A previous paper showed that the real numbers between 0 and 1 could be represented by an infinite tree structure, called the ‘infinity tree’, which contains only a countably infinite number of nodes and arcs. This p...A previous paper showed that the real numbers between 0 and 1 could be represented by an infinite tree structure, called the ‘infinity tree’, which contains only a countably infinite number of nodes and arcs. This paper discusses how a finite-state Turing machine could, in a countably infinite number of state transitions, write all the infinite paths in the infinity tree to a countably infinite tape. Hence it is argued that the real numbers in the interval [0, 1] are countably infinite in a non-Cantorian theory of infinity based on Turing machines using countably infinite space and time. In this theory, Cantor’s Continuum Hypothesis can also be proved. And in this theory, it follows that the power set of the natural numbers P(ℕ) is countably infinite, which contradicts the claim of Cantor’s Theorem for the natural numbers. However, this paper does not claim there is an error in Cantor’s arguments that [0, 1] is uncountably infinite. Rather, this paper considers the situation as a paradox, resulting from different choices about how to represent and count the continuum of real numbers.展开更多
This study uses Baidu News data and introduces a novel proxy for the rate of information flow to examine its relationship with return volatility in Chinese commodity futures and to test two competing hypotheses.We exa...This study uses Baidu News data and introduces a novel proxy for the rate of information flow to examine its relationship with return volatility in Chinese commodity futures and to test two competing hypotheses.We examine the contemporaneous relationships using correlation coefficient analysis,and find apparent differences between the information flow-return volatility relationship and the information flowtrading volume relationship.The empirical evidence contradicts the mixture of distribution hypothesis(MDH)and suggests that the rate of information flow distinctly affects trading volume and volatility.We conducted linear and nonlinear Granger causality tests to explore the sequential information arrival hypothesis(SIAH).The empirical results prove that a lead-lag linear and nonlinear causality exists between the information flow and return volatility of commodity futures,which is consistent with SIAH.In other words,a partial equilibrium exists before reaching the ultimate equilibrium when the new information arrives in the market.Finally,these findings are robust to alternative measurement of return volatility and subperiod analysis.Our findings reject the MDH and support the SIAH in the context of Chinese commodity futures.展开更多
This paper attempts to form a bridge between a sum of the divisors function and the gamma function, proposing a novel approach that could have significant implications for classical problems in number theory, specific...This paper attempts to form a bridge between a sum of the divisors function and the gamma function, proposing a novel approach that could have significant implications for classical problems in number theory, specifically the Robin inequality and the Riemann hypothesis. The exploration of using invariant properties of these functions to derive insights into twin primes and sequential primes is a potentially innovative concept that deserves careful consideration by the mathematical community.展开更多
Dilatancy is referred to the phenomenon of volume increase that occurs when a material is deformed.Dilatancy theory originated in geomechanics for the study of the behavior of granular materials.Later it is expanded t...Dilatancy is referred to the phenomenon of volume increase that occurs when a material is deformed.Dilatancy theory originated in geomechanics for the study of the behavior of granular materials.Later it is expanded to the case of more brittle materials like rocks when it is subjected to the load of varying effective stress and starts to crack and deform,then named the dilatancy-diffusion hypothesis.This hypothesis was developed to explain the changes in rock volume and pore pressure that occur prior to and during fault slip,which can influence earthquake dynamics.Dilatancy-fluid diffusion is a significant concept in understanding the seismogenic process and has served as the major theoretical pillar for earthquake prediction by its classic definition.This paper starts with the recount of fundamental laboratory experiments on granular materials and rocks,then conducts review and examination of the history for using the dilatancy-diffusion hypothesis to interpret the‘prediction’of the 1975 Haicheng Earthquake and other events.The Haicheng Earthquake is the first significant event to be interpreted with the dilatancy-diffusion hypothesis in the world.As one pivotal figure in the development of the dilatancy-diffusion hypothesis for earthquake prediction Professor Amos Nur of Stanford University worked tirelessly to attract societal attention to this important scientific and humanistic issue.As a deterministic physical model the dilatancy-diffusion hypothesis intrinsically bears the deficit to interpret the stochastic seismogenic process.With the emergence of deep learning and its successful applications to many science and technology fields,we may see a possibility to overcome the shortcoming of the current state of the theory with the addition of empirical statistics to push the operational earthquake forecasting approach with the addition of the physicallyinformed neural networks which adopt the dilatancy-diffusion hypothesis as one of its embedded physical relations,to uplift the seismic risk reduction to a new level for saving lives and reducing the losses.展开更多
This paper explores the applicability of the generalized wave impedance hypothesis in split Hopkinson pressure bar(SHPB)experiments,particularly under non-ideal conditions.The study investigates the effects of changes...This paper explores the applicability of the generalized wave impedance hypothesis in split Hopkinson pressure bar(SHPB)experiments,particularly under non-ideal conditions.The study investigates the effects of changes in wave impedance ratio and cross-sectional area ratio on the dynamic response of materials at high strain rates.Through theoretical analysis and numerical simulation,the impact of different wave impedance and cross-sectional area ratios on stress wave propagation characteristics is discussed in detail.It is found that when the cross-sections of two bars differ,shear strain occurs at the abrupt cross-section,leading to waveform distortion in the transmitted and reflected waves.The force balance condition does not always align with the momentum conservation theorem,and only when the three waveforms and wavelengths are completely consistent do they align.The research shows that when the wave impedance ratio and cross-sectional area ratio are within a specific range,the generalized wave impedance hypothesis can accurately predict changes in Young’s modulus and density.Additionally,the study extends the exploration to key factors such as wave impedance ratio,wave speed,Young’s modulus,density,and area ratio.展开更多
