Mathematics, Volume 8, Issue 9 (September 2020) – 250 articles

In this paper, the sinc-derivative collocation approach is used to solve second order integro-differential boundary value problems. While the derivative of the unknown variables is interpolated using sinc numerical methods, the desired solution and the integral terms are evaluated through numerical integration and all higher order derivatives are approximated through successive numerical differentiation. Suitable transformations are used to reduce non-homogeneous boundary conditions to homogeneous. Comparison of the proposed method with different approaches that were previously considered in the literature is carried out in order to test its accuracy and efficiency. The results show that the sinc-derivative collocation method performs well. Full article

The techniques of halftoning are widely used in marketing because they reduce the cost of impression and maintain the quality of graphics. Halftoning converts a digital image into a binary image conformed by dots. The output of the halftoning contains less visual information; a possible benefit of this task is the reduction of ink when graphics are printed. The human eye is not able to detect the absence of information, but the printed image stills have good quality. The most used method for halftoning is called Floyd-Steinberger, and it defines a specific matrix for the halftoning conversion. However, most of the proposed techniques in halftoning use predefined kernels that do not permit adaptation to different images. This article introduces the use of the harmony search algorithm (HSA) for halftoning. The HSA is a popular evolutionary algorithm inspired by the musical improvisation. The different operators of the HSA permit an efficient exploration of the search space. The HSA is applied to find the best configuration of the kernel in halftoning; meanwhile, as an objective function, the use of the structural similarity index (SSIM) is proposed. A set of rules are also introduced to reduce the regular patterns that could be created by non-appropriate kernels. The SSIM is used due to the fact that it is a perception model used as a metric that permits comparing images to interpret the differences between them numerically. The aim of combining the HSA with the SSIM for halftoning is to generate an adaptive method that permits estimating the best kernel for each image based on its intrinsic attributes. The graphical quality of the proposed algorithm has been compared with classical halftoning methodologies. Experimental results and comparisons provide evidence regarding the quality of the images obtained by the proposed optimization-based approach. In this context, classical algorithms have a lower graphical quality in comparison with our proposal. The results have been validated by a statistical analysis based on independent experiments over the set of benchmark images by using the mean and standard deviation. Full article

The socioeconomic costs of occupational accidents represent an important factor in the safety and healthy development of a country’s economy. Insurance payments (which cover workplace incidents, such as wounds or illness, disability and fatality) can be considered a proxy for the socioeconomic cost of occupational accidents. Occupational accidents in different industries cause important variations in these three socioeconomic costs—for example, in their frequency and severity. One of the most commonly used mathematical programming approaches that analyze the performance of inputs, economic outputs and occupational accidents is data envelopment analysis (DEA), which has also been used in recent years to estimate the relative performance related to occupational injuries. This study measures the safety and healthy economic performance of Taiwan’s 17 industrial sectors by incorporating the varying importance of the three socioeconomic costs of occupational accidents into a weighted DEA Model. The empirical results demonstrate that integrating the varying importance of the three socioeconomic costs of occupational accidents in the evaluation of safety and healthy economic performance is very important. To improve the occupational safety and healthy economic performance of Taiwan’s main industrial sectors, efforts should focus on reducing fatalities, which are very costly. These findings could help Taiwan’s policy makers effectively improve their safety and healthy economic performance, based on the specific context of each industry, especially the mining and quarrying industry. Full article

In the modeling and analysis of reliability data via the Lindley distribution, the maximum likelihood estimator is the most commonly used for parameter estimation. However, the maximum likelihood estimator is highly sensitive to the presence of outliers. In this paper, based on the probability integral transform statistic, a robust and efficient estimator of the parameter of the Lindley distribution is proposed. We investigate the relative efficiency of the new estimator compared to that of the maximum likelihood estimator, as well as its robustness based on the breakdown point and influence function. It is found that this new estimator provides reasonable protection against outliers while also being simple to compute. Using a Monte Carlo simulation, we compare the performance of the new estimator and several well-known methods, including the maximum likelihood, ordinary least-squares and weighted least-squares methods in the absence and presence of outliers. The results reveal that the new estimator is highly competitive with the maximum likelihood estimator in the absence of outliers and outperforms the other methods in the presence of outliers. Finally, we conduct a statistical analysis of four reliability data sets, the results of which support the simulation results. Full article

