Concept Of Commutativity Research Articles

Verification of Adjoint Solution Commutativity with the New OpenNode Nodal Diffusion Code

This paper presents in-depth exploration and verification of the OpenNode nodal diffusion code, a robust tool designed for multigroup neutron diffusion simulations under steady-state conditions. Leveraging the Nodal Expansion Method with a quartic polynomial and moments weighting method, OpenNode demonstrates exceptional accuracy in approximating nodal surface fluxes, further enhanced by the Quadratic Transverse Leakage approximation. The critical concept of commutativity between adjoint and forward solutions is thoroughly investigated, serving as a benchmark for the code’s reliability in predicting system responses, determining single-point reactor kinetics parameters, and facilitating perturbation analyses. The paper meticulously details OpenNode’s methodology for adjoint neutron flux computation, unraveling its rigorous approach through transposition operations and intricate mathematical transformations. Noteworthy features, including support for second and fourth polynomial orders; versatile computation modes; different mesh points; and seamless integration with Python, PyQt5, and Blender, underscore OpenNode’s adaptability. Results from comprehensive analysis of the two-dimensional and three-dimensional International Atomic Energy Agency core benchmark problem showcase OpenNode’s prowess. The code excels in reactor geometry visualizations, benchmark parameters, and neutronic analysis, with a particular emphasis on commutativity verification against various benchmarked codes. The precision of OpenNode is further demonstrated in power distribution analyses, revealing remarkable proximity to reference values and symmetrical power distribution patterns.

Common Fixed Point Theorems for Weakly Compatible Mapping by (CLR) Property in Dislocated Metric Spaces

In this paper, we employ the concepts of commutativity, weak compatibility and common limit in the range (CLR) property to derive some common fixed point theorems for six mappings satisfying integral type contractive conditions in complete dislocated metric spaces. Our findings improve and extends some previous results found in the literature. 2010 Mathematical Sciences Classification: 54H25, 47H10

Right Central CNZ Property Skewed by Ring Endomorphisms

The concept of the reversible ring property concerning nilpotent elements was introduced by A.M. Abdul-Jabbar and C. A. Ahmed, who introduced the concept of commutativity of nilpotent elements at zero, termed as a CNZ ring, as an extension of reversible rings. In this paper, we extend the CNZ property through the influence of a central ring endomorphism alpha , introducing a new type of ring called a right alpha -skew central CNZ ring. This concept not only expands upon CNZ rings but also serves as a generalization of right alpha -skew central reversible rings. We explore various properties of these rings and delve into extensions of right alpha -skew central CNZ rings, along with examining several established results, which emerge as corollaries of our findings.

Commutativity, Majorization, and Reduction in Fan–Theobald–von Neumann Systems

A Fan–Theobald–von Neumann system (Gowda in Optimizing certain combinations of linear/distance functions over spectral sets, 2019. arXiv:1902.06640v2 ) is a triple $$({{\mathcal {V}}},{{\mathcal {W}}},\lambda )$$ , where $${{\mathcal {V}}}$$ and $${{\mathcal {W}}}$$ are real inner product spaces and $$\lambda :{{\mathcal {V}}}\rightarrow {{\mathcal {W}}}$$ is a norm-preserving map satisfying a Fan–Theobald–von Neumann type inequality together with a condition for equality. Examples include Euclidean Jordan algebras, systems induced by certain hyperbolic polynomials, and normal decompositions systems (Eaton triples). In Gowda (Optimizing certain combinations of linear/distance functions over spectral sets, 2019. arXiv:1902.06640v2 ), we presented some basic properties of such systems and described results on optimization problems dealing with certain combinations of linear/distance and spectral functions. We also introduced the concept of commutativity via the equality in the Fan–Theobald–von Neumann-type inequality. In the present paper, we elaborate on the concept of commutativity and introduce/study automorphisms, majorization, and reduction in Fan–Theobald–von Neumann systems.

Orbital Continuity and Common Fixed Points in Menger PM-Spaces

In this paper, we prove that if a pair of semi R-commuting self-mappings defined on Menger PM-spaces with a nonlinear contractive condition posses a unique common fixed point, then these mappings are orbitally continuous. Also, we investigate whether this assertion and it converse holds if we replace semi R-commutativity with some other concept of commutativity in the weaker sense.

Commutativity degree of chains of finite groups

The concepts of commutativity of two chains, and the commutativity degree of the chains of a finite group such as G which ends in G are introduced. Then, the relation between the commutativity degree of the chains of a finite group is examined, and eventually this measure is calculated for some finite groups and fuzzy subgroups.