Aiming at gradually developing and perfecting the task-based teaching method, the essay, with enlightment from the Krashen＇s Input Hypothesis, discusses some issues about input, output, activities and teacher＇s role...Aiming at gradually developing and perfecting the task-based teaching method, the essay, with enlightment from the Krashen＇s Input Hypothesis, discusses some issues about input, output, activities and teacher＇s role in this method.展开更多
Aim To study the rules governing pressure distribution of traveling charge under the condition of Lagrange hypothesis. Methods\ The study is based on the laws of conservation of momentum and energy. Results\ The gas ...Aim To study the rules governing pressure distribution of traveling charge under the condition of Lagrange hypothesis. Methods\ The study is based on the laws of conservation of momentum and energy. Results\ The gas flow velocity distribution formula at the back of a projectile and the momentum equation of a traveling charge are deduced, and rules governing their pressure distribution under the Lagrange hypothesis conditions are established. The pressure distribution of a traveling charge is compared with that of a conventional charge. Conclusion\ The pressure distribution in the bore of a traveling charge can be accurately predicted. A parabolic pressure distribution type is revealed.展开更多
Amyloid-β(Aβ)and tau,the two hallmark proteins associated with Alzheimer’s disease(AD),exhibit distinct toxic effects but also interact synergistically within the disease pathology.The prevailing theory in AD patho...Amyloid-β(Aβ)and tau,the two hallmark proteins associated with Alzheimer’s disease(AD),exhibit distinct toxic effects but also interact synergistically within the disease pathology.The prevailing theory in AD pathology-the amyloid cascade hypothesis-highlights the pivotal role of increased processing of the amyloid precursor protein(APP).Initially cleaved by the majorβ-secretase(β-amyloid cleaving enzyme-1,BACE1)in the brain,then undergoes further cleavage by theγ-secretase complex,resulting in the production of Aβ_(40-42)and a set of intracellular C-terminal peptides known as Aβand APP intracellular domain(β-AICDs)and soluble amyloid precursor proteinβ(sAPPβ)(Orobets and Karamyshev,2023).展开更多
Currently,our understanding of the pathogenesis of major neurodegenerative disorders,such as Alzheimer's,Parkinson's,and Huntington's diseases,is largely shaped by the amyloid cascade hypothesis.Pa rticula...Currently,our understanding of the pathogenesis of major neurodegenerative disorders,such as Alzheimer's,Parkinson's,and Huntington's diseases,is largely shaped by the amyloid cascade hypothesis.Pa rticularly,this hypothesis posits that in Alzheimer's disease,the aggregation of amyloid-beta peptide initiates a series of pathological processes leading to neuronal dysfunction and death(Zhang et al.,2024).展开更多
“Sapir-Whorf hypothesis"holds that human thoughts are shaped by their native languages,and speakers of different languages think differently relevantly.The hypothesis is controversial partly because it seems to ...“Sapir-Whorf hypothesis"holds that human thoughts are shaped by their native languages,and speakers of different languages think differently relevantly.The hypothesis is controversial partly because it seems to deny the possibility of a general principle for human cognition,and partly because some findings taken to support it have not reliably replicated.The author argued that considering this hypothesis through the lens of probabilistic inference has the potential to figure out both issues,at least with respect to certain prominent findings in the two languages—Chinese and English.After exploring on the inner relationship among language,thought and culture with the comparison between English and Chinese based on a series of examples including“numbers,Wuhan dialect and some different understandings of idioms”,the author made an inference that language can somewhat affect human thought under the different culture contexts.Besides,it also provides some reference for educators to take in-depth studies on the relationship among language,thought and culture,which is vitally significant for ESL educators and learners.展开更多
Sapir-Whorf hypothesis has its implication in translation studies. Each language is a peculiar whole. It is a product, even an expression, of the spiritual personality and the cultural particularity. Translation is a ...Sapir-Whorf hypothesis has its implication in translation studies. Each language is a peculiar whole. It is a product, even an expression, of the spiritual personality and the cultural particularity. Translation is a kind of interlingual and intercultural communication. It involves not only the transference from one language into another, but a whole set of extra-linguistic criteria. In translating we are always crossing a greater or lesser barrier or divide.展开更多
文摘A previous paper showed that the real numbers between 0 and 1 could be represented by an infinite tree structure, called the ‘infinity tree’, which contains only a countably infinite number of nodes and arcs. This paper discusses how a finite-state Turing machine could, in a countably infinite number of state transitions, write all the infinite paths in the infinity tree to a countably infinite tape. Hence it is argued that the real numbers in the interval [0, 1] are countably infinite in a non-Cantorian theory of infinity based on Turing machines using countably infinite space and time. In this theory, Cantor’s Continuum Hypothesis can also be proved. And in this theory, it follows that the power set of the natural numbers P(ℕ) is countably infinite, which contradicts the claim of Cantor’s Theorem for the natural numbers. However, this paper does not claim there is an error in Cantor’s arguments that [0, 1] is uncountably infinite. Rather, this paper considers the situation as a paradox, resulting from different choices about how to represent and count the continuum of real numbers.
