In this article, we present, after a survey carried out on the ground, in the City of Bandundu, estimated measurements of the quantities (weight, number and nutritional value) of some products sold ...by the market gardeners of this city and that the Bandundians consume regularly. We bought some products sold by the market gardeners of this city which we counted, weighed and evaluated the nutritional value in order to say at the end if the inhabitants of this city know how to evaluate what they consume.
In this paper, we define split quaternions with components including Pell and Pell-Lucas number sequences. By using Binet's formulas and Cayley-Dickson's notation we introduce a new polar ...representation for split quaternions. This alternative representation, based on two complex number sequences, provides a new perspective on the structure of Pell and Pell-Lucas split quaternions and give a deeper understanding of their geometric interpretations and transformations. Furthermore, some fundamental properties and identities for these type of Pell and Pell-Lucas split quaternions are studied. In further the current paper, it would be valuable to replicate similar approaches polar representationin with Pell and Pell-Lucas Split quaternions.
Let wr be a given integer sequence in arithmetic progression with a common difference d. The study of diophantine equations, which are polynomial equations seeking integer solutions, has been a very ...interesting journey in the field of number theory. Historically, these equations have attracted the attention of many mathematicians due to their intrinsic challenges and their significance in understanding the properties of integers. In this current study, we examine a diophantine equation relating the sum of squared integers from specific sequences to a variable d: In particular, the diophantine equation \(\sum_{r=1}^n w_r^2+\frac{n}{3} d^2=3\left(\frac{n d^2}{3}+\sum_{r=1}^{\frac{n}{3}} w_{3 r-1}^2\right)\) is introduced and partially characterized. The objective is to determine the conditions under which integer solutions for (wr,d) exist within this diophantine equation.The methodology of solving this problem entails, decomposing polynomials, factorizing polynomials, and exploring the solution set of the given equation.
The increasing significance of addressing data loss, has led to a heightened focus on missing data imputation (MDI). Autoencoder (AE) models, renowned for their ability to autonomously learn and ...impute missing data, are gaining prominence in MDI. These models exhibit adaptability to diverse datasets, and their unsupervised nature makes them robust in handling data lacking clear labels. This study aims to explore the scope and objectives of AE training, which encompass critical elements such as optimization algorithms, loss functions, and training epochs. We specifically investigate the impact of updating input data during AE training, a topic that has been insufficiently explored in existing research. Traditionally, AEs are trained on the original data, assuming it contains latent information. However, in the context of MDI, where data may be corrupted, it becomes imperative to evaluate whether updating input data can lead to superior results. The objective of this research is to introduce and evaluate two methods inspired by Gradient Boosting Machines: Short-Term Reconstruction with Iterative Updates (STR-IU) and Long-Term Reconstruction with a Single Update (LTR-SU). We utilize Denoising Autoencoder (DAE) models and examine how various optimization mechanisms affect our proposed methods. We conduct comparisons between Stochastic Gradient Descent (SGD) and the Adam optimization algorithm, and transform three distinct datasets into synthetic datasets with varying levels of missing data (5%, 15%, 25%). The results indicate that, while performance may not consistently excel across all training epoch settings, there is a noticeable overall improvement when updating input data, whether using SGD or Adam. Additionally, LTR-SU outperforms STR-IU, and models with DAE using SGD exhibit greater optimization compared to those using Adam.
This paper presents Po-Shen Loh’s method as an alternate method for solving quadratic equations, which is seen as an efficient and natural method for solving general quadratic equations. The study is ...an action research involving a sample of forty – five (45) students of Kumasi Wesley Girls High School, randomly selected for the study. Prior to the study, it was observed that the students did not know about any other method of solving quadratic equation other than the four traditional methods (factorisation, formula, completing squares and graphical) in the mathematics curriculum at the senior high school level in Ghana. The pre-test and post-test scores obtained by the students were analysed quantitatively and an inferential and descriptive analysis were performed. Comparatively, the scores obtained from the pre-test and post-test showed a significant improvement in the students’ ability to solve quadratic equations using the Po-Shen Loh’s method. The authors therefore recommend for it to be introduced into the senior high school mathematics curriculum in Ghana.
