Additional Commutation Research Articles

Conditions on Lie ideals in rings

We show that if [Formula: see text] is a non-central Lie ideal of a ring [Formula: see text] with Char[Formula: see text], such that all of its nonzero elements are invertible, then [Formula: see text] is a division ring. We prove that if [Formula: see text] is an [Formula: see text]-central algebra and [Formula: see text] is a Lie ideal without zero divisor such that the set of multiplicative cosets [Formula: see text] is of finite cardinality, then either [Formula: see text] is a field or [Formula: see text] is central. We show the only non-central Lie ideal without zero divisor of a non-commutative central [Formula: see text]-algebra [Formula: see text] with Char[Formula: see text] and radical over the center is [Formula: see text], the additive commutator subgroup of [Formula: see text] and in this case [Formula: see text] is a generalized quaternion algebra. Finally we prove that if [Formula: see text] is a Lie ideal without zero divisor in a central [Formula: see text]-algebra with characteristic not 2 and if [Formula: see text] is a finite residual group, then [Formula: see text] is central.

Serial-Parallel IGBT Connection Method Based on Overvoltage Measurement

This paper deals with a novel method which allows the serial connection of Insulated Gate Bipolar Transistors (IGBTs). The different dynamic characteristics of serially connected IGBTs during turn ON and OFF cause a short-term overvoltage stress in the transistors. In contrary to the commonly used techniques, the presented method reduces additional commutation losses by actively correcting turn ON and OFF delays. The presented method uses overvoltages as measured by a peak detector. The correction circuit doesn’t require a high speed Analog-Digital converter (ADC) or high speed computation. The target power switch unit consists of two serial connected transistors with two identical parallel branches. The well-known 2-level inverter topology equipped with the power switch unit can be connected directly to the high-voltage grid. This converter topology was demanded by our industry partner for 11 MW mining machines. The paper contains a laboratory experiment conducted on a serial-parallel IGBT power switch unit with a tested output power of 1 kW. DOI: http://dx.doi.org/10.5755/j01.eee.22.1.14110

Relativity of arithmetic as a fundamental symmetry of physics

Arithmetic operations can be defined in various ways, even if one assumes commutativity and associativity of addition and multiplication, and distributivity of multiplication with respect to addition. In consequence, whenever one encounters `plus' or `times' one has certain freedom of interpreting this operation. This leads to some freedom in definitions of derivatives, integrals and, thus, practically all equations occurring in natural sciences. A change of realization of arithmetic, without altering the remaining structures of a given equation, plays the same role as a symmetry transformation. An appropriate construction of arithmetic turns out to be particularly important for dynamical systems in fractal space-times. Simple examples from classical and quantum, relativistic and nonrelativistic physics are discussed, including the eigenvalue problem for a quantum harmonic oscillator. It is explained why the change of arithmetic is not equivalent to the usual change of variables, and why it may have implications for the Bell theorem.

On semigroup ideals and n-derivations in near-rings

A non-empty subset U of a near-ring N is said to be a semigroup left (resp. right) ideal of N if NU⊆U (resp. UN⊆U) and if U is both a semigroup left ideal and a semigroup right ideal, it will be called a semigroup ideal. In the present paper, we investigate the commutativity of addition and multiplication of near-rings satisfying certain identities involving n-derivations on semigroup ideals and ideals. Furthermore, we study the conditions with semigroup ideals for n-derivations D1 and D2 of N which imply that D1=D2.

ON (σ, τ)-n-DERIVATIONS IN NEAR-RINGS

In the present paper, we introduce the notion of (σ, τ)-n-derivation in near-ring N and investigate some properties involving (σ, τ)-n-derivations of a prime near-ring N which force N to be a commutative ring. Additive commutativity of near-ring N satisfying certain identities involving (σ, τ)-n-derivations of a prime near-ring N has also been obtained. Related examples to justify the hypotheses in various theorems have also been provided.

