This manuscript provides a comparison of the Hypersphere World-Universe Model (WUM) with the prevailing Big Bang Model (BBM) of the Standard Cosmology. The performed analysis of BBM shows that the Four Pillars of the ...This manuscript provides a comparison of the Hypersphere World-Universe Model (WUM) with the prevailing Big Bang Model (BBM) of the Standard Cosmology. The performed analysis of BBM shows that the Four Pillars of the Standard Cosmology are model-dependent and not strong enough to support the model. The angular momentum problem is one of the most critical problems in BBM. Standard Cosmology cannot explain how Galaxies and Extra Solar systems obtained their substantial orbital and rotational angular momenta, and why the orbital momentum of Jupiter is considerably larger than the rotational momentum of the Sun. WUM is the only cosmological model in existence that is consistent with the Law of Conservation of Angular Momentum. To be consistent with this Fundamental Law, WUM discusses in detail the Beginning of the World. The Model introduces Dark Epoch (spanning from the Beginning of the World for 0.4 billion years) when only Dark Matter Particles (DMPs) existed, and Luminous Epoch (ever since for 13.8 billion years). Big Bang discussed in Standard Cosmology is, in our view, transition from Dark Epoch to Luminous Epoch due to Rotational Fission of Overspinning Dark Matter (DM) Supercluster’s Cores. WUM envisions Matter carried from the Universe into the World from the fourth spatial dimension by DMPs. Ordinary Matter is a byproduct of DM annihilation. WUM solves a number of physical problems in contemporary Cosmology and Astrophysics through DMPs and their interactions: Angular Momentum problem in birth and subsequent evolution of Galaxies and Extrasolar systems—how do they obtain it;Fermi Bubbles—two large structures in gamma-rays and X-rays above and below Galactic center;Diversity of Gravitationally-Rounded Objects in Solar system;some problems in Solar and Geophysics [1]. WUM reveals Inter-Connectivity of Primary Cosmological Parameters and calculates their values, which are in good agreement with the latest results of their measurements.展开更多
Potassium-ion batteries(PIBs)are considered promising alternatives to lithium-ion batteries owing to cost-effective potassium resources and a suitable redox potential of-2.93 V(vs.-3.04 V for Li+/Li).However,the explo...Potassium-ion batteries(PIBs)are considered promising alternatives to lithium-ion batteries owing to cost-effective potassium resources and a suitable redox potential of-2.93 V(vs.-3.04 V for Li+/Li).However,the exploration of appro-priate electrode materials with the correct size for reversibly accommodating large K+ions presents a significant challenge.In addition,the reaction mecha-nisms and origins of enhanced performance remain elusive.Here,tetragonal FeSe nanoflakes of different sizes are designed to serve as an anode for PIBs,and their live and atomic-scale potassiation/depotassiation mechanisms are revealed for the first time through in situ high-resolution transmission electron micros-copy.We found that FeSe undergoes two distinct structural evolutions,sequen-tially characterized by intercalation and conversion reactions,and the initial intercalation behavior is size-dependent.Apparent expansion induced by the intercalation of K+ions is observed in small-sized FeSe nanoflakes,whereas unexpected cracks are formed along the direction of ionic diffusion in large-sized nanoflakes.The significant stress generation and crack extension originating from the combined effect of mechanical and electrochemical interactions are elucidated by geometric phase analysis and finite-element analysis.Despite the different intercalation behaviors,the formed products of Fe and K_(2)Se after full potassiation can be converted back into the original FeSe phase upon depotassiation.In particular,small-sized nanoflakes exhibit better cycling perfor-mance with well-maintained structural integrity.This article presents the first successful demonstration of atomic-scale visualization that can reveal size-dependent potassiation dynamics.Moreover,it provides valuable guidelines for optimizing the dimensions of electrode materials for advanced PIBs.展开更多
