This is the second paper in a cycle investigating the exact solution of loop equations in decaying turbulence. We perform numerical simulations of the Euler ensemble, suggested in the previous work, as a solution to the loop equations. We designed novel algorithms for simulation, which take a small amount of computer RAM so that only the CPU time grows linearly with the size of the system and its statistics. This algorithm allows us to simulate systems with billions of discontinuity points on our fractal curve, dual to the decaying turbulence. For the vorticity correlation function, we obtain \textbf{quantum fractal laws} with regime changes between universal discrete values of indexes. The traditional description of turbulence with fractal or multifractal scaling laws does not apply here. The measured conditional probabilities of fluctuating variables are smooth functions of the logarithm of scale, with statistical errors being negligible at our large number of random samples $T = 167,772,160$ with $N = 200,000,000$ points on a fractal curve. The quantum jumps arise from the analytical distribution of scaling variable $X = \frac{\cot^2(\pi p/q)}{q^2}$ where $\frac{p}{q}$ is a random fraction. This distribution is related to the totient summatory function and is a discontinuous function of $X$. In particular, the energy spectrum is a devil's staircase with tilted uneven steps with slopes between $-1$ and $-2.03$. The logarithmic derivative of energy decay $n(t)$ as a function of time is jumping down the stairs of universal levels between $1.50$ and $1.53$. The quantitative verification of this quantization would require more precise experimental data.

This paper presents the results of investigations into the pyrolysis of waste polypropylene in a laboratory fixed-bed batch reactor. The experiments were designed and verified in such a way as to allow the application of the Response Surface Methodology (RSM) in the development of an empirical mathematical model that quantifies the impacts mentioned above. The influence of the mass of the raw material (50, 100 and 150 g), together with the reactor temperature (450, 475 and 500 °C) and the reaction time (45, 50 and 75 min) was examined. It has been shown that the mass of the raw material, i.e. the filling volume of the reactor, has a significant influence on the pyrolysis oil yield. This influence exceeds the influence of reactor temperature and reaction time. This was explained by observing the temperature change inside the reactor at three different spots at the bottom, middle and top of the reactor. Recorded temperature diagrams show that with greater masses of feedstock, local overheating occurs in the middle part of the reactor, which leads to overcracking of vapor products, and from there to an increased formation of non-condensable gases, i.e. reduced yield of pyrolytic oil.

This paper presents a mathematical modeling approach utilizing a fuzzy modeling framework for fixed wing aircraft systems with the goal of creating a highly desirable mathematical representation for model-based control design applications. The starting point is a mathematical model comprised of fifteen non-linear ordinary differential equations representing the dynamic and kinematic behavior applicable to a wide range of fixed wing aircraft systems. Here the proposed mathematical modeling framework is applied to the AIRBUS A310 model developed by ONERA. The proposed fuzzy modeling framework takes advantage of sector non-linearity techniquesto recast all the non-linear terms from the original model to a set of combined fuzzy rules. The result of this fuzzification is a more suitable mathematical description from the control system design point of view. Therefore, the combination of this fuzzy model and the wide range of control techniques available in the literature for such kind of models will enable us to avoid common control design methods, such as gain scheduling, where stability issues can be extremely challenging.

Monge-Ampere equations have important research significance in many fields such as geometry, convex geometry and mathematical physics. In this paper, under some superlinear and sublinear conditions, the existence of nontrivial solutions for a system arising from Monge-Ampere equations with two parameters is investigated based on Guo-Krasnosel'skii fixed point theorem. In the end, two examples are given to illustrate our main results.

Efficient fixed crane position analysis is critical in precast buildings construction to maximize lifting efficiency for precast elements. The primary objective is to minimize the travel distances of fixed cranes, thereby enhancing operational efficiency and cost control. This involves strategically reducing the distances between the transport truck parking, where elements are stored, the fixed crane, and the construction installation point. Despite its significance, existing studies often overlook the dynamic movement efficiency of transport trucks, particularly when dealing with multiple transport trucks and various models of fixed cranes, rendering the opti-mization of this scenario a challenging NP-hard problem susceptible to combinatorial explosion. This study presents a novel mathematical model leveraging the Genetic Algorithm (GA). The model aims to solve optimal model and position of fixed cranes, along with identifying ideal positions for transport truck parking. The study's methodology is validated and demonstrated through a project case study. Comparative analyses between the proposed model and the original planning underscore a noteworthy 6% reduction in both duration and costs when lifting elements directly from transport trucks, as opposed to establishing an on-site stock yard. Furthermore, the developed GA exhibits a substantial improvement in final solutions, achieving a remarkable 30% reduction in both operational duration and costs. This research contributes valuable insights into fixed crane position analysis of precast building construction, providing foundation for enhanced operational efficiency and cost-effectiveness in the industry.

In this paper, a class of coupled competitive neural networks, which subject to disturbance and discontinuous activation functions, is concerned. To realize the fixed-time quasi-bipartite synchronization, an aperiodic intermittent controller is initially designed. Subsequently, by combining the fixed-time stability theory and nonsmooth analysis, several criteria are established to ensure the bipartite synchronization in fixed time. Moreover, synchronization error bounds and settling time estimates are provided. Finally, numerical simulations are presented to verify the main results.

Due to the retrognathic mandible, an orthodontist frequently observes skeletal class II malocclusion in growing patients. The preferred technique for analyzing and monitoring the temporomandibular joint alterations caused by the functional device is magnetic resonance imaging [MRI]. The study aimed to assess and compare changes in the articular disc's dimension and location before and following the use of various class II correctors to correct the class II molar relation using MRI technology. Methods: 39 adolescent patients aged 15-23 years old [24 girls and 15 boys] who were diagnosed with skeletal Class II division 1 malocclusion based on clearly defined criteria underwent treatment with either the power scope II [PS], Sabbagh Advanced Repositioning Appliance [SARA] and or Dynaflex [DF] with fixed appliances. For fixed functional treatment, the average length of treatment was 5-7 months. The changes in the articular disc dimension and position and condylar position were assessed. The study was done at the Department of Orthodontics at the College of Dentistry, Hawler Medical University in Erbil City. Results: Group DF has a significant effect on the condylar position index and posterior joint space on the closed mouth and disc length on both open and close mouth techniques, and in the group SARA, disc position, and condylar position index on closed mouth technique have shown that significant differences were observed. Conclusion: Class II malocclusions can be effectively corrected by fixed functional appliances. The statistical significance forward movement of the condyle in the glenoid fossa and the posterior movement of the articular disc concerning the condylar head was observed. The mechanism of action of functional appliances appears to include the forward migration of the C-GF complex.