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This paper analyzes and studies the structure and parameters of the VGGNet network model and selects the most commonly used and efficient VGG-16 as the prototype of the improved model. A multiscale sampling layer is added at the end of the VGG-16 convolution part so that the model can input images of any size for training and testing while reducing the number of neurons in the fully connected layer. This improves the training speed of the model under the premise of ensuring the accuracy. This paper uses multisource street spatial data combined with geographic information spatial analysis technology to measure and evaluate the spatial quality of streets in the main urban area. From the three dimensions of vitality, safety, and greenness of urban street space quality, a systematic structure for evaluation and analysis of street space quality is constructed. Street vitality includes eight index factors: entrance and exit density, street furniture density, street sketch density, street characteristic landscape density, POI density, POI diversity, commercial POI ratio, and street population density. There are five index factors: degree, roadside parking occupancy ratio, traffic signal system density, sidewalk width proportion, and street facility density. We use ArcGIS to build an index factor information database for statistical analysis and visualization. According to the natural discontinuous point classification method, the safety level of urban street public space is divided into five grades. The sample size of the first four grades has a small fluctuation range. The sample sizes are 153, 172, 153, and 158, respectively, accounting for 21%, 23%, 21%, and 21% of the total street samples, of which the first two grades occupy a total of 44%, so 44% of the streets in the main urban area have a low-quality level of street space. Level 5 has a sample of 102 streets, accounting for 14%, with an average street space quality value of 0.43. [ABSTRACT FROM AUTHOR]

The structure of the urban road network affects the mode of urban development and the position of urban social and economic activities, families, and employment centers. Therefore, it is necessary to consider the supply inequality of urban road network and its impact on urban development so as to form a sustainable and fair urban development model in cities. Based on the fractal analysis, this paper seeks the evaluation index of urban road network layout and internal structure characteristics to guide the optimization and adjustment of the urban road network, which is of great significance for guiding urban land use, effectively utilizing geospatial space, and promoting sustainable urban development, and attempts to apply the fractal analysis concept to evaluate the urban road network in Harbin, China. It is found that there is a good relationship between the length of the urban road network and the build-up area. Therefore, fractal analysis is used to reasonably determine the spatial demand of incremental road networks, considering the impact of road network increase on development mode. This paper argues that fractal analysis is an auspicious tool for the evaluation of urban road networks, including solving the problem of supply inequality in urban road networks, which is very suitable for the gradual construction of road networks in urban situations, especially in the development environment of road networks with scarce resources. [ABSTRACT FROM AUTHOR]

In recent years, there are many problems in the construction of street landscape spatial pattern, such as emphasizing the surface, ignoring the substance, focusing on construction, and ignoring protection. The reason is closely related to the lack of visual evaluation of streetscape for guidance. This research mainly discusses the numerical analysis and calculation for the spatial pattern of urban streetscape. This study clarifies the related concepts of visual evaluation of urban streetscape and discusses the formation process, overall characteristics, and constituent elements of streetscape. It emphasizes the importance of two subjective and objective factors of "landscape" and "vision" for evaluation. This paper studies this spatial composition relationship from the perspective of street space and the building itself. In the research process, it selects the pedestrian street in the northwest of the city as the object and uses the questionnaire survey method and the multifactor evaluation method to carry out the visual evaluation of the streetscape. It deeply discusses the application of evaluation methods in practice and counts the relevant evaluation results. In the urban street space proportion curve and the corresponding comparative analysis, it is found that most of the street space proportion is between 0.6 and 3.0. This kind of space composition has mutual inclusive symmetry, which enhances the order and communication of urban architecture. This somewhat improves this alienated spatial morphological pattern. This research is helpful to promote the development of streetscape visual evaluation. [ABSTRACT FROM AUTHOR]

In this paper, a new geometric structure of projective invariants is proposed. Compared with the traditional invariant calculation method based on 3D reconstruction, this method is comparable in the reliability of invariant calculation. According to this method, the only thing needed to find out is the geometric relationship between 3D points and 2D points, and the invariant can be obtained by using a single frame image. In the method based on 3D reconstruction, the basic matrix of two images is estimated first, and then, the 3D projective invariants are calculated according to the basic matrix. Therefore, in terms of algorithm complexity, the method proposed in this paper is superior to the traditional method. In this paper, we also study the projection transformation from a 3D point to a 2D point in space. According to this relationship, the geometric invariant relationships of other point structures can be easily derived, which have important applications in model-based object recognition. At the same time, the experimental results show that the eight-point structure invariants proposed in this paper can effectively describe the essential characteristics of the 3D structure of the target, without the influence of view, scaling, lighting, and other link factors, and have good stability and reliability. [ABSTRACT FROM AUTHOR]