ON PERMUTING n-DERIVATIONS IN NEAR-RINGS

In this paper, we introduce the notion of permuting <TEX>$n$</TEX>-derivations in near-ring N and investigate commutativity of addition and multiplication of N. Further, under certain constrants on a <TEX>$n!$</TEX>-torsion free prime near-ring N, it is shown that a permuting <TEX>$n$</TEX>-additive mapping D on N is zero if the trace <TEX>$d$</TEX> of D is zero. Finally, some more related results are also obtained.

NOTES ON LIE IDEALS OF SIMPLE ARTINIAN RINGS

Let R be a ring. If we replace the original associative product of R with their canonic Lie product, or [a, b] = ab - ba for every a, b in R, then R would be a Lie ring. With this new product the additive commutator subgroup of R or [R, R] is a Lie subring of R. Herstein has shown that in a simple ring R with characteristic unequal to 2, any Lie ideal of R either is contained in Z(R), the center of R or contains [R, R]. He also showed that in this situation the Lie ring [R, R]/Z[R, R] is simple. We give an alternative matrix proof of these results for the special case of simple artinian rings and show that in this case the characteristic condition can be more restricted.

High Response and Precision Control of Electronic Throttle Controller Module without Hall Position Sensor for Detecting Rotor Position of BLDCM

This paper describes the characteristics of Electronic Throttle Controller (ETC) module in BLDC motor without the hall sensor for detecting a rotor position. The proposed ETC control system, which is mainly consisted of a BLDC motor, a throttle plate, a return spring and reduction gear, has a position sensor with an analogue voltage output on the throttle valve instead of BLDC motor for detecting the rotor position. So the additional commutation information is necessarily needed to control the ETC module. For this, the estimation method is applied. In order to improve and obtain the high resolution for the position control, it is generally needed to change the gear ratio of the module or the electrical switching method etc. In this paper, the 3-phase switching between successive commutations is adapted instead of the 2-phase switching that is conventionally used. In addition, the position control with a variable PI gain is applied to improve a dynamic response during a transient period and reduce vibration at a stop in case of matching position reference. The mentioned method can be used to estimate the commutation state and operate the high-precision position control for the ETC module and the high response characteristics. The validity of the proposed method is examined through the experimental results.

Security analysis of key agreement protocol based on matrix power function

Key agreement protocol (KAP) using Burau braid groups representation and matrix power function (MPF) is analyzed. MPF arguments are Burau representation matrices defined over finite field or ring. It is shown that KAP security relies on the solution of matrix multivariate quadratic system of equations over the ring with additional commutation constraints for matrices to be found. We are making a conjecture that proposed KAP is a candidate one-way function since its inversion is related with the solution of known multivariate quadratic problem which is NP-complete over any field. The one of advantages of proposed KAP is its possible effective realization even in restricted computational environments by avoiding arithmetic operations with big integers.

INTERSECTION OF YANG–MILLS THEORY WITH GAUGE DESCRIPTION OF GENERAL RELATIVITY

An intersection of Yang–Mills theory with the gauge description of general relativity is considered. This intersection has its origin in a generalized algebra, where the generators of the SO(3, 1) group as gauge group of general relativity and the generators of a SU(N) group as gauge group of Yang–Mills theory are not separated anymore but are related by fulfilling nontrivial commutation relations with each other. Because of the Coleman–Mandula theorem this algebra cannot be postulated as Lie algebra. As consequence, extended gauge transformations as well as an extended expression for the field strength tensor is obtained, which contains a term consisting of products of the Yang–Mills connection and the connection of general relativity. Accordingly a new gauge invariant action incorporating the additional term of the generalized field strength tensor is built, which depends of course on the corresponding tensor determining the additional intersection commutation relations. This means that the theory describes a decisively modified interaction structure between the Yang–Mills gauge field and the gravitational field leading to a violation of the equivalence principle.

