In this paper, we consider the composition operators on harmonic Bloch-type spaces. Then first we compute their spectra on harmonic α-Bloch spaces and harmonic little α-Bloch space and then we characterize isometric composition operators on harmonic α-Bloch-type spaces. Indeed we obtain a relation between the properties of the inducing function φ and the isometricity of the composition operator Cφ.

The OCDMA network using two Dimensional Variable-Weight Optical Orthogonal Codes (2D VWOOC) can support diverse Quality of Services (QoS) classes and multimedia services, and make the better use of bandwidth resources in fiber optical networks. To simplify practical implementation, the At Most One-Pulse Per Wavelength (AM-OPPW) restriction is often appended to a 2D VWOOC. In this paper, the upper bound on the size of AM-OPPW 2D VWOOCs is derived, semicyclic group divisible designs are introduced to construct AM-OPPW 2D VWOOCs, and an equivalence between optimal AM-OPPW 2D VWOOCs and Semicyclic Group Divisible Designs (SCGDDs) is established. Some direct and recursive constructions for SCGDDs are also presented. Consequently, several infinite families of optimal AM-OPPW 2D VWOOCs are obtained.

This paper further develops a previously proposed method of computer analogy, based on the formalization of core computational properties: a finite number of digits and the transfer from one rank to another. Aimed at constructing new analytical solutions for nonlinear differential systems, the key outcome of this method is semi-analytical solution. We obtained new results compared to our earlier publications. Namely, the construction of an analytical solution was demonstrated for Carleman kinetic system. Two semi-analytical approximations are proposed for the Van der Pol equation, reduced to a system of two nonlinear equations. The semi-analytical approximation derived for the Shimizu-Morioka system—based on the probabilistic properties of the coefficients of the highest-degree terms—demonstrates the presence of a strange attractor.

Student engagement in online learning is very important for assessing learning effectiveness. However, the process of learners' engagement, including its rise, stability, and decline, is complex and uncertain. Therefore, the student's online learning engagement assessment method is developed based on q-Rung Orthogonal Trapezoidal Fuzzy Numbers (q-ROFTrNs) in this paper. First, an q-rung orthogonal trapezoidal fuzzy Yager operator is designed. Second, a derived feature weight method is developed based on the Criteria Importance Through Intercriteria Correlation (CRITIC) under the q-ROFTrNs environment, which not only overcomes the shortcomings of specified weights but also has objectivity. Third, an integrated q-Rung Orthogonal Trapezoidal Fuzzy Number Decision-Making (q-ROFTrNDM) method is explored. This method combines fuzzy distance, Yager operator, CRITIC method, and score function to achieve a comprehensive and dynamic assessment of students' engagement. The assessment results of the q-ROFTrNDM method indicate that students' online learning engagement aligns with expert assessment outcomes. Parameter sensitivity analysis reveals that the proposed q-ROFTrNDM method does not alter the assessment results of the most engaged students. Comparative analysis demonstrates that q-ROFTrNDM achieves a higher engagement score than 0.929, outperforming competing methods. Additionally, the q-ROFTrNDM method boasts a computation time of less than 10 ms. Therefore, the implementation outcomes confirm the feasibility and effectiveness of q-ROFTrNDM.

This article presents the Godunov method applied to solve the Riemann problem for the isentropic Cargo LeRoux model. The pressure-density relation for this model yields Riemann invariants that are complicated and computationally challenging to process. Only the exact solution has been developed for this model, and no numerical method has been applied thus far. Incorporating many computational checks is necessary for the numerical simulations of this model. Hence, it is ensured that variables and related quantities in the pressure equation remain positive, and the integrals converge within given accuracy conditions without casting complex values. Two nonlinear equations are obtained for possible wave configurations in the exact solutions. This system of two nonlinear algebraic equations is solved with the Newton-Raphson method. This root-finding process is sensitive to the initial guess values. A special algorithm is used to guess the initial values for the Newton-Raphson procedure. It is based on evaluating the residual functions and finding appropriate initial guesses by sorting the answers. These steps effectively simulate complex terms. The system is hyperbolic, with three distinct eigenvalues of the Jacobian matrix, and the solution consists of three waves. The tests showed that the Godunov scheme is applicable and achieves good accuracy for this model. However, the central scheme fails to solve this problem. This study bridges the gap between model analysis and developing numerical methods for solving isentropic Euler equation models.

An overview of a Neutrosophic Deep Neural Network (NDNN) is given here to illustrate how artificial neural networks and neutrosophic sets can be combined to profit from the comprehensive truth, indeterminate, and falsity degrees known in neutrosophic logic. The investigation details how the NDNN architecture was gradually enriched from its initial and simplest structure, which was a Neutrosophic Neural Network (NNN) with only a one-layer neuron. Next, it progresses to an NNN with one layer and one multi-input neuron, and then becomes even more sophisticated as an NNN with one layer and several multi-input neurons. As a result, the framework concludes with a real NDNN made up of multiple layers, and every layer includes several multi-input neurons. For each network structure, new sets of formulas are given to estimate the parameters of neural networks as neutrosophic triplets for weights and activations. The use of the NDNN in soil microbe processing is demonstrated to prove its usefulness in handling situations with uncertainty and indeterminacy.

The Bullwhip Effect (BWE) occurs when orders made to suppliers have a bigger variation than sales to the buyer. This is a major concern that businesses are working on eliminating, as it has numerous side effects, such as excessive inventory, stock-outs, insufficient production, increased costs, etc. The new study adds to the literature by demonstrating how to quantify and assess the bullwhip impact on any supply chain. The results show that when consumer demand is unstable, the BWE is magnified. This was achieved by using the proposed formula which was based on an explanation and graph of the traditional BWE. A stochastic simulation based on a case study that replicates the behavior of a generic supply chain in a real-world market was used to evaluate the formula.

In this paper, we introduce a new linear operator Drq(λ , ℓ)f(ζ ) and employ it to define a q-analogue of a differential operator acting on a newly developed subclass of meromorphic functions in the punctured unit disk. The subclass, denoted Σq∗, r (Θ, λ , ℓ), is examined comprehensively, and several of its key analytic and geometric properties are established. Specifically, we derive coefficient conditions for functions in this class and study convolution properties, closure results, convex combination criteria, and the interaction of the class with the q-Bernardi integral operator. Moreover, we address and resolve the neighborhoods problem associated with this subclass. These findings offer new insights into meromorphic function theory within the framework of q-calculus operators and underscore the potential for further development of operator generated function classes in geometric function theory.

In this paper, we propose an extended iteration of the generalized Fibonacci-Mann technique to establish an escape condition for functions of the form ，where a and c are complex constants, n ≥ 2, and is a complex variable. Using an s-convex combination framework, the proposed approach refines existing procedures and enables the generation of novel Mandelbrot and Julia sets. Furthermore, we provide numerical examples and graphic demonstrations to illustrate the efficiency of this novel technique.