In this paper, a stability-driven optimal disturbance observer (DO) is proposed. The proposed method does not require any plant inverse dynamics to detect introduced disturbances or a stabilizing Q filter. It does not require additional compensators to resolve causality problems, due to the relative degree, or filters to solve instability problems of non-minimum phase plants. Using this method enables wideband and narrowband disturbances to be attenuated by simply multiplying the corresponding peak filters by the baseline weight function. Furthermore, the proposed DO guarantees the stability of closed-loop systems because the already designed outer-loop systems are considered as a target plant to be stabilized and because of the Lyapunov stability-based $H_{\infty }$ control. In the application example, it was confirmed that the proposed method is effective, and the position error signals were improved by 20.9% in commercial hard disk drives and 36.6% in optical image stabilization systems. Full article

In the present paper, we consider an important problem from the point of view of application in sciences and engineering, namely, a new class of nonlinear Love-equation with infinite memory in the presence of source term that takes general nonlinearity form. New minimal conditions on the relaxation function and the relationship between the weights of source term are used to show a very general decay rate for solution by certain properties of convex functions combined with some estimates. Investigations on the propagation of surface waves of Love-type have been made by many authors in different models and many attempts to solve Love’s equation have been performed, in view of its wide applicability. To our knowledge, there are no decay results for damped equations of Love waves or Love type waves. However, the existence of solution or blow up results, with different boundary conditions, have been extensively studied by many authors. Our interest in this paper arose in the first place in consequence of a query for a new decay rate, which is related to those for infinite memory $\varpi$ in the third section. We found that the system energy decreased according to a very general rate that includes all previous results. Full article

The incubation period of coronavirus disease 2019 (COVID-19) is not always observed exactly due to uncertain onset times of infection and disease symptoms. In this paper, we demonstrate how to estimate the distribution of incubation and its association with patient demographic factors when the exact dates of infection and symptoms’ onset may not be observed. The findings from analysis of the confirmed COVID-19 cases indicate that age could be associated with the incubation period, and an age-specific quarantine policy might be more efficient than a unified one in confining COVID-19. Full article

In this paper, we find the solution of the following quadratic functional equation $n{\sum }_{1\le i<j\le n}Q\left(x_i-x_j\right)={\sum }_{i=1}^{n}Q\left({\sum }_{j\ne i}{x}_j-(n-1)x_i\right)$, which is derived from the gravity of the n distinct vectors $x_1,\cdots ,x_n$ in an inner product space, and prove that the stability results of the $\mathcal{A}$-quadratic mappings in $\mu$-complete convex fuzzy modular ∗-algebras without using lower semicontinuity and $\beta$-homogeneous property. Full article

In the paper, we consider some fixed point results of $\mathcal{F}$-contractions for triangular $\alpha$-admissible and triangular weak $\alpha$-admissible mappings in metric-like spaces. The results on $\mathcal{F}$-contraction type mappings in the context of metric-like spaces are generalized, improved, unified, and enriched. We prove the main result but using only the property ($\mathcal{F}1$) of the strictly increasing mapping $\mathcal{F}:\left(0,,,+,\infty \right)\to \left(-,\infty ,,,+,\infty \right)$. Our approach gives a proper generalization of several results given in current literature. Full article