Estimating the 3D pose of the space object from a single image is an important but challenging work. Most of the existing methods estimate the 3D pose of known space objects and assume that the detailed geometry of a specific object is known. These methods are not available for unknown objects without the known geometry of the object. In contrast to previous works, this paper devotes to estimate the 3D pose of the unknown space object from a single image. Our method estimates not only the pose but also the shape of the unknown object from a single image. In this paper, a hierarchical shape model is proposed to represent the prior structure information of typical space objects. On this basis, the parameters of the pose and shape are estimated simultaneously for unknown space objects. Experimental results demonstrate the effectiveness of our method to estimate the 3D pose and infer the geometry of unknown typical space objects from a single image. Moreover, experimental results show the advantage of our approach over the methods relying on the known geometry of the object. [ABSTRACT FROM AUTHOR]

Object detection in public spaces on urban streets has always been an important research topic in the field of computer vision networks. Due to the complex and changeable scene in the prediction of public space art design indicators, there are still problems in the research of target detection algorithms in practical applications. Based on the DCNN, this paper studies the accurate detection algorithm and implementation of urban streets in complex scenes. This paper uses the characteristics of DCNN coding to collect and compress data at the same time, studies the prediction module of urban street saliency detection algorithm, and combines saliency map to determine the saliency of urban street art design indicators in the measurement domain. The experimental method can greatly shorten the index prediction scan time and solve the problems of high window calibration redundancy and long positioning time in index prediction. The experimental results show that the proposed method combining urban street mask and public space feature information can reduce other interference information, the average accuracy of target detection is increased by 0.398, and the error is reduced to 3.12%, which significantly promotes urban streets and improves recognition accuracy. [ABSTRACT FROM AUTHOR]

Urban commercial complex is the product of social and economic development, as well as the inevitable trend of commercial development. The public space design of urban complex project is an important link in its development process, which is the link between the contact and the building, the city and the building, and the external image display of the complex. Therefore, choosing a suitable and excellent public space design scheme is of great significance to show the superiority of the complex project and improve the project satisfaction and the sustainable operation in the later stage. This paper first defines the concept of urban complex public space and focuses on the analysis of the urban complex public space from four aspects of constituent elements, functional classification, design theory, and principle. Then, the Delphi method is used to determine 26 evaluation indicators to evaluate the urban complex public space design scheme, and the relevant index data of 20 urban complex public space design schemes are collected. The grey correlation analysis method is used to analyze the correlation degree between each indicator and the scheme winning bid. The final evaluation system of urban complex public space design scheme is obtained after removing the 8 indicators with low correlation degree. Support vector mechanism was used to build the optimization model of urban complex public space design scheme, and its accuracy was verified, which provides a relatively simple and quantitative method for urban public space design in the future, helps to improve the city's business structure, improves the business environment of the city, makes the commercial complex more effectively play its own characteristics and advantages, effectively stimulates the vitality of urban space, and creates more perfect architectural space and urban space for people. [ABSTRACT FROM AUTHOR]

By analyzing the historical background of the times and summarizing the current situation of urban development research at home and abroad, we find that there is a lack of theoretical and practical research related to intelligent park cities. Therefore, this paper first starts with the connotation of park city theory, focuses on the improvement of planning methods, and studies the application paths of big data technology in the planning and construction of park cities. Taking Jinzhai Country as the research object, this paper further illustrates the applicability of this research method at the macrolevel. In the context of the park city, we analyze the problems of the current status of city construction in general and explore the path of "planning concept first, big data-assisted design" for innovative and intelligent city construction. According to the study, the overlook corridor control has an impact on the building height. In terms of landscape protection, overlook system simulation is the other key factor. In addition, the analytic hierarchy process is the basis for development intensity control. The results show that big data technology can assist in the landscape conservation, morphology formation, and efficient operation of Jinzhai Country Park City. Our aim is to achieve the protection and utilization of its ecological environment and natural resources and thus to comprehensively coordinate the multidimensional urban spaces and build a park city model. As an urban development model that meets the requirements of being "people-oriented, efficient, green, and aesthetic" in the new stage, park cities need to be faced by researchers in order to further realize the overall city goal and vision for the whole society to be smart. It also provides relevant design ideas and methods for the planning and construction of park cities in other similar cities or regions. [ABSTRACT FROM AUTHOR]