Rumors are a type of false information, a consequence of an asymmetrical informational structure. This paper focuses on the social mechanisms of rumor fulfilling. Rumors with important contents related to people’s pe...Rumors are a type of false information, a consequence of an asymmetrical informational structure. This paper focuses on the social mechanisms of rumor fulfilling. Rumors with important contents related to people’s personal interests win acceptance through changing people’s expected payoffs, misleading people to the belief that acceptance of the rumor would beneficially outperform rejection of it. Nevertheless, it is risky to believe rumors; therefore, people make their decision whether to believe a rumor or not by referring to other people’s choices. An analysis was performed first within a game model that incorporated the variables of an individual’s expectancy and other people’s impact to predict whether the individual would accept or reject a rumor. Another analysis followed to further examine the functions of some dynamic mechanisms in rumor fulfilling when group pressure and network effects were introduced. Finally, an exploratory discussion on how to prevent rumors and erase their effects via information management strategies was presented.展开更多
Minimizing disorder and defects is crucial for realizing the full potential of two-dimensional transition metal dichalcogenides(TMDs) materials and improving device performance to desired properties. However, the meth...Minimizing disorder and defects is crucial for realizing the full potential of two-dimensional transition metal dichalcogenides(TMDs) materials and improving device performance to desired properties. However, the methods in defect controlcurrently face challenges with overly large operational areas and a lack of precision in targeting specific defects. Therefore,we propose a new method for the precise and universal defect healing of TMD materials, integrating real-time imaging withscanning transmission electron microscopy (STEM). This method employs electron beam irradiation to stimulate the diffusionmigration of surface-adsorbed adatoms on TMD materials grown by low-temperature molecular beam epitaxy (MBE),and heal defects within the diffusion range. This approach covers defect repairs ranging from zero-dimensional vacancydefects to two-dimensional grain orientation alignment, demonstrating its universality in terms of the types of samples anddefects. These findings offer insights into the use of atomic-level focused electron beams at appropriate voltages in STEMfor defect healing, providing valuable experience for achieving atomic-level precise fabrication of TMD materials.展开更多
The emergence of the middle class was closely related to the appearance of industrial society and its consequential constant changes in the social structure. Karl Marx and other theorists in the same camp were among t...The emergence of the middle class was closely related to the appearance of industrial society and its consequential constant changes in the social structure. Karl Marx and other theorists in the same camp were among the earliest scholars who discussed that topic. For a quite long period of time, the debate was mainly focused on the characteristics of the “new middle class.” The middle class, however, has undergone a categorical transformation from the old to the new middle-class, and furthermore, this transformation itself has signified the transition in social patterns from industrial to post-industrial society as well as economic globalization, both of which have contributed to the growth and global expansion of the middle class, having thus fundamentally renovated the middle class.展开更多
In Advances in Pure Mathematics (www.scirp.org/journal/apm), Vol. 1, No. 4 (July 2011), pp. 136-154, the mathematical structure of the much discussed problem of probability known as the Monty Hall problem was mapped i...In Advances in Pure Mathematics (www.scirp.org/journal/apm), Vol. 1, No. 4 (July 2011), pp. 136-154, the mathematical structure of the much discussed problem of probability known as the Monty Hall problem was mapped in detail. It is styled here as Monty Hall 1.0. The proposed analysis was then generalized to related cases involving any number of doors (d), cars (c), and opened doors (o) (Monty Hall 2.0) and 1 specific case involving more than 1 picked door (p) (Monty Hall 3.0). In cognitive terms, this analysis was interpreted in function of the presumed digital nature of rational thought and language. In the present paper, Monty Hall 1.0 and 2.0 are briefly reviewed (§§2-3). Additional generalizations of the problem are then presented in §§4-7. They concern expansions of the problem to the following items: (1) to any number of picked doors, with p denoting the number of doors initially picked and q the number of doors picked when switching doors after doors have