The Black–Scholes equation is one of the most important partial differential equations governing the value of financial derivatives in financial markets.The Black–Scholes model for pricing stock options has been app...The Black–Scholes equation is one of the most important partial differential equations governing the value of financial derivatives in financial markets.The Black–Scholes model for pricing stock options has been applied to various payoff structures,and options trading is based on Black and Scholes’principle of dynamic hedging to estimate and assess option prices over time.However,the Black–Scholes model requires severe constraints,assumptions,and conditions to be applied to real-life financial and economic problems.Several methods and approaches have been developed to approach these conditions,such as fractional Black–Scholes models based on fractional derivatives.These fractional models are expected since the Black–Scholes equation is derived using Ito’s lemma from stochastic calculus,where fractional derivatives play a leading role.Hence,a fractional stochastic model that includes the basic Black–Scholes model as a special case is expected.However,these fractional financial models require computational tools and advanced analytical methods to solve the associated fractional Black–Scholes equations.Nevertheless,it is believed that the fractal nature of economic processes permits to model economical and financial markets problems more accurately compared to the conventional model.The relationship between fractional calculus and fractals is well-known in the literature.This study introduces a generalized Black–Scholes equation in fractal dimensions and discusses its role in financial marketing.In our analysis,we consider power-laws properties for volatility,interest rated,and dividend payout,which emerge in several empirical regularities in quantitative finance and economics.We apply our model to study the problem of pricing barrier option and we estimate the values of fractal dimensions in both time and in space.Our model can be used to obtain the prices of many pay-off models.We observe that fractal dimensions considerably affect the solutions of the Black–Scholes equation and that,for fractal dimensions much smaller than unity,the call option increases significantly.We prove that fractal dimensions are a powerful tool to obtain new results.Further details are analyzed and discussed.展开更多
In this article,we first establish a recollement related to projectively coresolved Gorenstein flat(PGF)complexes.Secondly,we define and study PGF dimension of complexes,we denote it PG F(X)for a complex X.It is shown...In this article,we first establish a recollement related to projectively coresolved Gorenstein flat(PGF)complexes.Secondly,we define and study PGF dimension of complexes,we denote it PG F(X)for a complex X.It is shown that the PGF(X)is equal to the infimum of the set{supA|there exists a diagram of morphisms of complexes A←G→X,such that G→X is a special PGF precover of X and G→A is a PGF almost isomorphism}.展开更多
Different from the previous qualitative analysis of linear systems in time and frequency domains, the method for describing nonlinear systems quantitatively is proposed based on correlated dimensions. Nonlinear dynami...Different from the previous qualitative analysis of linear systems in time and frequency domains, the method for describing nonlinear systems quantitatively is proposed based on correlated dimensions. Nonlinear dynamics theory is used to analyze the pressure data of a contrarotating axial flow fan. The delay time is 18 and the embedded dimension varies from 1 to 25 through phase-space reconstruction. In addition, the correlated dimensions are calculated before and after stalling. The results show that the correlated dimensions drop from 1. 428 before stalling to 1. 198 after stalling, so they are sensitive to the stalling signal of the fan and can be used as a characteristic quantity for the judging of the fan stalling.展开更多
[Objective] The aim was to discuss the spatial pattern changes of land use in Tianjin new coastal area based on fractal dimensions.[Method] By dint of remote and geographic information system technology to obtain the ...[Objective] The aim was to discuss the spatial pattern changes of land use in Tianjin new coastal area based on fractal dimensions.[Method] By dint of remote and geographic information system technology to obtain the data of urban land use in new coastal area from 1993 to 2008,the boundary dimension,radius dimension and information dimension of each land use type were calculated based on fractal dimension.In addition,the revealed land use spatial dimension changes characteristics were analyzed.[Result] The spatial distribution of each land use type in new costal area had distinct fractal characteristics.And,the amount and changes of three types of dimension values effectively revealed the changes of complicatedness,centeredness and evenness of spatial pattern of land use in the study area.The boundary dimension of unused land and salty earth increased incessantly,which suggested its increasing complicatedness.The boundary of the port and wharf and shoal land was getting simpler.The radius dimension of the cultivated land was larger than 2,which suggested that its area spread from center to the surroundings;the one in salty land and waters distributed evenly within different radius space to the center of the city;the one in other land use types reduced gradually from center to the surroundings.The information dimension value in the woodland and orchard land,unused land and shoal land was small,and was in obvious concentrated distribution;the spatial distribution of cultivated and salty land concentrated in the outside area;the construction area in the port and wharf spread gradually on the basis of original state;the spatial distribution of waters and residents and mines were even.[Conclusion] Applying fractal dimensions to the study of spatial pattern changes of urban land use can make up for some disadvantages in classical urban spatial pattern quantitative research,which has favorable practical value.展开更多