$K$-Theory of Azumaya algebras

For an Azumaya algebra $A$ which is free over its centre $R$, we prove that the $K$-theory of $A$ is isomorphic to $K$-theory of $R$ up to its rank torsion. We observe that a graded central simple algebra, graded by an abelian group, is a graded Azumaya algebra and it is free over its centre. So the above result, from the non-graded setting, covers graded central simple algebras. For a graded central simple algebra $A$, we can also consider graded projective modules. Let $\Pgr (R)$ be the category of graded finitely generated projective $R$-modules and $K_i, i\geq 0$, be the Quillen $K$-groups. Then $K_i^{\gr} (R)$ is defined to be $K_i( \Pgr (R))$. We give some examples to show that the graded $K$-theory of $A$ does not necessarily coincide with its usual $K$-theory. For a graded Azumaya algebra $A$, free over its centre $R$ and subject to some conditions, we show that $K_i^{\gr} (A)$ is ``very close'' to $K_i^{\gr}(R)$. Further, we consider additive commutators in the setting of graded division algebras. For a graded division algebra $D$ with a totally ordered abelian grade group, we show how the submodule generated by the additive commutators in $QD$ relates to that of $D$, where $QD$ is the quotient division ring.

Noncommutative classical and quantum mechanics for quadratic Lagrangians (Hamiltonians)

Classical and quantum mechanics based on an extended Heisenberg algebra with additional canonical commutation relations for position and momentum coordinates are considered. In this approach additional noncommutativity is removed from the algebra by a linear transformation of coordinates and transferred to the Hamiltonian (Lagrangian). This linear transformation does not change the quadratic form of the Hamiltonian (Lagrangian), and Feynman’s path integral preserves its exact expression for quadratic models. The compact general formalism presented here can be easily illustrated in any particular quadratic case. As an important result of phenomenological interest, we give the path integral for a charged particle in the noncommutative plane with a perpendicular magnetic field. We also present an effective Planck constant ħ eff which depends on additional noncommutativity.

From numerical concepts to concepts of number

Many experiments with infants suggest that they possess quantitative abilities, and many experimentalists believe that these abilities set the stage for later mathematics: natural numbers and arithmetic. However, the connection between these early and later skills is far from obvious. We evaluate two possible routes to mathematics and argue that neither is sufficient: (1) We first sketch what we think is the most likely model for infant abilities in this domain, and we examine proposals for extrapolating the natural number concept from these beginnings. Proposals for arriving at natural number by (empirical) induction presuppose the mathematical concepts they seek to explain. Moreover, standard experimental tests for children's understanding of number terms do not necessarily tap these concepts. (2) True concepts of number do appear, however, when children are able to understand generalizations over all numbers; for example, the principle of additive commutativity (a+b=b+a). Theories of how children learn such principles usually rely on a process of mapping from physical object groupings. But both experimental results and theoretical considerations imply that direct mapping is insufficient for acquiring these principles. We suggest instead that children may arrive at natural numbers and arithmetic in a more top-down way, by constructing mathematical schemas.

Novel ZCS-PFM Series Resonant High Frequency Inverter for Electromagnetic Induction Eddy Current-Heated Roller

This paper presents a novel prototype of zero current switching pulse frequency modulation (ZCS-PFM )high frequency series resonant inverter using IGBT power module for electromagnetic induction eddy current heated roller in copy and printing machines. The operating principle and unique features of this voltage-fed half bridge inverter with two additional soft commutation inductor snubber are presented including the transformer modeling of induction heated rolling drum This soft switching inverter can achieve stable zero current soft commutation under a discontinuous and continuous resonant load current for a widely specified power regulation processing. The experimental results and computer-aided analysis of this inverter are discussed from a practical point of view.

