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Background: Spatial complexity is always associated with spatial autocorrelation. Spatial autocorrelation coefficients including Moran's index proved to be an eigenvalue of the spatial correlation matrixes. An eigenvalue represents a kind of characteristic length for quantitative analysis. However, if a spatial correlation process is based on self-organized evolution, complex structure, and the distributions without characteristic scale, the eigenvalue will be ineffective. In this case, a scaling exponent such as fractal dimension can be used to compensate for the shortcoming of characteristic length parameters such as Moran's index. Method: This paper is devoted to finding an intrinsic relationship between Moran's index and fractal dimension by means of spatial correlation modeling. Using relative step function as spatial contiguity function, we can convert spatial autocorrelation coefficients into spatial autocorrelation functions. Result: By decomposition of spatial autocorrelation functions, we can derive the relation between spatial correlation dimension and spatial autocorrelation functions. As results, a series of useful mathematical models are constructed, including the functional relation between Moran's index and fractal parameters. Correlation dimension proved to be a scaling exponent in the spatial correlation equation based on Moran's index. As for empirical analysis, the scaling exponent of spatial autocorrelation of Chinese cities is Dc = 1.3623±0.0358, which is equal to the spatial correlation dimension of the same urban system, D2. The goodness of fit is about R2 = 0.9965. This fractal parameter value suggests weak spatial autocorrelation of Chinese cities. Conclusion: A conclusion can be drawn that we can utilize spatial correlation dimension to make deep spatial autocorrelation analysis, and employ spatial autocorrelation functions to make complex spatial autocorrelation analysis. This study reveals the inherent association of fractal patterns with spatial autocorrelation processes. The work may inspire new ideas for spatial modeling and exploration of complex systems such as cities. [ABSTRACT FROM AUTHOR]

The local indicators of spatial association (LISA) are important measures for spatial autocorrelation analysis. However, there is an inadvertent fault in the mathematical processes of deriving LISA in literature so that the local Moran and Geary indicators do not satisfy the second basic requirement for LISA: the sum of the local indicators is proportional to a global indicator. This paper aims at reconstructing the calculation formulae of the local Moran indexes and Geary coefficients through mathematical derivation and empirical evidence. Two sets of LISAs were clarified by new mathematical reasoning. One set of LISAs is based on non-normalized weights and non-centralized variable (MI1 and GC1), and the other set is based on row normalized weights and standardized variable (MI2 and GC2). The results show that the first set of LISAs satisfy the above-mentioned second requirement, but the second the set cannot. Then, the third set of LISA was proposed and can be treated as canonical forms (MI3 and GC3). This set of LISAs satisfies the second requirement. The observational data of city population and traffic mileage in Beijing-Tianjin-Hebei region of China were employed to verify the theoretical results. This study helps to clarify the misunderstandings about LISAs in the field of geospatial analysis. [ABSTRACT FROM AUTHOR]

Revealing spatio-temporal evolution regularity in the spatial diffusion of epidemics is helpful for preventing and controlling the spread of epidemics. Based on the real-time COVID-19 datasets by prefecture-level cities, this paper is devoted to exploring the multifractal scaling in spatial diffusion pattern of COVID-19 pandemic and its evolution characteristics in Chinese mainland. The ArcGIS technology and box-counting method are employed to extract spatial data and the least square regression based on rescaling probability (μ-weight method) is used to calculate fractal parameters. The results show multifractal distribution of COVID-19 pandemic in China. The generalized correlation dimension spectrums are inverse S-shaped curves, but the fractal dimension values significantly exceed the Euclidean dimension of embedding space when moment order q«0. The local singularity spectrums are asymmetric unimodal curves, which slant to right. The fractal dimension growth curves are shown as quasi S-shaped curves. From these spectrums and growth curves, the main conclusions can be drawn as follows: First, self-similar patterns developed in the process of COVID-19 pandemic, which seems to be dominated by multifractal scaling law. Second, the spatial pattern of COVID-19 across China can be characterized by global clustering with local disordered diffusion. Third, the spatial diffusion process of COVID-19 in China experienced four stages, i.e., initial stage, the rapid diffusion stage, the hierarchical diffusion stage, and finally the contraction stage. This study suggests that multifractal theory can be utilized to characterize spatio-temporal diffusion of COVID-19 pandemic, and the case analyses may be instructive for further exploring natural laws of spatial diffusion. [ABSTRACT FROM AUTHOR]

Moran's index is an important spatial statistical measure used to determine the presence or absence of spatial autocorrelation, thereby determining the selection orientation of spatial statistical methods. However, Moran's index is chiefly a statistical measurement rather than a mathematical model. This paper is devoted to establishing spatial autocorrelation models by means of linear regression analysis. Using standardized vector as independent variable, and spatial weighted vector as dependent variable, we can obtain a set of normalized linear autocorrelation equations based on quadratic form and vector inner product. The inherent structure of the models' parameters are revealed by mathematical derivation. The slope of the equation gives Moran's index, while the intercept indicates the average value of standardized spatial weight variable. The square of the intercept is negatively correlated with the square of Moran's index, but omitting the intercept does not affect the estimation of the slope value. The datasets of a real urban system are taken as an example to verify the reasoning results. A conclusion can be reached that the inner product equation of spatial autocorrelation based on Moran's index is effective. The models extend the function of spatial analysis, and help to understand the boundary values of Moran's index. [ABSTRACT FROM AUTHOR]

Revealing spatio-temporal evolution regularity in the spatial diffusion of epidemics is helpful for preventing and controlling the spread of epidemics. Based on the real-time COVID-19 datasets by prefecture-level cities, this paper is devoted to exploring the multifractal scaling in spatial diffusion pattern of COVID-19 pandemic and its evolution characteristics in Chinese mainland. The ArcGIS technology and box-counting method are employed to extract spatial data and the least square regression based on rescaling probability (μ-weight method) is used to calculate fractal parameters. The results show multifractal distribution of COVID-19 pandemic in China. The generalized correlation dimension spectrums are inverse S-shaped curves, but the fractal dimension values significantly exceed the Euclidean dimension of embedding space when moment order q«0. The local singularity spectrums are asymmetric unimodal curves, which slant to right. The fractal dimension growth curves are shown as quasi S-shaped curves. From these spectrums and growth curves, the main conclusions can be drawn as follows: First, self-similar patterns developed in the process of COVID-19 pandemic, which seems to be dominated by multifractal scaling law. Second, the spatial pattern of COVID-19 across China can be characterized by global clustering with local disordered diffusion. Third, the spatial diffusion process of COVID-19 in China experienced four stages, i.e., initial stage, the rapid diffusion stage, the hierarchical diffusion stage, and finally the contraction stage. This study suggests that multifractal theory can be utilized to characterize spatio-temporal diffusion of COVID-19 pandemic, and the case analyses may be instructive for further exploring natural laws of spatial diffusion. [ABSTRACT FROM AUTHOR]