The present status of self-elevating drilling units was analysed. Based on statistics of the main dimensions of self-elevating drilling units, a mathematical model was established using stepwise return procedures and ...The present status of self-elevating drilling units was analysed. Based on statistics of the main dimensions of self-elevating drilling units, a mathematical model was established using stepwise return procedures and a back-propagation neural network. mathematical model is applicable and reliable. The of the main dimensions of self-elevating drilling Analysis of examples of calculations showed that the model is useful for mastering the essential variations units and can be used for technical and economic analysis as well as in conceptual designs of drilling units.展开更多
To investigate the pore structure of graphene oxide modified polymer cement mortar(GOPM)under salt-freeze-thaw(SFT)coupling effects and its impact on deterioration,this study modifies polymer cement mortar(EMCM)with g...To investigate the pore structure of graphene oxide modified polymer cement mortar(GOPM)under salt-freeze-thaw(SFT)coupling effects and its impact on deterioration,this study modifies polymer cement mortar(EMCM)with graphene oxide(GO).The micro-pore structure of GOPM is characterized using LF-NMR and SEM.Fractal theory is applied to calculate the fractal dimension of pore volume,and the deterioration patterns are analyzed based on the evolution characteristics of capillary pores.The experimental results indicate that,after 25 salt-freeze-thaw cycles(SFTc),SO2-4 ions penetrate the matrix,generating corrosion products that fill existing pores and enhance the compactness of the specimen.As the number of cycles increases,the ongoing formation and expansion of corrosion products within the matrix,combined with persistent freezing forces,and result in the degradation of the pore structure.Therefore,the mass loss rate(MLR)of the specimens shows a trend of first decreasing and then increasing,while the relative dynamic elastic modulus(RDEM)initially increases and then decreases.Compared to the PC group specimens,the G3PM group specimens show a 28.71% reduction in MLR and a 31.42% increase in RDEM after 150 SFTc.The fractal dimensions of the transition pores,capillary pores,and macropores in the G3PM specimens first increase and then decrease as the number of SFTc increases.Among them,the capillary pores show the highest correlation with MLR and RDEM,with correlation coefficients of 0.97438 and 0.98555,respectively.展开更多
Mine filling materials urgently need to improve mechanical properties and achieve low-carbon transformation.This study explores the mechanism of the synergistic effect of optimizing aggregate fractal grading and intro...Mine filling materials urgently need to improve mechanical properties and achieve low-carbon transformation.This study explores the mechanism of the synergistic effect of optimizing aggregate fractal grading and introducing CO_(2)nanobubble technology to improve the performance of cement-fly ash-based backfill materials(CFB).The properties including fluidity,setting time,uniaxial compressive strength,elastic modulus,porosity,microstructure and CO_(2)storage performance were systematically studied through methods such as fluidity evaluation,time test,uniaxial compression test,mercury intrusion porosimetry(MIP),scanning electron microscopy-energy dispersive spectroscopy analysis(SEM-EDS),and thermogravimetric-differential thermogravimetric analysis(TG-DTG).The experimental results show that the density and strength of the material are significantly improved under the synergistic effect of fractal dimension and CO_(2)nanobubbles.When the fractal dimension reaches 2.65,the mass ratio of coarse and fine aggregates reaches the optimal balance,and the structural density is greatly improved at the same time.At this time,the uniaxial compressive strength and elastic modulus reach their peak values,with increases of up to 13.46%and 27.47%,respectively.CO_(2)nanobubbles enhance the material properties by promoting hydration reaction and carbonization.At the microscopic level,CO_(2)nanobubble water promotes the formation of C-S-H(hydrated calcium silicate),C-A-S-H(hydrated calcium aluminium silicate)gel and CaCO_(3),which is the main way to enhance the performance.Thermogravimetric studies have shown that when the fractal dimension is 2.65,the dehydration of hydration products and the decarbonization process of CaCO_(3)are most obvious,and CO_(2)nanobubble water promotes the carbonization reaction,making it surpass the natural state.The CO_(2)sequestration quality of cement-fly ash-based materials treated with CO_(2)nanobubble water at different fractal dimensions increased by 12.4wt%to 99.8wt%.The results not only provide scientific insights for the design and implementation of low-carbon filling materials,but also provide a solid theoretical basis for strengthening green mining practices and promoting sustainable resource utilization.展开更多
Intercultural communication competence can help us adapt better to the host culture and deal with culture shock successfully. This paper mainly discusses the dimensions of intercultural communication competence.