Space target identification is key to missile defense. Micromotion, as an inherent attribute of the target, can be used as the theoretical basis for target recognition. Meanwhile, time-varying micro-Doppler (m-D) frequency shifts induce frequency modulations on the target echo, which can be referred to as the m-D effect. m-D features are widely used in space target recognition as it can reflect the physical attributes of the space targets. However, the traditional recognition method requires human participation, which often leads to misjudgment. In this paper, an intelligent recognition method for space target micromotion is proposed. First, accurate and suitable models of warhead and decoy are derived, and then the m-D formulae are offered. Moreover, we present a deep-learning (DL) model composed of a one-dimensional parallel structure and long short-term memory (LSTM). Then, we utilize this DL model to recognize time-frequency distribution (TFD) of different targets. Finally, simulations are performed to validate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Several fixed point results for the existence of common fixed points of multivalued contractive mappings have been established in complex-valued metric space. In this paper, we study the existence of common fixed points for a pair of multivalued contractive mappings satisfying some rational inequalities in the framework of complex-valued b -metric spaces. The contractive condition used in this paper generalizes many contractive conditions used by other authors in the literature. Employing our results, we check the existence solution to the Riemann-Liouville equation. [ABSTRACT FROM AUTHOR]

Aiming at a space manipulator with a joint-locked failure, a halt optimization strategy is proposed in this paper. Firstly, a halt configuration optimization model (HCOM) is constructed, to select an optimal configuration where the kinematic ability of the manipulator is the best. Secondly, considering the constraint of joint running parameters and the disturbance torque of the base, we construct and solve the halt motion optimization model (HMOM), which can achieve a steady halt and ensure the safety of the manipulator. The correctness and effectiveness of the proposed strategy in this paper are verified with a 7-DOF space manipulator. This strategy firstly puts forward the idea of halt configuration optimization and realizes the minimum global disturbance torque of the base in the halt process. [ABSTRACT FROM AUTHOR]

The paper is regarding the fair distribution of several files having different sizes to several storage supports. With the existence of several storage supports and different files, we search for a method that makes an appropriate backup. The appropriate backup guarantees a fair distribution of the big data (files). Fairness is related to the used spaces of storage support distribution. The problem is how to find a fair method that stores all files on the available storage supports, where each file is characterized by its size. We propose in this paper some fairness methods that seek to minimize the gap between used spaces of all storage supports. In this paper, several algorithms are developed to solve the proposed problem, and the experimental study shows the performance of these developed algorithms. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a generalization of rectangular b -metric spaces, by changing the rectangular inequality as follows: D ζ a , b ≤ ζ a , b , u , v D ζ a , u + D ζ u , v + D ζ v , b , for all distinct a , b , u , v ∈ X. We prove some fixed point theorems, and we use our results to present a nice application in the last section of this paper. [ABSTRACT FROM AUTHOR]

Let ℒ = − Δ + V be a Schrödinger operator on ℝ d , d ≥ 3 , where Δ is the Laplacian operator on ℝ d , and the nonnegative potential V belongs to the reverse Hölder class RH s with s ≥ d / 2 . For given 0 < α < d , the fractional integrals associated with the Schrödinger operator ℒ is defined by ℐ α = ℒ − α / 2 . Suppose that b is a locally integrable function on ℝ d and the commutator generated by b and ℐ α is defined by b. ℐ α f x = b x ⋅ ℐ α f x − ℐ α b f x . In this paper, we first introduce some kinds of weighted Morrey spaces related to certain nonnegative potentials belonging to the reverse Hölder class RH s with s ≥ d / 2 . Then, we will establish the boundedness properties of the fractional integrals ℐ α on these new spaces. Furthermore, weighted strong-type estimate for the corresponding commutator b , ℐ α in the framework of Morrey space is also obtained. The classes of weights, the classes of symbol functions, as well as weighted Morrey spaces discussed in this paper are larger than A p , q , BMO ℝ d , and L p , κ μ , ν corresponding to the classical case (that is V ≡ 0). [ABSTRACT FROM AUTHOR]

This paper is devoted to the maximal regularity of sectorial operators in Lebesgue spaces L p ⋅ with a variable exponent. By extending the boundedness of singular integral operators in variable Lebesgue spaces from scalar type to abstract-valued type, the maximal L p ⋅ − regularity of sectorial operators is established. This paper also investigates the trace of the maximal regularity space E 0 1 , p ⋅ I , together with the imbedding property of E 0 1 , p ⋅ I into the range-varying function space C − I , X 1 − 1 / p ⋅ , p ⋅ . Finally, a type of semilinear evolution equations with domain-varying nonlinearities is taken into account. [ABSTRACT FROM AUTHOR]