Commutativity of first‐order discrete‐time linear time‐varying systems

After introducing the concept of commutativity for continuous‐time linear time‐varying systems, the related literature and the results obtained so far are presented. For a simple introduction of the commutativity of discrete‐time linear time‐varying systems, the problem is formulated for first‐order systems. Finally, explicit necessary and sufficient conditions for the commutativity of first‐order discrete‐time linear time‐varying systems are derived, and their advantageous use in digital system design is illustrated, which are the main objectives of the paper. The results are verified by examples which include an application in amplitude modulation for digital telecommunication.

Investigation of an Active Current Injection DC Circuit Breaker Based on a Magnetic Induction Current Commutation Module

Active current injection circuit breakers (ACICBs), which utilize the mechanical switch and a parallel-connected precharged capacitor, have broad application prospects in future multiterminal dc grids. However, with the increase of system voltage, the precharged capacitor leads to the great cost and size being spent on the charging circuit and auxiliary commutating appliances. To address this shortcoming, an innovative dc circuit breaker (DCCB) based on a magnetic induction current commutation module (MICCM) is proposed. The influence of the main component parameters on the commutation performance is investigated by calculation, in which the self-, mutual, and stray inductances are involved. Besides, the validity of calculation is experimentally proved. Then, by applying the MICCM to the ACICB, the breaking characteristics of the ACICB are analyzed in detail. Finally, a 10-kV DCCB prototype is developed, verifying the feasibility of current commutation concept and the validity of simulated interruption results. Our studies show that a 10-kA bidirectional fault current can be interrupted successfully with a commutation duration less than 250 μs.

Commutativity of the strain energy density expression for the benefit of the FEM implementation of Koiter's initial postbuckling theory

SummaryThe concept of full commutativity of displacements in the expression for strain energy density for the geometrically nonlinear problem has been introduced for the first time and fully established in this paper. Its consequences for the FEM formulation have been demonstrated. As a result, the strain energy, equilibrium equation, and incremental equilibrium equation for the geometrically nonlinear problem can all be presented in a unified manner involving various stiffness matrices that are all symmetric, unique, and explicitly expressed. As an important application, the framework has been employed in the FEM implementation of Koiter's initial postbuckling theory, which has been handicapped by its mesh sensitivity in evaluating one of the initial postbuckling coefficients. This has largely prevented it from being incorporated in mainstream commercial FEM codes. Based on the outcomes of this paper, the mesh sensitivity problem has been completely resolved without the need to use any specially formulated element. As a result, Koiter's theory can be practically and straightforwardly implemented in any FEM code. The results have been verified against those found in the literature.

Perturbations of spectra of closed subspaces in Banach spaces

This paper studies the variation of spectra of closed subspaces (i.e., linear relations) in Banach spaces under some perturbations. A concept of commutativity for subspaces in Banach spaces is introduced and its properties are studied. It is shown that boundedness of the inverse of a closed subspace is preserved under relatively bounded and small gap perturbations and perturbation about spectral condition, separately. By using these results, upper semi-continuity of spectra of closed subspaces is obtained and an error estimate of spectra of closed subspaces is given under bounded perturbation. In the special case that the space is a Hilbert space, invariance of self-adjointness of subspaces under relatively bounded and small gap perturbations and the variation of spectrum of a self-adjoint subspace under bounded and Hermitian perturbation are discussed. The results obtained in the present paper generalize the corresponding results for closed operators to closed subspaces and some of which weaken certain assumptions of the related existing results.

Zero commutativity of nilpotent elements skewed by ring endomorphisms

ABSTRACTThe reversible property is an important role in noncommutative ring theory. Recently, the study of the reversible ring property on nilpotent elements is established by Abdul-Jabbar et al., introducing the concept of commutativity of nilpotent elements at zero (simply, a CNZ ring) as a generalization of reversible rings. We here study this property skewed by a ring endomorphism α, and such ring is called a right α-skew CNZ ring which is an extension of CNZ rings as well as a generalization of right α-skew reversible rings, and then investigate the structure of right α-skew CNZ rings and their related properties. Consequently, several known results are obtained as corollaries of our results.

Г-invariant operators associated with locally compact groups

Let G be a locally compact group and let ? be a closed subgroup of G x G. In this paper, the concept of commutativity with respect to a closed subgroup of a product group, which is a generalization of multipliers under the usual sense, is introduced. As a consequence, we obtain characterization of operators on L2(G) which commute with left translation when G is amenable.