随着电力系统的发展,现行的IEC标准IEC 60120《Dimensions of ball and socket couplings of string insulator units》(Third edition) 1984版已经无法涵盖和适应新的特高压大吨位绝缘子产品和技术的发展,包括对应于36和40两种新的联...随着电力系统的发展,现行的IEC标准IEC 60120《Dimensions of ball and socket couplings of string insulator units》(Third edition) 1984版已经无法涵盖和适应新的特高压大吨位绝缘子产品和技术的发展,包括对应于36和40两种新的联接标记的更高的强度等级的绝缘子。笔者介绍了IEC TC36/MT21工作组维护IEC 60120标准的主要内容:包括结合国际工程实践经验,将已经被广泛应用的36、40两个联接标记加入到本标准中;对Smin的表征意义进行重新理解和计算,并将其列入资料性附录供参考;解决了28B W型锁紧销是否在本次修订中纳入标准的问题;对socket章节的内容进行重新理解和研究,修正了原有的表述等。展开更多
The waterway in the middle and lower reaches of the Yangtze River has long been known as the Golden Waterway and has served as an important link in the construction of the Yangtze River Economic Belt.Therefore,expandi...The waterway in the middle and lower reaches of the Yangtze River has long been known as the Golden Waterway and has served as an important link in the construction of the Yangtze River Economic Belt.Therefore,expanding its dimensions is a significant goal,particularly given the long-range cumulative erosion occurring downstream of the Three Gorges Dam (TGD),which has been concentrated in the dry river channel.With the regulation of the volume from upstream reservoirs and the TGD,the minimum discharge and water level of the river downstream are increasing,and creating favorable conditions for the increase of the depth of the waterway.The discharge compensation effect during the dry season offsets the decline in the water level of the river channel caused by the down-cutting of part of the riverbed,but the minimum navigable water level of the segment near the dam still shows a declining trend.In recent years,several waterway remediation projects have been implemented in the downstream reaches of the TGD and although the waterway depth and width have been increased,the channel dimensions are still insufficient in the Yichang-Anqing reach (with a total length of 1026 km),as compared to the upstream reservoir area and the deep water channel in the downstream tidal reaches.A comprehensive analysis of the water depth and the number and length of shoals in the waterway indicates that its dimensions can be increased to 4.5 m ×200 m and 6.0 m×200 m in the Yichang-Wuhan and Wuhan-Anqing reaches,respectively.This is also feasible given the remediation technologies currently available,but remediation projects need to be coordinated with those for flood prevention and ecological protection.展开更多
Potassium ion batteries(PIBs)with the prominent advantages of sufficient reserves and economical cost are attractive candidates of new rechargeable batteries for large-grid electrochemical energy storage systems(EESs)...Potassium ion batteries(PIBs)with the prominent advantages of sufficient reserves and economical cost are attractive candidates of new rechargeable batteries for large-grid electrochemical energy storage systems(EESs).However,there are still some obstacles like large size of K+to commercial PIBs applications.Therefore,rational structural design based on appropriate materials is essential to obtain practical PIBs anode with K+accommodated and fast diffused.Nanostructural design has been considered as one of the effective strategies to solve these issues owing to unique physicochemical properties.Accordingly,quite a few recent anode materials with different dimensions in PIBs have been reported,mainly involving in carbon materials,metal-based chalcogenides(MCs),metal-based oxides(MOs),and alloying materials.Among these anodes,nanostructural carbon materials with shorter ionic transfer path are beneficial for decreasing the resistances of transportation.Besides,MCs,MOs,and alloying materials with nanostructures can effectively alleviate their stress changes.Herein,these materials are classified into 0D,1D,2D,and 3D.Particularly,the relationship between different dimensional structures and the corresponding electrochemical performances has been outlined.Meanwhile,some strategies are proposed to deal with the current disadvantages.Hope that the readers are enlightened from this review to carry out further experiments better.展开更多
基金Rami Ahmad El-Nabulsi has received funding from the Czech National Agency of Agricultural 533 Research,project QK22020134“Innovative fisheries management of a large reservoir”.
