Kenric Nelson, Ph.D. on LinkedIn: Independent Approximates provide a maximum likelihood estimate for… (2024)

📃Scientific paper: A New Class of Linear CodesAbstract:Let $n$ be a prime power, $r$ be a prime with $r\mid n-1$, and$\varepsilon\in \(0,1/2\)$.Using the theory of multiplicative character sums andsuperelliptic curves, we construct new codes over $\mathbb F\_r$ having length$n$, relative distance $\(r-1\)/r+O\(n^\{-\varepsilon\}\)$ and rate$n^\{-1/2-\varepsilon\}$.When $r=2$, our binary codes have exponential size whencompared to all previously known families of linear and non-linear codes withrelative distance asymptotic to $1/2$, such as Delsarte--Goethals codes.Moreover, our codes are linear.Continued on ES/IODE ➡️ https://etcse.fr/8YE-------If you find this interesting, feel free to follow, comment and share.We need your help to enhance our visibility, so that our platform continues to serve you.

I am delighted to share that my recent research paper titled "Mittag-Leffler wavelets and their applications for solving fractional optimal control problems" has been published in the "Journal of Vibration and Control".#alzahra_university #optimal_control_problem#wavelet#fractional_calculushttps://lnkd.in/dwjGpznS

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The concept of entropy in nature of the five elements involves understanding the dynamic interplay between these elements and their complementary characteristics. The five elements typically refer to earth, water, fire, air, and ether (or space) in various philosophies.In this context, "currents" can be interpreted as the flow or movement of energy, information, or matter between these elements, forming complex relationships and feedback loops. These currents can be described using positive algebraic equations, which represent the interactions and balance between the elements.Statistical mechanisms come into play when analyzing the distribution and behavior of these currents over time. By applying statistical inputs, such as probability distributions or time-series analysis, we can gain insights into the patterns and trends of the elemental interplay.Elaborating on the interplay of "n," it is possible to extend this concept beyond the traditional five elements. Here, "n" represents the number of elements involved, allowing us to consider more diverse and intricate systems. This expansion could involve incorporating additional elements or abstract concepts that interact with each other, contributing to a deeper understanding of natural processes.In summary, the executive summary outlines a statistical approach to comprehend the entropy and interactions of the five elements and beyond, using positive algebraic equations and statistical mechanisms to analyze the complex interplay of currents between these elements or "n" elements. The study seeks to offer a quantitative perspective on the dynamic and interconnected nature of natural processes and systems.

Differential Equations: Projector Analysis on Time ScalesFrom the Editor's web site:This book presents a projector analysis of dynamic systems on time scales. The dynamic systems are classified as first, second, third and fourth kinds. For each classes of dynamic systems the basic matrix chains are constructed. The proposed theory is applied for decoupling of dynamic equations on time scales. Properly involved derivatives, constraints and consistent initial values for the considered equations are defined. A linearization for nonlinear dynamic systems is introduced and the total derivative for regular linearized equations with tractability index one is investigated.The first book devoted on projector analysis of dynamic equations on time scalesProvides decoupling of all classes of linear time-varying dynamic equations.Provides with many examples illustrated the main theory. https://lnkd.in/dV5uiHrQ

A paper titled "Fractional Differential Equations with the General Fractional Derivatives of Arbitrary Order in the Riemann-Liouville Sense " may raise your interest https://buff.ly/3QGkOxC 🔎 AbstractIn this paper, we first consider the general fractional derivatives of arbitrary order defined in the Riemann–Liouville sense. In particular, we deduce an explicit form of their null space and prove the second fundamental theorem of fractional calculus that leads to a closed form formula for their projector operator. These results allow us to formulate the natural initial conditions for the fractional differential equations with the general fractional derivatives of arbitrary order in the Riemann–Liouville sense. In the second part of the paper, we develop an operational calculus of the Mikusiński type for the general fractional derivatives of arbitrary order in the Riemann–Liouville sense and apply it for derivation of an explicit form of solutions to the Cauchy problems for the single- and multi-term linear fractional differential equations with these derivatives. The solutions are provided in form of the convolution series generated by the kernels of the corresponding general fractional integrals.Keywords: #Soninekernel; #Soninecondition; #fractionalintegral; #operationalcalculus; #MDPIOpenAccess #ComSciMath_Mdpi #BerlinUniversity