基金supported by the National Social Science Fund of China(24CGL027)the National Natural Science Foundation of China(72101009,72141304,72201122)National Key Research and Development Program of China(2022YFC3303304).
文摘This study uses Baidu News data and introduces a novel proxy for the rate of information flow to examine its relationship with return volatility in Chinese commodity futures and to test two competing hypotheses.We examine the contemporaneous relationships using correlation coefficient analysis,and find apparent differences between the information flow-return volatility relationship and the information flowtrading volume relationship.The empirical evidence contradicts the mixture of distribution hypothesis(MDH)and suggests that the rate of information flow distinctly affects trading volume and volatility.We conducted linear and nonlinear Granger causality tests to explore the sequential information arrival hypothesis(SIAH).The empirical results prove that a lead-lag linear and nonlinear causality exists between the information flow and return volatility of commodity futures,which is consistent with SIAH.In other words,a partial equilibrium exists before reaching the ultimate equilibrium when the new information arrives in the market.Finally,these findings are robust to alternative measurement of return volatility and subperiod analysis.Our findings reject the MDH and support the SIAH in the context of Chinese commodity futures.
文摘This paper attempts to form a bridge between a sum of the divisors function and the gamma function, proposing a novel approach that could have significant implications for classical problems in number theory, specifically the Robin inequality and the Riemann hypothesis. The exploration of using invariant properties of these functions to derive insights into twin primes and sequential primes is a potentially innovative concept that deserves careful consideration by the mathematical community.
基金sponsored by the National Research Foundation of Korea(RS-2023-00220913).
文摘Dilatancy is referred to the phenomenon of volume increase that occurs when a material is deformed.Dilatancy theory originated in geomechanics for the study of the behavior of granular materials.Later it is expanded to the case of more brittle materials like rocks when it is subjected to the load of varying effective stress and starts to crack and deform,then named the dilatancy-diffusion hypothesis.This hypothesis was developed to explain the changes in rock volume and pore pressure that occur prior to and during fault slip,which can influence earthquake dynamics.Dilatancy-fluid diffusion is a significant concept in understanding the seismogenic process and has served as the major theoretical pillar for earthquake prediction by its classic definition.This paper starts with the recount of fundamental laboratory experiments on granular materials and rocks,then conducts review and examination of the history for using the dilatancy-diffusion hypothesis to interpret the‘prediction’of the 1975 Haicheng Earthquake and other events.The Haicheng Earthquake is the first significant event to be interpreted with the dilatancy-diffusion hypothesis in the world.As one pivotal figure in the development of the dilatancy-diffusion hypothesis for earthquake prediction Professor Amos Nur of Stanford University worked tirelessly to attract societal attention to this important scientific and humanistic issue.As a deterministic physical model the dilatancy-diffusion hypothesis intrinsically bears the deficit to interpret the stochastic seismogenic process.With the emergence of deep learning and its successful applications to many science and technology fields,we may see a possibility to overcome the shortcoming of the current state of the theory with the addition of empirical statistics to push the operational earthquake forecasting approach with the addition of the physicallyinformed neural networks which adopt the dilatancy-diffusion hypothesis as one of its embedded physical relations,to uplift the seismic risk reduction to a new level for saving lives and reducing the losses.
