In this paper, we investigate intuitionistic fuzzy Poisson equation with uncertain parameters, considering the parameters as intuitionistic fuzzy numbers. We apply a finite difference method to solve ’Intuitionistic fuzzy Poisson equation’. The continuity of the membership and non-membership functions (which imply the continuity of the hesitancy function) is used to obtain qualitative properties on regular α-cut and β-cut of the intuitionistic fuzzy solution. The fuzzification of the deterministic α-cut and β-cut solutions obtained lead to the intuitionistic fuzzy solution. Finally, an example is presented to illustrate the proposed methodology as well as to show a graphical representation of its corresponding intuitionistic fuzzy solution.

Numerous lifetime distributions have been developed to assist researchers in various fields. In this paper, a new continuous three-parameter lifetime distribution is proposed by combining the distribution of the maximum of a sequence of independently identical gamma-distributed random variables with zero-truncated Poisson random variables, defined as the complementary gamma zero-truncated Poisson distribution (CGZTP). The proposed distribution's properties, including proofs of the probability density function, cumulative distribution function, survival function, hazard function, and moments, are discussed. The unknown parameters are estimated using the maximum likelihood method, whose asymptotic properties are examined. In addition, Wald confidence intervals are constructed for the CGZTP parameters. Simulation studies are conducted to evaluate the efficacy of parameter estimation, and a real-world application demonstrates the application of the proposed distribution.

An algebraic hypercompositional structure is a non-empty set H endowed with at least one hyperoperation, i.e., a multivalued function that associates to any pair of elements x, y in H their hyperproduct x o y representing a subset of H. 1934 is the year when the first hypercompositional structure was introduced. In fact, F. Marty defined the hypergroup as a pair (H, o) formed by a non-empty set H and a multivalued operation (hyperoperation) on the cartesian product H x H with values in the set of non-empty subsets of H, satisfying two axioms: i) the associativity, (x o y) o z=x o (y o z), for any x, y, z in H and ii) the reproductivity, x o H=H= H o x, for any x in H. The aim of this presentation is to recall and gather the main properties of one class of hypergroups, with similar behavior as groups, that attracted (and still attracts) the attention of many researchers during the last 50 years. These are the complete hypergroups, defined in 1970 by Koskas using the notion of complete part. Briefly, a complete part A is a subset of a hypergroup H containing all the hyperproducts of the elements in H having non-empty intersection with A and a hypergroup (H, o) is called complete if the complete closure C(x o y) of any hyperproduct x o y, i.e., the intersection of all complete parts of H containing x o y, is exactly x o y. A very useful characterization of the complete hypergroups was provided later on by P. Corsini, that emphasizes the strong connections that exists between hypergroups and groups. He proved that any complete hypergroup (H, o) may be represented as a union of its non-empty subsets A_g, with g in G, where i) (G, +) is a group; ii) the family {A_g / g in G} is a partition of H; iii) the hyperoperation on H is defined as: if (x,y) in A_g x A_h, with g, h in G, then x o y=A_g+h. The presentation will focus on several properties related to: i) the core (or the heart) of a complete hypergroup; ii) the reversibility and regularity properties; iii) the class equation; iv) the reducibility and fuzzy reducibility properties; v) the grade fuzzy set; vi) the commutativity degree; vii) the Euler's totient function defined on complete hypergroups. These are just some of the topics related to complete hypergroups developed in the last period, that for sure will open new lines of research on hypergroups.

Forecasting and modeling time series data is a crucial aspect of financial research for academics and business practitioners. The volatility of stock market returns impacts different economic and financial sectors worldwide. The ability to predict the direction of stock prices is vital for creating an investment plan or determining the optimal time to make a trade. However, stock price movements can be complex to predict, non-linear and chaotic, making it difficult to forecast their evolution. In this paper, we investigate modeling and forecasting the daily prices of the new Morocco Stock Index 20 (MSI 20). To this aim, we propose a comparative study between the results obtained from applying the following machine learning methods: Support Vector Regression (SVR), eXtreme Gradient Boosting (XGBoost), Long Short-Term Memory (LSTM), Convolutional-LSTM (CNN-LSTM), and Multilayer Perceptron (MLP) models. The results show that the LSTM and SVR models perform better than the other models and achieve high forecasting accuracy for daily prices.

The study of Fe3O4/water nanofluid in a lid-driven cavity under mixed convection conditions has been carried out with a focus on the effect of a non-uniform magnetic field on the heat exchange process. The governing equations, including continuity, momentum, and energy, were resolved using the Finite Volume Method-based in-house solver. Several parameters were considered in the analysis, including Magnetic number, the shape of nanoparticles (cylindrical, spherical, platelet, and brick), and the Reynolds number. The results were presented in the form of isotherms and streamlines, local and average Nusselt numbers. The results showed that applying a non-uniform magnetic field positively impacts the heat exchange process. In addition, an optimal condition was defined based on the shape of nanoparticles, Magnetic number, and Reynolds number. These findings contribute to understanding the dynamics and thermals of ferrofluids in lid-driven cavities and have implications for improving heat transfer applications.

Presented in this work is a trigonometrically fitted scheme based on a class of improved hybrid method for the numerical integration of oscillatory problems. The trigonometric conditions are constructed through which a third algebraic order scheme is derived. Numerical properties of the scheme are analyzed. Numerical experiment is conducted to validate the scheme. Results obtained reveal the superiority of the scheme over its equals in the literature.

