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A note on a general sequence of λ-Szász Kantorovich type operators
In the present manuscript, we study the approximation properties of modified Szász Kantorovich operators with a new modification of blending type which depends on parameters,
λ
∈
[
-
1
,
1
]
and
ρ
>
0
. Further, we prove a Korovkin-type approximation theorem and obtain the rate of convergence of these operators. Next, their graphical depiction, error analysis and convergence behaviour of these operators for the different functional spaces are discussed. Moreover, univariate and bivariate version of these sequences of operators are introduced in their respective blocks. Rate of convergence, order of approximation, local approximation, global approximation in terms of weight function and
A
-statistical approximation results are investigated via first and second-order modulus of smoothness, Lipschitz classes, Peetre’s
K
-functional in different spaces of functions.
Journal Article
A computational framework to systematize uncertainty analysis in the sediment fingerprinting approach using least square methods
Simulating sediment transfer processes in catchments has contributed significantly to solving environmental problems due to its importance in the silting of rivers and reservoirs and for controlling the pollution of water bodies. Among the methods used to improve data collection and modelling, the “sediment fingerprinting approach” uses tracers reflecting the composition of eroded soils and sediments in multivariate statistical analyses and mathematical models for optimizing equation systems. Based on generalized least squares (GLS) method and Mahalanobis distance, this study sought to present a computational framework to solve over-determined systems applied to sediment tracing, systematize the uncertainty analysis and sample number optimization. Hence, this approach takes into account the influence of collinearity among the chemical variables that compose the tracer set to be evaluated by the presence of the variance-covariance matrix. A dataset from the Arvorezinha experimental catchment in southern Brazil was used to validate the modeling, and our findings confirmed the assumption of increased uncertainty as the number of target samples decreases in the sources or eroded sediment samples. Sharing the code files with the PySASF (Python package for Source Apportionment with Sediment Fingerprinting) contributes to improving the technique as it allows other researchers to systematically improve the definition of the number of samples required based on the uncertainty analysis.
Journal Article
A mathematical model to the melanoma dynamics involving CAR T-cells
Melanoma is one of the most aggressive types of cancer. Although it has a low percentage of incidence in the population, a high degree of lethality is observed due to its rapid metastasis. As melanoma is a highly immunogenic cancer, it has been used as an experimental model in several studies aimed at developing therapies, such as immunotherapy with Chimeric Antigen Receptor (CAR) T-cells. We propose a mathematical model of three ordinary differential equations to describe the dynamics of melanoma in the presence of Tumor-Associated Macrophages (TAMs) and CAR T-cell therapy, to assess the role of TAMs cells in the failure of this melanoma therapy. We examine the existence and asymptotic stability of equilibrium points of this system, giving a biological interpretation to each of them. Based on our theoretical and numerical results, we conclude that immunosuppression has a negative impact on CAR T-cell immunotherapy and that increasing the immunotherapy dose can improve tumor control. Furthermore, an increase in the action of the TAMs population on tumor proliferation can induce oscillations that eventually become periodic.
Journal Article
How to implement market models using VBA
\"Accessible VBA coding for complex financial modellingImplementing Market Models Using VBA makes solving complex valuation issues accessible to any financial professional with a taste for mathematics. With a focus on the clarity of code, this practical introductory guide includes chapters on VBA fundamentals and essential mathematical techniques, helping readers master the numerical methods to build an algorithm that can be used in a wide range of pricing problems. Coverage includes general algorithms, vanilla instruments, multi-asset instruments, yield curve models, interest rate exotics, and more, guiding readers thoroughly through pricing in the capital markets area. The companion website features additional VBA code and algorithmic techniques, and the interactive blog provides a forum for discussion of code with programmers and financial engineers, giving readers insight into the different applications and customisations possible for even more advanced problem solving..Financial engineers implement models from a mathematical representation of an asset's performance by building a program that performs a valuation of securities based on this asset. Implementing Market Models Using VBA makes this technical process understandable, with well-explained algorithms, VBA code, and accessible theoretical explanations. Decide which numerical method to use in which scenario Identify the necessary building blocks of an algorithm Write clear, functional VBA code for a variety of problems Apply algorithms to different instruments and models Designed for finance professionals, this book brings more accurate modelling within reach for anyone with interest in the market. For clearer code, patient explanation, and practical instruction, Implementing Market Models Using VBA is an essential introductory guide\"-- Provided by publisher.
Book
Energy estimate for Oldroyd-B model under Tresca boundary condition: scheme preserving properties
This paper is concerned with the design of a numerical scheme that preserves; the symmetry, positive definiteness, and
a priori
estimate for the Oldroyd-B model with Tresca boundary condition. Such a scheme is important for its numerical stability, and for investigation of long time behaviour of macro-macro models. The theoretical findings are validated with simulations for lid driven cavity.
Journal Article
Mathematical modelling and computational reduction of molten glass fluid flow in a furnace melting basin
In this work, we present the modelling and numerical simulation of a molten glass fluid flow in a furnace melting basin. We first derive a model for a molten glass fluid flow and present numerical simulations based on the finite element method (FEM). We further discuss and validate the results obtained from the simulations by comparing them with experimental results. Finally, we also present a non-intrusive proper orthogonal decomposition (POD) based on artificial neural networks (ANN) to efficiently handle scenarios which require multiple simulations of the fluid flow upon changing parameters of relevant industrial interest. This approach lets us obtain solutions of a complex 3D model, with good accuracy with respect to the FEM solution, yet with negligible associated computational times.
Journal Article