As cyber-attacks targeting public cloud infrastructure increase in severity, it is essential to have strong network security measures for Linux machines. 1 Recent statistics underscore the severity ...of the situation, with a significant 39% of businesses experiencing security breaches within their cloud environments in 2022. This data shows a notable 35% increase in security attacks from the previous year. These breaches affected around 400 million individuals, emphasizing the urgent need for action. As organizations increasingly migrate their operations to the cloud, addressing security risks is paramount. This needs a comprehensive approach to cloud security, focusing on monitoring and surveillance of cloud infrastructure usage by customers. Effective security observability requires deploying monitoring and alerting systems capable of promptly detecting and mitigating potential threats in real-time. 2 The Linux community has embraced Berkeley Packet Filter (BPF) technology as a cornerstone in this effort. BPF's flexibility and extensibility have led to the development of sophisticated tools, offering unparalleled capabilities in enhancing security observability and response mechanisms. This study begins by examining legacy solutions like auditd, which help auditing of all aspects of Linux machines. It also explores the origins and evolution of BPF within the Linux ecosystem, highlighting its transformative impact. The study further delves into BPF-based monitoring tools tailored for scrutinizing Linux system processes. It elucidates their functionalities and meticulously assesses the performance of select tools and technologies. Rigorous experimental method, involving virtual machines with identical specifications subjected to network load simulations, ensures reliable and unbiased performance evaluations. Through this experimentation, valuable insights into resource consumption patterns for each tool are gleaned, aiding informed decision-making in tool selection and deployment strategies.
We developed an algorithm based on combination of regularization and wavelet collocation method to solve Fredholm integral equations of the first kind. As first kind Fredholm integral equations are ...often ill-posed problems, regularization method is implemented to convert it into an approximate well posed Fredholm integral equation of the second kind whose solution converges to the solution of the original problem. Then wavelet collocation method is applied to obtain the numerical solution of the resulting problem. We have applied proposed method using Legendre and Chebyshev wavelets to some examples and compared their efficiency.
The mean value estimation of arithmetical function is closely related to many problems in number theory. Let f be an arithmetical function satisfying some conditions. Let r be the integral part of r. ...This paper proves that the asymptotic expression $$S_f(y):=\sum_{n \leq y} f(y / n) /\left(y / n^{k-1}\right)\left(k \in \mathbb{N}^{+}\right)$$ and the error term of this asymptotic formula is \(\Omega\)(y). The arithmetical function in this paper satisfies certain conditions, and the Dirichlet hyperbolic principle is used in the proof of the conclusion. With the different values of the independent variable of the function, the function value of the arithmetical function is often irregular, and the property of the mean value of the arithmetical function is more regular than that of the arithmetical function itself. Therefore, with the help of the mean value estimation results of the arithmetical function, we can have a deeper understanding of the nature of the arithmetical function itself, and then provide ideas for solving more problems.
The paper introduces a comprehensive stochastic model for the reserving process and the corresponding probability of ruin for a life insurance policy or, equivalently, for a portfolio of life ...policies. Within this framework, a discounted surplus process is established using a general probability space equipped with the natural filtration of past events and a suitable probability measure. Subsequently, it is demonstrated that the surplus process behaves as a submartingale and explores its impact on the probability of ruin, along with the inherent trade-off between the initial expense level and the adjustment factor applied to the net reserves of the life policy. Finally, a thorough numerical analysis is conducted focusing on a whole life insurance policy. In this specific case, a comprehensive range of values for the adjustment factor necessary to uphold the desired probability of ruin is ascertained, considering the corresponding values of the initial expense level.
This study focuses on the construction of (25SOR) in Three Dimensions (3D) engaging trigonometric functions. Designing experiments in multiple dimensions is crucial for efficiently exploring complex ...systems and optimizing various processes. The proposed methodology utilizes trigonometric functions to generate a set of experimental points that exhibit desirable properties, such as rotatability, orthogonality, and uniformity, in the three-dimensional space. By employing trigonometric transformations, a design with twenty-five equally spaced points is constructed, ensuring the ability to conduct thorough investigations across the entire experimental region. The advantages of utilizing trigonometric functions in the design construction process include the flexibility to achieve rotational symmetry and the capability to control the distribution of points systematically. The resulting 25SOR design facilitates comprehensive experimentation and enables researchers to efficiently evaluate response surfaces and identify optimal operating conditions in three-dimensional spaces. This approach holds promise for applications in various fields, including agriculture, where the exploration of multidimensional parameter spaces is essential for enhancing performance and efficiency.