Spontaneous Usage of Different Shortcuts Based on the Commutativity Principle

Based on research on expertise a person can be said to possess integrated conceptual knowledge when she/he is able to spontaneously identify task relevant information in order to solve a problem efficiently. Despite the lack of instruction or explicit cueing, the person should be able to recognize which shortcut strategy can be applied – even when the task context differs from the one in which procedural knowledge about the shortcut was originally acquired. For mental arithmetic, first signs of such adaptive flexibility should develop already in primary school. The current study introduces a paper-and-pencil-based as well as an eyetracking-based approach to unobtrusively measure how students spot and apply (known) shortcut options in mental arithmetic. We investigated the development and the relation of the spontaneous use of two strategies derived from the mathematical concept of commutativity. Children from grade 2 to grade 7 and university students solved three-addends addition problems, which are rarely used in class. Some problems allowed the use of either of two commutativity-based shortcut strategies. Results suggest that from grade three onwards both of the shortcuts were used spontaneously and application of one shortcut correlated positively with application of the other. Rate of spontaneous usage was substantial but smaller than in an instructed variant. Eyetracking data suggested similar fixation patterns for spontaneous an instructed shortcut application. The data are consistent with the development of an integrated concept of the mathematical principle so that it can be spontaneously applied in different contexts and strategies.

Lumpability and Commutativity of Markov Processes

We introduce the concepts of lumpability and commutativity of a continuous time discrete state space Markov process, and provide a necessary and sufficient condition for a lumpable Markov process to be commutative. Under suitable conditions we recover some of the basic quantities of the original Markov process from the jump chain of the lumped Markov process.

Evolution of the commutation concept associated with the development of flow analysis

Evolution of the commutation concept has lead to the proposal and development of different generations of flow analyzers. Since the inception of the air-segmented flow systems till the availability of modern flow injection, sequential-injection and other flow-based analytical systems, a noteworthy improvement of the commutating devices has been noted. Multi-functional manifold is described as a polyvalent approach for methodology implementation in a flow analyzer. It permits the investigation of mixing conditions under different flow patterns (unsegmented, segmented, monosegmented) with optional exploitation of the stopped-flow approach. For this purpose, spectrophotometric or turbidimetric measurements eventually affected by Schlieren noise were considered. Potentialities and limitations of the manifold are discussed in relation with methods based on relatively fast or slow chemical reactions. As applications, phosphate and chloride determinations in plant digests and natural waters were selected. The manifold is characterized by high versatility and may work in connection with different flow configurations. Development will certainly lead to simple, versatile and miniaturized analyzers, able to run samples in a personalized fashion. In addition, random reagent selection, full automation, expansion of the analytical application range and increasing potentialities of the already existing methodologies are devised.

Particles and quantum symmetries

A system of interacting particles equipped with a quantum symmetry is described in an abstract algebraic way. The concept of quantum commutativity is used for the description of algebra of quantum states of the system. The graded commutativity and particles in a singular magnetic field are considered as an example. The generalized Pauli exclusion principle is also mentioned.

An ac-dc converter with reduced electromagnetic interference

The circuit proposed in this paper causes considerably reduced electromagnetic interference (EMI) and harmonic current distortion on the utility supply network in comparison to existing power supplies that are used in electronic equipment (computers, television sets, etc.). The proposed circuit can also be used in providing variable-voltage power supplies for the control of motors and other applications in electro-technologies. The effect of a distorted mains current waveform in distribution systems is to increase the heating of distribution transformers and interfere with radio-frequency equipment such as radios and TVs, and even to disturb the reliable operation of other electronic equipment. The multiphase commutation concept proposed for the circuit topology permits an appreciable reduction in the amplitude of current harmonics generated by modern switching power supplies. The proposed circuit thereby operates at a higher efficiency and reduces the constraints on the switching elements. The multiphase commutation concept can be applied to the development of DC-AC converters that are used mainly in uninterruptible power supplies (UPSs), where it makes possible an output current with very low distortion by using low-weight and less bulky filter elements.

Nearly commuting projections

It is well known that projection operators are typical elements in Boolean algebras, and a number of relevant theorems have been proved for commutative projections. We propose an extension of the concept of commutativity, which we call near-commutativity. We extend to this concept the main theorems on commutative projections, and in various ways we frame the class of nearly commutative projections in Boolean algebras.

New current source inverters with DC-side commutation and load-side energy recovery circuit

Two all-thyristor-type current source inverters (CSIs) with DC-side commutation and load-side energy recovery are proposed to reduce the device voltage stress and to eliminate the commutation failure problems. The inverter circuits are analyzed approximately to give guidelines for commutation circuit design and are compared with the autosequentially commutated inverter (ASCI). The inverters overcome most of the drawbacks of conventional CSIs-high device voltage stress, low operating frequency range, large commutation capacitance-by using a simultaneous recovery and commutation concept. The CSIs use only one commutation capacitor and can be built with considerably low cost. The commutation energies are temporarily stored in a large DC capacitor and recovered to the load side, which makes the device voltage stress low and the efficiency high. The operation of the proposed inverters is verified through computer simulation. Experimental results are shown for a 5-hp induction motor drive.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Two common fixed point theorems for weakly commuting mappings

Two theorems concerning common fixed points of set-valued mappings and singlevalued mappings are established using the concept of weak commutativity indebted to the second author. The first theorem generalizes a recent result of the first author and suitable examples are also given.