Urban morphology exhibits fractal characteristics, which can be described by multifractal scaling. Multifractal parameters under positive moment orders primarily capture information about central areas characterized by relatively stable growth, while those under negative moment orders mainly reflect information about marginal areas that experience more active growth. However, effectively utilizing multifractal spectra to uncover the spatio-temporal variations of urban growth remains a challenge. To addresses this issue, this paper proposes a multifractal measurement by combining theoretical principles and empirical analysis. To capture the difference between growth stability in central areas and growth activity in marginal areas, an index based on generalized correlation dimension Dq is defined. This index takes the growth rate of Dq at extreme negative moment order as the numerator and that at extreme positive moment order as the denominator. During the stable stage of urban growth, the index demonstrates a consistent pattern over time, while during the active stage, the index may exhibit abnormal fluctuations or even jumps. This indicates that the index can reveal spatio-temporal information about urban evolution that cannot be directly observed through multifractal spectra alone. By integrating this index with multifractal spectra, we can more comprehensively characterize the evolutionary characteristics of urban spatial structure. [ABSTRACT FROM AUTHOR]

The phenomenon of Iks was first found by anthropologists and biologists, but it is actually a problem of human geography. However, it has not yet drawn extensive attention of geographers. Based on the relationship between urbanization and ikization, this paper is devoted to constructing a model to explain ikization. The research methods include literature-based analogy, mathematical modeling, empirical analysis, and numerical experiments. The main findings are as follows. First, the generalized production function can be used to model the behavior of ikization resulting from dramatic changes in the geographical environment and sudden cultural rupture. Second, nonlinear replacement dynamic models can be used to explain the possibility of rapid urbanization leading to ikization. Observational data is utilized to verify the fast urbanization mode, and numerical experimentation is employed to reveal the possible key factor causing ikization. The principal conclusions can be reached that social transition should adopt a relatively mild approach to changing, and protecting the geographical environment and reviving traditional culture contribute to national sustainable development. [ABSTRACT FROM AUTHOR]

To deeply understand the role of P in hydrodeoxygenation (HDO), SiO2-supported Ni and Ni–P catalysts with different P/Ni ratios (x) were prepared. The as-prepared samples were characterized by various characterization methods. The HDO activity and product distribution over the Ni/SiO2 and N–P/SiO2-x were compared and the effects of x on the structure, acidity, formation mechanism of active phases and HDO performance were studied taking m-cresol HDO as a model reaction. The results showed that the introduction of P promotes the formation of smaller active sites and contributes to the creation of weak and medium strength acid sites through the formation of P–OH groups and Niδ+ in Ni2P. HDO over the Ni/SiO2 catalyst occurs mainly via the hydrogenation (HYD) route with 3-methyl-cyclohexanol (3-MCHnol) as the main product. However, for Ni–P/SiO2-x catalysts, methyl-cyclohexane (MCH) selectivity increases first and then decreases with the increase of x, reaching a maximum of 95% at x = 1. The acidity generated by the introduction of P contributes to increased MCH selectivity, while the dehydration of 3-MCHnol to MCH occurs mainly on acid sites. However, the excessively high P content (x ≥ 2.0) leads to a significant increase of MB (toluene) selectivity, which is associated with the increase in Ni(I) sites. About 100% m-cresol conversion was achieved with Ni–P/SiO2-1.0 when the m-cresol (g)/catalyst (g) ratio was 3, with MCH (99.4%) as the major product, showing great promise for deep HDO catalysis. [ABSTRACT FROM AUTHOR]

Geographical gravity models can be employed to quantitatively describe and predict spatial flows, including migration flows, passenger flows, daily commuting flows, etc. However, how to model spatial flows and reveal the structure of urban traffic networks in the case of missing partial data is still a problem to be solved. This paper is devoted to characterizing the interurban passenger flows in the Beijing–Tianjin–Hebei region of China using dual gravity models and Tencent location big data. The method of parameter estimation is the least squares regression. The main results are as follows. First, both the railway and highway passenger flows can be effectively described by dual gravity models. A small part of missing spatial data can be compensated for by predicted values. Second, the fractal properties of traffic flows can be revealed. The railway passenger flows follow the gravity scaling law better than the highway passenger flows. Third, the prediction residuals indicate the changing trend of interurban connections in the study area in recent years. The center of gravity of the spatial dynamics has shifted from the Beijing–Tianjin–Tangshan triangle to the Beijing–Baoding–Shijiazhuang axis. A conclusion can be reached that the dual gravity model is an effective tool for analyzing spatial structures and dynamics of traffic networks and flows. Moreover, the model provides a new approach to estimating the fractal dimensions of traffic networks and spatial flow patterns. [ABSTRACT FROM AUTHOR]

The spatial diffusion of epidemic disease follows distance decay law in geography and social physics, but the mathematical models of distance decay depend on concrete spatio-temporal conditions. This paper is devoted to modeling spatial diffusion patterns of COVID-19 stemming from Wuhan city to Hubei province, China. The modeling approach is to integrate analytical method and experimental method. The local gravity model is derived from allometric scaling and global gravity model, and then the parameters of the local gravity model are estimated by observational data and least squares calculation. The main results are as below. The local gravity model based on power law decay can effectively describe the diffusion patterns and process of COVID-19 in Hubei Province, and the goodness of fit of the gravity model based on negative exponential decay to the observational data is not satisfactory. Further, the goodness of fit of the model to data entirely became better and better over time, the size elasticity coefficient increases first and then decreases, and the distance attenuation exponent decreases first and then increases. Moreover, the significance of spatial autoregressive coefficient in the model is low, and the confidence level is less than 80%. The conclusions can be reached as follows. (1) The spatial diffusion of COVID-19 of Hubei bears long range effect, and the size of a city and the distance of the city to Wuhan affect the total number of confirmed cases. (2) Wuhan direct transmission is the main process in the spatial diffusion of COVID-19 in Hubei at the early stage, and the horizontal transmission between regions is not significant. (3) The effect of spatial lockdown and isolation measures taken by Chinese government against the transmission of COVID-19 is obvious. This study suggests that the role of urban gravity (size and distance) should be taken into account to prevent and control epidemic disease. [ABSTRACT FROM AUTHOR]

