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Countability of Infinite Paths in the Infinity Tree: Proof of the Continuum Hypothesis in a Non-Cantorian Infinity Theory
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作者 Philip C. Jackson 《Advances in Pure Mathematics》 2025年第1期73-90,共18页
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
关键词 INFINITY Countable UNCOUNTABLE Diagonalization Real Numbers Infinity Tree Continuum hypothesis Turing Machine Infinite Time Turing Machine Non-Cantorian
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Review and Evaluation on the Sociocultural Theory and Bottleneck Hypothesis 被引量:1
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作者 Fan Xu 《Review of Educational Theory》 2020年第4期58-63,共6页
Over the past three decades,a growing number of different theories in second language acquisition field have come out in an effort to provide explanations as to how language learning takes place,to figure out what var... Over the past three decades,a growing number of different theories in second language acquisition field have come out in an effort to provide explanations as to how language learning takes place,to figure out what variables are effective for second language acquisition as well as to offer guidance to mass second language learners and language teachers.Because behind every teaching approach exists certain kind of theory of language acquisition and good theory in turn can help students master language skills in an effective and efficient way.Each theory is considered to have contributed to the field by highlighting a specific aspect of the language acquisition process.Second language acquisition theories are intrinsically related with various disciplines such as applied linguistics,psychology,education,sociolinguistics,neurology,etc.Considering the impossibility to elaborate all second language theories,I will focus on sociocultural theory and bottleneck hypothesis in second language acquisition.There is an overview which follows the introduction to the Sociocultural Theory and Bottleneck Hypothesis and its contribution to second language acquisition respectively,and then I will evaluate them to see their contributions to the SLA disciplinary development. 展开更多
关键词 Sociocultural theory Bottleneck hypothesis theory evaluation
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Classical Quantum Field Theory Based on the Hypothesis of the Absolute Reference System 被引量:1
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作者 Konstantinos Patrinos 《Journal of Applied Mathematics and Physics》 2019年第4期747-780,共34页
The quantum field theory based on the hypothesis of the absolute reference system is a classical non-relativistic theory, which is compatible with current quantum theory. This conclusion arises when one compares the t... The quantum field theory based on the hypothesis of the absolute reference system is a classical non-relativistic theory, which is compatible with current quantum theory. This conclusion arises when one compares the theoretical results of quantum electrodynamics using the basic principles of this hypothesis. Wave equation, which replaces this of Schrodinger, is the classical wave equation of a peculiar electromagnetic wave, derived from the study of particle structure. 展开更多
关键词 PARTICLE MECHANICS Field theory QUANTUM ELECTRODYNAMICS QUANTUM MECHANICS Experimental CONFIRMATION of PARTICLE Dynamics
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Baidu News and the return volatility of Chinese commodity futures:evidence for the sequential information arrival hypothesis
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作者 Ruwei Zhao Xiong Xiong +2 位作者 Junjun Ma Yuzhao Zhang Yongjie Zhang 《Financial Innovation》 2025年第1期2279-2302,共24页
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
关键词 Baidu News Chinese commodity futures Return volatility Sequential information arrival hypothesis Mixture of distribution hypothesis
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Riemann Hypothesis and Value Distribution Theory
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作者 Jinhua Fei 《Journal of Applied Mathematics and Physics》 2017年第3期734-740,共7页