文摘The Black–Scholes equation is one of the most important partial differential equations governing the value of financial derivatives in financial markets.The Black–Scholes model for pricing stock options has been applied to various payoff structures,and options trading is based on Black and Scholes’principle of dynamic hedging to estimate and assess option prices over time.However,the Black–Scholes model requires severe constraints,assumptions,and conditions to be applied to real-life financial and economic problems.Several methods and approaches have been developed to approach these conditions,such as fractional Black–Scholes models based on fractional derivatives.These fractional models are expected since the Black–Scholes equation is derived using Ito’s lemma from stochastic calculus,where fractional derivatives play a leading role.Hence,a fractional stochastic model that includes the basic Black–Scholes model as a special case is expected.However,these fractional financial models require computational tools and advanced analytical methods to solve the associated fractional Black–Scholes equations.Nevertheless,it is believed that the fractal nature of economic processes permits to model economical and financial markets problems more accurately compared to the conventional model.The relationship between fractional calculus and fractals is well-known in the literature.This study introduces a generalized Black–Scholes equation in fractal dimensions and discusses its role in financial marketing.In our analysis,we consider power-laws properties for volatility,interest rated,and dividend payout,which emerge in several empirical regularities in quantitative finance and economics.We apply our model to study the problem of pricing barrier option and we estimate the values of fractal dimensions in both time and in space.Our model can be used to obtain the prices of many pay-off models.We observe that fractal dimensions considerably affect the solutions of the Black–Scholes equation and that,for fractal dimensions much smaller than unity,the call option increases significantly.We prove that fractal dimensions are a powerful tool to obtain new results.Further details are analyzed and discussed.
基金Supported by the National Natural Science Foundation of China(12061061)Young Talents Team Project of Gansu Province(2025QNTD49)+1 种基金Lanshan Talents Project of Northwest Minzu University(Xbmulsrc202412)Longyuan Young Talents of Gansu Province。
文摘In this article,we first establish a recollement related to projectively coresolved Gorenstein flat(PGF)complexes.Secondly,we define and study PGF dimension of complexes,we denote it PG F(X)for a complex X.It is shown that the PGF(X)is equal to the infimum of the set{supA|there exists a diagram of morphisms of complexes A←G→X,such that G→X is a special PGF precover of X and G→A is a PGF almost isomorphism}.
基金Supported by the Natural Science Foundation of Jiangsu Province(BK2005018)the Graduate Research and Innovation Plan of Jiangsu Province(CX07B-061Z)~~
文摘Different from the previous qualitative analysis of linear systems in time and frequency domains, the method for describing nonlinear systems quantitatively is proposed based on correlated dimensions. Nonlinear dynamics theory is used to analyze the pressure data of a contrarotating axial flow fan. The delay time is 18 and the embedded dimension varies from 1 to 25 through phase-space reconstruction. In addition, the correlated dimensions are calculated before and after stalling. The results show that the correlated dimensions drop from 1. 428 before stalling to 1. 198 after stalling, so they are sensitive to the stalling signal of the fan and can be used as a characteristic quantity for the judging of the fan stalling.