A series of bimetallic NixCu(10-x)/SiO2 (where x is the mass fraction of Ni and the total metal loading was fixed at 10 wt%.) catalysts with different Ni/Cu mass ratio are prepared and characterized by X-Ray diffraction (XRD), N2 adsorption-desorption, inductively coupled plasma mass spectrometry (ICP-MS), H2 temperature-programmed reduction (H2-TPR) and transmission electron microscope (TEM). The benzofuran (BF) hydrodeoxygenation (HDO) performance of as-prepared catalysts are evaluated in a fixed flow reactor. The results showed that the incorporation of Cu to Ni/SiO2 catalyst can increase surface area of catalyst and improve the reducibility of nickel oxide species, which contributed to higher catalytic activity and total deoxygenated compounds yield. Moreover, the strong synergistic effect between Ni and Cu led to the formation of NiCu alloy at the Ni mass fraction of 5 wt% and thus induced smaller crystallite size and exposure of more active particles, which inevitably contributed to the improved HDO performance for Ni5Cu5/SiO2 catalyst. At 300 °C, 3.0 MPa, MHSV=3.0 h−1 and H2/oil = 500(v/v), the total yield of deoxygenated products over Ni5Cu5/SiO2 catalyst reached 86.0%, which is increased by 10.8% and 77.4% as compared to those of monometallic Ni/SiO2 (75.2%) and Cu/SiO2 catalysts (8.8%), respectively. Finally, a possible reaction network for HDO of BF on Ni5Cu5/SiO2 catalyst was proposed. [ABSTRACT FROM AUTHOR]

A number of spatial statistic measurements such as Moran's I and Geary's C can be used for spatial autocorrelation analysis. Spatial autocorrelation modeling proceeded from the 1-dimension autocorrelation of time series analysis, with time lag replaced by spatial weights so that the autocorrelation functions degenerated to autocorrelation coefficients. This paper develops 2-dimensional spatial autocorrelation functions based on the Moran index using the relative staircase function as a weight function to yield a spatial weight matrix with a displacement parameter. The displacement bears analogy with the time lag in time series analysis. Based on the spatial displacement parameter, two types of spatial autocorrelation functions are constructed for 2-dimensional spatial analysis. Then the partial spatial autocorrelation functions are derived by using the Yule-Walker recursive equation. The spatial autocorrelation functions are generalized to the autocorrelation functions based on Geary's coefficient and Getis' index. As an example, the new analytical framework was applied to the spatial autocorrelation modeling of Chinese cities. A conclusion can be reached that it is an effective method to build an autocorrelation function based on the relative step function. The spatial autocorrelation functions can be employed to reveal deep geographical information and perform spatial dynamic analysis, and lay the foundation for the scaling analysis of spatial correlation. [ABSTRACT FROM AUTHOR]

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Traffic networks have been proved to be fractal systems. However, previous studies mainly focused on monofractal networks, while complex systems are of multifractal structure. This paper is devoted to exploring the general regularities of multifractal scaling processes in the street network of 12 Chinese cities. The city clustering algorithm is employed to identify urban boundaries for defining comparable study areas; box-counting method and the direct determination method are utilized to extract spatial data; the least squares calculation is employed to estimate the global and local multifractal parameters. The results showed multifractal structure of urban street networks. The global multifractal dimension spectrums are inverse S-shaped curves, while the local singularity spectrums are asymmetric unimodal curves. If the moment order q approaches negative infinity, the generalized correlation dimension will seriously exceed the embedding space dimension 2, and the local fractal dimension curve displays an abnormal decrease for most cities. The scaling relation of local fractal dimension gradually breaks if the q value is too high, but the different levels of the network always keep the scaling reflecting singularity exponent. The main conclusions are as follows. First, urban street networks follow multifractal scaling law, and scaling precedes local fractal structure. Second, the patterns of traffic networks take on characteristics of spatial concentration, but they also show the implied trend of spatial deconcentration. Third, the development space of central area and network intensive areas is limited, while the fringe zone and network sparse areas show the phenomenon of disordered evolution. This work may be revealing for understanding and further research on complex spatial networks by using multifractal theory. [ABSTRACT FROM AUTHOR]

A number of mathematical methods have been developed to make temporal signal analyses based on time series. However, no effective method for spatial signal analysis, which are as important as temporal signal analyses for geographical systems, has been devised. Nonstationary spatial and temporal processes are associated with nonlinearity, and cannot be effectively analyzed by conventional analytical approaches. Fractal theory provides a powerful tool for exploring spatial complexity and is helpful for spatio-temporal signal analysis. This paper is devoted to developing an approach for analyzing spatial signals of geographical systems by means of wave-spectrum scaling. The traffic networks of 10 Chinese cities are taken as cases for positive studies. Fast Fourier transform (FFT) and ordinary least squares (OLS) regression methods are employed to calculate spectral exponents. The results show that the wave-spectrum density distribution of all these urban traffic networks follows scaling law, and that the spectral scaling exponents can be converted into fractal dimension values. Using the fractal parameters, we can make spatial analyses for the geographical signals. The wave-spectrum scaling methods can be applied to both self-similar fractal signals and self-affine fractal signals in the geographical world. This study has implications for the further development of fractal-based spatiotemporal signal analysis in the future. [ABSTRACT FROM AUTHOR]

Entropy is one of the physical bases for the fractal dimension definition, and the generalized fractal dimension was defined by Renyi entropy. Using the fractal dimension, we can describe urban growth and form and characterize spatial complexity. A number of fractal models and measurements have been proposed for urban studies. However, the precondition for fractal dimension application is to find scaling relations in cities. In the absence of the scaling property, we can make use of the entropy function and measurements. This paper is devoted to researching how to describe urban growth by using spatial entropy. By analogy with fractal dimension growth models of cities, a pair of entropy increase models can be derived, and a set of entropy-based measurements can be constructed to describe urban growing process and patterns. First, logistic function and Boltzmann equation are utilized to model the entropy increase curves of urban growth. Second, a series of indexes based on spatial entropy are used to characterize urban form. Furthermore, multifractal dimension spectra are generalized to spatial entropy spectra. Conclusions are drawn as follows. Entropy and fractal dimension have both intersection and different spheres of application to urban research. Thus, for a given spatial measurement scale, fractal dimension can often be replaced by spatial entropy for simplicity. The models and measurements presented in this work are significant for integrating entropy and fractal dimension into the same framework of urban spatial analysis and understanding spatial complexity of cities. [ABSTRACT FROM AUTHOR]