Riemann Hypothesis was posed by Riemann in early 50’s of the 19th century in his thesis titled “The Number of Primes less than a Given Number”. It is one of the unsolved “Supper” problems of mathematics. The Riem... Riemann Hypothesis was posed by Riemann in early 50’s of the 19th century in his thesis titled “The Number of Primes less than a Given Number”. It is one of the unsolved “Supper” problems of mathematics. The Riemann Hypothesis is closely related to the well-known Prime Number Theorem. The Riemann Hypothesis states that all the nontrivial zeros of the zeta-function lie on the “critical line” . In this paper, we use Nevanlinna’s Second Main Theorem in the value distribution theory, refute the Riemann Hypothesis. In reference [7], we have already given a proof of refute the Riemann Hypothesis. In this paper, we gave out the second proof, please read the reference. 展开更多
关键词 VALUE Distribution theory Nevanlinna’s SECOND MAIN THEOREMS RIEMANN hypothesis
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Consequences of Invariant Functions for the Riemann Hypothesis
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作者 Michael Mark Anthony 《Advances in Pure Mathematics》 2025年第1期36-72,共37页
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
关键词 LambertW Function Principal Branch Riemann hypothesis ITERATIONS Robin Inequality Robin Integers INVARIANCE Gauss Gamma Function Li-Function Prime Counting Function Sums of Divisors INVARIANCE PRIMES Twin Primes
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The dilatancy-diffusion hypothesis,earthquake prediction,and operational earthquake forecasting:In memory of Professor Amos Nur on the 50th Anniversary of the 1975 Haicheng Earthquake
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作者 Lanbo Liu 《Earthquake Science》 2025年第5期465-484,共20页
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
关键词 dilatancy-diffusion hypothesis Amos Nur Haicheng Earthquake earthquake prediction operational earthquake forecasting(OEF) physically-informed neural networks(PINNs)
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A Theory of Evolving Natural Constants Based on the Unification of General Theory of Relativity and Dirac’s Large Number Hypothesis
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作者 PENGHuan-Wu 《Communications in Theoretical Physics》 SCIE CAS CSCD 2005年第1期81-88,共8页
Talcing Dirac's large number hypothesis as true, we have shown [Commun.Theor. Phys. (Beijing, China) 42 (2004) 703] the inconsistency of applying Einstein's theory ofgeneral relativity with fixed gravitation c... Talcing Dirac's large number hypothesis as true, we have shown [Commun.Theor. Phys. (Beijing, China) 42 (2004) 703] the inconsistency of applying Einstein's theory ofgeneral relativity with fixed gravitation constant G to cosmology, and a modified theory for varyingG is found, which reduces to Einstein's theory outside the gravitating body for phenomena of shortduration in small distances, thereby agrees with all the crucial tests formerly supportingEinstein's theory. The modified theory, when applied to the usual homogeneous cosmological model,gives rise to a variable cosmological tensor term determined by the derivatives of G, in place ofthe cosmological constant term usually introduced ad hoc. Without any free parameter thetheoretical Hubble's relation obtained from the modified theory seems not in contradiction toobservations, as Dr. Wang's preliminary analysis of the recent data indicates [Commun. Theor. Phys.(Beijing, China) 42 (2004) 703]. As a complement to Commun. Theor. Phys. (Beijing, China) 42 (2004)703 we shall study in this paper the modification of electromagnetism due to Dirac's large numberhypothesis in more detail to show that the approximation of geometric optics still leads to nullgeodesies for the path of light, and that the general relation between the luminosity distance andthe proper geometric distance is still valid in our theory as in Einstein's theory, and give theequations for homogeneous cosmological model involving matter plus electromagnetic radiation.Finally we consider the impact of the modification to quantum mechanics and statistical mechanics,and arrive at a systematic theory of evolving natural constants including Planck's h as well asBoltzmann's k_B by finding out their cosmologically combined counterparts with factors ofappropriate powers of G that may remain truly constant to cosmologically long time. 展开更多
关键词 general theory of relativity natural constants dirac's large numberhypothesis
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The Application of Affective Filter Hypothesis Theory in English Grammar Teaching
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作者 Cuicui Chen 《Journal of Contemporary Educational Research》 2020年第6期71-74,共4页
