loops defined in parametric form. In particular, three phase shifts are included in the model, which permits us to tilt the hysteresis loop smoothly by the required angle at the split point as well as to smoothly change the curvature of the loop. As a result, the error of approximation of a hysteresis loop by the improved model does not exceed 1%, which is several times less than the error of the existing model. The improved model is capable of approximating most of the known types of rate-independent symmetrical hysteresis loops encountered in the practice of physical measurements. The model allows building smooth, piecewise-linear, hybrid, minor, mirror-reflected, inverse, reverse, double, and triple loops. One of the possible applications of the model developed is linearization of a probe microscope piezoscanner. The improved model can be found useful for the tasks of simulation of scientific instruments that contain hysteresis elements.

Longitudinal Vehicle Dynamics: A Comparison of Physical and Data-Driven Models Under Large-Scale Real-World Driving Conditions

Mathematical models of vehicle dynamics will form essential components of future autonomous vehicles. They may be used within inverse or forward control loops, or within predictive learning systems. Often, nonlinear physical models are used in this context, which, though conceptually simple (especially for decoupled, longitudinal dynamics), may be computationally costly to parameterise and also inaccurate if they omit vehicle-specific dynamics. In this study we sought to determine the relative merits of a commonly used nonlinear physical model of vehicle dynamics versus data-driven models in large-scale real-world driving conditions. To this end, we compared the performance of a standard nonlinear physical model with a linear state-space model and a neural network model. The large-scale experimental data was obtained from two vehicles; a Lancia Delta car and a Jeep Renegade sport utility vehicle. The vehicles were driven on regular, public roads, during normal human driving, across a range of road gradients. Both data-driven models outperformed the physical model. The neural network model performed best for both vehicles; the state-space model performed almost as well as the neural network for the Lancia Delta, but fell short for the Jeep Renegade whose dynamics were more strongly nonlinear. Our results suggest that the linear data-driven model gives a good trade-off in accuracy and simplicity, whilst the neural network model is most accurate and is extensible to more nonlinear operating conditions, and finally that the widely used physical model may not be the best choice for control design.

Formation and Eruption of Sigmoidal Structure from a Weak Field Region of NOAA 11942

Abstract Using observations from the Solar Dynamics Observatory, we studied an interesting example of a sigmoid formation and eruption from small-scale flux-canceling regions of active region (AR) 11942. Through an analysis of Helioseismic and Magnetic Imager and Atmospheric Imaging Assembly observations we infer that initially the AR is compact and bipolar in nature, evolved to a sheared configuration consisting of inverse J-shaped loops hosting a filament channel over a couple of days. By tracking the photospheric magnetic features, shearing and converging motions are observed to play a prime role in the development of S-shaped loops and further flux cancellation leads to tether-cutting reconnection of J loops. This phase is cotemporal with the filament rise motion, followed by sigmoid eruption at 21:32 UT on January 6. The flux rope rises in phases of slow (v avg = 26 km s−1) and fast (a avg = 55 m s−2) rise motion categorizing the coronal mass ejection (CME) as slow with an associated weak C1.0 class X-ray flare. The flare ribbon separation velocity peaks at around the peak time of the flare at which the maximum reconnection rate (2.14 V cm−1) occurs. Furthermore, the extreme ultraviolet light curves of 131, 171 Å have delayed peaks of 130 minutes compared to 94 Å and are explained by differential emission measure. Our analysis suggests that the energy release is proceeded by a much longer time duration, manifesting the onset of the filament rise and an eventual eruption driven by converging and canceling flux in the photosphere. Unlike strong eruption events, the observed slow CME and weak flare are indications of slow runway tether-cutting reconnection in which most of the sheared arcade is relaxed during the extended phase after the eruption.