Spatial autocorrelation and spatial interaction are two important analytical processes for geographical analyses. However, the internal relations between the two types of models have not been brought to light. This paper is devoted to integrating spatial autocorrelation analysis and spatial interaction analysis into a logic framework by means of Getis-Ord's indexes. Based on mathematical derivation and transform, the spatial autocorrelation measurements of Getis-Ord's indexes are reconstructed in a new and simple form. A finding is that the local Getis-Ord's indexes of spatial autocorrelation are equivalent to the rescaled potential energy indexes of spatial interaction theory based on power-law distance decay. The normalized scatterplot is introduced into the spatial analysis based on Getis-Ord's indexes, and the potential energy indexes are proposed as a complementary measurement. The global Getis-Ord's index proved to be the weighted sum of the potential energy indexes and the direct sum of total potential energy. The empirical analysis of the system of Chinese cities are taken as an example to illustrate the effect of the improved methods and measurements. The mathematical framework newly derived from Getis-Ord's work is helpful for further developing the methodology of geographical spatial modeling and quantitative analysis. [ABSTRACT FROM AUTHOR]

Irregular boundary lines can be characterized by fractal dimension, which provides important information for spatial analysis of complex geographical phenomena such as cities. However, it is difficult to calculate fractal dimension of boundaries systematically when image data are limited. An approximation estimation formula of boundary dimension based on square is widely applied in urban and ecological studies. But the boundary dimension is sometimes overestimated. This paper is devoted to developing a series of practicable formulae for boundary dimension estimation using ideas from fractals. A number of regular figures are employed as reference shapes, from which the corresponding geometric measure relations are constructed; from these measure relations, two sets of fractal dimension estimation formulae are derived for describing fractal-like boundaries. Correspondingly, a group of shape indexes can be defined. A finding is that different formulae have different merits and spheres of application, and the second set of boundary dimensions is a function of the shape indexes. Under condition of data shortage, these formulae can be utilized to estimate boundary dimension values rapidly. Moreover, the relationships between boundary dimension and shape indexes are instructive to understand the association and differences between characteristic scales and scaling. The formulae may be useful for the prefractal studies in geography, geomorphology, ecology, landscape science, and especially, urban science. [ABSTRACT FROM AUTHOR]

A series of APTMS ((3-aminopropyl)trimethoxysilane)-modified silicate MCM-41 adsorbents (x -APTMS/MCM-41, x is the volume of APTMS per 1 g of silicate MCM-41) with different APTMS contents was prepared, and the effects of APTMS content on the desulfurization performance of the APTMS/MCM-41 adsorbents were studied in a fixed adsorption bed using H2S and N2 mixture as a model gas. The as-prepared adsorbents were characterized by X-ray diffraction analysis, N2 adsorption–desorption, Fourier transform infrared spectroscopy, transmission electron microscopy, scanning electron microscopy, and energy-dispersive spectroscopy. The results showed that all the APTMS-modified x -APTMS/MCM-41 adsorbents retained the mesoporous silica structure of MCM-41. The Brunauer–Emmett–Teller-specific surface area of x -APTMS/MCM-41 increased slightly with increasing x at first and then decreased with further increasing APTMS content. The H2S removal performances of x -APTMS/MCM-41 adsorbents decreased in the order 0.6-APTMS/MCM-41 > 0.7-APTMS/MCM-41 > 0.5-APTMS/MCM-41 > 0.4-APTMS/MCM-41 > 0.8-APTMS/MCM-41. At x = 0.6, the maximum H2S removal rate of 54.2% and H2S saturated capacity of 134.4 mg g−1 were observed. The regeneration experiment of 0.6-APTMS/MCM-41 adsorbent after three times regeneration at 423 K for 3 h in nitrogen confirmed that it possessed a good regenerability. [ABSTRACT FROM AUTHOR]

Here, a novel approach has been proposed to synthesize NaP zeolite adsorbents doped with transition metals (M‐NaP) using the Na2SiO3 and NaAlO2 compounds extracted from fly ash via activation and stage treatment. The preparation process of M‐NaP employed the in‐situ synthesis in combination with organic complexation method. The effects of the addition amounts and valence state of transition metals on the zeolite products were investigated. The crystalline phase, morphology, and particle size of M‐NaP were characterized using X‐ray diffractometry (XRD), Scanning electron microscopy (SEM), and Laser particle size analyzer (PSD). The doping process was investigated using X‐ray photoelectron spectroscopy (XPS) and Materials Studio. The adsorption performance of M‐NaP was tested by the adsorption of Zn2+. The optimal molar ratio of n(Al2O3)/n(M) was identified as 8:1 for Co–NaP, Ni–NaP, and Fe–NaP, compared with 6:1 for Ti–NaP. The influence of transition metals on adsorption was: Co–NaP > Ni–NaP > Ti–NaP > Fe‐NaP. Due to largest surface area of Co–NaP (162.5 m2/g, five times than that of NaP‐RAW), the maximum removal rate of Zn2+ was above 99.50% at 25°C. The existence state of transition metals in M‐NaP primarily included: isomorphous substitution and balance of the skeletal charge, with the latter in majority. The simulation of Materials Studio indicates that Si at T4 was first substituted and then, Si at T3 opposite T4 was replaced when the replacement of Si in different sites occurred. [ABSTRACT FROM AUTHOR]