基金supported by the National Natural Science Foundation of China(Grant Nos.U2341244,12172179,11772160,and 12202207)China Postdoctoral Science Foundation(Grant No.2022M711623)+3 种基金the Natural Science Foundation of Jiangsu Province(Grant No.BK20220968)Open Funds for Key Laboratory of Impact and Safety Engineering(Ningbo University)Ministry of Education(Grant No.CJ202201)Open Funds for Shock and Vibration of Engineering Materials and Structures Key Laboratory of Sichuan Province(Grant No.22kfgk03).
文摘This paper explores the applicability of the generalized wave impedance hypothesis in split Hopkinson pressure bar(SHPB)experiments,particularly under non-ideal conditions.The study investigates the effects of changes in wave impedance ratio and cross-sectional area ratio on the dynamic response of materials at high strain rates.Through theoretical analysis and numerical simulation,the impact of different wave impedance and cross-sectional area ratios on stress wave propagation characteristics is discussed in detail.It is found that when the cross-sections of two bars differ,shear strain occurs at the abrupt cross-section,leading to waveform distortion in the transmitted and reflected waves.The force balance condition does not always align with the momentum conservation theorem,and only when the three waveforms and wavelengths are completely consistent do they align.The research shows that when the wave impedance ratio and cross-sectional area ratio are within a specific range,the generalized wave impedance hypothesis can accurately predict changes in Young’s modulus and density.Additionally,the study extends the exploration to key factors such as wave impedance ratio,wave speed,Young’s modulus,density,and area ratio.
文摘Aiming at gradually developing and perfecting the task-based teaching method, the essay, with enlightment from the Krashen＇s Input Hypothesis, discusses some issues about input, output, activities and teacher＇s role in this method.
文摘Aim To study the rules governing pressure distribution of traveling charge under the condition of Lagrange hypothesis. Methods\ The study is based on the laws of conservation of momentum and energy. Results\ The gas flow velocity distribution formula at the back of a projectile and the momentum equation of a traveling charge are deduced, and rules governing their pressure distribution under the Lagrange hypothesis conditions are established. The pressure distribution of a traveling charge is compared with that of a conventional charge. Conclusion\ The pressure distribution in the bore of a traveling charge can be accurately predicted. A parabolic pressure distribution type is revealed.
文摘Amyloid-β(Aβ)and tau,the two hallmark proteins associated with Alzheimer’s disease(AD),exhibit distinct toxic effects but also interact synergistically within the disease pathology.The prevailing theory in AD pathology-the amyloid cascade hypothesis-highlights the pivotal role of increased processing of the amyloid precursor protein(APP).Initially cleaved by the majorβ-secretase(β-amyloid cleaving enzyme-1,BACE1)in the brain,then undergoes further cleavage by theγ-secretase complex,resulting in the production of Aβ_(40-42)and a set of intracellular C-terminal peptides known as Aβand APP intracellular domain(β-AICDs)and soluble amyloid precursor proteinβ(sAPPβ)(Orobets and Karamyshev,2023).
基金funded by the Russian Science Foundation(grant No.23-74-10092)(to AIS)。
文摘Currently,our understanding of the pathogenesis of major neurodegenerative disorders,such as Alzheimer's,Parkinson's,and Huntington's diseases,is largely shaped by the amyloid cascade hypothesis.Pa rticularly,this hypothesis posits that in Alzheimer's disease,the aggregation of amyloid-beta peptide initiates a series of pathological processes leading to neuronal dysfunction and death(Zhang et al.,2024).
基金国家自然科学基金面上项目“基于高压人群身心健康的工作环境绿色空间体系研究”(编号51978364)国家自然科学基金青年科学基金项目“北京地区城市森林疗养空间特征识别及健康效益定量评价”(编号51908310)Tsinghua-Toyota Joint Research Institute Cross discipline Program共同资助。
文摘“Sapir-Whorf hypothesis"holds that human thoughts are shaped by their native languages,and speakers of different languages think differently relevantly.The hypothesis is controversial partly because it seems to deny the possibility of a general principle for human cognition,and partly because some findings taken to support it have not reliably replicated.The author argued that considering this hypothesis through the lens of probabilistic inference has the potential to figure out both issues,at least with respect to certain prominent findings in the two languages—Chinese and English.After exploring on the inner relationship among language,thought and culture with the comparison between English and Chinese based on a series of examples including“numbers,Wuhan dialect and some different understandings of idioms”,the author made an inference that language can somewhat affect human thought under the different culture contexts.Besides,it also provides some reference for educators to take in-depth studies on the relationship among language,thought and culture,which is vitally significant for ESL educators and learners.
文摘Sapir-Whorf hypothesis has its implication in translation studies. Each language is a peculiar whole. It is a product, even an expression, of the spiritual personality and the cultural particularity. Translation is a kind of interlingual and intercultural communication. It involves not only the transference from one language into another, but a whole set of extra-linguistic criteria. In translating we are always crossing a greater or lesser barrier or divide.
