Applied mathematics and Modelling

Problem: Existing approaches to creating Artificial General Intelligence (AGI) face a fundamental challenge in evaluating information processes and their connection to the real world. Methods based on reinforcement learning depend on artificial and subjective reward systems designed by humans. Meanwhile, unsupervised learning models, despite reducing this dependency, lack a universal principle for aligning their internal information processes with real physical changes in the environment. Consequently, modern architectures—even with significant increases in computational power and data volume—demonstrate a limited capacity for true adaptation, failing to generalize beyond their training data or to form fundamentally new adaptive responses that are coherent with physical reality.
Solution: This paper proposes a theoretical model of adaptive artificial intelligence based on biological principles, designed to overcome these limitations. A key feature of the model is the replacement of traditional gradient-based optimization with an emulation of synaptic plasticity. The model is engineered for individual adaptation to each incoming stimulus through the continuous stabilization of synaptic parameters within unique permissible ranges.
Methodology: The solution is based on two core principles. First, a direct link is established between changes in the physical parameters of an external stimulus and the temporal characteristics of the model's response (frequency and/or phase). Second, a mechanism of synaptic plasticity is implemented, where synapses act as dynamic parameters that change after each neuron activation cycle, thereby forming the system's dynamic memory.
Conclusion: By emulating biological mechanisms such as the Hebbian rule (changes in temporal synchronization Tij​ in a pair of neurons), internal architectural self-regulation, synaptic weight modification (analogous to LTP and LTD), feedback loops, and group differentiation of neurons, the proposed model opens a potential pathway toward creating truly adaptive systems and lays the foundation for a future AGI architecture.

Two, the most simple cases of special-relativistic flows of a viscous, incompressible fluid are considered: plane Couette flow and plane Poiseuille flow. Considering only the regular motion of the fluid we found the distribution of velocity in the fluid (velocity profiles) and the friction force, acting on immovable wall. The results are expressed through simple analytical functions for the Couette flow, while for the Poiseiulle flow they are expressed by higher transcendental functions (Jacobi's elliptic functions).

The human body is a marvel of natural design exhibiting both intricate mathematical patterns and profound spiritual significance. This paper presents a comprehensive study that bridges the rigorous frameworks of mathematical modeling and computation with the rich insights of religious teachings, particularly from the Quran and Islamic scholars. It explores the geometry, proportionality, and fractal nature of the human body through mathematical lenses such as symmetry, the golden ratio, Navier-Stokes fluid dynamics, and neural network models. Simultaneously, it discusses religious perspectives emphasizing the human body as a purposeful creation reflecting divine wisdom. By integrating scientific and spiritual approaches, this study encourages a holistic appreciation of human complexity, underscoring the complementary relationship between mathematics and faith in understanding the structure and function of the human body.

In this paper we first present the known disagreement between the law of a second grade fluid and the statement concerning the asymptotic stability of the rest state. After that we put into evidence that for a third grade fluid (which is not considered in the framework described by Coleman's and Noll Approximation Theorem (ATh» the rest state is asymptotically stable, for any value of the constitutive modulus (tIl.

In this work, we extend the analyses devoted to Newtonian viscous fluids previously reported by Ribe [Physical Review E 68, 036305 (2003)], by investigating shear thickening (dilatant) and shear thinning (pseudoplastic) effects on the development of folding instabilities in non-Newtonian viscous sheets of which viscosity is given by a power-law constitutive equation. Such instabilities are trigged by compression stresses acting on viscous sheets that leave a channel at a very small initial velocity, fall, and then hit a solid surface or a fluid substrate. Our study is conducted through a mixed approach combining direct numerical simulations, energy budget analyses, scaling laws, and experiments. The numerical results are based on an adaptive variational multi-scale method for multiphase flows, while Carpobol gel sheets are considered for the conducted experiments. Two folding regimes are observed: (1) the viscous regime; and (2) the gravitational one. Interestingly, only the latter ...

Amorphous solids increase their stress as a function of an applied strain until a mechanical yield point whereupon the stress cannot increase anymore, afterward exhibiting a steady state with a constant mean stress. In stress-controlled experiments, the system simply breaks when pushed beyond this mean stress. The ubiquity of this phenomenon over a huge variety of amorphous solids calls for a generic theory that is free of microscopic details. Here, we offer such a theory: The mechanical yield is a thermodynamic phase transition, where yield occurs as a spinodal phenomenon. At the spinodal point, there exists a divergent correlation length that is associated with the system-spanning instabilities (also known as shear bands), which are typical to the mechanical yield. The theory, the order parameter used, and the correlation functions that exhibit the divergent correlation length are universal in nature and can be applied to any amorphous solids that undergo mechanical yield.