A novel method for preparing Ni2P/C-x (x = preparation temperature, °C) catalysts in a flowing N2 atmosphere by decomposition of hypophosphites was proposed, and the effect of preparation temperature on the hydrodeoxygenation performance of the catalysts was further investigated. X-ray diffraction (XRD), N2-adsorption specific surface area measurements, CO uptake, and X-ray photoelectron spectroscopy (XPS) were applied. The performances of the Ni2P/C-x catalysts prepared at different preparation temperatures were tested in the benzofuran hydrodeoxygenation (BF HDO) reaction. The diffraction peaks related to Ni2P can be seen when x≧ 400 °C. With increasing x, the Ni2P crystallite size and CO uptake amount of the Ni2P/C-x catalysts increased, and the amount of phosphorous decreased. The BF conversion and yield of total O-free products over the Ni2P/C-x catalysts increased with increasing preparation temperature. The Ni2P/C-550 catalyst showed a BF HDO conversion of 91.6% and a yield of total O-free products of 70.2% under the reaction conditions of 300 °C, 3.0 MPa, a H2/oil ratio of 500 (V/V), and a weight hourly space velocity (WHSV) of 4.0 h−1. [ABSTRACT FROM AUTHOR]

The law of allometric scaling based on Zipf distributions can be employed to research hierarchies of cities in a geographical region. However, the allometric patterns are easily influenced by random disturbance from the noises in observational data. In theory, both the allometric growth law and Zipf’s law are related to the hierarchical scaling laws associated with fractal structure. In this paper, the scaling laws of hierarchies with cascade structure are used to study Chinese cities, and the method of R/S analysis is applied to analyzing the change trend of the allometric scaling exponents. The results show that the hierarchical scaling relations of Chinese cities became clearer and clearer from 1991 to 2014 year; the global allometric scaling exponent values fluctuated around 0.85, and the local scaling exponent approached 0.85. The Hurst exponent of the allometric parameter change is greater than 0.5, indicating persistence and a long-term memory of urban evolution. The main conclusions can be reached as follows: the allometric scaling law of cities represents an evolutionary order rather than an invariable rule, which emerges from self-organized process of urbanization, and the ideas from allometry and fractals can be combined to optimize spatial and hierarchical structure of urban systems in future city planning. [ABSTRACT FROM AUTHOR]

BACKGROUND Coal fly ash ( CFA) is a solid waste generated during combustion and transformation of coal that causes serious environmental pollution because of the huge amount of emissions and subsequent accumulation. In this work, coal fly ash was selected as a source of silicon and aluminum components to synthesize zeolites Na-P and Na-X. RESULTS High purity zeolites Na-P and Na-X were synthesized under hydrothermal conditions. The influences of an organic steric agent and different sodium salts on the preparation were investigated and the process parameters of the hydrothermal system optimized. The synthesized product was further characterized by XRD, SEM, ICP, FTIR, and BET surface area measurements. Adsorption tests of Na-P and Na-X zeolite for Ni2+ were performed and flame atomic absorption spectrometry ( FAAS) was used for the detailed analysis. CONCLUSION Pretreatment and purification of CFA favors the preparation of pure Na-P and Na-X zeolite. The organic steric agent and different sodium salts were used to decrease the grain size of the product and control the purity and yield, respectively. Zeolite Na-P synthesized with the addition of TEA (triethanolamine) had the best Ni2+ adsorption performance and a hypothesis for Ni2+ adsorption is proposed. Preliminary analysis proved that Van der Waals absorption is the main type of adsorption for the porous zeolite but ion exchange could also occur with the effect of metal ion exchange contributing a maximum of 13.56% to the total adsorption capacity. © 2015 Society of Chemical Industry [ABSTRACT FROM AUTHOR]

The spatial pattern of the urban-rural regional system is associated with the dynamic process of urbanization. How to characterize the urban-rural terrain using quantitative measurement is a difficult problem remaining to be solved. This paper is devoted to defining urban and rural regions using ideas from fractals. A basic postulate is that human geographical systems are of self-similar patterns correlated with recursive processes. Then multifractal geometry can be employed to describe or define the urban and rural terrain with the level of urbanization. A space-filling index of urban-rural region based on a generalized correlation dimension is presented to reflect the degree of geo-spatial utilization in terms of urbanism. The census data of America and China are used to show how to make empirical analyses of urban-rural multifractals. This work is a normative study rather than a positive study, and it proposes a new way of investigating urban and rural regional systems using fractal theory. [ABSTRACT FROM AUTHOR]

The area-perimeter allometric scaling is an important approach for researching fractal cities, and the basic ideas and models have been researched for a long time. However, the fractal parameters based on this scaling relation have not been efficiently utilized in urban studies. This paper is devoted to developing a description method of urban evolution using the fractal parameter sets based on the area-perimeter measure relation. The novelty of this methodology is as follows: first, the form dimension and boundary dimension are integrated to characterize the urban structure and texture; second, the global and local parameters are combined to characterize an urban system and individual cities; third, an entire analytical process based on the area-perimeter scaling is illustrated. Two discoveries are made in this work: first, a dynamic proportionality factor can be employed to estimate the local boundary dimension; second, the average values of the local fractal parameters are approximately equal to the corresponding global fractal parameters of cities. By illustrating how to carry out the area-perimeter scaling analysis of Chinese cities in Yangtze River Delta in the case of remote sensing images with low resolution, we propose a possible new approach to exploring fractal systems of cities. [ABSTRACT FROM AUTHOR]

In geo-statistics, the Durbin-Watson test is frequently employed to detect the presence of residual serial correlation from least squares regression analyses. However, the Durbin-Watson statistic is only suitable for ordered time or spatial series. If the variables comprise cross-sectional data coming from spatial random sampling, the test will be ineffectual because the value of Durbin-Watson’s statistic depends on the sequence of data points. This paper develops two new statistics for testing serial correlation of residuals from least squares regression based on spatial samples. By analogy with the new form of Moran’s index, an autocorrelation coefficient is defined with a standardized residual vector and a normalized spatial weight matrix. Then by analogy with the Durbin-Watson statistic, two types of new serial correlation indices are constructed. As a case study, the two newly presented statistics are applied to a spatial sample of 29 China’s regions. These results show that the new spatial autocorrelation models can be used to test the serial correlation of residuals from regression analysis. In practice, the new statistics can make up for the deficiencies of the Durbin-Watson test. [ABSTRACT FROM AUTHOR]

