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Mathematics ◽  
2022 ◽  
Vol 10 (2) ◽  
pp. 272
Author(s):  
Chenyu Wu ◽  
Haoran Li ◽  
Yufei Zhang ◽  
Haixin Chen

The accuracy of an airfoil stall prediction heavily depends on the computation of the separated shear layer. Capturing the strong non-equilibrium turbulence in the shear layer is crucial for the accuracy of a stall prediction. In this paper, different Reynolds-averaged Navier–Stokes turbulence models are adopted and compared for airfoil stall prediction. The results show that the separated shear layer fixed k−v2¯−ω (abbreviated as SPF k−v2¯−ω) turbulence model captures the non-equilibrium turbulence in the separated shear layer well and gives satisfactory predictions of both thin-airfoil stall and trailing-edge stall. At small Reynolds numbers (Re~105), the relative error between the predicted CL,max of NACA64A010 by the SPF k−v2¯−ω model and the experimental data is less than 3.5%. At high Reynolds numbers (Re~106), the CL,max of NACA64A010 and NACA64A006 predicted by the SPF k−v2¯−ω model also has an error of less than 5.5% relative to the experimental data. The stall of the NACA0012 airfoil, which features trailing-edge stall, is also computed by the SPF k−v2¯−ω model. The SPF k−v2¯−ω model is also applied to a NACA0012 airfoil, which features trailing-edge stall and an error of CL relative to the experiment at CL>1.0 is smaller than 3.5%. The SPF k−v2¯−ω model shows higher accuracy than other turbulence models.


Mathematics ◽  
2022 ◽  
Vol 10 (2) ◽  
pp. 274
Author(s):  
Álvaro Gómez-Rubio ◽  
Ricardo Soto ◽  
Broderick Crawford ◽  
Adrián Jaramillo ◽  
David Mancilla ◽  
...  

In the world of optimization, especially concerning metaheuristics, solving complex problems represented by applying big data and constraint instances can be difficult. This is mainly due to the difficulty of implementing efficient solutions that can solve complex optimization problems in adequate time, which do exist in different industries. Big data has demonstrated its efficiency in solving different concerns in information management. In this paper, an approach based on multiprocessing is proposed wherein clusterization and parallelism are used together to improve the search process of metaheuristics when solving large instances of complex optimization problems, incorporating collaborative elements that enhance the quality of the solution. The proposal deals with machine learning algorithms to improve the segmentation of the search space. Particularly, two different clustering methods belonging to automatic learning techniques, are implemented on bio-inspired algorithms to smartly initialize their solution population, and then organize the resolution from the beginning of the search. The results show that this approach is competitive with other techniques in solving a large set of cases of a well-known NP-hard problem without incorporating too much additional complexity into the metaheuristic algorithms.


Mathematics ◽  
2022 ◽  
Vol 10 (2) ◽  
pp. 275
Author(s):  
Jun-Seok Yun ◽  
Seok-Bong Yoo

Among various developments in the field of computer vision, single image super-resolution of images is one of the most essential tasks. However, compared to the integer magnification model for super-resolution, research on arbitrary magnification has been overlooked. In addition, the importance of single image super-resolution at arbitrary magnification is emphasized for tasks such as object recognition and satellite image magnification. In this study, we propose a model that performs arbitrary magnification while retaining the advantages of integer magnification. The proposed model extends the integer magnification image to the target magnification in the discrete cosine transform (DCT) spectral domain. The broadening of the DCT spectral domain results in a lack of high-frequency components. To solve this problem, we propose a high-frequency attention network for arbitrary magnification so that high-frequency information can be restored. In addition, only high-frequency components are extracted from the image with a mask generated by a hyperparameter in the DCT domain. Therefore, the high-frequency components that have a substantial impact on image quality are recovered by this procedure. The proposed framework achieves the performance of an integer magnification and correctly retrieves the high-frequency components lost between the arbitrary magnifications. We experimentally validated our model’s superiority over state-of-the-art models.


Mathematics ◽  
2022 ◽  
Vol 10 (2) ◽  
pp. 263
Author(s):  
Le Xuan Hoang Khoa ◽  
Ioan Pop ◽  
Mikhail A. Sheremet

The development of different industrial fields, including mechanical and power engineering and electronics, demands the augmentation of heat transfer in engineering devices. Such enhancement can be achieved by adding extended heat transfer surfaces to the heated walls or heat-generating elements. This investigation is devoted to the numerical analysis of natural convective energy transport in a differentially heated chamber with isothermal vertical walls and a fin system mounted on the heated wall. The developed in-house computational code has been comprehensively validated. The Forchheimer–Brinkman extended Darcy model has been employed for the numerical simulation of transport phenomena in a porous material. The partial differential equations written, employing non-primitive variables, have been worked out by the finite difference technique. Analysis has been performed for solid and porous fins with various fin materials, amounts and heights. It has been revealed that porous fins provide a very good technique for the intensification of energy removal from heated surfaces.