This paper investigates the application method of architectural decoration space transformation construction, constructs the architectural decoration model based on virtual reality technology, realizes the three-dimensional display of architectural decoration space structure, and optimizes the construction of architectural decoration space transformations in order to solve the unreasonable problem of architectural decoration space combined with virtual reality technology. The experimental results show that using virtual reality technology in the construction of architectural decoration space transformation can better ensure the rationality of building structure and improve the construction efficiency of architectural decoration space transformation, thereby simplifying the space transformation process and improving space transformation quality. [ABSTRACT FROM AUTHOR]

In order to pay attention to the protection of the third tier industrial heritage, this paper puts forward the protection measures of combining the third tier industrial heritage with tourism based on the concept of urban image. The tourism value of the tertiary industrial heritage is evaluated by using the comprehensive evaluation method. Through the analysis of the tourism value evaluation system combining the three-level industrial heritage and rural tourism in a certain city, the following conclusions are drawn. In the comprehensive evaluation layer, the value of the third tier industrial heritage accounts for the largest weight of 0.5581, indicating that the third tier industrial heritage resources occupy an important position in the third tier industrial heritage tourism value system. Tourism development conditions also account for a large proportion, which explains that while adhering to the principle of third tier industrial heritage protection, we should pay attention to the consideration of tourism development conditions. It once again emphasizes the importance of the third tier industrial heritage for the development of industrial heritage tourism and the significance of the protection of the third tier industrial heritage for tourism development. In the three-level evaluation layer of industrial heritage and rural tourism, the historical and cultural value and social and cultural value have the largest weight. They are the leading factor of the combined value of tertiary industrial heritage and rural tourism. Historical and cultural value is one of the important meanings of three-level industrial heritage protection and also the essence of the combined development of third-level industrial heritage tourism and rural tourism. Social value determines the recognition of tourists and people to participate in the development of tourism. In the evaluation layer of tourism development conditions, the development potential is particularly prominent. The development potential is the characteristic of the third tier industrial heritage tourism of a city. The development of the third tier industrial heritage tourism of a city must be combined with the local characteristics to highlight the differences. [ABSTRACT FROM AUTHOR]

With the development of the times, intelligent space simulation technology has gradually emerged in the design of ceramic forms, and the development of modern ceramics has gradually transformed into artistic development. The development of ceramics must conform to the design trend, adjust the rhythm, and seek development opportunities. Organic design opens up a green channel for ceramics and integrates into the lives of today's people. This paper mainly discusses the external form of ceramics and studies from two levels of curve form and bionic form. Through the intelligent space simulation technology, the shape design of ceramics is studied, and the optimal shape of ceramics is obtained, which enables people to have a better understanding of ceramic art. [ABSTRACT FROM AUTHOR]

Although hydraulic fracturing has been practiced all over the world, the research on how the fracture height develops in time and space still leaves some missing gaps. The fracture height has been considered in most cases equal to the pay zone thickness, and the influence of temperature in this process has been omitted. Therefore, the aim of this paper is to study the effect of temperature, rock mechanical properties, and fluid injection rate on the development of the fracture geometry, especially on the fracture height. A multiphysics model was implemented using cohesive elements in a finite element model generated with equations in fracture mechanics. Once the model was calibrated with experimental data, it was used to conduct sensitivity studies to reveal the influence of main contributed factors such as the properties of rocks and fluids used in hydraulic fracturing, the injection rate of fracturing liquid, and especially the influence of temperature because this last aspect was omitted in literature review from previous studies. The results indicated that the fracture height depended strongly on the rock properties, not only the rock in the pay zone but also the ones in the adjacent layers. Besides, the influence of the fluid injection rate on the fracturing height is so great that it overwhelms the influence of temperature and mechanical parameters. Moreover, the impact of the leak-off coefficient is much less remarkable than that of the fluid viscosity, which demonstrates why in reality it is important to control the viscosity to achieve desirable results. This study can be applied in real life problems to predict fracture's geometry generated in well stimulations. [ABSTRACT FROM AUTHOR]

The proposal and development of edge computing provide new ideas for the management of industrial space forms in high-density cities. With the acceleration of China's urbanization process, the spatial distribution system of industries in cities is relatively complicated and is not suitable for benefit and suitability evaluation. There is still a lack of in-depth quantitative analysis and research on the industrial spatial form of Macau's high-density cities, which is restricted by factors such as shortage of land and simplification of industries. Therefore, it is necessary to explore the relationship between Macau's industrial spatial pattern and its urban spatial pattern, deepen its industrial system reform, and put forward suggestions that are more in line with the needs of urbanization. Among them, the sports, leisure, and entertainment industry account for a relatively large proportion of the industrial structure of Macau city, which is a very important part. This paper studies the aggregation and correlation of its spatial distribution through the method of nuclear density analysis and aims to provide a better basis and support for its more reasonable industrial upgrading. [ABSTRACT FROM AUTHOR]