The difference between the inverse power function and the negative exponential function is significant. The former suggests a complex distribution, while the latter indicates a simple distribution. However, the association of the power-law distribution with the exponential distribution has been seldom researched. This paper is devoted to exploring the relationships between exponential laws and power laws from the angle of view of urban geography. Using mathematical derivation and numerical experiments, I reveal that a power-law distribution can be created through a semi-moving average process of an exponential distribution. For the distributions defined in a one-dimension space (e.g. Zipf's law), the power exponent is 1; while for those defined in a two-dimension space (e.g. Clark's law), the power exponent is 2. The findings of this study are as follows. First, the exponential distributions suggest a hidden scaling, but the scaling exponents suggest a Euclidean dimension. Second, special power-law distributions can be derived from exponential distributions, but they differ from the typical power-law distributions. Third, it is the real power-law distributions that can be related with fractal dimension. This study discloses an inherent link between simplicity and complexity. In practice, maybe the result presented in this paper can be employed to distinguish the real power laws from spurious power laws (e.g. the fake Zipf distribution). [ABSTRACT FROM AUTHOR]

Spatial correlation modeling comprises both spatial autocorrelation and spatial cross-correlation processes. The spatial autocorrelation theory has been well-developed. It is necessary to advance the method of spatial cross-correlation analysis to supplement the autocorrelation analysis. This paper presents a set of models and analytical procedures for spatial cross-correlation analysis. By analogy with Moran’s index newly expressed in a spatial quadratic form, a theoretical framework is derived for geographical cross-correlation modeling. First, two sets of spatial cross-correlation coefficients are defined, including a global spatial cross-correlation coefficient and local spatial cross-correlation coefficients. Second, a pair of scatterplots of spatial cross-correlation is proposed, and the plots can be used to visually reveal the causality behind spatial systems. Based on the global cross-correlation coefficient, Pearson’s correlation coefficient can be decomposed into two parts: direct correlation (partial correlation) and indirect correlation (spatial cross-correlation). As an example, the methodology is applied to the relationships between China’s urbanization and economic development to illustrate how to model spatial cross-correlation phenomena. This study is an introduction to developing the theory of spatial cross-correlation, and future geographical spatial analysis might benefit from these models and indexes. [ABSTRACT FROM AUTHOR]

Efficient and environmentally friendly conversion of methane into syngas is a topic of practical relevance for the production of hydrogen, chemicals, and synthetic fuels. At present, methane-derived syngas is produced primarily through the steam methane reforming processes. The efficiencies of such processes are limited owing to the endothermic steam methane reforming reaction and the high steam to methane ratio required by the reforming catalysts. Chemical looping reforming represents an alternative approach for methane conversion. In the chemical looping reforming scheme, a solid oxygen carrier or 'redox catalyst' is used to partially oxidize methane to syngas. The reduced redox catalyst is then regenerated with air. The cyclic redox operation reduces the steam usage while simplifying the heat integration scheme. Herein, a new Fe2O3@La xSr1− xFeO3 (LSF) core-shell redox catalyst is synthesized and investigated. Compared with several other commonly investigated iron-based redox catalysts, the newly developed core-shell redox catalyst is significantly more active and selective for syngas production from methane. It is also more resistant toward carbon formation and maintains high activity over cyclic redox operations. [ABSTRACT FROM AUTHOR]

Spatial autocorrelation plays an important role in geographical analysis; however, there is still room for improvement of this method. The formula for Moran’s index is complicated, and several basic problems remain to be solved. Therefore, I will reconstruct its mathematical framework using mathematical derivation based on linear algebra and present four simple approaches to calculating Moran’s index. Moran’s scatterplot will be ameliorated, and new test methods will be proposed. The relationship between the global Moran’s index and Geary’s coefficient will be discussed from two different vantage points: spatial population and spatial sample. The sphere of applications for both Moran’s index and Geary’s coefficient will be clarified and defined. One of theoretical findings is that Moran’s index is a characteristic parameter of spatial weight matrices, so the selection of weight functions is very significant for autocorrelation analysis of geographical systems. A case study of 29 Chinese cities in 2000 will be employed to validate the innovatory models and methods. This work is a methodological study, which will simplify the process of autocorrelation analysis. The results of this study will lay the foundation for the scaling analysis of spatial autocorrelation. [ABSTRACT FROM AUTHOR]

The studies of spatial complexity have resulted in new understanding of the distance-decay functions of geography. The weight functions of spatial autocorrelation should be consistent with the functions of spatial distribution and interaction. This paper is on 'spatial autocorrelation analysis' of spatial autocorrelation. The 1-dimension spatial autocorrelation function (ACF) and partial autocorrelation function (PACF) of space series are employed to analyze four kinds of weight function in common use for the 2-dimensional spatial autocorrelation model. The aim of this study is at how to select a proper weight function to construct a spatial contiguity matrix for spatial analysis. The scopes of application of different weight functions are defined in terms of the characters of their ACFs and PACFs. [ABSTRACT FROM AUTHOR]

A city with fractal structure used to be thought of as a kind of spatial chaotic attractor. Several chaotic attractors indeed can be found by simulating urbanization dynamics through numerical iterations. However, the results lend little support to the suggestion that real cities are chaotic systems. The rural-urban population interaction model does not display chaotic behavior in normal state, but chaos will happen only if the parameter values of the model deviate from the reality. Accordingly, whether or not complex urban systems are chaotic is posed as a pending question. Varied simulation experiments based on the urbanization dynamics imply that the complex patterns of cities occur on the edge of chaos rather than in chaotic state. This result presents an angle of view for us to understand Holland’s question, i.e., why the interactions that form a city are typically stable in the real world. [ABSTRACT FROM AUTHOR]

Fractal structure of a system suggests the optimal way in which parts are arranged or put together to form a whole. The ideas from fractals have a potential application to the researches on urban sustainable development. To characterise fractal cities, we need the measure of fractional dimension. However, if the fractal organisation is concealed in the complex spatial distributions of geographical phenomena, the common methods of evaluating fractal parameter will be disabled. In this article, a new model is proposed to describe urban density and estimate fractal dimension of urban form. If urban density takes on quasi-fractal pattern or the self-similar pattern is hidden in the negative exponential distribution, the generalised gamma function may be used to model the urban landscape and estimate its latent fractal dimension. As a case study, the method is applied to the city of Hangzhou, China. The results show that urban form evolves from simple to complex structure with time. [ABSTRACT FROM AUTHOR]

A nonlinear analysis of urban evolution is made by using of spatial autocorrelation theory. A first-order nonlinear autoregression model based on Clark’s negative exponential model is proposed to show urban population density. The new method and model are applied to Hangzhou City, China, as an example. The average distance of population activities, the auto-correlation coefficient of urban population density, and the auto-regressive function values all show trends of gradual increase from 1964 to 2000, but there always is a sharp first-order cutoff in the partial autocorrelations. These results indicate that urban development is a process of localization. The discovery of urban locality is significant to improve the cellular-automata-based urban simulation of modeling spatial complexity. [ABSTRACT FROM AUTHOR]