Critical operators for the degree of the minimal polynomial of derivations restricted to Grassmann spaces

Let V be a finite dimension vector space. For a linear operator on V, f, D( f) denotes the restriction of the derivation associated with f to the mth Grassmann space of V. In [Cyclic spaces for Grassmann derivatives and additive theory, Bull. London Math. Soc. 26 (1994) 140–146] Dias da Silva and Hamidoune obtained a lower bound for the degree of the minimal polynomial of D( f), over an arbitrary field. Over a field of zero characteristic that lower bound is given by deg ( P D ( f ) ) ⩾ m ( deg ( P f ) - m ) + 1 . Using additive number theory results, results on the elementary divisors of D( f) and methods presented by Marcus and Ali in [Minimal polynomials of additive commutators and jordan products, J. Algebra 22 (1972) 12–33] we obtain a characterization of equality cases in the former inequality, over a field of zero characteristic, whenever m does not exceed the number of distinct eigenvalues of f.

Commutator rings

A ring is called a commutator ring if every element is a sum of additive commutators. In this note we give examples of such rings. In particular, we show that given any ring R, a right R-module N, and a nonempty set Ω, EndR(⌖ΩN) and EndR(ΠΩN) are commutator rings if and only if either Ω is infinite or EndR(N) is itself a commutator ring. We also prove that over any ring, a matrix having trace zero can be expressed as a sum of two commutators.

On similarity invariants of matrix commutators and Jordan products

Denote by [ X, Y] the additive commutator XY − YX of two square matrices X, Y over a field F. In a previous paper, the possible eigenvalues, ranks and numbers of nonconstant invariant polynomials of [⋯[[ A, X 1], X 2], …, X k ], when A is a fixed matrix and X 1, …, X k vary, were studied. Moreover given any expression g( X 1, …, X k ), obtained from distinct noncommuting variables X 1, …, X k by applying recursively the Lie product [· , ·] and without using the same variable twice, the possible eigenvalues, ranks and numbers of nonconstant invariant polynomials of g( X 1, …, X k ) when one of the variables X 1, …, X k takes a fixed value in F n× n and the others vary, were studied. The purpose of the present paper is to show that analogous results can be obtained when additive commutators are replaced with multiplicative commutators or Jordan products.

On division rings with algebraic commutators of bounded degree

We shall answer several questions concerning additive or multiplicative commutators in a division ring which are algebraic of bounded degree over its center.

Getting off Death Row: Commuted Sentences and the Deterrent Effect of Capital Punishment

This paper merges a state‐level panel data set that includes crime and deterrence measures and state characteristics with information on all death sentences handed out in the United States between 1977 and 1997. Because the exact month and year of each execution and removal from death row can be identified, they are matched with state‐level criminal activity in the relevant time frame. Controlling for a variety of state characteristics, the paper investigates the impact of the execution rate, commutation and removal rates, homicide arrest rate, sentencing rate, imprisonment rate, and prison death rate on the rate of homicide. The results show that each additional execution decreases homicides by about five, and each additional commutation increases homicides by the same amount, while an additional removal from death row generates one additional murder. Executions, commutations, and removals have no impact on robberies, burglaries, assaults, or motor‐vehicle thefts.

Young Children's Understanding of Addition Concepts

Children's knowledge of concrete versions of additive composition, commutativity and associativity was investigated in two studies. In Study 1, 24 four- to five-year-olds and 25 five- to six-year-olds judged the equivalence of conceptually related addition problems presented using groups of objects. In Study 2, 45 five- to six-year-olds judged related problems and solved addition problems. Both studies indicated that concrete versions of principles were salient to most children although associativity was more difficult than commutativity and there were considerable individual differences in children's understanding. Study 1 results indicated that schoolchildren were more accurate at recognising additive composition than preschoolers and Study 2 results suggested that commutativity knowledge was related to using advanced counting strategies for solving addition problems. Overall, the research supports the claim that examining early knowledge of addition principles provides important insights into children's emerging part-whole knowledge and mathematical development.