This study evaluates the effectiveness of Recurrent
Neural Networks (RNNs) and Transformer-based
models in predicting the Air Quality Index (AQI). Accurate AQI prediction is critical for mitigating the significant health impacts of air pollution and plays a vital role in public health protection and environmental
management. The research compares traditional RNN
models, including Long Short-Term Memory (LSTM)
and Gated Recurrent Unit (GRU) networks, with advanced Transformer architectures. Data were collected
from a weather station in Cuenca, Ecuador, focusing
on key pollutants such as CO, NO2, O3, PM2.5, and
SO2. Model performance was assessed using Root
Mean Square Error (RMSE), Mean Absolute Error
(MAE), and the Coefficient of Determination (R2
).
The findings reveal that the LSTM model achieved superior performance, with an R2 of 0.701, an RMSE of
0.087, and an MAE of 0.056, demonstrating superior
capability in capturing temporal dependencies within
complex datasets. Conversely, while Transformerbased models exhibited potential, they were less effective in handling intricate time-series data, resulting
in comparatively lower accuracy. These results position the LSTM model as the most reliable approach
for AQI prediction, offering an optimal balance between predictive accuracy and computational efficiency. This research contributes to improving AQI
forecasting and underscores the importance of timely
interventions to mitigate the harmful effects of air
pollution.

Elementary demonstrations of the 3-body Efimov effect are provided for several models involving a light particle and two heavy ones, and differing by the nature of the 2-body (local or non-local) potentials which bind at zero energy the light particle to each of the heavy ones. The proofs rely on Born-Oppenheimer approximations, which are actually projections of the Hamiltonian into suitable subspaces, and they use the correct reduced mass. A numerical estimate of the long range potential responsible for the accumulation of Efimov bound states is obtained through Padé approximants.

In some cases people are interested in certain kinds of networks and want them to be of small size. Usually these kinds of networks are defined by certain requirements on the connectivity between their inputs and outputs. One trick that sometimes yields the desired networks is counting argument. One considers a certain family of graphs of size n and counts how many of these graphs do not satisfy the requirements (the bad ones). In case the number of bad ones is smaller than the number of graphs in the family, the existence of a good graph (the desired network) is established. In fact, in many of the cases one shows that most of the graphs in the family are good. (The fraction of bad graphs tends to zero as n grows.) The weakness of this approach is that it is nonconstructive: although one knows that many of these graphs are good, he cannot construct one such graph. An (n, m, k) concentrator is a directed acyclic graph (dag) with n inputs, m < n outputs, and at most kn edges, such that for every subset of m inputs there are m vertex disjoint paths going from these m inputs to the outputs. An (n, k) superconentrator (s.c.) is a dag with n inputs, n outputs and at most kn edges, such that for every 1 < r < it and any two sets of r inputs and r outputs there are r vertex disjoint paths connecting the two sets. A family of linear concentrators [superconcentrators] of density k is a set of (n, m, k + o(l)) concentrators [(n, k + o(l)) s.c.'s] for 1 <m < n<cn [for I<n<oo]. In (61 Pinsker constructed a family of linear concentrators of density 29. His construction uses counting argument. Valiant [9] used Pinsker's linear concentrators to construct a family of linear s.c.'s of density 238. By doing so he disproved a conjecture that superconcentrators require more than a linear number of edges p. 450, research problem 12.371. Pippenger [7] has discovered a direct way to construct a family of linear s.c.'s of density 39. His construction used a certain type of graphs. the existence of which is

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The shift toward online education has been accelerated by factors such as fear of COVID-19, rising fuel costs, and enhanced internet connectivity, leading both educational institutions and students to embrace elearning, particularly in English as a Second Language (ESL) contexts. This study examines the influence of elearning on ESL learners' satisfaction, focusing on critical factors such as instructor interaction, student collaboration, and learning content, with e-learning quality as a mediating factor. The data were collected online via Google Forms from 478 ESL students enrolled in online programs in Pakistan. Subsequently, it was analysed using Partial Least Squared (PLS) structural equation modelling. The research concluded that student collaboration had the least significant impact and reliability compared to other independent variables. This study will have practical implications for English language teaching institutions.

An efficient automatic quadrature procedure is developed for numerically computing the integrals 0 , where the function is smooth and nonoscillatory at infinity and is the Bessel functions of order ν =1,0 and 1/4. The procedure involves the use of an automatic integration scheme of modified FFT used for evaluating Fourier integrals and product type integration, and the modified W-transformation used for computing oscillatory infinite integrals.

This study develops deteriorating items production inventory models with random machine breakdown and stochastic repair time. The model assumes the machine repair time is independent of the machine breakdown rate. The classical optimization technique is used to derive an optimal solution. A numerical example and sensitivity analysis are shown to illustrate the models. The stochastic repair models with uniformly distributed repair time tends to have a larger optimal total cost than the fixed repair time model, however the production up time is less than the fixed repair time model. Production and demand rate are the most sensitive parameters for the optimal production up time, and demand rate is the most sensitive parameter to the optimal total cost for the stochastic model with exponential distribution repair time.

1 Department of Mechanical, Aerospace and Nuclear Engineering, 2 Center for Multiphase Research, Rensselaer Polytechnic Institute, Troy, NY 12180, USA (*) Tel: 518-276-4000, Fax: 518-276-3055 Email: podowm@ rpi. edu Key words: Membrane filtration; Dean ...