The evolution of city size distribution in China has gained a great deal of scholarly attention. However, little is known about the effect of economic transition on the reorganization of city size distribution in China. Using an urban hierarchy with cascade structure model, we decompose Zipf's law into two exponential functions that provide a new way of examining the dynamic processes of urban system evolution. This study aims to investigate the dominating latent forces that affect China's city size distribution through mathematical modeling of the hierarchical scaling laws based on census data of 1982, 1990, 2000, and 2010. A number of features of China's city size distribution are found. First, the size distribution of Chinese cities displayed a clear trend of evolving toward the Zipf distribution, which is the result of economic transition from planned to market. Second, the rank-size pattern still deviates slightly from the standard Zipf distribution, as indicated by the narrow scaling range and departure of the scaling exponent from the theoretically expected value. We argue that the top-down state regulation is a critical cause of deviation of China's city size distribution from Zipf's law. [ABSTRACT FROM AUTHOR]

Radio-frequency (RF) surface acoustic wave (SAW) resonators used as filters and duplexers are mass-produced and widely used in current mobile phones. With the numerous emergences of the diverse device structure, a universal method used for the accurate and fast simulation of the SAW resonator calls for urgent demand. However, there are too many instances where the behavior of the entire acoustic resonator cannot be characterized rapidly and efficiently due to limitations in the current computer memory and speed. This is especially true for SAW resonators configured with long arrays of inter-digital transducers (IDTs), and we have to resort to a periodic analysis. In this paper, the previously reported generalized partial differential equations (PDE) based on the two-dimensional finite element method (2D-FEM) model is extended to analysis for the periodic structure of the SAW resonator. We present model order reduction (MOR) techniques based on FEM and periodic boundary conditions to achieve a dimensionally reduced PDE model without decreasing the accuracy of computations. Examples of different SAW devices, including the regular SAW, IHP-SAW and TC-SAW resonators, are provided which shows the results of the periodic analysis compared with the experimental results of the actual resonators. The investigation results demonstrate the properties of the proposed methodology and prove its effectiveness and accuracy. [ABSTRACT FROM AUTHOR]

Urban population density provides a good perspective for understanding urban growth and socio-spatial dynamics. Based on sub-district data of the five national censuses in 1964, 1982, 1990, 2000, and 2010, this paper is devoted to analyzing of urban growth and the spatial restructuring of the population in the city of Hangzhou, China. Research methods are based on mathematical modeling and field investigation. The modeling result shows that the negative exponential function and the power-exponential function can be well fitted to Hangzhou's observational data of urban density. The negative exponential model reflects the expected state, while the power-exponential model reflects the real state of urban density distribution. The parameters of these models are linearly correlated to the spatial information entropy of population distribution. The fact that the density gradient in the negative exponential function flattened in the 1990s and 2000s is closely related to the development of suburbanization. In terms of investigation materials and the changing trend of model parameters, we can reveal the spatio-temporal features of Hangzhou's urban growth. The main conclusions can be reached as follows. The policy of reformation and opening-up and the establishment of a market economy improved the development mode of Hangzhou. As long as a city has a good social and economic environment, it will automatically tend to the optimal state through self-organization. [ABSTRACT FROM AUTHOR]

Fractal dimension curves of urban growth can be modeled with sigmoid functions, including logistic function and quadratic logistic function. Different types of logistic functions indicate different spatial dynamics. The fractal dimension curves of urban growth in Western countries follow the common logistic function, while the fractal dimension growth curves of cities in northern China follow the quadratic logistic function. Now, we want to investigate whether other Chinese cities, especially cities in South China, follow the same rules of urban evolution and attempt to analyze the reasons. This paper is devoted to exploring the fractals and fractal dimension properties of the city of Shenzhen in southern China. The urban region is divided into four subareas using ArcGIS technology, the box-counting method is adopted to extract spatial datasets, and the least squares regression method is employed to estimate fractal parameters. The results show that (1) the urban form of Shenzhen city has a clear fractal structure, but fractal dimension values of different subareas are different; (2) the fractal dimension growth curves of all the four study areas can only be modeled by the common logistic function, and the goodness of fit increases over time; (3) the peak of urban growth in Shenzhen had passed before 1986 and the fractal dimension growth is approaching its maximum capacity. It can be concluded that the urban form of Shenzhen bears characteristics of multifractals and the fractal structure has been becoming better, gradually, through self-organization, but its land resources are reaching the limits of growth. The fractal dimension curves of Shenzhen's urban growth are similar to those of European and American cities but differ from those of cities in northern China. This suggests that there are subtle different dynamic mechanisms of city development between northern and southern China. [ABSTRACT FROM AUTHOR]

The conventional mathematical methods are based on characteristic length, while urban form has no characteristic length in many aspects. Urban area is a scale-dependence measure, which indicates the scale-free distribution of urban patterns. Thus, the urban description based on characteristic lengths should be replaced by urban characterization based on scaling. Fractal geometry is one powerful tool for the scaling analysis of cities. Fractal parameters can be defined by entropy and correlation functions. However, the question of how to understand city fractals is still pending. By means of logic deduction and ideas from fractal theory, this paper is devoted to discussing fractals and fractal dimensions of urban landscape. The main points of this work are as follows. Firstly, urban form can be treated as pre-fractals rather than real fractals, and fractal properties of cities are only valid within certain scaling ranges. Secondly, the topological dimension of city fractals based on the urban area is 0; thus, the minimum fractal dimension value of fractal cities is equal to or greater than 0. Thirdly, the fractal dimension of urban form is used to substitute the urban area, and it is better to define city fractals in a two-dimensional embedding space; thus, the maximum fractal dimension value of urban form is 2. A conclusion can be reached that urban form can be explored as fractals within certain ranges of scales and fractal geometry can be applied to the spatial analysis of the scale-free aspects of urban morphology. [ABSTRACT FROM AUTHOR]