With the continuous development of the social economy, the urban residential structure is also changing, and people have higher and higher requirements for the living environment. Moreover, the landscape construction of public spaces in cities is an important part of the city. It is easy to neglect the comprehensive consideration of historical development and regional culture in architectural projects. The overall lack of individuality in urban design, the lack of characteristics of adapting measures to local conditions, and the blind emphasis on architectural landscaping have led to a serious lack of regional cultural characteristics and spiritual culture in public places. Therefore, in terms of the problems of insufficient landscape construction quality and green concepts being insufficient in the construction environment of cities, an evaluation method system is established in the paper to further study the shortcomings of the scenic area architecture. What is more, relying on the personal experience of the users in the scenic spot and understanding the real needs of the public space landscape environment around the scenic spot, scientific methods and a complete system are applied to make an overall assessment of the public space in the built residential area. Besides, according to the data analysis of the simulation experiment, the advantages and disadvantages of the public space in the residential area are extracted. Combined with the current research status, the green concept design strategy of the public space landscape environment in the scenic spot is summarized. Lastly, according to the data analysis of the simulation experiment, the evaluation satisfaction of the activity atmosphere, plant configuration, and overall layout is improved by 4.2%, 3.7%, and 3.1% compared with other methods, which proves that this study has a more reasonable planning program to meet the various needs of public open space. The development of urban landscape design provides a valuable reference. [ABSTRACT FROM AUTHOR]

The three-dimensional organic growth features of buildings have been given more and more attention according to the unique view representation regulations of the indoor construction industry, in order to optimize the usage and allocation efficiency of building space. To explore the configuration structure of building function space, the three-dimensional box dimension algorithm is used to measure the fractal dimension of the indoor and outdoor form of building space, and the two-dimensional and three-dimensional fractal characteristics of building space are compared and analyzed; the method of the second derivative is utilized for the automatic recognition of fractal scale-free areas, aiming at the imprecise problem of the artificial judgment of scale-free areas in earlier fractal research of interior and outdoor forms of architectural space. The experimental results show that the second derivative method can effectively and automatically identify the scale-free region. The coefficients of linear fitting are above 0.990, and the indoor and outdoor forms of architectural space have clear fractal characteristics. After applying the method, the three-dimensional fractal dimension grows, indicating that the interior and outdoor form usage of architectural space in this area is generally effective and compact. [ABSTRACT FROM AUTHOR]

Economic development leads to the widespread use of energy, which results in carbon emissions. In order to determine the correlation between different urban carbon emissions and fiscal growth, a coupling and coordination model of urban carbon emissions and economic growth based on discrete Fourier transform (DFT) is constructed. According to the coupling and coordinated development characteristics of economic growth and carbon emissions, the evaluation index system of the regional economy and carbon emissions is constructed. This paper examines the proportion of primary energy consumption and the influencing factors of carbon emission in a city and constructs the economic growth computational intelligence model and urban carbon emission model. The coupling degree among economic growth, carbon emission, and energy consumption is studied; the coupling standard between economic growth and energy consumption carbon emission is determined; and the carbon emission factor under the method of DFT is introduced. The coupling coordination model between economic growth and carbon emission is constructed, and the interaction mechanism between carbon emission, economic development, and environmental protection is determined. The experimental findings demonstrate that when energy consumption intensity and carbon emission are relatively low, the model's change in the trend of coupling coordination index is comparable with the real/actual condition and the model is more reliable. [ABSTRACT FROM AUTHOR]

In this paper, the authors obtain the boundedness of the fractional integral operators with variable kernels on the variable exponent weak Morrey spaces based on the results of Lebesgue space with variable exponent as the infimum of exponent function p(·) equals 1. The corresponding commutators generated by BMO and Lipschitz functions are considered, respectively. [ABSTRACT FROM AUTHOR]

The discrete Gel'fand–Yaglom theorem was studied several years ago. In the present paper, we generalize the discrete Gel'fand–Yaglom method to obtain the determinants of mass matrices which appear in current works in particle physics, such as dimensional deconstruction and clockwork theory. Using the results, we show the expressions for vacuum energies in such various models. [ABSTRACT FROM AUTHOR]