On dihedral 2-groups as inner mapping groups of finite commutative inverse property loops

On dihedral 2-groups as inner mapping groups of finite commutative inverse property loops

Semiautomorphic inverse property loops

ABSTRACTWe define a variety of loops called semiautomorphic, inverse property loops that generalize Moufang and Steiner loops. We first show an equivalence between a previously studied variety of loops. Next we extend several known results for Moufang and Steiner loops. That is, the commutant is a subloop and if a is in the commutant, then a2 is a Moufang element, a3 is a c-element and a6 is in the center. Finally, we give two constructions for semiautomorphic inverse property loops based on Chein’s and de Barros and Juriaans’ doubling constructions.

Engineering magnetic nanostructures with inverse hysteresis loops

Top-down lithography techniques allow the fabrication of nanostructured elements with novel spin configurations, which provide a new route to engineer and manipulate the magnetic response of sensors and electronic devices and understand the role of fundamental interactions in materials science. In this study, shallow nanostructure-patterned thin films were designed to present inverse magnetization curves, i.e., an anomalous magnetic mechanism characterized by a negative coercivity and negative remanence. This procedure involved a method for manipulating the spin configuration that yielded a negative coercivity after the patterning of a single material layer. Patterned NiFe thin films with trench depths between 15%–25% of the total film thickness exhibited inverse hysteresis loops for a wide angular range of the applied field and the trench axis. A model based on two exchange-coupled subsystems accounts for the experimental results and thus predicts the conditions for the appearance of this magnetic behavior. The findings of the study not only advance our understanding of patterning effects and confined magnetic systems but also enable the local design and control of the magnetic response of thin materials with potential use in sensor engineering.

ON THE UNIVERSALITY OF SOME SMARANDACHE LOOPS OF BOL-MOUFANG TYPE

A Smarandache quasigroup(loop) is shown to be universal if all its f, g-principal isotopes are Smarandache f, g-principal isotopes. Also, weak Smarandache loops of Bol-Moufang type such as Smarandache: left(right) Bol, Moufang and extra loops are shown to be universal if all their f, g-principal isotopes are Smarandache f, gprincipal isotopes. Conversely, it is shown that if these weak Smarandache loops of Bol-Moufang type are universal, then some autotopisms are true in the weak Smarandache sub-loops of the weak Smarandache loops of Bol-Moufang type relative to some Smarandache elements. Futhermore, a Smarandache left(right) inverse property loop in which all its f, g-principal isotopes are Smarandache f, g-principal isotopes is shown to be universal if and only if it is a Smarandache left(right) Bol loop in which all its f, g-principal isotopes are Smarandache f, g-principal isotopes. Also, it is established that a Smarandache inverse property loop in which all its f, g-principal isotopes are Smarandache f, g-principal isotopes is universal if and only if it is a Smarandache Moufang loop in which all its f, g-principal isotopes are Smarandache f, g-principal isotopes. Hence, some of the autotopisms earlier mentioned are found to be true in the Smarandache sub-loops of universal Smarandache: left(right) inverse property loops and inverse property loops.

Inverse Magnetoresistance Loops in Nearly Percolating Co–Ag Nanostructures and Two-Phase Model

We observed unusual inverse magnetoresistance (MR) loops in the transverse configuration for nearly percolating Co–Ag granular thin films deposited by a coevaporation technique onto a room-temperature glass substrate. When the substrate was heated above about 60°C during evaporation, the inverse MR loops disappeared and converted into normal loops. On the other hand, when the sample was annealed below about 120°C after deposition onto a room-temperature substrate, the inverse MR loops remained, whereas when annealed from about 120 to 300°C, the inverse MR loops were converted into “normal+inverse”-type loops and finally into totally normal loops when annealed above about 350°C. The unusual MR loops may have originated from magnetic nanostructures in nearly percolating Co–Ag granular films. A two-phase model incorporating uniaxial anisotropy, exchange interaction and spin-dependent scattering is presented, which is able to qualitatively explain some of the observed results.