Heat transfer enhancement for a steady, laminar, incompressible and axially fully developed flow of nonlinear viscoelastic shear-thinning fluids abiding by the Giesekus constitutive structure in straight microtubes of arbitrary non-circular contour under constant heat flux at the walls is investigated. The governing equations are solved based on an embedded double asymptotic series expansion pivoted around the elasticity measure Weissenberg number 𝑊𝑖 and a mapping parameter 𝜀. The effects of the constitutive parameters of the Giesekus model as well as the dimensionless flow parameters on the flow and heat transfer in microtubes of a wide-ranging spectrum of non-circular cross-sectional contours are investigated. The flow and thermal fields of representative tubes with equilateral triangular, square, rectangular, and pentagonal cross-sections are investigated in detail. The analysis reveals that the constitutive mobility parameter 𝛼, viscosity ratio 𝛽 and the Weissenberg number 𝑊𝑖 significantly influence the Nusselt number 𝑁𝑢 together with the flow characteristics, the Péclet Pe, Brinkman Br and Reynolds Re numbers. Effects of the viscous dissipation in wall cooling and wall heating is studied. At a given value of 𝑊𝑖 heat transfer is enhanced regardless the process considered at the boundary. In all cases, heat transfer is improved compared to Newtonian fluids, with the strongest enhancement observed in rectangular microtubes for low-inertia flows.

This paper introduces advances in the geometry of the transforms for cross ratio of four points in a line in the Desargues affine plane. The results given here have a clean, based Desargues affine plan axiomatics and definitions of addition and multiplication of points on a line in this plane, and for skew field properties. In this paper are studied, properties and results related to the some transforms for cross ratio for 4-points, in a line, which we divide into two categories, Invariant and Preserving transforms for cross ratio. The results in this paper are (1) the cross-ratio of four points is Invariant under transforms: Inversion, Natural Translation, Natural Dilation, Mobiüs Transform, in a line of Desargues affine plane. (2) the cross-ratio of four points is Preserved under transforms: parallel projection, translations and dilation's in the Desargues affine plane.

In this paper, as a continuation of our work on the determinants of cubic matrices of order 2 and order 3, we have investigated the possibilities of developing the concept of determinants of cubic matrices with three indexes, as well as the possibility of calculating them using the Laplace expansion method. We have observed that the notion of permutation expansion, which is used for square determinants, and the concept of the Laplace expansion method, which is used for square and non-square (rectangular) determinants, may be applied to this novel concept of 3D determinants. In this research, we demonstrated that the Laplace expansion approach is also applicable to cubic matrices of the second and third orders. These results are presented simply and with extensive proof. The findings are also supported by illustrated cases. In addition, we provided an algorithmic explanation for the Laplace expansion approach applied to cubic matrices.

Ky libër është një përpjekje për të shpjeguar disa nga konceptet më thelbësore dhe të rëndësishme në fushën e matematikës dhe aplikimeve të saj, të cilat janë thelbësore për shumë degë të shkencave të natyrshme dhe inxhinierisë. Ky libër ka për qëllim të shërbejë si një udhëzues shumë i dobishëm dhe i detajuar për studentët, dhe profesionistët që dëshirojnë të thellohen në përdorimin dhe aplikimet e matematikës në fushën e ekonomisë, inxhinerisë, etje.. Me një strukturë të qartë dhe të organizuar, libri ofron një cikël leksionesh që mbulojnë një gamë të gjerë temash nga matematikora teorike dhe e aplikuar, duke i shpjeguar ato me shembuj praktikë dhe ushtrime të shumta të zgjidhura, për të ndihmuar lexuesit të kuptojnë thellë dhe të aplikojnë teorinë në situata të ndryshme ekonomike.
Libri nis me konceptet themelore të hapësirave vektoriale, matricave dhe përcaktorëve, duke e trajtuar secilin aspekt në mënyrë të detajuar. Pjesa e parë e librit shpjegon bazat e hapësirave vektoriale dhe dimensionin e tyre në Rn, duke përfshirë shumëzimin numerik të vektorëve dhe veprimet që mund të kryhen me matricat, të tilla si mbledhja, shumëzimi, kuptimi i determinantëve (përcaktorëve), ekuacionet matricore, etje. Kjo pjesë është e mbushur me ushtrime dhe shembuj të ndryshëm, që ndihmojnë në forcimin e kuptimit të këtyre koncepteve dhe aplikimin e tyre në zgjidhjen e problemeve. Një nga seksionet më të rëndësishme të librit është ai i sistemeve të ekuacioneve lineare dhe metodave për zgjidhjen e tyre. Këtu, lexuesi do të njihet me metoda, si ’metoda e Kramerit’, ’eliminimi Gauss’ dhe ’Gauss-Jordan’, të cilat janë të domosdoshme për zgjidhjen e sistemeve të ekuacioneve linearë, që shpeshherë shfaqen në modelet ekonomike dhe financiare. Po ashtu, bëhet një përshkrim i detajuar për "transformimet lineare", vlerat dhe vektorët vetiakë ku ofrohet një kuptim i thelluar i lidhjeve ndërmjet hapësirave vektoriale dhe përdorimit të këtyre
konceptëve në analizën e sistemeve të ndryshme komplekse. Gjithashtu, ky libër trajton funksionet me shumë variabla, duke ofruar një analizë interesante të derivateve dhe aplikimeve të tyre në fushën e ekonomisë, përfshirë "elasticitetin e kërkesës"’, ’elasticitetin e të ardhurave’ dhe  aplikime të tjera të dobishme. Trajtimi i funksioneve implicite dhe derivimi i funksioneve implicite është një pjesë që ndihmon lexuesit të kuptojnë dhe të aplikojnë këto teknika në problematika të ndryshme, duke mundësuar një trajtim të saktë të ekuacioneve që nuk mund të shprehen drejtpërdrejt. Një nga temat më të rëndësishme të këtij libri është ’optimizimi i kushtëzuar’, një aspekt kyç i matematikës ekonomike, ku diskutohet përdorimi i ’metodës së shumëzuesve të Lagrange’ dhe zgjidhja e problemeve të optimizimit të kushtëzuar, duke e lidhur me aplikime të mundshme në menaxhimin e burimeve dhe maksimizimin e fitimeve. Po ashtu, problemi i ’katrorëve më të vegjël’ dhe ’problemet e mosbarazimeve lineare’ janë shpjeguar përmes ushtrimeve dhe shembujve që ndihmojnë në aplikimin praktik të këtyre metodave në ekonomi.