COVID-19, known as Coronavirus disease 2019, is caused by a coronavirus called SARS-CoV-2. As coronavirus restrictions ease and cause changes to social and business activities around the world, and in the United States in particular, including social distancing, reopening states, reopening schools, and the face mask mandates, COVID-19 outbreaks are on the rise in many states across the United States and several other countries around the world. The United States recorded more than 1.9 million new infections in July, which is nearly 36 percent of the more than 5.4 million cases reported nationwide since the pandemic began, including more than 170,000 deaths from the disease, according to data from Johns Hopkins University as of 16 August 2020. In April 2020, the author of this paper presented a model to estimate the number of deaths related to COVID-19, which assumed that there would be no significant change in the COVID-19 restrictions and guidelines in the coming days. This paper, which presents the evolved version of the previous model published in April, discusses a new explicit mathematical model that considers the time-dependent effects of various pandemic restrictions and changes related to COVID-19, such as reopening states, social distancing, reopening schools, and face mask mandates in communities, along with a set of selected indicators, including the COVID-19 recovered cases and daily new cases. We analyzed and compared the modeling results to two recent models based on several model selection criteria. The model could predict the death toll related to the COVID-19 virus in the United States and worldwide based on the data available from Worldometer. The results show the proposed model fit the data significantly better for the United States and worldwide COVID-19 data that were available on 16 August 2020. The results show very encouraging predictability that reflected the time-dependent effects of various pandemic restrictions for the proposed model. The proposed model predicted that the total number of U.S. deaths could reach 208,375 by 1 October 2020, with a possible range of approximately 199,265 to 217,480 deaths based on data available on 16 August 2020. The model also projected that the death toll could reach 233,840 by 1 November 2020, with a possible range of 220,170 to 247,500 American deaths. The modeling result could serve as a baseline to help decision-makers to create a scientific framework to quantify their guidelines related to COVID-19 affairs. The model predicted that the death toll worldwide related to COVID-19 virus could reach 977,625 by 1 October 2020, with a possible range of approximately 910,820 to 1,044,430 deaths worldwide based on data available on 16 August 2020. It also predicted that the global death toll would reach nearly 1,131,000 by 1 November 2020, with a possible range of 1,030,765 to 1,231,175 deaths. The proposed model also predicted that the global death toll could reach 1.47 million deaths worldwide as a result of the SARS CoV-2 coronavirus that causes COVID-19. We plan to apply or refine the proposed model in the near future to further study the COVID-19 death tolls for India and Brazil, where the two countries currently have the second and third highest total COVID-19 cases after the United States. Full article

This paper develops a dispersion trading strategy based on a statistical index subsetting procedure and applies it to the S&P 500 constituents from January 2000 to December 2017. In particular, our selection process determines appropriate subset weights by exploiting a principal component analysis to specify the individual index explanatory power of each stock. In the following out-of-sample trading period, we trade the most suitable stocks using a hedged and unhedged approach. Within the large-scale back-testing study, the trading frameworks achieve statistically and economically significant returns of 14.52 and 26.51 percent p.a. after transaction costs, as well as a Sharpe ratio of 0.40 and 0.34, respectively. Furthermore, the trading performance is robust across varying market conditions. By benchmarking our strategies against a naive subsetting scheme and a buy-and-hold approach, we find that our statistical trading systems possess superior risk-return characteristics. Finally, a deep dive analysis shows synchronous developments between the chosen number of principal components and the S&P 500 index. Full article

The paper is concerned with complex fuzzy numbers and complex fuzzy inner product spaces. In the classical complex number set, a complex number can be expressed using the Cartesian form or polar form. Both expressions are needed because one expression is better than the other depending on the situation. Likewise, the Cartesian form and the polar form can be defined in a complex fuzzy number set. First, the complex fuzzy numbers (CFNs) are categorized into two types, the polar form and the Cartesian form, as type I and type II. The properties of the complex fuzzy number set of those two expressions are discussed, and how the expressions can be used practically is shown through an example. Second, we study the complex fuzzy inner product structure in each category and find the non-existence of an inner product on CFNs of type I. Several properties of the fuzzy inner product space for type II are proposed from the modulus that is newly defined. Specfically, the Cauchy-Schwartz inequality for type II is proven in a compact way, not only the one for fuzzy real numbers. In fact, it was already discussed by Hasanhani et al; however, they proved every case in a very complicated way. In this paper, we prove the Cauchy-Schwartz inequality in a much simpler way from a general point of view. Finally, we introduce a complex fuzzy scalar product for the generalization of a complex fuzzy inner product and propose to study the condition for its existence on CFNs of type I. Full article

