| viXra.org > Functions and Analysis > 2409 |
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| viXra.org > Functions and Analysis > 2409 |
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[8] viXra:2409.0162 [pdf] submitted on 2024-09-29 16:03:16
Authors: Juan Elias Millas Vera
Comments: 5 Pages.
In this paper I show a several generalizations of the Ramanujan’s Mock θ-functions. Using sigma and pi operators and defining the series.
Category: Functions and Analysis
[7] viXra:2409.0140 [pdf] submitted on 2024-09-25 03:36:18
Authors: Hyon Sung-Yun, Sung Chol U, Sung Chol Kim, Myong hyok Sin
Comments: 15 Pages.
Proportional-Integral-Derivative controller is remained as the most widely used controller for many industrial applications even though it was developed decades ago. This is because of its simplicity, satisfactory control performance and robustness. The classical and empirical PID tuning rules are applicable only to the FOPDT and cannot guarantee its optimality. The Ziegler-Nichols frequency response method is regarded as a basis of relay feedback auto-tuning because it uses the only information at the phase crossover frequency. The Ziegler-Nichols tunings are quite aggressive for lag- dominant processes but sluggish for delay-dominant processes. The IMC-PID settings yield good servo performance and robustness, they result in poor LD (load disturbance) rejection for lag-dominant plants. We have proposed a new method of determining LQ index in consideration of dominant pole placement for desired performance and derive a simple LQR-PID tuning formula via IMC-like H∞ approach for first order plus dead-time systems. We have determined the weight for sensitivity function so that LQ optimization is equivalent to the H∞ optimization of the weighted sensitivity function. The proposed PID controller has the same performance as LQR controller and the tuning method is simple, since it does not need to solve the Riccati algebraic equation. We also present other two tuning methods for PID controller: LQR-like and pole-placement-like ones. The new contributions in this paper are: determination of LQ index for dominant poles placement and optimal weight for sensitivity, and derivation of LQR-PID tuning methods via IMC-like approach, LQR and pole-placement approaches. The effectiveness of the proposed methodology and the identity of the PID parameters tuned by those three methods have been demonstrated via simulation.
Category: Functions and Analysis
[6] viXra:2409.0120 [pdf] submitted on 2024-09-24 02:09:26
Authors: KumSosng Jang, YongKwon Pak, MyongHyok Sin1, NamHo Kim
Comments: 10 Pages.
Classical fractional derivative does not reflect hysteresis characteristic, the unique characteristic of fractional derivative. In order to overcome it, identification approach for the system with input delay expressed by conformable fractional order derivative is proposed. Simulation results shows that the proposed approach infers systematic parameters with high accuracy.
Category: Functions and Analysis
[5] viXra:2409.0114 [pdf] submitted on 2024-09-23 02:00:30
Authors: Parker Emerson
Comments: 34 Pages.
Spinor theory and its applications are indispensable in many areas of theoretical physics, especiallyin quantum mechanics, general relativity, and string theory. Spinors are complex objects thattransform under specific representations of the Lorentz or rotation groups, capturing the intrinsicspin properties of particles. Recent developments in mathematical abstraction have provided newinsights and tools for exploring spinor dynamics, particularly through the lens of motivic operatorsand M-Posit transforms.This paper delves into the intricate dynamics of spinors subjected to motivic operators and MPosit transforms. Motivic operators encapsulate intrinsic algebraic properties and perturbations,leading to highly evolved spinor states without reliance on external coordinate systems. The M-Posittransform, a novel operator designed for spinors, leverages fractal morphic properties, topologicalcongruence, and quantum-inspired perturbations to manipulate spinor structures within an infinitedimensional oneness geometry calculus.Drawing on the foundations laid by twistor theory, we aim to redefine the evolution of spinorsusing intrinsic properties derived from phenomenological velocity equations. By interpreting spinorsas self-propelled twistors, we offer new perspectives on spinor transformations and dynamics. Thisintrinsic approach not only simplifies the mathematical treatment but also enhances the physicaland geometric interpretation of spinor behaviors.The structure of this paper is organized as follows: We begin with the formal definition andcomputation of spinor components using motivic operators, highlighting the steps involved in theirtransformations. Following this, we introduce the M-Posit transform and explore its applicationto spinors, providing detailed mathematical formulations and examples. We also examine theimplications of these transformations in higher-dimensional twistor spaces and non-commutativestructures. Finally, we extend our analysis to practical applications in quantum computing, fractalimage processing, and quantum field theory.The potential of spinning theory redefined through motivic operators and M-posit transformsoffers promising avenues for further research in various domains of theoretical physics and mathematics. This paper sets a foundation for these explorations, emphasizing the importance of intrinsicproperties and algebraic dynamics in understanding complex spinor evolutions.
Category: Functions and Analysis
[4] viXra:2409.0110 [pdf] submitted on 2024-09-22 01:22:50
Authors: Bin Wang
Comments: 10 Pages.
We extend the convergence for mollifiers to that for differential forms of arbitrary degrees.
Category: Functions and Analysis
[3] viXra:2409.0103 [pdf] submitted on 2024-09-19 23:01:08
Authors: SonUng Hong, Kwang Ri, CholRyong Kim
Comments: 10 Pages.
In this paper, we provide some useful lemmas to construct continued fraction based on a given power series. Then we establish new continued fraction approximations for the gamma function via the Tri-gamma function. Especially, we analytically determine all parameters of the continued fraction by Bernoulli numbers.
Category: Functions and Analysis
[2] viXra:2409.0023 [pdf] submitted on 2024-09-06 16:30:37
Authors: Richard J. Mathar
Comments: 11 Pages.
Definite integrals along the real axis from zero to infinity with functions with denominator 1+x^n*sin^2 x suffer from dominant peaks at all x-values that are close to Pi, which impedes sampling the function with generic discrete numerical methods. We demonstrate the method of integrating along a closed contour around a circular sector in the complex x-plane and collecting the sum of all (infinitely many) residues inside the sector with an adapted series acceleration.
Category: Functions and Analysis
[1] viXra:2409.0007 [pdf] submitted on 2024-09-02 20:37:38
Authors: Mamadou Ndao
Comments: 4 Pages. (Note by viXra Admin: Please cite and list scientific references)
This document presents a new method for solving constrained optimization problems, an alternative to the Lagrange multipliers. We introduce the Vector Product Approach for Optimization Resolution (VPAOR), which uses properties of vector products to simplify optimization problems. Our results demonstrate that this approach is an alternative to traditional methods, offering an effective solution for various problems.
Category: Functions and Analysis
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