In an earlier paper by the author [A. Sidi, SIAM J. Math. Anal., 16 (1985), pp. 896-906], asymptotic expansions for Mellin transforms f (z) = ∞ 0 t z-1 f (t) dt as z → ∞, with z real and positive, were derived. In particular, it was shown there that, for certain classes of functions u k (t), k = 0, 1, . . . , that form asymptotic scales as In this note, we show that, for two of the cases considered there, f (z) ∼ ∞ k=0 A k u k (z) as z → ∞, also when z is complex and |ℑz| ≤ η(ℜz) c , for some c ∈ (0, 1) and some fixed, but otherwise arbitrary, η > 0.

In this paper, we discuss the application of the author's d(m) transformation to accelerate the convergence of infinite series ∞ n=1 a n when the terms a n have asymptotic expansions that can be expressed in the form We discuss the implementation of the d(m) transformation via the recursive Walgorithm of the author. We show how to apply this transformation and how to assess in a reliable way the accuracies of the approximations it produces, whether the series converge or they diverge. We classify the different cases that exhibit unique numerical stability issues in floating-point arithmetic. We show that the d(m) transformation can also be used efficiently to accelerate the convergence of infinite products Finally, we give several numerical examples that attest the high efficiency of the d(m) transformation for the different cases.

In an earlier paper by the author [A. Sidi, SIAM J. Math. Anal., 16 (1985), pp. 896-906], asymptotic expansions for Mellin transforms f (z) = ∞ 0 t z-1 f (t) dt as z → ∞, with z real and positive, were derived. In particular, it was shown there that, for certain classes of functions u k (t), k = 0, 1, . . . , that form asymptotic scales as In this note, we show that, for two of the cases considered there, f (z) ∼ ∞ k=0 A k u k (z) as z → ∞, also when z is complex and |ℑz| ≤ η(ℜz) c , for some c ∈ (0, 1) and some fixed, but otherwise arbitrary, η > 0.

This chapter was originally published in the book Proceedings of MEST 2012: Electronic Structure Methods with Applications to Experimental Chemistry. The copy attached is provided by Elsevier for the author's benefit and for the benefit of the author's institution, for non-commercial research, and educational use. This includes without limitation use in instruction at your institution, distribution to specific colleagues, and providing a copy to your institution's administrator.

We suggest certain effects, caused by interaction between rotation and gravitation with turbulence structure, for the cooling/heating of dispersed phase of non-isothermal particles in rotating turbulent fluid flows. These effects are obtained through the derivation of kinetic or probability density function based macroscopic equations for the particles. In doing so, for one-way temperature coupling, we also show that homogeneous, isotropic non-isothermal fluid turbulence does not influence the mean temperature (though it influences mean velocity) of the dispersed phase of particles settling due to gravitational force in the isotropic turbulence.

Numerical solutions for laminar heat transfer of a non-Newtonian fluid in the thermal entrance region for triangular, square, sinusoidal, etc. ducts are presented for constant wall temperature. The continuity equation and parabolic forms of the energy and momentum equations in Cartesian coordinates are transformed by the elliptic grid generation technique into new non-orthogonal coordinates with the boundary of the duct coinciding with the coordinate surface. The effects of axial heat conduction, viscous dissipation and thermal energy sources within the fluid are neglected. The transformed equations are solved by the finite difference technique. As an application of the method, flow and heat transfer results are presented for ducts with triangular, square, sinusoidal and four-cusped cross sections and square cross sections with four indented corners. The results are compared with the results of previous works.