In this paper, we characterize the closure of the Morrey space in the Bloch space. Furthermore, the boundedness and compactness of composition operators from the Bloch space to the closure of the Morrey space in the Bloch space are investigated. [ABSTRACT FROM AUTHOR]

Structured light has been widely applied to 3D shape measurement with the capabilities of rapidness, high-accuracy, and noncontact. Because of uneven illumination and noise, it is difficult to distinguish the light stripes and background of the image, which reduces the measurement accuracy. In this paper, an adaptive Canny edge detection method with two phases is proposed for structured light stripes. Firstly, the idea of dynamic granularity is introduced and the dynamic granularity matrix space is established, in which image segmentation problems are described as the transformations and jumping of image at different granularity layers. The hierarchical structure and optimal granularity layer of image are obtained as the basis of adaptive edge detection. Secondly, a quantum-inspired group leader hybrid algorithm is adopted to calculate the optimal threshold from the optimal granularity layer, which is taken as the adaptive threshold for Canny operator. Finally, experimental tests and comparisons have been conducted to verify the effectiveness of the adaptive method proposed. The experiments show that the proposed method achieves high segmentation accuracy, improves the segmentation efficiency, and has strong robustness to noise. [ABSTRACT FROM AUTHOR]

Unlike outdoor trajectory prediction that has been studied many years, predicting the movement of a large number of users in indoor space like shopping mall has just been a hot and challenging issue due to the ubiquitous emerging of mobile devices and free Wi-Fi services in shopping centers in recent years. Aimed at solving the indoor trajectory prediction problem, in this paper, a hybrid method based on Hidden Markov approach is proposed. The proposed approach clusters Wi-Fi access points according to their similarities first; then, a frequent subtrajectory based HMM which captures the moving patterns of users has been investigated. In addition, we assume that a customer's visiting history has certain patterns; thus, we integrate trajectory prediction with shop category prediction into a unified framework which further improves the predicting ability. Comprehensive performance evaluation using a large-scale real dataset collected between September 2012 and October 2013 from over 120,000 anonymized, opt-in consumers in a large shopping center in Sydney was conducted; the experimental results show that the proposed method outperforms the traditional HMM and perform well enough to be usable in practice. [ABSTRACT FROM AUTHOR]

Significant advancements in developing earth-air heat exchanger models have been detected in the past several decades. It is worth mentioning that this type of device takes advantage of the Earth's constant temperature to cool or heat spaces in buildings so that the identification of its most appropriate geometric configurations to reduce energy consumption is still an actual challenge. In this context, the present paper is focused on the geometric evaluation of several earth-air heat exchangers arrangements according to the Constructal Design method. The performance indicators are the minimization of its soil volume occupation, the minimization of its airflow pressure drop, and the maximization of its thermal potential. Therefore, from a straight duct named Reference Installation, 26 complex geometries have been outlined here using the numerical-analytical investigation. Many ideas emerged from this study: the use of serpentine with low spacing between ducts reduced nearly 39% of the soil volume occupied by the device compared to Reference Installation, showing its applicability in urban regions. In addition, configurations with few curves benefited the decrease of air pressure drop, allowing a performance 30% superior to the most complex shapes. Instead, complex designs can be recommended for thermal potential increase, although the influence of the different configurations over this indicator was not substantial since the maximum improvement achieved between the best and worst shapes proved to be around 6%. Finally, when the three performance indicators are concomitantly considered, several complex geometries reached an overall performance superior to the Reference Installation. [ABSTRACT FROM AUTHOR]

In this paper, we consider an auxiliary function G to combine and unify several existing fixed point theorems in the setting of the complete partial b -metric space. We consider also some examples to support the observed main results. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notion of R -partial b -metric spaces and prove some related fixed point results in the context of this notion. We also discuss an example to validate our result. Finally, as applications, we evince the importance of our work by discussing some fixed point results on graphical-partial b -metric spaces and on partially-ordered-partial b -metric spaces. [ABSTRACT FROM AUTHOR]

In this paper, we prove the existence and uniqueness of fixed points for F -contractions in complete Branciari b -metric spaces. Furthermore, an example for supporting the related result is shown. We also present the concept of the weak well-posedness of the fixed-point problem of the mapping T and discuss the weak well-posedness of the fixed-point problem of an F -contraction in complete Branciari b -metric spaces. Besides, we investigate the problem of common fixed points for F -contractions in above spaces. As an application, we apply our main results to solving the existence and uniqueness of solutions for a class of the integral equation and the dynamic programming problem, respectively. [ABSTRACT FROM AUTHOR]