基金Supported by National Natural Science Fund Program(40705038)~~
文摘[Objective] The aim was to discuss the spatial pattern changes of land use in Tianjin new coastal area based on fractal dimensions.[Method] By dint of remote and geographic information system technology to obtain the data of urban land use in new coastal area from 1993 to 2008,the boundary dimension,radius dimension and information dimension of each land use type were calculated based on fractal dimension.In addition,the revealed land use spatial dimension changes characteristics were analyzed.[Result] The spatial distribution of each land use type in new costal area had distinct fractal characteristics.And,the amount and changes of three types of dimension values effectively revealed the changes of complicatedness,centeredness and evenness of spatial pattern of land use in the study area.The boundary dimension of unused land and salty earth increased incessantly,which suggested its increasing complicatedness.The boundary of the port and wharf and shoal land was getting simpler.The radius dimension of the cultivated land was larger than 2,which suggested that its area spread from center to the surroundings;the one in salty land and waters distributed evenly within different radius space to the center of the city;the one in other land use types reduced gradually from center to the surroundings.The information dimension value in the woodland and orchard land,unused land and shoal land was small,and was in obvious concentrated distribution;the spatial distribution of cultivated and salty land concentrated in the outside area;the construction area in the port and wharf spread gradually on the basis of original state;the spatial distribution of waters and residents and mines were even.[Conclusion] Applying fractal dimensions to the study of spatial pattern changes of urban land use can make up for some disadvantages in classical urban spatial pattern quantitative research,which has favorable practical value.
基金Supported by the National 863 Plan Foundation under Grant No.2003AA414060
文摘The present status of self-elevating drilling units was analysed. Based on statistics of the main dimensions of self-elevating drilling units, a mathematical model was established using stepwise return procedures and a back-propagation neural network. mathematical model is applicable and reliable. The of the main dimensions of self-elevating drilling Analysis of examples of calculations showed that the model is useful for mastering the essential variations units and can be used for technical and economic analysis as well as in conceptual designs of drilling units.
基金Funded by the National Natural Science Foundation of China(Nos.5226804252468035)。
文摘To investigate the pore structure of graphene oxide modified polymer cement mortar(GOPM)under salt-freeze-thaw(SFT)coupling effects and its impact on deterioration,this study modifies polymer cement mortar(EMCM)with graphene oxide(GO).The micro-pore structure of GOPM is characterized using LF-NMR and SEM.Fractal theory is applied to calculate the fractal dimension of pore volume,and the deterioration patterns are analyzed based on the evolution characteristics of capillary pores.The experimental results indicate that,after 25 salt-freeze-thaw cycles(SFTc),SO2-4 ions penetrate the matrix,generating corrosion products that fill existing pores and enhance the compactness of the specimen.As the number of cycles increases,the ongoing formation and expansion of corrosion products within the matrix,combined with persistent freezing forces,and result in the degradation of the pore structure.Therefore,the mass loss rate(MLR)of the specimens shows a trend of first decreasing and then increasing,while the relative dynamic elastic modulus(RDEM)initially increases and then decreases.Compared to the PC group specimens,the G3PM group specimens show a 28.71% reduction in MLR and a 31.42% increase in RDEM after 150 SFTc.The fractal dimensions of the transition pores,capillary pores,and macropores in the G3PM specimens first increase and then decrease as the number of SFTc increases.Among them,the capillary pores show the highest correlation with MLR and RDEM,with correlation coefficients of 0.97438 and 0.98555,respectively.
基金financially supported by the China Scholarship Council(CSC)。
文摘Mine filling materials urgently need to improve mechanical properties and achieve low-carbon transformation.This study explores the mechanism of the synergistic effect of optimizing aggregate fractal grading and introducing CO_(2)nanobubble technology to improve the performance of cement-fly ash-based backfill materials(CFB).The properties including fluidity,setting time,uniaxial compressive strength,elastic modulus,porosity,microstructure and CO_(2)storage performance were systematically studied through methods such as fluidity evaluation,time test,uniaxial compression test,mercury intrusion porosimetry(MIP),scanning electron microscopy-energy dispersive spectroscopy analysis(SEM-EDS),and thermogravimetric-differential thermogravimetric analysis(TG-DTG).The experimental results show that the density and strength of the material are significantly improved under the synergistic effect of fractal dimension and CO_(2)nanobubbles.When the fractal dimension reaches 2.65,the mass ratio of coarse and fine aggregates reaches the optimal balance,and the structural density is greatly improved at the same time.At this time,the uniaxial compressive strength and elastic modulus reach their peak values,with increases of up to 13.46%and 27.47%,respectively.CO_(2)nanobubbles enhance the material properties by promoting hydration reaction and carbonization.At the microscopic level,CO_(2)nanobubble water promotes the formation of C-S-H(hydrated calcium silicate),C-A-S-H(hydrated calcium aluminium silicate)gel and CaCO_(3),which is the main way to enhance the performance.Thermogravimetric studies have shown that when the fractal dimension is 2.65,the dehydration of hydration products and the decarbonization process of CaCO_(3)are most obvious,and CO_(2)nanobubble water promotes the carbonization reaction,making it surpass the natural state.The CO_(2)sequestration quality of cement-fly ash-based materials treated with CO_(2)nanobubble water at different fractal dimensions increased by 12.4wt%to 99.8wt%.The results not only provide scientific insights for the design and implementation of low-carbon filling materials,but also provide a solid theoretical basis for strengthening green mining practices and promoting sustainable resource utilization.