Bayesian Network is one of the famous network models, and the loop cutset is one of the crucial structures for Bayesian Inference. In the Bayesian Network and its inference, how to measure the relationship between nodes is very important, because the relationship between different nodes has significant influence on the node-probability of the loop cutset. To analyse the relationship between two nodes in a graph, we define the shared node, prove the upper and lower bounds of the shared nodes number, and affirm that the shared node influences the node-probability of the loop cutset according to the theorems and experiments. These results can explain the problems that we found in studying on the statistical node-probability belonging to the loop cutset. The shared nodes are performed not only to improve the theoretical analysis on the loop cutset, but also to the loop cutset solving algorithms, especially the heuristic algorithms, in which the heuristic strategy can be optimized by a shared node. Our results provide a new tool to gauge the relationship between different nodes, a new perspective to estimate the loop cutset, and it is helpful to the loop cutset algorithm and network analysis. Full article

In the context of CAD CAM CAE (Computer-Aided Design, Manufacturing and Engineering) and Additive Manufacturing, the computation of level sets of closed 2-manifold triangular meshes (mesh slicing) is relevant for the generation of 3D printing patterns. Current slicing methods rely on the assumption that the function used to compute the level sets satisfies strong Morse conditions, rendering incorrect results when such a function is not a Morse one. To overcome this limitation, this manuscript presents an algorithm for the computation of mesh level sets under the presence of non-Morse degeneracies. To accomplish this, our method defines weak-Morse conditions, and presents a characterization of the possible types of degeneracies. This classification relies on the position of vertices, edges and faces in the neighborhood outside of the slicing plane. Finally, our algorithm produces oriented 1-manifold contours. Each contour orientation defines whether it belongs to a hole or to an external border. This definition is central for Additive Manufacturing purposes. We set up tests encompassing all known non-Morse degeneracies. Our algorithm successfully processes every generated case. Ongoing work addresses (a) a theoretical proof of completeness for our algorithm, (b) implementation of interval trees to improve the algorithm efficiency and, (c) integration into an Additive Manufacturing framework for industry applications. Full article

A deeper game-tree search can yield a higher decision quality in a heuristic minimax algorithm. However, exceptions can occur as a result of pathological nodes, which are considered to exist in all game trees and can cause a deeper game-tree search, resulting in worse play. To reduce the impact of pathological nodes on the search quality, we propose an iterative optimal minimax (IOM) algorithm by optimizing the backup rule of the classic minimax algorithm. The main idea is that calculating the state values of the intermediate nodes involves not only the static evaluation function involved but also a search into the future, where the latter is given a higher weight. We experimentally demonstrated that the proposed IOM algorithm improved game-playing performance compared to the existing algorithms. Full article

In the early 20th century, B.-Y. Chen introduced the concept of CR-warped products and obtained several fundamental results, such as inequality for the length of second fundamental form. In this paper, we obtain B.-Y. Chen’s inequality for CR-slant warped products in nearly cosymplectic manifolds, which are the more general classes of manifolds. The equality case of this inequality is also investigated. Furthermore, the inequality is discussed for some important subclasses of CR-slant warped products. Full article

Vendor selection is an established problem in supply chain management. It is regarded as a strategic resource by manufacturers, which must be managed efficiently. Any inappropriate selection of the vendors may lead to severe issues in the supply chain network. Hence, the desire to develop a model that minimizes the combination of transportation, deliveries, and ordering costs under uncertainty situation. In this paper, a multi-objective vendor selection problem under fuzzy environment is solved using a fuzzy goal programming approach. The vendor selection problem was modeled as a multi-objective problem, including three primary objectives of minimizing the transportation cost; the late deliveries; and the net ordering cost subject to constraints related to aggregate demand; vendor capacity; budget allocation; purchasing value; vendors’ quota; and quantity rejected. The proposed model input parameters are considered to be LR fuzzy numbers. The effectiveness of the model is illustrated with simulated data using R statistical package based on a real-life case study which was analyzed using LINGO 16.0 optimization software. The decision on the vendor’s quota allocation and selection under different degree of vagueness in the information was provided. The proposed model can address realistic vendor selection problem in the fuzzy environment and can serve as a useful tool for multi-criteria decision-making in supply chain management. Full article