Krashen’s theories of second language acquisition play a vital role in English teaching,in which“affective filter hypothesis”analyzes the influence of various affective factors on English learning.This paper focuse... Krashen’s theories of second language acquisition play a vital role in English teaching,in which“affective filter hypothesis”analyzes the influence of various affective factors on English learning.This paper focuses on Klashen’s“affective filter hypothesis”,analyzes the application of affective factors in the teaching practice of English grammar,and puts forward some teaching suggestions.The purpose of the study is to reduce the anxiety of the students in the second language grammar learning class,and then to find the most conducive state of English grammar learning,and to achieve the goal of English grammar teaching. 展开更多
关键词 Affective filter hypothesis English teaching Grammar teaching
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Integration of Ideological and Political Education into the Probability Theory and Mathematical Statistics Course:A Teaching Design Based on Estimation and Hypothesis Testing
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作者 Guangyu Li 《Journal of Contemporary Educational Research》 2024年第9期248-254,共7页
With the rapid development of higher education in China,colleges and universities are facing new challenges and impacts in talent training.Probability Theory and Mathematical Statistics is one of the important courses... With the rapid development of higher education in China,colleges and universities are facing new challenges and impacts in talent training.Probability Theory and Mathematical Statistics is one of the important courses in higher education for science and engineering majors and economics and management majors.Its critical role in cultivating students’thinking skills and improving their problem-solving skills is self-evident.Course ideological and political education construction is an important link in college talent training work.Combining ideological and political education with course teaching can help students establish correct value concepts and play a certain role in improving their comprehensive ability and quality.At present,the construction of ideological and political education in the Probability Theory and Mathematical Statistics course still faces some problems,mainly manifested in the lack of attention paid by teachers to course ideological and political education,insufficient exploitation of ideological and political elements,and the simplification of ideological and political education implementation methods.In order to comprehensively deepen the construction of course ideological and political education in line with the actual needs of Probability Theory and Mathematical Statistics course teaching,we should strengthen the construction of teacher teams,improve teachers’ability to carry out course ideological and political education,integrate educational resources,develop educational resources for ideological and political education,and innovate teaching methods to improve the overall effect of ideological and political education integration. 展开更多
关键词 Probability theory and Mathematical Statistics Course education Teaching strategy
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科学工作假说(Working Hypothesis)是科学创新的基础 被引量:12
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作者 刘东生 《第四纪研究》 CAS CSCD 北大核心 2006年第5期673-677,共5页
中国第四纪研究委员会成立50年来,第四纪科学已进于一个新的后第四纪研究时代了。显著的特点是研究工作由描述性向理念性,由区域性向全球性,由学科性向系统科学性迈进。在此过程中“科学工作假说”的不断出现,是促进其生长的动力。在195... 中国第四纪研究委员会成立50年来,第四纪科学已进于一个新的后第四纪研究时代了。显著的特点是研究工作由描述性向理念性,由区域性向全球性,由学科性向系统科学性迈进。在此过程中“科学工作假说”的不断出现,是促进其生长的动力。在1950年代对中国黄土成因的许多不同的假说促进了后来中国黄土研究的发展。当前中国第四纪研究的许多关于全球变化问题的科学假说,将开辟一个第四纪研究的新时代。 展开更多
关键词 科学工作假说 科学创新
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The Enlightment on Task-based Teaching Derived from Input Hypothesis 被引量:1
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作者 周春红 《Sino-US English Teaching》 2006年第4期36-38,43,共4页
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
关键词 task-based teaching input hypothesis INPUT OUTPUT ACTIVITIES teacher's role
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Rules Governing Pressure Distribution for a Traveling Charge Under the Condition of Lagrange Hypothesis
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作者 罗运军 谭惠民 陈福泰 《Journal of Beijing Institute of Technology》 EI CAS 1999年第2期43-49,共7页
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
关键词 GUN traveling charge interior ballistics pressure distribution Lagrange hypothesis