In this paper, we propose a non-parametric estimator of the conditional hazard function weighted on the recursive kernel method in the context of functional stationary ergodic process with the explanatory variable taking values in a semi-metric space and a censored response. The conditional hazard rate plays an important role in the statistcis, it arise in a variety of fields inculding econometrics, epidemiology environmental science and many others. We consider the case of functional ergodic data because it has been an increasing interest in this area in recent year. This ergodic hypothesis is a fundamental axiom of statistical physics in order to examine the thermodynamic properties of gases, atoms, electrons or plasmas , also makes it possible to avoid complicated probabilistic calculations of the mixing condition. We consider a recursive estimate when the observations are strictly stationary ergodic data, it should be noted that the advantage of the recursive estimate is that the smoothing parameter is linked to the observation (Xi,Yi), wich permits to update our estimator for each additional observation. Under hypothesis, we establish the almost surely convergence of the proposed estimator.

In this study, we have dealt with a scheduling problem that has not been studied enough, the parallel flow-shop scheduling problem. Its difficulty lies in the fact that it consists of two sub-problems: the assignment of jobs to workshops and the scheduling of these jobs once assigned. Due to the complexity of the research problem, we propose a hybridization of two well-known optimization algorithms, a bio-inspired meta-heuristic (Particle Swarm Optimization, PSO) and a local search algorithm (Tabu Search, TS); with the aim of minimizing the maximum execution time of all jobs within constraints. The purpose of this hybridization is to combine the strengths of the two methods in order to obtain more efficient results than those achieved by classic methods. The concept of the proposed method is to start by generating a set of near-optimal solutions by the PSO meta-heuristic. Then the TS algorithm refines and improves these solutions in order to attain the optimal solution.

The well-known optical absorption J-band arises as a result of the formation of J-aggregates of polymethine dyes in their aqueous solutions. Compared to dye monomers, this band is narrow and high intensity, and redshifted. The narrowness and high intensity of the J-band are used in many applications, in particular, in the development of modern dye lasers. The J-band was discovered experimentally by Jelley and independently by Scheibe in 1936 [1,2]. In 1938, Franck and Teller [3] gave a theoretical explanation of the J-band based on the Frenkel exciton model. In 1984, based on the same exciton model, Knapp explained the shape of the J-band [4]. Subsequently, within the framework of the Frenkel exciton model, the shape of the J-band was studied by a large number of theorists, including the author of this abstract [5]. The author's reviews [6,7] provide a detailed critique of the explanation of the nature of the J-band based on the Frenkel exciton model. In particular, a significant drawback of this model is its inability to explain in principle the nature and shape of the optical bands of polymethine dye monomers from which J-aggregates are formed [6–8]. The author gives an alternative explanation of the nature of the J-band in the framework of a new fundamental physical theory, namely, in the framework of quantum-classical mechanics of elementary electron transfers in condensed media, which includes an explanation of the nature and shape of the bands of polymethine monomers that form J-aggregates [8] . Quantum-classical mechanics is a significantly modified quantum mechanics, in which the initial and final states of the "electron + nuclear environment" system for its "quantum" transitions are quantum in the adiabatic approximation, and the transient chaotic electron-nuclear(-vibrational) state due to chaos is classical [8]. This chaos is called dozy chaos. The new explanation of the nature and shape of the J-band is based on the so-called Egorov nano-resonance discovered in quantum-classical mechanics [8]. Egorov nano-resonance is a resonance between the electron motion and the motion of the reorganization of the nuclei of the environment during quantum-classical transitions in the optical chromophore under the condition of weak dozy chaos in the electron-nuclear(-vibrational) transient state.

[1] Jelley, E.E. Spectral absorption and fluorescence of dyes in the molecular state. Nature 1936, 138, 1009–1010.

[2] Scheibe, G. Variability of the absorption spectra of some sensitizing dyes and its cause. Angew. Chem. 1936, 49, 563.

[3] Franck, J.; Teller, E. Migration and photochemical action of excitation energy in crystals. J. Chem. Phys. 1938, 6, 861–872.

[4] Knapp, E.W. Lineshapes of molecular aggregates, exchange narrowing and intersite correlation. Chem. Phys. 1984, 85, 73–82.

[5] Makhov, D.V.; Egorov, V.V.; Bagatur’yants, A.A.; Alfimov, M.V. Efficient approach to the numerical calculation of optical line shapes for molecular aggregates. J. Chem. Phys. 1999, 110, 3196–3199.

[6] Egorov, V.V.; Alfimov, M.V. Theory of the J-band: From the Frenkel exciton to charge transfer. Phys. Uspekhi 2007, 50, 985–1029.

[7] Egorov, V.V. Theory of the J-band: From the Frenkel exciton to charge transfer. Phys. Procedia 2009, 2, 223–326.

[8] Egorov, V.V. Quantum–classical mechanics: Nano-resonance in polymethine dyes. Mathematics 2022, 10(9), 1443-1–1443-25.

Abstract

Obtaining an approximation for the majority of sparse linear systems found in engineering and applied sciences requires efficient iteration approaches. Solving such linear systems using iterative techniques is possible, but the number of iterations is high. To acquire approximate solutions with rapid convergence, the need arises to redesign or make changes to the current approaches. In this study, a modified approach, termed the "third refinement" of the Gauss-Seidel algorithm, for solving linear systems is proposed. The primary objective of this research is to optimize for convergence speed by reducing the number of iterations and the spectral radius. Decomposing the coefficient matrix using a standard splitting strategy and performing an interpolation operation on the resulting simpler matrices led to the development of the proposed method. We investigated and established the convergence of the proposed accelerated technique for some classes of matrices. The efficiency of the proposed technique was examined numerically, and the findings revealed a substantial enhancement over its previous modifications.