Let L = − Δ ℍ n + V be a Schrödinger operator on the Heisenberg group ℍ n , where Δ ℍ n is the sub-Laplacian on ℍ n and the nonnegative potential V belongs to the reverse Hölder class B q with q ∈ Q / 2 , ∞ . Here, Q = 2 n + 2 is the homogeneous dimension of ℍ n . Assume that e − t L t > 0 is the heat semigroup generated by L. The semigroup maximal function related to the Schrödinger operator L is defined by T L ∗ f u ≔ sup t > 0 e − t L f u . The Riesz transform associated with the operator L is defined by R L = ∇ ℍ n L − 1 / 2 , and the dual Riesz transform is defined by R L ∗ = L − 1 / 2 ∇ ℍ n , where ∇ ℍ n is the gradient operator on ℍ n . In this paper, the author first introduces a class of Morrey spaces associated with the Schrödinger operator L on ℍ n . Then, by using some pointwise estimates of the kernels related to the nonnegative potential, the author establishes the boundedness properties of these operators T L ∗ , R L , and R L ∗ acting on the Morrey spaces. In addition, it is shown that the Riesz transform R L = ∇ ℍ n L − 1 / 2 is of weak-type 1 , 1 . It can be shown that the same conclusions are also true for these operators on generalized Morrey spaces. [ABSTRACT FROM AUTHOR]

In this paper, the concept of sequential p -metric spaces has been introduced as a generalization of usual metric spaces, b -metric spaces and specially of p -metric spaces. Several topological properties of such spaces have been discussed here. In view of this notion, we prove fixed point theorems for some classes of contractive mappings over such spaces. Supporting examples have been given in order to examine the validity of the underlying space and in respect to our proven fixed point theorems. [ABSTRACT FROM AUTHOR]

This paper investigates the network coordination, self-regulation mode, and autonomous control spatial planning of microgrid. To do this, the cooperative self-discipline model of multi-microgrid intelligent distribution network is constructed. Based on combing the power control of multi-microgrid with high penetration situation, the concept and characteristics of distribution network and self-regulation mode are defined according to the new requirements, and the basic framework and decision-making process of self-regulation mode are put forward. Further, the formulation method of autonomous spatial planning for multi-micronetworks is described. By constructing cooperative self-discipline space scheme and its reward and punishment mechanism, the network operation behavior is restrained and guided, and the control dimension of the distribution network is reduced. Finally, a typical case is given to illustrate the effectiveness of cooperative self-discipline supervision mode in reducing the space-time dimension of distribution network supervision. [ABSTRACT FROM AUTHOR]

Recently, a notion of b -hybrid contraction for single-valued mappings in the framework of b -metric spaces which unify and improve several significant existing results in the corresponding literature was introduced. This paper presents a multivalued generalization for such contraction. Moreover, one of our obtained results is applied to analyze some solvability conditions of Fredholm-type integral inclusions. Nontrivial examples are also provided to support the assertions of our theorems. [ABSTRACT FROM AUTHOR]

In this paper, we have established some fixed-point results for the class of multivalued φ -contractions in the setting of extended b -metric space. An example is furnished to show the validity of our results. The results we have obtained generalize/extend many recent results by Asl, Bota, Samreen et al., and those contained therein. [ABSTRACT FROM AUTHOR]

The Banach contraction principle is the most celebrated fixed point theorem and has been generalized in various directions. In this paper, inspired by the concept of θ ‐ ϕ -contraction in metric spaces, introduced by Zheng et al., we present the notion of θ ‐ ϕ -contraction in b -rectangular metric spaces and study the existence and uniqueness of a fixed point for the mappings in this space. Our results improve many existing results. [ABSTRACT FROM AUTHOR]

In this paper, we present a common fixed point result for a pair of mappings defined on a b-metric space, which satisfies quasi-contractive inequality with nonlinear comparison functions. An application in solving a class of integral equations will support our results. [ABSTRACT FROM AUTHOR]

This paper aims to disclose the compound topological and directional relationships of three simple regions in the three-dimensional (3D) space. For this purpose, the directional model and the 8-intersection model were coupled into an R5DOS-intersection model and used to represent three simple regions in the 3D space. The matrices represented by the model were found to be complete and mutually exclusive. Then, a self-designed algorithm was adopted to solve the model, yielding 11,038 achievable topological and directional relationships. Compared with the minimum bounding rectangle (MBR) model, the proposed model boasts strong expressive power. Finally, our model was applied to derive the topological and directional relationships between simple regions A and C from the known relationships between simple regions A and B and those between B and C. Based on the results, a compound relationship reasoning table was established for A and C. The research results shed new light on the representation and reasoning of 3D spatial relationships. [ABSTRACT FROM AUTHOR]