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人类“绿色基因”假说(Human"Green-Gene"Hypothesis):核心内容、科学佐证与实践意义 被引量:13
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作者 李树华 康宁 +1 位作者 向鹏天 孟令爽 《中国园林》 CSCD 北大核心 2023年第2期6-12,共7页
首先,对人类“绿色基因”的形成进行探讨,包括人类(动物)与植物共同维持大气中碳氧平衡、人类(动物)与植物互为食物链关系、人体功能中存在植物性功能、绿色是人类眼睛最易看到的颜色、人类血红蛋白的结构相似于叶绿素结构、作为人体呼... 首先,对人类“绿色基因”的形成进行探讨,包括人类(动物)与植物共同维持大气中碳氧平衡、人类(动物)与植物互为食物链关系、人体功能中存在植物性功能、绿色是人类眼睛最易看到的颜色、人类血红蛋白的结构相似于叶绿素结构、作为人体呼吸器官的肺部相似于树木地上部形状(树形)、人类肠道绒毛相似于植物根系毛细根等方面。进而对支持早期人类生活的植物类型与栽培植物诞生进行研究。在此基础上,提出人类“绿色基因”假说及其核心内容,归纳该假说的科学佐证。人类“绿色基因”假说从整体的、发展的思维解释人类与植物关系,奠定了园艺疗法、园林康养、森林康养的坚实基础,并指出接触植物、进行园艺操作与田园劳作是人们实现接地、激发触觉潜在功能的途径。 展开更多
关键词 风景园林 人类与植物关系 人类“绿色基因”假说 绿色脉络 园林康养 园艺疗法
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分析族群冲突问题的新模式——试评Ethnic Conflict:Commerce,Culture,and Contact Hypothesis 被引量:1
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作者 岳小国 《三峡论坛》 2012年第2期144-146,150,共3页
加拿大多伦多大学政治学系福布斯(H.D.Forbes)教授的著作《族群冲突:贸易、文化及接触理论》在分析、借鉴其它社会科学研究成果的基础上,向人们展示了一种理解和诠释族群冲突问题的新视角。该著作通过评析"接触理论"的利弊,... 加拿大多伦多大学政治学系福布斯(H.D.Forbes)教授的著作《族群冲突:贸易、文化及接触理论》在分析、借鉴其它社会科学研究成果的基础上,向人们展示了一种理解和诠释族群冲突问题的新视角。该著作通过评析"接触理论"的利弊,提出了一个替代性的"语言模型"。以"语言模型"为基础的研究表明接触怎样能够同时改善和恶化族群关系:在个人层面上,接触能使族群关系更加和谐;但在群体层面上,接触可能会激发人们保留各自的群体认同,从而避免他们在同化中付出沉重代价。福布斯认为,接触是一个过程,而不是一个结果,它能打破社会分层,减少文化差异,但同化威胁到一个群体的存在,因此增加了彼此间的紧张关系。毋庸置疑,族群间的差异是冲突合理存在且不可避免的重要原因。 展开更多
关键词 《族群冲突:贸易、文化及接触理论》 族群冲突 接触理论 语言模型
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Multi-Angle Exploration on the Inner Relationship among Language,Thought and Culture with “Sapir-Whorf Hypothesis”
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作者 李芳 《海外英语》 2019年第12期85-86,共2页
“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
关键词 Sapir-Whorf hypothesis INNER relationship LANGUAGE THOUGHT CULTURE
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Sapir-Whorf Hypothesis and Translation
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作者 姜海清 《海外英语》 2013年第5X期4-6,共3页
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
关键词 Sapir-Whorf hypothesis IMPLICATION LINGUISTIC tran
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A Critical Review of Critical Period Hypothesis in Second Language Acquisition
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作者 黄一平 《海外英语》 2011年第7X期296-298,310,共4页
The researches on Critical Period Hypothesis(CPH) aims to explain the importance of the age factor in the process of learning a second language.In this essay,a critical review of the theoretical issues and empirical r... The researches on Critical Period Hypothesis(CPH) aims to explain the importance of the age factor in the process of learning a second language.In this essay,a critical review of the theoretical issues and empirical research on the CPH will spread out.Meanwhile,the discussion of implication and limitation of the CPH research will be concerned as well. 展开更多
关键词 CRITICAL PERIOD hypothesis SECOND LANGUAGE ACQUISITION age
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A Brief Analysis of Contrastive Analysis Hypothesis
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作者 佘阿莉 《海外英语》 2017年第24期21-21,共1页
This paper makes a brief analysis on the contrastive analysis hypothesis, and it is hoped to be helpful for the English teachers.
关键词 contrastive analysis hypothesis second language acquisition
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Comparing Three of the Leadership Theories: Leader-Member Exchange Theory,transformational Leadership and Team Leadership
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作者 王子涵 《中国校外教育(上旬)》 2013年第S2期122-124,共3页
Leadership is a complex process.It is one of the most researched areas around the world.It has gained importance in every walk of life from politics to business and from education to social organizations.According to ... Leadership is a complex process.It is one of the most researched areas around the world.It has gained importance in every walk of life from politics to business and from education to social organizations.According to the study of"Leadership in Adult Education Venues",here has a much more clear recognition of leadership:leadership is a process whereby an individual influences a group of individuals to achieve a common goal.There are many approaches of leadership throughout the study of this class,the three theories of leadership I choose to describe in this paper are:Leader-Member Exchange(LMX)Theory,Transformational Leadership,and Team Leadership. 展开更多
关键词 Leader-Member EXCHANGE theory Transformational LEA
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