A Novel low power 2-D to 3-D Array Priority Encoder using Split-Logic Technique for Data Path Applications

In this work, an ascendable low power 64-bit priority encoder is designed using a two-directional array to three-directional array conversion, and Split-logic technique and 6-bit is obtained as the output. By using this method, the high performance priority encoder can be achieved. In the conventional priority encoder, a single bit is set as an input, but for a priority encoder with 3-Darray, every input are specified in the matrix form. The I-bit input file is split hooked on M × N bits, similar to 2-D Matrix. In priority encoder with 3-Darray, three directional output comes out, unlike traditional priority encoder, where the output is received from one direction. The development can be achieved by implementing the two-directional array to three-directional array technique. Simulation results show that the proposed 2-D and 3-D priority encoder consumes 0.087039mW and 0.184014mW which is less when compared with the conventional priority encoder. The priority encoders are simulated and synthesized using VHDL in Xilinx Vivado version 2019.2 and the Oasys synthesis tool.

Characteristics of Regular Functions Defined on a Semicommutative Subalgebra of 4-Dimensional Complex Matrix Algebra

In this paper, we give an extended quaternion as a matrix form involving complex components. We introduce a semicommutative subalgebra ℂ ℂ 2 of the complex matrix algebra M 4 , ℂ . We exhibit regular functions defined on a domain in ℂ 4 but taking values in ℂ ℂ 2 . By using the characteristics of these regular functions, we propose the corresponding Cauchy–Riemann equations. In addition, we demonstrate several properties of these regular functions using these novel Cauchy–Riemann equations. Mathematical Subject Classification is 32G35, 32W50, 32A99, and 11E88.

Corrigendum to “The Oresme sequence: The generalization of its matrix form and its hybridization process” [Notes on Number Theory and Discrete Mathematics, Vol. 27, 2021, No. 1, 101–111]

The present Corrigendum contains a list of corrections applicable to the authors’ paper [1].

Green’s Functions of Multi-Layered Plane Media with Arbitrary Boundary Conditions and Its Application on the Analysis of the Meander Line Slow-Wave Structure

A method was proposed for solving the dyadic Green’s functions (DGF) and scalar Green’s functions (SGF) of multi-layered plane media in this paper. The DGF and SGF were expressed in matrix form, where the variables of the boundary conditions (BCs) can be separated in matrix form. The obtained DGF and SGF are in explicit form and suitable for arbitrary boundary conditions, owing to the matrix form expression and the separable variables of the BCs. The Green’s functions with typical BCs were obtained, and the dispersion characteristic of the meander line slow-wave structure (ML-SWS) is analyzed based on the proposed DGF. The relative error between the theoretical results and the simulated ones with different relative permittivity is under 3%, which demonstrates that the proposed DGF is suitable for electromagnetic analysis to complicated structure including the ML-SWS.

Convergence of the Nelder-Mead method

We develop a matrix form of the Nelder-Mead simplex method and show that its convergence is related to the convergence of infinite matrix products. We then characterize the spectra of the involved matrices necessary for the study of convergence. Using these results, we discuss several examples of possible convergence or failure modes. Then, we prove a general convergence theorem for the simplex sequences generated by the method. The key assumption of the convergence theorem is proved in low-dimensional spaces up to 8 dimensions.

Decomposed 2*2 games - a conceptual review

2*2 games, such as the Prisoner's Dilemma, are a common tool for studying cooperation and social decision-making. In experiments, 2*2 games are usually presented in matrix form, such that participants see only the possible outcomes. Some 2*2 games can be decomposed into payoffs for self and other, such that participants see the direct consequences of two actions. While the final outcomes of the decomposed form and the matrix-form can be identical, the framing differs: the matrix form emphasises the outcome, the decomposed form emphasises the action. This allows decomposed games to address questions that could not be answered with matrix games. Here, we provide a conceptual overview of decomposed games that is accessible without knowing the underlying mathematics. We explain which 2*2 games can be decomposed, why the same payoff matrix can be decomposed into infinitely many decompositions, and we apply this to (a)symmetric games, (a)symmetric decompositions, and games with ties. Finally, we show how to calculate all decompositions for a given game and we suggest when the decomposed form might be more appropriate than the matrix form for an experimental design.

A New Recursive Composite Adaptive Controller for Robot Manipulators

In this paper, a new recursive implementation of composite adaptive control for robot manipulators is proposed. We investigate the recursive composite adaptive algorithm and prove the stability directly based on the Newton-Euler equations in matrix form, which, to our knowledge, is the first result on this point in the literature. The proposed algorithm has an amount of computation On, which is less than any existing similar algorithms and can satisfy the computation need of the complicated multidegree manipulators. The manipulator of the Chinese Space Station is employed as a simulation example, and the results verify the effectiveness of this proposed recursive algorithm.

Simultaneous Collision of the Rigid Body at Two Points

We present a new approach based on the notion of inertance for the simultaneous collisions without friction of a rigid solid. The calculations are performed using the screw (plückerian) coordinates, while the results are obtained in matrix form, and they may be easily implemented for different practical situations. One calculates the velocities after collision, the energy of lost velocities, and the loss of the kinetic energy. The general algorithm of calculation is described in the paper. The main assumption is that the normal velocities at the contact points vanish simultaneously. The coefficients of restitution at the contact points may be equal or not. Some completely solved applications are also presented, and the numerical results are discussed. The numerical values depend on which coefficient of restitution is used.

A new method for creating Mivar knowledge bases in tabular-matrix form for ground intelligent vehicle control systems

This research presents a methodology for creating mivar knowledge bases in tabular-matrix form for ground intelligent vehicle control systems. At its core, this methodology is kind of instruction for analysts facing the task of formalizing knowledge in a given subject area. The result of this formalization is a “knowledge map” created according to a special proposed template. In the future, this template allows forming a knowledge base for a given subject area in the formalism of bipartite oriented mivar networks. As an example, the subject area of ground-based intelligent vehicle control systems is used as a template. The proposed methodology of knowledge formalization makes it possible to simplify the process of creating models in Wi!Mi “Razumator-Consultant” 2.1 and also to level the probability of logical collisions when designing a knowledge model in the formalism of bipartite oriented mivar networks.

Minimax Design of 2D FIR Half-Band Filters Using an Efficient Matrix-Based IRLS Algorithm

This paper considers the minimax design of two-dimensional (2D) finite impulse response (FIR) half-band filters. First, the design problem is formulated in a matrix form, where the half-band constraints are expressed as a pair of matrix equations. By matrix transformations, the constrained minimax problem is transformed into an unconstrained one. Then, we propose an efficient iterative reweighted least squares (IRLS) algorithm to solve this problem. The weighted least squares (WLS) subproblems arising from the IRLS algorithm are solved using a generalized conjugate gradient (GCG) algorithm. Moreover, the GCG algorithm is guaranteed to converge in a finite number of iterations. In the proposed algorithm, the design coefficients of filters are solved in their matrix form, leading to a great saving in computations and memory space. Design examples and comparisons with existing methods are provided to demonstrate the effectiveness and efficiency of the proposed algorithm.