been opened to reveal goats (Monty Hall 3.0;see §4);(3) to the precise conditions under which one’s chances increase or decrease in instances of Monty Hall 3.0 (Monty Hall 3.2;see §6);and (4) to any number of switches of doors (s) (Monty Hall 4.0;see §7). The afore-mentioned article in APM, Vol. 1, No. 4 may serve as a useful introduction to the analysis of the higher variations of the Monty Hall problem offered in the present article. The body of the article is by Leo Depuydt. An appendix by Richard D. Gill (see §8) provides additional context by building a bridge to modern probability theory in its conventional notation and by pointing to the benefits of certain interesting and relevant tools of computation now available on the Internet. The cognitive component of the earlier investigation is extended in §9 by reflections on the foundations of mathematics. It will be proposed, in the footsteps of George Boole, that the phenomenon of mathematics needs to be defined in empirical terms as something that happens to the brain or something that the brain does. It is generally assumed that mathematics is a property of nature or reality or whatever one may call it. There is not the slightest intention in this paper to falsify this assumption because it cannot be falsified, just as it cannot be empirically or positively proven. But there is no way that this assumption can be a factual observation. It can be no more than an altogether reasonable, yet fully secondary, inference derived mainly from the fact that mathematics appears to work, even if some may deem the fact of this match to constitute proof. On the deepest empirical level, mathematics can only be directly observed and therefore directly analyzed as an activity of the brain. The study of mathematics therefore becomes an essential part of the study of cognition and human intelligence. The reflections on mathematics as a phenomenon offered in the present article will serve as a prelude to planned articles on how to redefine the foundations of probability as one type of mathematics in cognitive fashion and on how exactly Boole’s theory of probability subsumes, supersedes, and completes classical probability theory. §§2-7 combined, on the one hand, and §9, on the other hand, are both self-sufficient units and can be read independently from one another. The ultimate design of the larger project of which this paper is part remains the increase of digitalization of the analysis of rational thought and language, that is, of (rational, not emotional) human intelligence. To reach out to other disciplines, an effort is made to describe the mathematics more explicitly than is usual.展开更多
A novel coordination polymer of [Ca(2-OPA)2(H2O)2]n (2-OPA-=2-oxo-1(4H)-pyridineacetate anion) was synthesized and characterized by elemental analysis, IR, TG and single crystal X-ray diffraction. The title complex cr...A novel coordination polymer of [Ca(2-OPA)2(H2O)2]n (2-OPA-=2-oxo-1(4H)-pyridineacetate anion) was synthesized and characterized by elemental analysis, IR, TG and single crystal X-ray diffraction. The title complex crystallizes in orthorhombic with space group Pna21, a=0.799 96(16) nm, b=0.823 77(16) nm, c=2.415 3(5) nm, V=1.591 6(6) nm3, Z=4, R=0.030 3, wR=0.070 0. The Ca atom is eight-coordinated by six O atoms of four 2-OPA- ligands and two water molecules, and displays a dodecahedron coordination geometry. Each 2-OPA- ligand bridges two adjacent Ca atoms, forming a infinite chain along the a direction. The Ca...Ca distance is 0.4102 2(8)nm. A two-dimensional supramolecular framework is further constructed by the hydrogen bonds and the weak π-π interactions. The results of TG analysis show the chain structure of the title complex was stable under 297.5 ℃. CCDC: 251669.展开更多
new coordination polymer {[Zn(CF3COO)2(C5H5ON)]·H2O}n was synthesized based on the reaction of zinc(Ⅱ) trifluoroacetate and 3-hydroxypyridine(C5H5ON) in methanol medium for the first time. The structure of the c...new coordination polymer {[Zn(CF3COO)2(C5H5ON)]·H2O}n was synthesized based on the reaction of zinc(Ⅱ) trifluoroacetate and 3-hydroxypyridine(C5H5ON) in methanol medium for the first time. The structure of the coordination polymer was confirmed by IR, 1H NMR, elemental analysis and thermal analysis. The crystal structure of the coordination polymer was also determined by X-ray single crystal diffraction. The crystal belongs to monoclinic system with space group P21/m, and crystallographic data of the coordination polymer are: a= 0.863 1(4) nm, b=0.717 7(3) nm, c=1.116 4(5) nm, α=γ=90°, β=107.542(6)°, V=0.659 4(5) nm3; Dc=2.037 g·cm-3; Z=2; F(000)=400; μ=1.969 mm-1. Zinc(Ⅱ) atom lies at the center of an octahedron formed by the coordination of zinc atom and six O atoms which come from four different trifluoroacetate ions and two different 3-hydroxypyridine molecules where each trifluoroacetate ion and 3-hydroxypyridine are coordinated to two different zinc ions to form coordination polymer. CCDC: 253909.展开更多