Initiation of CMEs: the role of magnetic twist

Recent multiwavelength observations, modelling results and theoretical developments indicate the importance of twisted magnetic configurations in solar active regions (ARs) in the initiation of coronal mass ejections (CMEs). Through multiwavelength analysis of a few representative events we make an attempt to provide constraints for CME models. The two events presented here in detail start with the expansion of sigmoids (S- or inverse S-shaped loops) observed in soft X-rays. Both events (on 25 October 1994 and 14 October 1995) occurred before the launch of the SOHO spacecraft, but indirect evidences (i.e. signatures of an outward propagation traced up to ≈20 solar radii and an associated magnetic cloud) suggest that both of them were related to CMEs. We show evidence that sigmoids are the coronal manifestations of twisted magnetic flux tubes, which start expanding presumably due to a loss of equilibrium. It is noteworthy that the analysed CMEs occurred in a complex (not simply bipolar) magnetic environment and in all cases we found evidences of the interaction (magnetic reconnection) with the surrounding fields. We propose a scenario for sigmoid expansion related CME events and suggest that twisted magnetic configurations are good candidates for being source regions of CMEs.

Influence of the tensile and torsional stress on the magnetic parameters of a Co-rich stress annealed amorphous wire

Measurements of axial and inverse Wiedemann effect hysteresis loops have been performed on a stress-annealed Co-rich amorphous wire. The influence of both tensile and torsional stress at room temperature on the reduced remanence and coercive field of the treated wires is analyzed. The magnetic behavior of the stressed or twisted wire can be explained by taking into account the fact that this treatment gives rise to structural relaxation and induction of magnetic anisotropy, and depending on the annealing parameters, one of these effects may predominate. >

Torsion dependence of the magnetization process in magnetostrictive amorphous wire

The torsion dependence of axial and inverse Wiedemann-effect hysteresis loops for a highly magnetostrictive wire has been experimentally determined for the as-quenched state and after thermal treatment. Particular emphasis has been given to the study of the evolution of the remanence and switching field for bistable behavior with applied torsional strain. The switching process for both kinds of loops is discussed. From the analysis of the results the existence of a small component of the magnetization along a helical direction for the as-quenched state may be concluded.

EXTENSIONS OF INVERSE LOOPS

EXTENSIONS OF INVERSE LOOPS

Constructions of weak inverse property loops

Constructions of weak inverse property loops

Construction of commutative weak inverse property loops of most orders

Construction of commutative weak inverse property loops of most orders

Combinatorial structures in loops I. Elements of the decomposition theory

Difference sets have been extensively studied in groups, principally in Abelian groups. Here we extend the notion of a difference set to loops. This entails considering the class of 〈 υ, k〉 systems and the special subclasses of 〈 υ, k, λ〉 principal block partial designs (PBPDs) and 〈 υ, k, λ〉 designs. By means of a certain permutation matrix decomposition of the incidence matrices of a system and its complement, we can isomorphically identify an abstract 〈 υ, k〉 system with a corresponding system in a loop. Special properties of this decomposition correspond to special algebraic properties of the loop. Here we investigate the situation when some or all of the elements of the loop are right inversive. We identify certain classes of 〈 υ, k, λ〉 designs, including skew-Hadamard designs and finite projective planes, with designs and difference sets in right inverse property loops and prove a universal existence theorem for 〈 υ, k, λ〉 PBPDs and corresponding difference sets in such loops.

純流体逆形フィードバック発振器の発振原理

A new wall attachment type pure fluid oscillator was developed by means of inverse feedback loops. These loops are generally called positive feedback loops between right outlet and left control inlet and between left outlet and right control inlet. This inverse feedback oscillator itself is not self-excited, but needs one trigger pulse in order to begin oscillation.The principle of the oscillation of the inverse feedback oscillators was studied theoretically and experimentally. It was found that their frequencies were about twice as much as that of the conventional feedback oscillator. The pulse width of the inverse feedback oscillations was decided by the phase lag between two cycles, right to left cycle and left to right cycle. If these two cycles are different from each other, the oscillation will soon be stopped as the oscillation continues. However, these two cycles were experimentally found to be the same and the stable oscillation did not stop even when the device was asymmetrical. The reason why these two cycles were the same was studied and the stable conditions for the pulse width were discovered.

Inverse Loops as Groupoids with One Law

Inverse Loops as Groupoids with One Law