Extracting information from individual risk factors provides an effective way to identify diabetes risk and associated complications, such as retinopathy, at an early stage. Deep learning and machine learning algorithms are being utilized to extract information from individual risk factors to improve early-stage diagnosis. This study proposes a deep neural network (DNN) combined with recursive feature elimination (RFE) to provide early prediction of diabetic retinopathy (DR) based on individual risk factors. The proposed model uses RFE to remove irrelevant features and DNN to classify the diseases. A publicly available dataset was utilized to predict DR during initial stages, for the proposed and several current best-practice models. The proposed model achieved 82.033% prediction accuracy, which was a significantly better performance than the current models. Thus, important risk factors for retinopathy can be successfully extracted using RFE. In addition, to evaluate the proposed prediction model robustness and generalization, we compared it with other machine learning models and datasets (nephropathy and hypertension–diabetes). The proposed prediction model will help improve early-stage retinopathy diagnosis based on individual risk factors. Full article

The fluid-structure interaction of solid objects freely falling in a Newtonian fluid was investigated numerically by direct-forcing immersed boundary (DFIB) method. The Navier–Stokes equations are coupled with equations of motion through virtual force to describe the motion of solid objects. Here, we rigorously derived the equations of motion by taking control-volume integration of momentum equation. The method was validated by a popular numerical test example describing the 2D flow caused by the free fall of a circular disk inside a tank of fluid, as well as 3D experimental measurements in the sedimentation of a sphere. Then, we demonstrated the method by a few more 2D sedimentation examples: (1) free fall of two tandem circular disks showing drafting, kissing and tumbling phenomena; (2) sedimentation of multiple circular disks; (3) free fall of a regular triangle, in which the rotation of solid object is significant; (4) free fall of a dropping ellipse to mimic the falling of a leaf. In the last example, we found rich falling patterns exhibiting fluttering, tumbling, and chaotic falling. Full article

This paper proposes NetVote, an internet voting protocol where usability and ease in deployment are a priority. We introduce the notion of strict coercion resistance, to distinguish between vote-buying and coercion resistance. We propose a protocol with ballot secrecy, practical everlasting privacy, verifiability and strict coercion resistance in the re-voting setting. Coercion is mitigated via a random dummy vote padding strategy to hide voting patterns and make re-voting deniable. This allows us to build a filtering phase with linear complexity, based on zero knowledge proofs to ensure correctness while maintaining privacy of the process. Voting tokens are formed by anonymous credentials and pseudorandom identifiers, achieving practical everlasting privacy, where even if dealing with a future computationally unbounded adversary, vote intention is still hidden. It is not assumed for voters to own cryptographic keys prior to the election, nor store cryptographic material during the election. This property allows voters not only to vote multiple times, but also from different devices each time, granting the voter a vote-from-anywhere experience. This paper builds on top of the paper published in CISIS’19. In this version, we modify the filtering. Moreover, we formally define the padding technique, which allows us to perform the linear filtering scheme. Similarly we provide more details on the protocol itself and include a section of the security analysis, where we include the formal definitions of strict coercion resistance and a game based definition of practical everlasting privacy. Finally, we prove that NetVote satisfies them all. Full article