文摘Intercultural communication competence can help us adapt better to the host culture and deal with culture shock successfully. This paper mainly discusses the dimensions of intercultural communication competence.
基金supported by the National Key Research and Development Program of China(Grants No.2016YFC0402306 and 2016YFC0402106)the National Natural Science Foundation of China(Grant No.51809131)+1 种基金the Key Laboratory of Yellow River Sediment Research,Ministry of Water Resources of China(Grant No.2016002)the Fundamental Research Funds for Central Public Welfare Research Institutes(Grants No.TKS160103,TKS180201,and TKS180411)
文摘The waterway in the middle and lower reaches of the Yangtze River has long been known as the Golden Waterway and has served as an important link in the construction of the Yangtze River Economic Belt.Therefore,expanding its dimensions is a significant goal,particularly given the long-range cumulative erosion occurring downstream of the Three Gorges Dam (TGD),which has been concentrated in the dry river channel.With the regulation of the volume from upstream reservoirs and the TGD,the minimum discharge and water level of the river downstream are increasing,and creating favorable conditions for the increase of the depth of the waterway.The discharge compensation effect during the dry season offsets the decline in the water level of the river channel caused by the down-cutting of part of the riverbed,but the minimum navigable water level of the segment near the dam still shows a declining trend.In recent years,several waterway remediation projects have been implemented in the downstream reaches of the TGD and although the waterway depth and width have been increased,the channel dimensions are still insufficient in the Yichang-Anqing reach (with a total length of 1026 km),as compared to the upstream reservoir area and the deep water channel in the downstream tidal reaches.A comprehensive analysis of the water depth and the number and length of shoals in the waterway indicates that its dimensions can be increased to 4.5 m ×200 m and 6.0 m×200 m in the Yichang-Wuhan and Wuhan-Anqing reaches,respectively.This is also feasible given the remediation technologies currently available,but remediation projects need to be coordinated with those for flood prevention and ecological protection.
基金the Start-up Funding of Jinan University(Grant No.88016105 and Grant No.55800001)the discipline construction outstanding young backbone project(Grant No.12819023)the Fundamental Research Funds for the Central Universities(Grant No.11620317).
文摘Potassium ion batteries(PIBs)with the prominent advantages of sufficient reserves and economical cost are attractive candidates of new rechargeable batteries for large-grid electrochemical energy storage systems(EESs).However,there are still some obstacles like large size of K+to commercial PIBs applications.Therefore,rational structural design based on appropriate materials is essential to obtain practical PIBs anode with K+accommodated and fast diffused.Nanostructural design has been considered as one of the effective strategies to solve these issues owing to unique physicochemical properties.Accordingly,quite a few recent anode materials with different dimensions in PIBs have been reported,mainly involving in carbon materials,metal-based chalcogenides(MCs),metal-based oxides(MOs),and alloying materials.Among these anodes,nanostructural carbon materials with shorter ionic transfer path are beneficial for decreasing the resistances of transportation.Besides,MCs,MOs,and alloying materials with nanostructures can effectively alleviate their stress changes.Herein,these materials are classified into 0D,1D,2D,and 3D.Particularly,the relationship between different dimensional structures and the corresponding electrochemical performances has been outlined.Meanwhile,some strategies are proposed to deal with the current disadvantages.Hope that the readers are enlightened from this review to carry out further experiments better.