Due to fluctuating environmental conditions
many losses occurs on solar panels, soiling losses are one of
them. To ensure grid stability prediction of soiling loss is
essential. The two unique approaches for estimating the effect of
soiling on small-scale solar plants are compared in this research.
Neural network strategy is used to predict losses due to soiling.
Different training-to-validation proportion is carried to choose
the leading proportion for the show. There are customary
strategies proposed to deterministically assess the solar power
loss caused by ruining. In any case, the error of deterministic
estimation cannot be disposed of due to the characteristic
instability of solar power. Hence, this paper proposes a
probabilistic evaluation strategy, ANN, LSTM to appraise the
power loss by soiling on solar PV board. Test results indicates
that R-square value and predicted power loss in LSTM is more
accurate

The paper considers the numerical stability of the backward recurrence algorithm (BR-algorithm) for computing approximants of the continued fraction with complex elements. The new method establishes sufficient conditions for the numerical stability of this algorithm and the error bounds of the calculation of the nth approximant of the continued fraction with complex elements. It follows from the obtained conditions that the numerical stability of the algorithm depends not only on the rounding errors of the elements and errors of machine operations but also on the value sets and the element sets of the continued fraction. The obtained results were used to study the numerical stability of the BR-algorithm for computing the approximants of the continued fraction expansion of the ratio of Horn’s confluent functions H7. Bidisc and bicardioid regions are established, which guarantee the numerical stability of the BR-algorithm. The obtained result is applied to the study of the numerical stability of computing approximants of the continued fraction expansion of the ratio of Horn’s confluent function H7 with complex parameters. In addition, the analysis of the relative errors arising from the computation of approximants using the backward recurrence algorithm, the forward recurrence algorithm, and Lenz’s algorithm is given. The method for studying the numerical stability of the BR-algorithm proposed in the paper can be used to study the numerical stability of the branched continued fraction expansions and numerical branched continued fractions with elements in angular and parabolic domains. © (2024), (VNTL Publishers). All rights reserved.

The temporal mode stability of incompressible submerged axisymmetric gas jets is comprehensively investigated by linear stability analysis. The basic velocity profile is constructed using the hyperbolic tangent function approach. The influences of basic velocity profile, Reynolds Re, and Weber We numbers, and physical properties of the surrounding liquid on the stability of the gas jet are investigated and stability maps are constructed. We find that the jet breakup propagation velocity shows a strong linear relationship with the velocity of the two-phase interface, and the shear on the interface can greatly change the instability modes of submerged gas jet system. Large surface tension triggers long-wave instability of the jet and local shear at the interface leads to the unsteady transition to short-wave instability. Moreover, it is found that there is a strong linear relationship between the most unstable growth rate and dimensionless parameters directly or indirectly, and R2 is above 0.95. In addition, the instability of the submerged gas jet shows a double-mode feature when the velocity profile parameters exceed their thresholds.

Pertussis (Whooping Cough) resurgence possess a formidable threat to public health systems, particularly
due to disruptions in basic immunization programs induced by the recent COVID-19 Pandemic. Whooping cough
predominantly affects infants and young children even in some developed countries with complete immunization
programs. Therefore, reemergence of this disease stands as a double burden to developing countries with poor
immunization scheme.
In this Paper, we present a comprehensive five non-linear mathematical model to undersee the dynamics of pertussis
transmission. The developed model puts into account the impact of vaccination during pregnancy (maternally
derived immunity), vaccinated individuals, treatment of caregivers, adolescents and young adults who are usually
disease reservoir (asymptomatic carriers. The stability of the equilibrium point was analyzed and the Basic
reproduction number derived using the next generation matrix method. Furthermore, the normalized forward
sensitivity analysis index was performed to pinpoint the most crucial parameter for targeted control and intervention
strategies.
Numerical simulations were done using MATLAB 2021a to validate theoretical findings, relevant results are
displayed.

Currently, the disruptions to routine vaccination programs induced during COVID-19 pandemic have raised worries about possible resurgence of vaccine-preventable diseases like diphtheria
and pertussis, particularly in infants and children with zero vaccination. This study aims to assess
the risk of diphtheria-pertussis co-dynamics and control strategies in the post-pandemic era using
modified SIR-type mathematical model. Our research is hinged on the premise that pathogens
can coexist in a host and that diphtheria-pertussis are both preventable by (Diphtheria-TetanusPertussis) DTAP vaccine. Therefore, the presented model captures epidemiological parameters and
varying disease control coverage inputs to simulate disease behaviour in a population susceptible to
both infections. Key non-optimal control parameters used are vaccination at birth, maternal derived immunity and partial quarantine for diphtheria only. The next generation matrix was used to
derive the basic reproduction number R0 , after which stability analysis was conducted and it was
observed that the formulated model exhibits four equilibrium points. The disease-free equilibrium
and endemic equilibrium are shown to be locally and globally asymptotically stable. The forward
sensitivity index was employed to pinpoint the effects of the hierarchy of parameters within R0.
Furthermore, it was observed that the model would undergo backward bifurcation under certain
conditions, Consequently, optimal control inputs should be considered for future research. Finally,
theoretical accuracy of the diseases co-existence is validated via Numerical simulations and relevant
graphical illustrations are displayed using MATLAB 2021a.