A magnetic heterogeneous α‐Fe2O3/CdS‐RGO (RGO: reduced graphene oxide) composite photocatalyst was synthesized using the one‐step hydrothermal method. The α‐Fe2O3 and CdS nanoparticles with a diameter range of 20~60 nm were synchronously loaded/distributed on the surface of RGO. The as‐synthesized α‐Fe2O3/CdS‐RGO nanocomposites were analyzed using X‐ray diffraction, Fourier transform‐infrared spectra, BET surface area, scanning electron microscopy, transmission electron microscopy, UV–Vis diffusive reflectance spectra and Raman spectroscopy. Compared with the pure CdS, α‐Fe2O3 and α‐Fe2O3/CdS nanoparticles, the α‐Fe2O3/CdS‐RGO nanocomposites expanded the adsorption range of visible‐light, and showed significant photocatalytic performance and cyclic stability for degradation of methylene blue in visible light. Also, the remarkable catalytic performances mainly depend on its special structure of the α‐Fe2O3/CdS‐RGO, which enabled the effective separation of the electron–hole pairs. These attractive features make the α‐Fe2O3/CdS‐RGO nanocomposite to be a photocatalyst with great application potential in water pollutants treatment. [ABSTRACT FROM AUTHOR]

Bimetallic NixCu(10−x)/γ-Al2O3 catalysts (where x is the mass fraction of Ni) with different Ni/Cu mass ratios were prepared. The catalysts were characterized by X-ray diffractometry, N2 adsorption–desorption, inductively coupled plasma mass spectrometry, X-ray photoelectron spectroscopy, H2-temperature programmed reduction, and transmission electron microscopy. The effect of Ni/Cu mass ratio on benzofuran hydrodeoxygenation was investigated in a fixed-flow reactor. Cu addition improved the NiO reducibility. The strong interaction of Ni and Cu led to the formation of smaller and highly dispersed CuO and NiO species over γ-Al2O3, which favors an improvement in catalytic activity. Among the as-prepared catalysts, the Ni5Cu5/γ-Al2O3 showed the highest deoxygenated product yield (79.9%) with an acceptable benzofuran conversion of 95.2%, which increased by 18.3% and 16.9% compared with that of the monometallic Ni/γ-Al2O3 catalyst. A possible reaction network was proposed, which would provide insight into benzofuran hydrodeoxygenation over the Ni5Cu5/γ-Al2O3 catalyst. [ABSTRACT FROM AUTHOR]

Fractal geometry provides a powerful tool for scale-free spatial analysis of cities, but the fractal dimension calculation results always depend on methods and scopes of the study area. This phenomenon has been puzzling many researchers. This paper is devoted to discussing the problem of uncertainty of fractal dimension estimation and the potential solutions to it. Using regular fractals as archetypes, we can reveal the causes and effects of the diversity of fractal dimension estimation results by analogy. The main factors influencing fractal dimension values of cities include prefractal structure, multi-scaling fractal patterns, and self-affine fractal growth. The solution to the problem is to substitute the real fractal dimension values with comparable fractal dimensions. The main measures are as follows. First, select a proper method for a special fractal study. Second, define a proper study area for a city according to a study aim, or define comparable study areas for different cities. These suggestions may be helpful for the students who take interest in or have already participated in the studies of fractal cities. [ABSTRACT FROM AUTHOR]

Fracturing wastewater is often highly emulsified, viscous, and has a high chemical oxygen demand (COD), which makes it difficult to treat and recycle. Ferrate(VI) is a green oxidant that has a high redox potential and has been adopted for the efficient oxidation of fracturing wastewater to achieve triple effects: demulsification, visbreaking, and COD removal. Firstly, optimal conditions were identified to build a model for fast and efficient treatment. Secondly, wastewater treatment using ferrate oxidation was investigated via demulsification, visbreaking, and COD removal. Finally, a mechanism for ferrate oxidation was proposed for the three effects using Fourier-transform infrared (FT-IR) spectroscopy and scanning electron microscopy (SEM). The theoretical and experimental data demonstrated that the ferrate oxidation achieved the three desired effects. When ferrate was added, the demulsification efficiency increased from 56.2% to 91.8%, the total viscosity dropped from 1.45 cp to 1.10 cp, and the total removal rate of COD significantly increased to 74.2%. A mechanistic analysis showed that the strongly-oxidizing ferrate easily and efficiently oxidized the O/W interfacial film materials, viscous polymers, and compounds responsible for the COD, which was a promising result for the triple effects. [ABSTRACT FROM AUTHOR]

One type of fractal dimension definition is based on the generalized entropy function. Both entropy and fractal dimensions can be employed to characterize complex spatial systems such as cities and regions. Despite the inherent connection between entropy and fractal dimensions, they have different application scopes and directions in urban studies. This paper focuses on exploring how to convert entropy measurements into fractal dimensions for the spatial analysis of scale-free urban phenomena using the ideas from scaling. Urban systems proved to be random prefractal and multifractal systems. The spatial entropy of fractal cities bears two properties. One is the scale dependence: the entropy values of urban systems always depend on the linear scales of spatial measurement. The other is entropy conservation: different fractal parts bear the same entropy value. Thus, entropy cannot reflect the simple rules of urban processes and the spatial heterogeneity of urban patterns. If we convert the generalized entropies into multifractal spectrums, the problems of scale dependence and entropy homogeneity can be solved to a degree for urban spatial analysis. Especially, the geographical analyses of urban evolution can be simplified. This study may be helpful for students in describing and explaining the spatial complexity of urban evolution. [ABSTRACT FROM AUTHOR]

Hierarchies can be modeled by a set of exponential functions, from which we can derive a set of power laws indicative of scaling. The solution to a scaling relation equation is always a power law. The scaling laws are followed by many natural and social phenomena such as cities, earthquakes, and rivers. This paper reveals the power law behaviors in systems of natural cities by reconstructing the urban hierarchy with cascade structure. Cities of the U.S.A., Britain, France, and Germany are taken as examples to perform empirical analyses. The hierarchical scaling relations can be well fitted to the data points within the scaling ranges of the number, size and area of the natural cities. The size-number and area-number scaling exponents are close to 1, and the size-area allometric scaling exponent is slightly less than 1. The results show that natural cities follow hierarchical scaling laws very well. The principle of entropy maximization of urban evolution is then employed to explain the hierarchical scaling laws, and differences entropy maximizing processes are used to interpret the scaling exponents. This study is helpful for scientists to understand the power law behavior in the development of cities and systems of cities. [ABSTRACT FROM AUTHOR]