In this article, we present a completeness characterization of b ∼ metric space via existence of fixed points of generalized multivalued quasicontractions. The purpose of this paper is twofold: (a) to establish the existence of fixed points of multivalued quasicontractions in the setup of b ∼ metric spaces and (b) to establish completeness of a b ∼ metric space which is a topological property in nature with existence of fixed points of generalized multivalued quasicontractions. Further, a comparison of our results with comparable results shows that the results obtained herein improve and unify the existing results in the literature applicable to the case where existing results fail. [ABSTRACT FROM AUTHOR]

In this paper, we obtain some characterizations of composition operators C φ , which are induced by an analytic self-map φ of the unit disk Δ , from hyperbolic Bloch type space β μ ∗ into hyperbolic type space Q K , p , q ∗ . [ABSTRACT FROM AUTHOR]

In this paper, we show that biharmonic hypersurfaces with at most two distinct principal curvatures in pseudo-Riemannian space form N s n + 1 c with constant sectional curvature c and index s have constant mean curvature. Furthermore, we find that such biharmonic hypersurfaces M r 2 k − 1 in even-dimensional pseudo-Euclidean space E s 2 k , M s − 1 2 k − 1 in even-dimensional de Sitter space S s 2 k c c > 0 , and M s 2 k − 1 in even-dimensional anti-de Sitter space ℍ s 2 k c c < 0 are minimal. [ABSTRACT FROM AUTHOR]

In this paper, we present some fixed point results for generalized θ ‐ ϕ ‐ contraction in the framework of α , η − compete rectangular b ‐ metric spaces. Further, we establish some fixed point theorems for this type of mappings defined on such spaces. Our results generalize and improve many of the well-known results. Moreover, to support our main results, we give an illustrative example. [ABSTRACT FROM AUTHOR]

Let T α 0 ≤ α < n be a class of sublinear operators satisfying certain size conditions introduced by Soria and Weiss, and let b , T α 0 ≤ α < n be the commutators generated by BMO R n functions and T α . This paper is concerned with two-weight, weak-type norm estimates for these sublinear operators and their commutators on the weighted Morrey and amalgam spaces. Some boundedness criteria for such operators are given, under the assumptions that weak-type norm inequalities on weighted Lebesgue spaces are satisfied. As applications of our main results, we can obtain the weak-type norm inequalities for several integral operators as well as the corresponding commutators in the framework of weighted Morrey and amalgam spaces. [ABSTRACT FROM AUTHOR]

In this paper, we discuss a class of mappings more general than ρ -nonexpansive mapping defined on a modular space endowed with a graph. In our investigation, we prove the existence of fixed point results of these mappings. Then, we also introduce an iterative scheme for which proves the convergence to a fixed point of such mapping in a modular space with a graph. [ABSTRACT FROM AUTHOR]

The boundedness, compactness, and essential norm of weighted composition operators from Besov Zygmund-type spaces into Zygmund-type spaces are investigated in this paper. [ABSTRACT FROM AUTHOR]

In this paper, we obtain some fixed point results for noncyclic monotone ρ -nonexpansive mappings in uniformly convex modular spaces and uniformly convex in every direction modular spaces. As an application, we prove the existence of the solution of an integral equation. [ABSTRACT FROM AUTHOR]

In this paper, we propose a computationally efficient direction-of-arrival (DoA) tracking scheme called the direct signal space construction Luenberger tracker (DSPCLT) with quadratic least square (QLS) regression. Also, we study analytically how the choice of observer gain affects the algorithm performance and illustrate how we can use the theoretical results in determining optimal observer gain value. The proposed scheme (DSPCLT) has several distinct features compared with existing algorithms. First, it requires only a fraction of computational complexity compared with other schemes. Secondly, it maintains robustness by treating separately the special case of object overlap in which subspace-based algorithms often suffer from lack of resolvability. Thirdly, the proposed scheme achieves enhanced performance by a method of delay compensation, which accounts for observation delay. Through numerical analysis, we show that DSPCLT achieves performance similar or superior to existing algorithms with only a fraction of computational requirement. [ABSTRACT FROM AUTHOR]

The main goal of the present paper is to obtain several fixed point theorems in the framework of F -quasi-metric spaces, which is an extension of F -metric spaces. Also, a Hausdorff δ -distance in these spaces is introduced, and a coincidence point theorem regarding this distance is proved. We also present some examples for the validity of the given results and consider an application to the Volterra-type integral equation. [ABSTRACT FROM AUTHOR]