arXiv subjects

Muneerah Al Nuwairan

Publications and source records attributed to Muneerah Al Nuwairan.

5 recordsLinked to original sources

arXiv2025

Periodic Fractional Control in Bioprocesses for Clean Water and Ecosystem Health

This paper introduces a novel fractional-order chemostat model (FOCM) incorporating Caputo fractional derivative with sliding memory (CFDS) to capture microbial memory effects in biological water treatment, addressing limitations of integer-order models that overlook time-dependent behaviors and fail to capture microbial memory such as delayed growth responses to past nutrient availability, history-dependent adaptation to inflow fluctuations, and persistent historical effects over hours to days, which are biologically critical in wastewater treatment. By optimizing periodic dilution rate control, we minimize the average pollutant output, constrained by treatment capacity and periodic boundaries. Key contributions include: (1) a rigorous fractional framework linking microbial kinetics to memory-driven control; (2) reduction to a 1D fractional-order differential equation (FDE) for computational efficiency; (3) proofs of optimal periodic solution (OPS) existence/uniqueness via Schauder's theorem and convexity; (4) bang-bang control derivation using fractional Pontryagin maximum principle (PMP) and Fourier-Gegenbauer pseudospectral (FG-PS) method with a specialized edge-detection technique to handle control discontinuities, ensuring efficient numerical resolution of switching points and discontinuities inherent in bang-bang strategies; and (5) a comprehensive sensitivity analysis revealing how the fractional order α, scaling parameter {\vartheta}, and memory length L critically influence system performance, with simulations showing up to 40% reduction in substrate concentrations versus steady-state and demonstrating computational tractability through efficient discretization that scales favorably for practical implementation. Scientifically, this advances fractional calculus in bioprocesses, revealing memory's role in improving responsiveness and efficiency.

math.OC↗

arXiv2020

An Algorithm for Verifying Some Norm Identities in Inner-Product Spaces

In this paper, we provide an algorithm for verifying the validity of identities of the form $\underset{A\subseteq\overline{n}}{\sum}c_{A}\left\Vert x_{A}\right\Vert ^{2}=0$, where $x_{A}=\underset{i\in A}{\sum}x_{i}$ and $\overline{n}=\{1,...,n\}$ in inner-product spaces. Such algorithm is used to verify the validity, in inner-product spaces, for a number of identities. These include a generalization of the parallelopiped law. We also show that such identities hold only in inner-product spaces. Thus, the algorithm can be used to deduce characterizations of inner-product spaces.

math.FA↗

arXiv2020

Inclusion-Exclusion-Like identities

An expression $E(X_{1},...,X_{n})$ built using union, intersection, and complements is called inclusion-exclusion-like if, like the union in the exclusion-inclusion principle, there are constants $c_{1},c_{2},...,c_{n}$ so that for any sequence of sets${ A=(A_{1},...,A_{n})}$ the cardinality of ${ E(A_{1},...,A_{n})}$ can be expressed as $\left|E(A_{1},...,A_{n})\right|=$$\sum_{k=1}^{n}c_{k}i_{n,k}(A)$ where $i_{n,k}(A)=\sum_{I\subseteq\overline{n},\left|I=k\right|}^{n}\left|\cap_{i\in I}A_{i}\right|$ is the sum of the cardinalities of all intersections of $k$ sets in the sequence $A$. In this paper, we construct, from the expression $E$, a set of nonempty subsets of $\left\{ 1,\ldots,n\right\} $ called the characteristic set of $E$, and using this set to give a necessary and sufficient condition for the expression to be inclusion-exclusion-like . Furthermore, we give a method for determining the constants $c_{1},c_{2},...,c_{n}$ in the expression for the cardinality of ${ E(A_{1},...,A_{n})}$ when it exists. The content of the paper is illustrated by a simple detailed example given in the introduction.

math.CO↗

arXiv2017

Potential Examples for Non-Additivity of the Minimal Output Entropy

In this paper, we study the minimal output entropy of EPOSIC channels. We determine the cases where their minimal output entropy is zero, and obtain some partial results on the fulfillment of their entanglement breaking property.Our results show that these channels provide potential examples for non-additivity of the minimal output entropy.

math-ph↗

arXiv2013

SU(2)-Irreducibly covariant and EPOSIC channels

In this paper we introduce EPOSIC channels, a class of SU(2)-covariant quantum channels. We give their definition, a Kraus representation of them, and compute their Choi matrices. We show that these channels form the set of extreme points of all SU(2)-irreducibly covariant channels. We also compute their complementary channels, and their dual maps. As application of these channel, we get a new example of positive map that is not completely positive.

math-ph↗