Let $C_k^{n,l}$ be a simple closed k-curves with l elements in ${\mathbb{Z}}^n$ and $W:=\stackrel{\mathrm{m}-\mathrm{times}}{\overbrace{C_k^{n,l}\vee \cdots \vee C_k^{n,l}}}$ be an m-iterated digital wedges of $C_k^{n,l}$, and $F\left(Co{n}_k\left(W\right)\right)$ be an alignment of fixed point sets of W. Then, the aim of the paper is devoted to investigating various properties of $F\left(Co{n}_k\left(W\right)\right)$. Furthermore, when proceeding with this work, this paper addresses several unsolved problems. To be specific, we firstly formulate an alignment of fixed point sets of $C_k^{n,l}$, denoted by $F\left(Co{n}_k\left(C_k^{n,l}\right)\right)$, where $l(\ge 7)$ is an odd natural number and $k\ne 2n$. Secondly, given a digital image $(X,k)$ with $X^{♯}=n$, we find a certain condition that supports $n-1,n-2\in F\left(Co{n}_k\left(X\right)\right)$. Thirdly, after finding some features of $F\left(Co{n}_k\left(W\right)\right)$, we develop a method of making $F\left(Co{n}_k\left(W\right)\right)$ perfect according to the (even or odd) number l of $C_k^{n,l}$. Finally, we prove that the perfectness of $F\left(Co{n}_k\left(W\right)\right)$ is equivalent to that of $F\left(Co{n}_k\left(C_k^{n,l}\right)\right)$. This can play an important role in studying fixed point theory and digital curve theory. This paper only deals with k-connected digital images $(X,k)$ such that $X^{♯}\ge 2$. Full article

In this study, we introduce set-valued Prešić type almost contractive mapping, Prešić type almost F-contractive mapping and set-valued Prešić type almost F-contractive mapping in metric space and prove some fixed point results for these mappings. Additionally, we give examples to show that our main theorems are applicable. These examples show that the new class of set-valued Prešić type almost F-contractive operators is not included in Prešić type class of set-valued Prešić type almost contractive operators. Full article

The dynamic behavior of n-firm oligopolies is examined without product differentiation and with linear price and cost functions. Continuous time scales are assumed with best response dynamics, in which case the equilibrium is asymptotically stable without delays. The firms are assumed to face both implementation and information delays. If the delays are equal, then the model is a single delay case, and the equilibrium is oscillatory stable if the delay is small, at the threshold stability is lost by Hopf bifurcation with cyclic behavior, and for larger delays, the trajectories show expanding cycles. In the case of the non-equal delays, the stability switching curves are constructed and the directions of stability switches are determined. In the case of growth rate dynamics, the local behavior of the trajectories is similar to that of the best response dynamics. Simulation studies verify and illustrate the theoretical findings. Full article

The arithmetic operations of fuzzy sets are completely different from the arithmetic operations of vectors of fuzzy sets. In this paper, the arithmetic operations of vectors of fuzzy intervals are studied by using the extension principle and a form of decomposition theorem. These two different methodologies lead to the different types of membership functions. We establish their equivalences under some mild conditions. On the other hand, the $\alpha$-level sets of addition, difference and scalar products of vectors of fuzzy intervals are also studied, which will be useful for the different usage in applications. Full article

A photomosaic is an image with two layers of visual information, including an overarching image that can be seen from a distance and a matrix of individual tile images when examined closely. This paper presents a method for generating photomosaics with an additional layer of quick response code (QR code) information that can be accessed by typical QR code scanners in cell phones. The basic idea is to carefully classify the tile images in different categories and generate the photomosaic patches by referring to the properties of QR code modules. Three levels of construction methods for generating the proposed photomosaics in different image resolutions are proposed. The results show that the generated photomosaics have good visual quality and high robustness for decoding the QR code. The proposed method endows conventional photomosaics with the QR code capability. It extends photomosaics from exhibiting purely visual information to the linkage of multimedia data. Furthermore, it increases the feasibility and potential of applying photomosaics in diverse applications, such as activity promotions or commercial product advertisements. Full article

To estimate age-specific natural mortality, we proposed an age-structured biomass model with an impulsive dynamical system. In the estimation of natural mortality, we considered growth rate and also reproduction rate, growth, and catch of sandfish, Arctoscopus japonicus. Assuming a linear relationship between observed values of the catch per unit effort (CPUE) and total biomass estimated by the age-structured biomass model, we estimated the age-specific natural mortality using the CPUE and catch data, from 1994 to 2009, for varying values of the assumed initial total biomass in 1994, by selecting the largest coefficient of determination ($R^2$). We suggested the following empirical formula: $M_i=\frac{q}{K{L}_{\infty }}\ln \left(\frac{e^{K\left(i+1-t_0\right)}-1}{e^{K\left(i-t_0\right)}-1}\right),$ which estimated natural mortality of sandfish, and the derived age-specific natural mortality was significantly related to fecundity and growth. The parameters of von Bertalanffy growth equation and a logistic equation of maturity with total length were derived from the data of otolith and gonad analysis of female sandfish collected from 2005 to 2008 and from 2005 to 2006, respectively. We also conducted sensitivity analysis by varying the exponent in the inverse function of total length. Full article