A deterministic model for controlling the neglected tropical filariasis disease known as elephantiasis, caused by a filarial worm, is developed. The model incorporates drug resistance in human and insecticide-resistant vector populations. An investigation into whether the model is of biological importance reveals that it is positively invariant, mathematically well posed, and tractable for epidemiological studies. The filariasis-free and filariasis-present equilibrium points were obtained. The next-generation matrix technique is used to derive the basic reproduction number R 0 , which is then used to determine the local stability analysis of the model. It is established that the system is locally asymptotically stable when R 0 < 1. The technique by Castillo-Chavez and a Lyapunov function were employed to prove the global stability of the model's fixed points. The results of this analysis of filariasis-free equilibrium show that the system is globally asymptotically stable when R 0 < 1 and unstable when R 0 > 1. Similarly, the filariasis-present equilibrium point is proved to be globally asymptotically stable when R 0 > 1 and unstable otherwise. This indicates that the fight against the spread of the disease is achievable. It is observed that increasing human-infected mosquito contacts or mosquito-infected human contacts raises the value of R 0 , whereas decreasing the progression of micro-filaria into infective larva and killing more mosquitoes will decrease the R 0 value according to the sensitivity analysis of the model. The variable precision arithmetic technique executed in MATLAB R2014a was used to determine the elasticity indices of the parameters of R 0 , which showed that the value of R 0 = 0.94639. Further investigations revealed that ω 2 has a significant influence on the reproduction number, suggesting that treatment of acute infections is crucial in the control of the disease. Pontryagin's Maximum Principle (PMP) is used for optimal control analysis. The numerical result revealed that strategy D is the most effective based on the infection averted ratio (IAR) value.

Dimitrov, P., Kamenova, I., Roumenina, E., Filchev, L., Ilieva, I., Jelev, G., Gikov, A., Banov, M., Krasteva, V., Kolchakov, V., Kercheva, M., Dimitrov. E., & Miteva. N. (2019) Estimation of biophysical and biochemical variables of winter wheat through Sentinel-2 vegetation indices. Bulgarian Journal of Agricultural Science, 25(5), 819–832 Traditionally, the growth and physiological status of winter wheat (Triticum aestivum L.) is monitored in the fi eld by measuring different biophysical and biochemical variables such as Above Ground Biomass (AGB), Nitrogen content (N), N uptake, Leaf Area Index (LAI), Fraction of vegetation Cover (fCover), Canopy Chlorophyll Content (CCC), and fraction of Absorbed Photosynthetically Active Radiation (fAPAR). The objective of this study was to investigate the possibility of estimating these crop variables through statistical regression modelling and spectral vegetation indices derived by the Sentinel-2 satellites. Field data were collected over tw...

The discrete autonomous/non-autonomous Toda equations and the discrete Lotka-Volterra system are important integrable discrete systems in fields such as mathematical physics, mathematical biology and statistical physics. They also have applications to numerical linear algebra. In this paper, we first simultaneously obtain their general solutions. Then, we show the asymptotic behavior of the solutions for any initial values as the discrete-time variables go to infinity. Our two main techniques for understanding the distinct integrable systems are to introduce two types of discrete-time variables and to examine properties of a restricted infinite sequence, its associated determinants and polynomials.

We study the limiting behavior of the zeros of the Euler polynomials. When linearly scaled, they approach a definite curve in the complex plane related to the Szegö curve which governs the behavior of the roots of the Taylor polynomials associated to the exponential function. Further, under a conformal transformation, the scaled zeros are uniformly distributed.

Robust estimators have been extensively developed in statistics since the pioneering work of Huber (1964) and Hampel (1968). The most popular robust alternative of the classical multivariate location and scatter estimators are minimum volume ellipsoid and the minimum covariance determinant estimators. In this paper multivariate location and scatter estimate with high breakdown point can be thought of as estimating the mean and covariance of the good part of the data. A study of these estimators providing certain numerical illustrations by using R software is carried out.

In this paper we discuss a kind of symbolic operator method by making use of the defined Sheffer-type polynomial sequences and their generalizations, which can be used to construct many power series transformation and expansion formulas. The convergence of the expansions are also discussed.

The distribution of equi-oscillation points (alternation points) for the error in best Chebyshev approximation on [−1, 1] by rational functions is investigated. In general, the alternation points need not be dense in [−1, 1] when rational functions of degree (n, m) are considered and asymptotically n/m → κ with κ ≥ 1. We show that the asymptotic behavior of the alternation points is closely related to the behavior of the poles of the rational approximants. Hence, poles of the rational approximations are attracting points of alternations such that the well-known equi-distribution for the polynomial case can be heavily disturbed.

