In this paper,we study two types of the Ding injective dimensions of complexes.First,we provide some equivalent characterizations of the dimension related to the special Ding injec-tive preenvelopes.Furthermore,we con...In this paper,we study two types of the Ding injective dimensions of complexes.First,we provide some equivalent characterizations of the dimension related to the special Ding injec-tive preenvelopes.Furthermore,we consider the relationship between the dimensions Dipd(Y)and Did(Y)of the complex Y,where Dipd(Y)denotes the dimension associated with special Ding injective preenvelopes,and Did(Y)denotes the dimension associated with DG-injective resolutions.It is demonstrated that Dipd(Y)=Did(Y)for any bounded complex Y.展开更多
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
We investigate the application of the on-shell unitarity method to compute the anomalous dimensions of effective field theory operators.We compute one-loop anomalous dimensions for the dimension-7 operator mixing in l...We investigate the application of the on-shell unitarity method to compute the anomalous dimensions of effective field theory operators.We compute one-loop anomalous dimensions for the dimension-7 operator mixing in low-energy effective field theory(LEFT).The on-shell method significantly simplifies the construction of scattering amplitudes.By leveraging the correspondence between the anomalous dimensions of operator form factors and the double-cut phase-space integrals,we bypass the need for direct loop integral calculations.The resulting renormalization group equations derived in this work provide crucial insights into the scale dependence of the LEFT dimension-7 Wilson coefficients,which will aid in precision experimental fitting of these coefficients.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
富碱性水环境将降低围岩承载力,诱发巷道不均匀变形和塌方冒顶,威胁巷道施工安全。以富碱性水环境浸泡砂质泥岩为研究对象,利用单轴压缩试验(uniaxial compression,简称UC)和核磁共振测试技术(nuclear magnetic resonance,简称NMR)研究...富碱性水环境将降低围岩承载力,诱发巷道不均匀变形和塌方冒顶,威胁巷道施工安全。以富碱性水环境浸泡砂质泥岩为研究对象,利用单轴压缩试验(uniaxial compression,简称UC)和核磁共振测试技术(nuclear magnetic resonance,简称NMR)研究了不同pH溶液浸泡后砂质泥岩强度劣化和孔隙结构演化特征,构建了孔隙分形维数D与单轴抗压强度R_(c)之间的关联函数,揭示了碱性水环境下砂质泥岩细观结构演化特性和宏观强度劣化机制。结果表明:(1)随着p H值的增大,砂质泥岩中微孔(孔径r1≤0.01μm)和中孔(孔径0.01μm<r2≤1.00μm)不断扩展且逐渐发育为大孔(孔径r3>1.00μm),导致砂质泥岩单轴抗压强度的降低;(2)富碱性水环境下砂质泥岩孔隙结构呈多重分形结构,砂质泥岩的力学强度与其内部孔隙结构与分布形态密切相关。(3)随着pH值的增大,岩样沿轴向的破裂面逐渐增多,主破裂面附近出现了大量的次生裂纹,且有明显的剥落现象;(4)碱性水的溶蚀作用和砂质泥岩吸水膨胀效应是导致砂质泥岩细观孔隙结构演化和宏观强度劣化的根本原因。研究成果有助于提高富碱性水环境下软岩巷道围岩变形控制和工程灾害防治能力。展开更多
基金Supported by the National Natural Science Foundation of China(Grant No.12061061)the Young Talents Team Project of Gansu Province(Grant No.2025QNTD49)+1 种基金Lanshan Talent Project of Northwest Minzu University(Grant No.Xbmulsrc202412)Longyuan Young Talents of Gansu Province.
文摘In this paper,we study two types of the Ding injective dimensions of complexes.First,we provide some equivalent characterizations of the dimension related to the special Ding injec-tive preenvelopes.Furthermore,we consider the relationship between the dimensions Dipd(Y)and Did(Y)of the complex Y,where Dipd(Y)denotes the dimension associated with special Ding injective preenvelopes,and Did(Y)denotes the dimension associated with DG-injective resolutions.It is demonstrated that Dipd(Y)=Did(Y)for any bounded complex Y.
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 Science Foundation of China under Grants Nos.12347145,12347105,12375099,and 12047503the National Key Research and Development Program of China Grant Nos.2020YFC2201501 and 2021YFA0718304。
文摘We investigate the application of the on-shell unitarity method to compute the anomalous dimensions of effective field theory operators.We compute one-loop anomalous dimensions for the dimension-7 operator mixing in low-energy effective field theory(LEFT).The on-shell method significantly simplifies the construction of scattering amplitudes.By leveraging the correspondence between the anomalous dimensions of operator form factors and the double-cut phase-space integrals,we bypass the need for direct loop integral calculations.The resulting renormalization group equations derived in this work provide crucial insights into the scale dependence of the LEFT dimension-7 Wilson coefficients,which will aid in precision experimental fitting of these coefficients.
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}.
文摘富碱性水环境将降低围岩承载力,诱发巷道不均匀变形和塌方冒顶,威胁巷道施工安全。以富碱性水环境浸泡砂质泥岩为研究对象,利用单轴压缩试验(uniaxial compression,简称UC)和核磁共振测试技术(nuclear magnetic resonance,简称NMR)研究了不同pH溶液浸泡后砂质泥岩强度劣化和孔隙结构演化特征,构建了孔隙分形维数D与单轴抗压强度R_(c)之间的关联函数,揭示了碱性水环境下砂质泥岩细观结构演化特性和宏观强度劣化机制。结果表明:(1)随着p H值的增大,砂质泥岩中微孔(孔径r1≤0.01μm)和中孔(孔径0.01μm<r2≤1.00μm)不断扩展且逐渐发育为大孔(孔径r3>1.00μm),导致砂质泥岩单轴抗压强度的降低;(2)富碱性水环境下砂质泥岩孔隙结构呈多重分形结构,砂质泥岩的力学强度与其内部孔隙结构与分布形态密切相关。(3)随着pH值的增大,岩样沿轴向的破裂面逐渐增多,主破裂面附近出现了大量的次生裂纹,且有明显的剥落现象;(4)碱性水的溶蚀作用和砂质泥岩吸水膨胀效应是导致砂质泥岩细观孔隙结构演化和宏观强度劣化的根本原因。研究成果有助于提高富碱性水环境下软岩巷道围岩变形控制和工程灾害防治能力。