In this paper we present an algorithm which counts the number of fixed point orbits of an AND-OR dynamical system. We further extend the algorithm in order to list all its fixed point orbits (FPOs) in polynomial time on the number of FPOs of the system. Full article

Since the 1990s, the notion of a circular economy has been developing globally; countries all over the world have been considering the development of a circular economy as an important means of achieving sustainable development. As the development of an industrial circular economy can help promote the efficient recycling of resources, it is an important starting point for industrial transformation and upgrading, and represents a key factor that will lead to the development of a circular economy in China. China’s varying provinces (municipalities and autonomous regions) have successively implemented circular economy practices in the industrial field. The research object of the present study is 30 provinces, autonomous regions, and municipalities directly under the control of central government (Hong Kong, Macao, Taiwan, and Tibet were not included owing to lack of data). Through the integration of geographic information systems (GIS) technology and the spatial analysis model, data envelopment analysis (DEA) model, and Tobit regression model, a measure model and index system are constructed, in order to carry out a multi-angle comprehensive study integrating the efficiency evaluation, spatial analysis, and influencing factors analysis of China’s industrial circular economy. It is an important innovation, and an important contribution to the existing research system. The conclusions are as follows: (1) In general, the overall level of China’s industrial circular economy’s efficiency was not high, and there was still a lot of room for improvement. The integrated efficiency of the industrial circular economy in the eastern region was relatively high, followed by that in the western region, and the lowest level in the middle region. (2) The efficiency of China’s industrial circular economy displayed obvious spatial aggregation characteristics at the provincial level, including clear spatial dependence and spatial heterogeneity. High-value aggregation areas were mainly distributed in the eastern coastal areas, and low-value aggregation areas were concentrated and contiguously distributed in the middle and western inland areas. (3) The four elements of economic level, openness to the outside, government regulation, and industrialization aggregation each impose a significant positive impact on the efficiency of China’s industrial circular economy, which can promote its efficiency. The level of industrialization exerts a significant negative impact on the efficiency of the industrial circular economy, which hampers its improvement. The impact of technological innovation on the efficiency of the industrial circular economy is not statistically significant. Full article

The present work is aimed at studying the effect of fractional order and thermal relaxation time on an unbounded fiber-reinforced medium. In the context of generalized thermoelasticity theory, the fractional time derivative and the thermal relaxation times are employed to study the thermophysical quantities. The techniques of Fourier and Laplace transformations are used to present the problem exact solutions in the transformed domain by the eigenvalue approach. The inversions of the Fourier-Laplace transforms hold analytical and numerically. The numerical outcomes for the fiber-reinforced material are presented and graphically depicted. A comparison of the results for different theories under the fractional time derivative is presented. The properties of the fiber-reinforced material with the fractional derivative act to reduce the magnitudes of the variables considered, which can be significant in some practical applications and can be easily considered and accurately evaluated. Full article

The aim of this article is to fill part of the existing gap between the mathematical modeling of a green roof and its computational treatment, focusing on the mathematical analysis. We first introduce a two-dimensional mathematical model of the thermal behavior of an extensive green roof based on previous models and secondly we analyze such a system of partial differential equations. The model is based on an energy balance for buildings with vegetation cover and it is presented for general shapes of roofs. The model considers a vegetable layer and the substratum and the energy exchange between them. The unknowns of the problem are the temperature of each layer described by a coupled system of two partial differential equations of parabolic type. The equation modeling the evolution of the temperature of the substratum also considers the change of phase of water described by a maximal monotone graph. The main result of the article is the proof of the existence of solutions of the system which is given in detail by using a regularization of the maximal monotone graph. Appropriate estimates are obtained to pass to the limit in a weak formulation of the problem. The result goes one step further from modeling to validate future numerical results. Full article