People in the current day aspire to make their lives simpler, safer, smarter, and more efficient, which is leading to growing industry and urbanisation, which produces air pollution. Air pollution has become a huge threat to human life, living beings, and mother nature, containing pollutant gases and particulate matter such as SO2, NO2, O3, CO, PM2.5, PM10, and so on, causing cardio-vascular disorders and respiratory issues. It is now necessary to estimate air quality in order to live a healthy and happy life. In this article, I used a famous deep learning methodology as well as machine learning methods to anticipate pollutant and particulate levels and estimate PM2.5 and PM10 values. LSTM delivers the best accurate forecasts among the different examined alternatives. Using the entire set of accessible variables yielded a more accurate result.

spatial and orientation distributions are measured for a suspension of fibers during pressure-driven flow. The fibers are rigid and non-colloidal, and two aspect ratios (length to diameter ratios) of 12 and 24 were tested; the suspending fluid is viscous, Newtonian, and density matched to the particles. As with the migration of spheres in parabolic flows, the fibers migrate toward the centerline of the channel if the concentration is sufficiently high. Migration is not observed for concentrations below a volume fraction of 0.035 for aspect ratio 24 and 0.07 for aspect ratio 12. The orientation distribution of the fibers is spatially dependent. Fibers near the center of the channel align closely with the flow direction, but fibers near the wall are observed to preferentially align in the vorticity (perpendicular to the flow and gradient) direction.

The global expansion of solar photovoltaics (PV) is central to the global energy transition. As governments aim to triple renewable energy capacity by 2030, solar PV is poised for rapid growth, particularly outside mid-latitude regions (China, Europe, US) where uptake has been highest. These new growth areas have diverse environmental conditions, where factors like higher temperatures and aerosol concentrations strongly impact solar power production. A comprehensive review of these effects therefore aids PV performance and siting optimization. This review examines six key influences: solar irradiance, ambient temperature, atmospheric conditions, terrain effects, extreme weather events, and long-term irradiance changes. First, solar irradiance has strong geographic and temporal variability, making it the most significant factor. Second, raising module temperature reduces efficiency by 0.4–0.5 % per degree Celsius, limiting productivity in hotter climates. Third, atmospheric conditions (clouds, aerosols, pollutants, and dust) can reduce electricity output by up to 60 %, especially in desert regions. Fourth, terrain factors like albedo and snow present mixed effects, with increased reflection boosting output but snow obstructing panels. Fifth, extreme weather like wildfires and hailstorms cause substantial damage, while solar eclipses lead to large but short-lived output losses. Finally, long-term changes in solar irradiance, driven by climate change and air pollutants, present future challenges for maintaining PV efficiency. Optimizing PV systems for diverse climates and mitigating environmental impacts on productivity is important to the continued success of solar photovoltaics. This review highlights the need for tailored strategies to maintain performance in varied and evolving environmental contexts.

In this note, the bottleneck product rate variation problem with square-deviation objective is considered. Bounds for the feasible solution of this problem are established explicitly. Existence of a perfect matching on the corresponding bipartite graph again turns out to be sufficient for the 1-bounded feasible solution to this problem as in the case of the problem with absolute-deviation objective. Furthermore, a pseudo-polynomial optimization algorithm that improves existing solution approaches is proposed. Like in the problem with absolute-deviation objective or the product rate variation problem with sum-deviation objective, the cyclic sequences are optimal. Keywords  Scheduling, mixed-model just-in-time, bottleneck objective, integer programming.

The accumulation of dust and other environmental contaminants on the photovoltaic (PV) modules, also known as PV module soiling, is a significant environmental influence reducing the output of the PV power plant. This problem is substantial for countries with low yearly precipitations level and dusty climates. In this paper, the influence of soiling on the performance of PV modules during a year in Yerevan (Armenia) is investigated. Two PV modules were tested, one of which is regularly cleaned with the use of a specially developed automated cleaning system, while the other is left to the soil naturally. The short circuit current, output power, and efficiency losses of two PV modules were measured. The measured data shows that the characterization of soiling losses by measuring the power losses is beneficiary since the output power is the main operational parameter of the PV module. The measurement of shirt circuit current is simpler, but it is not recommended use due to the dependence of short circuit current on the homogeneity of soiling. Meantime, if necessary, the measurement of the efficiency of a soiled PV module can be realized for indication of the amount of efficiency reduction due to the soiling.