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4. Discussion and ConclusionsThe main contribution of this work was to provide two strategies to generate different analytical solutions to the three-dimensional heat diffusion equation. Relevant proofs of the generated particular solutions for each strategies were provided.One aspect to keep in mind when using the presented solution strategies is that not all initial and boundary conditions can be used. Such conditions must be compatible with the dynamic behavior of the analytical solutions. This constitutes an important limitation when generating solutions for the heat diffusion equation. As seen in the generated solutions, the temperature increases with time, mainly at one end of the scalar field; therefore, a pertinent scenario in which these techniques can be applied occurs when the Newmann boundary condition is obtained, which is a finite flow of constant surface heat, which causes precisely this effect. Another way to take this to an advantage is to fit either the initial or boundary conditions to those of the given problem by a linear combination of several heat polynomials. Solutions with a stationary behavior in time and space are usually of greater interest.A numerical analysis was developed to validate the analytical solutions generated. This analysis was performed using a single spatial variable so that the scalar fields of the proposed solutions could be plotted. This numerical analysis contributed to the certainty that the analytical solutions generated were correct. The fact that the temperature graphically increases with time in both solution strategies is consistent with the algebraic information contained in the analytical solutions.https://lnkd.in/gTQyvguB

Our paper titled "Residual-based a posteriori error estimation for mixed virtual element methods" has been published by Computers & Mathematics with Applications.This paper presents an a posteriori error analysis for the mixed virtual element method (mixed-VEM) applied to general second-order elliptic equations. https://lnkd.in/eJNksj7t

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I am glad to share that my new paper 'Parametric risk-neutral density estimation via finite lognormal-Weibull mixtures', co-authored with Ingmar Nolte and Manh Cuong Pham from Lancaster University Management School, has been published in the Journal of Econometrics. The paper introduces a novel parametric mixture-of-density method to estimate the risk-neutral density (RND) from options data. Our key innovation is the inclusion of Weibull components in the classic mixture-of-lognormal density tailored to capture the stylized heavy left-tail of empirical RNDs for stock indices. This results in a highly flexible parametric family of densities which can fit complex RND shapes with relatively fewer parameters and higher precision than several existing (semi)-nonparametric methods. We carefully balance misspecification and overfitting to produce a parsimonious density estimate with a good fit to the observable option prices. Our empirical results reveal the reliability of our new method while highlighting the importance of diagnostic testing after RND estimation: blindly adopting (semi)-nonparametric RND estimators with 'recommended' tuning parameter choices can result in highly misleading RND estimates if one does not check the model-implied residuals. The paper is openly accessible via the link below. The supplementary materials and related codes are also available for download via the authors' personal websites. https://lnkd.in/edzVTDs3

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New paper with Christoph Knochenhauer and Alexander Merkelhttps://lnkd.in/ewebgRsWHere we look at controlling a stochastic process whose drift depends on an unobserved variable - so our control both affects our costs and our learning. We give a rigorous connection to a finite-dimensional PDE, which allows us to highlight the benefits of learning in a general context.

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We glad to share the top 3 most read publications in Nonlinear Analysis: Modelling and Control at 2023:Devi, Medisetty Padma, and Suripeddi Srinivas. "Heat transfer effects on the oscillatory MHD flow in a porous channel with two immiscible fluids." Nonlinear Analysis: Modelling and Control 28 (2023): 1-19. https://lnkd.in/eU36RN9rLuo, Cheng, Guo-Cheng Wu, and Lan-Lan Huang. "Fractional uncertain differential equations with general memory effects: Existences and alpha-path solutions." Nonlinear Analysis: Modelling and Control 28 (2023): 1-28. https://lnkd.in/eMZ8X7G7Reddy, Anala Subramanyam, et al. "MHD flow of non-Newtonian ferro nanofluid between two vertical porous walls with Cattaneo–Christov heat flux, entropy generation, and time-dependent pressure gradient." Nonlinear Analysis: Modelling and Control 28 (2023): 1-17. https://lnkd.in/eHe6yEsj