Mathematics ◽  
2022 ◽  
Vol 10 (2) ◽  
pp. 273
Author(s):  
Mujahid Abbas ◽  
Muhammad Waseem Asghar ◽  
Manuel De la Sen

The aim of this paper is to propose a new faster iterative scheme (called AA-iteration) to approximate the fixed point of (b,η)-enriched contraction mapping in the framework of Banach spaces. It is also proved that our iteration is stable and converges faster than many iterations existing in the literature. For validity of our proposed scheme, we presented some numerical examples. Further, we proved some strong and weak convergence results for b-enriched nonexpansive mapping in the uniformly convex Banach space. Finally, we approximate the solution of delay fractional differential equations using AA-iterative scheme.


Mathematics ◽  
2022 ◽  
Vol 10 (2) ◽  
pp. 267
Author(s):  
Richard Schweickert ◽  
Xiaofang Zheng

A Multinomial Processing Tree (MPT) is a directed tree with a probability associated with each arc and partitioned terminal vertices. We consider an additional parameter for each arc, a measure such as time. Each vertex represents a process. An arc descending from a vertex represents selection of a process outcome. A source vertex represents processing beginning with stimulus presentation and a terminal vertex represents a response. An experimental factor selectively influences a vertex if changing the factor level changes parameter values on arcs descending from that vertex and no others. Earlier work shows that if each of two factors selectively influences a different vertex in an arbitrary MPT it is equivalent to one of two simple MPTs. Which applies depends on whether the two selectively influenced vertices are ordered by the factors or not. A special case, the Standard Binary Tree for Ordered Processes, arises if the vertices are ordered and the factor selectively influencing the first vertex changes parameter values on only two arcs. We derive necessary and sufficient conditions, testable by bootstrapping, for this case. Parameter values are not unique. We give admissible transformations for them. We calculate degrees of freedom needed for goodness of fit tests.


Mathematics ◽  
2022 ◽  
Vol 10 (2) ◽  
pp. 271
Author(s):  
Vassilis G. Kaburlasos

By “model”, we mean a mathematical description of a world aspect [...]


Mathematics ◽  
2022 ◽  
Vol 10 (2) ◽  
pp. 276
Author(s):  
Helong Yu ◽  
Shimeng Qiao ◽  
Ali Asghar Heidari ◽  
Chunguang Bi ◽  
Huiling Chen

The seagull optimization algorithm (SOA) is a novel swarm intelligence algorithm proposed in recent years. The algorithm has some defects in the search process. To overcome the problem of poor convergence accuracy and easy to fall into local optimality of seagull optimization algorithm, this paper proposed a new variant SOA based on individual disturbance (ID) and attraction-repulsion (AR) strategy, called IDARSOA, which employed ID to enhance the ability to jump out of local optimum and adopted AR to increase the diversity of population and make the exploration of solution space more efficient. The effectiveness of the IDARSOA has been verified using representative comprehensive benchmark functions and six practical engineering optimization problems. The experimental results show that the proposed IDARSOA has the advantages of better convergence accuracy and a strong optimization ability than the original SOA.


Mathematics ◽  
2022 ◽  
Vol 10 (2) ◽  
pp. 265
Author(s):  
Marta Kornafel

The paper presents a theoretical framework for the phenomenon of the price war in the context of general equilibrium, with special attention to the production system. The natural question that arises is whether Nash-optimal production plans being the reactions to the changing prices can finally approximate a Nash-optimal production plan at the end of this war. To provide an answer, the production system is described as a parametric-multicriteria game. Referring to some results on the lower semicontinuty of the parametric weak-multicriteria Nash equilibria, we provide a positive answer for the stated problem.


Mathematics ◽  
2022 ◽  
Vol 10 (2) ◽  
pp. 266
Author(s):  
Wenzhi Cao ◽  
Jilin Deng ◽  
Yi Yang ◽  
Yangyan Zeng ◽  
Limei Liu

The scientific and reasonable evaluation of the carrying capacity of water resources is of guiding significance for solving the issues of water resource shortages and pollution control. It is also an important method for realizing the sustainable development of water resources. Aiming at an evaluation of the carrying capacity of water resources, an evaluation model based on the cloud model theory and evidential reasoning approach is studied. First, based on the existing indicators, a water resources evaluation index system based on the pressure-state-response (PSR) model is constructed, and a classification method of carrying capacity grade is designed. The cloud model theory is used to realize the transformation between the measured value of indicators and the degree of correlation. Second, to obtain the weight of the evaluation index, the weight method of the index weights model based on the entropy weight method and evidential reasoning approach is proposed. Then, the reliability distribution function of the evaluation index and the graded probability distribution of the carrying capacity of water resources are obtained by an evidential reasoning approach. Finally, the evaluation method of the carrying capacity of water resources is constructed, and specific steps are provided. The proposed method is applied to the evaluation of water resources carrying capacity for Hunan Province, which verifies the feasibility and effectiveness of the method proposed in the present study. This paper applies this method of the evaluation of the water resources carrying capacity of Hunan Province from 2010 to 2019. It is concluded that the water resources carrying capacity of Hunan Province belongs to III~V, which is between the critical state and the strong carrying capacity state. The carrying capacity of the province’s water resources is basically on the rise. This shows that the carrying capacity of water resources in Hunan Province is in good condition, and corresponding protective measures should be taken to continue the current state.


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