The dynamics of a single elastoviscoplastic drop immersed in plane shear flow of a Newtonian fluid is studied by three-dimensional direct numerical simulations using a finite-difference/level set method combined with the Saramito model for the elastoviscoplastic fluid. This model gives rise to a yield stress behavior, where the unyielded state of the material is described as a Kelvin-Voigt viscoelastic solid and the yielded state as a viscoelastic Oldroyd-B fluid. Yielding of an initially solid drop of Carbopol is simulated under successively increasing shear rates. We proceed to examine the roles of nondimensional parameters on the yielding process; in particular, the Bingham number, the capillary number, the Weissenberg number and the ratio of solvent and total drop viscosity are varied. We find that all of these parameters have a significant influence on the drop dynamics, and not only the Bingham number. Numerical simulations predict that the volume of the unyielded region inside the droplet increases with the Bingham number and the Weissenberg number, while it decreases with the capillary number at low Weissenberg and Bingham numbers. A new regime map is obtained for the prediction of the yielded, unyielded and partly yielded modes as a function of the Bingham and Weissenberg numbers. The drop deformation is studied and explained by examining the stresses in the vicinity of the drop interface. The deformation has a complex dependence on the Bingham and Weissenberg numbers. At low Bingham numbers, the droplet deformation shows a non-monotonic behaviour with an increasing drop viscoelasticity. In contrast, at moderate and high Bingham numbers, droplet deformation always increases with drop viscoelasticity. Moreover, it is found that the deformation increases with the capillary number and with the solvent to total drop viscosity ratio. A simple ordinary differential equation model is developed to explain the various behaviours observed numerically. The presented results are in contrast with the heuristic idea that viscoelasticity in the dispersed phase always inhibits deformation.

The aim of this research is to establish a relation between the derivatives of Hardy&#39;s Z function and the argument of the Riemann zeta function in the neighborhood of points where |Z| reaches a large maximum. In this paper, we make a step toward this goal by solving a problem of the same nature.

The dynamics of a model describing the human immunodeficiency virus (HIV) infection with cytotoxic T-lymphocyte (CTL), antibodies and two saturated rates is investigated and studied in this paper. The model includes five nonlinear differential equations describing the evolution of uninfected cells, infected ones, free HIV viruses, CTL immune response and antibodies. This model includes also two treatments that represent the efficiency of drug treatment in inhibiting viral production and preventing new infections. Existence, positivity and boundedness of solutions are given. Existence of the optimal control pair is established and the Pontryagin’s maximum principle is

For a given $\theta\in (-1,1)$, we find out all parameters $\alpha,\beta\in \{0,1\}$ such that, there exists a linear combination of Jacobi polynomials $J_{n+1}^{(\alpha,\beta)}(x)-C J_{n}^{(\alpha,\beta)}(x)$ which generates a Lobatto (Radau) positive quadrature formula of degree of exactness \textcolor{red}{$2n+2$ ($2n+1$)} and contains the point $\theta$ as a node. These positive quadratures are very useful in studying problems in one-sided polynomial $L_1$ approximation.

Asymptotic approximations are derived for integrals that depends on a Matrix. A matrix version analogous to Watson&#39;s lemma for scalar functions are obtained. Key Word: Special functions; Asymptotics; Asymptotic Approximations; Asymptotic Expansions; Matrix; Gamma function of Matrices; Jordan Canonical For Watson’s lemma. AMS Subject Classification: 33C05 , 33C15, 34A05, 15A60, 41A30,41A60. -------------------------------------------------------------------------------------------------------------------------------------Date of Submission: 07-10-2020 Date of Acceptance: 22-10-2020 -------------------------------------------------------------------------------------------------------------------------------------

The emergence of the COVID-19 pandemic highlighted the critical need for robust and adaptable models to predict and manage the spread of infectious diseases. This thesis explores the application of Bayesian statistical inference using the Markov Chain Monte Carlo (MCMC) method to estimate the parameters of an infectious disease model, with a focus on the COVID-19 pandemic. Employing PyMC3, a powerful library in Python based on Bayesian statistical modeling and probabilistic machine learning, we develop and validate a series of Bayesian models to derive robust estimates of model parameters. Specifically, we used a mathematical model that incorporates the dynamics of COVID-19 transmission and the impact of a double-dose vaccination strategy. Our dataset spans from February 24, 2021, to March 31, 2024, capturing a comprehensive timeline of the pandemic's progression in Malaysia. By applying Bayesian methods to this data, we estimate infection rates, providing critical insights into the rate at which susceptible individuals contract the virus and the subsequent spread within the population. Sensitivity analyses reveal the impact of varying priors and data quality on model outputs, emphasizing the importance of robust prior selection and data preprocessing. We observed after the simulation that the MCMC method converges asymptotically to the posterior distribution with 94\% probability, which makes this method better than the usual methods. Based on the normalized mean square error, which we use as the metric error to evaluate how accurately the model fits the real data, we obtained 88\% accuracy. This study enhances the understanding of Bayesian modeling using PyMC3 to have the best parameter estimation. It also provides a foundation for future research in this field. The findings offer valuable contributions to public health strategies, enabling better-informed decisions for managing and mitigating the effects of infectious diseases.

Keywords: Bayesian modeling; Mathematical model; COVID-19; Markov Chain Monte Carlo; PyMC3; Python

For a given $\theta\in (-1,1)$, we find out all parameters $\alpha,\beta\in \{0,1\}$ such that, there exists a linear combination of Jacobi polynomials $J_{n+1}^{(\alpha,\beta)}(x)-C J_{n}^{(\alpha,\beta)}(x)$ which generates a Lobatto (Radau) positive quadrature formula of degree of exactness \textcolor{red}{$2n+2$ ($2n+1$)} and contains the point $\theta$ as a node. These positive quadratures are very useful in studying problems in one-sided polynomial $L_1$ approximation.