s: Ultrafine A2La2Ti3O10 (A=K, Na) powders with laminar structure were successfully synthesized by citric acid sol-gel method using ANO3(A=K, Na)?La(NO3)3?Ti(OBu)4 and citric acid as starting precursors. The crystalli...s: Ultrafine A2La2Ti3O10 (A=K, Na) powders with laminar structure were successfully synthesized by citric acid sol-gel method using ANO3(A=K, Na)?La(NO3)3?Ti(OBu)4 and citric acid as starting precursors. The crystalline phase of A2La2Ti3O10 can be obtained by thermal decomposition of citrate complex precursors at a relatively low temperature of 800 ℃ (600 ℃ for A=Na), about 300 ℃(500 ℃ for A=Na) lower than that of conventional solid state reaction process. The properties of the citrate precursors and the calcined powders were characterized by Infrared spectroscopy (IR), X-ray diffraction (XRD), transmission electron microscopy (TEM), thermal-gravimetric-differential thermal analysis (TG-DTA), inductively coupled plasma (ICP) and Brunauer-Emmett-Teller (BET) techniques. Results show that the average size of A2La2Ti3O10 powders obtained by citric acid sol-gel route was reduced to 200 nm×250 nm and the specific surface area was up to 19 m2·g-1. At the same time, the product was with more regular morphological characteristics. The synthesis process and the formation of A2La2Ti3O10 were also discussed. The obtained A2La2Ti3O10 was found to be transformed from A2La2Ti3O9.5 during the formation process.展开更多
A new binuclear copper(Ⅱ) complex, [Cu2(phen)2(H2O)2( μ2-C2O4)](NO3)2, has been synthesized and characterized by elemental analysis, IR and UV-Vis spectrum. Its crystal structure was determined by single crystal X-r...A new binuclear copper(Ⅱ) complex, [Cu2(phen)2(H2O)2( μ2-C2O4)](NO3)2, has been synthesized and characterized by elemental analysis, IR and UV-Vis spectrum. Its crystal structure was determined by single crystal X-ray diffraction techniques. Crystal data: monoclinic, space group P21/c, a=0.712 21(8) nm, b=1.170 93(14) nm, c=1.783 7(2) nm, β=111.828(2)°, and V=1.380 8(3) nm3, Dc=1.769 Mg·m-3, Z=2, F(000)=744, R1=0.025 4, wR2=0.069 5, Gof=1.077, Δρ=328^-455 e·nm-3. The complex is packed by one centrosymmetry binuclear copper(Ⅱ) unit, oxalate dianion and NO3- anion. In the molecule structure of the title complex, two Cu(Ⅱ) ions are bridged by oxalate dianion and each Cu(Ⅱ) ions coordinates with two nitrogen atoms from 1,10-phenanthroline ligand and one oxygen atom from water to form a five-coordinate distorted square-pyramidal configuration. The hydrogen bonds are observed between coordinated water molecules and NO3- anions. The analysis of the crystal structure indicates that the complex has a two-dimensional stacking network structure, which is formed by intramolecular hydrogen bonds, intermolecular hydrogen bonds and stacking effect of aromatic ring. CCDC: 255345.展开更多
A one-dimensional double-chain coordination polymer [Mn(phen)(tsgluo)] was synthesized in a mixed solution and its crystal structure was determined by X-ray diffraction method. It crystallizes in orthorhombic system w...A one-dimensional double-chain coordination polymer [Mn(phen)(tsgluo)] was synthesized in a mixed solution and its crystal structure was determined by X-ray diffraction method. It crystallizes in orthorhombic system with space group P212121. The crystal data are: a=0.530 78(17) nm, b=1.723 9(5) nm, c=2.456 9(8) nm, Z=4, μ=0.729 mm-1, Dc=1.579 g·cm-3, V=2.248 1(12) nm3, R1=0.033 1, ωR2=0.078 9. In the title complex, each Mn(Ⅱ) ion presents a octahedral geometry with the coordination of two nitrogen atoms from 1,10-phenanthroline and four oxygen atoms from three different tsgluo2- ligands. The γ-carboxyl coordinates to Mn(Ⅱ) in the mode of bidentate chelate, while the α-carboxyl coordinates in a bidentate bridging mode. CCDC: 253910.展开更多
文摘This manuscript provides a comparison of the Hypersphere World-Universe Model (WUM) with the prevailing Big Bang Model (BBM) of the Standard Cosmology. The performed analysis of BBM shows that the Four Pillars of the Standard Cosmology are model-dependent and not strong enough to support the model. The angular momentum problem is one of the most critical problems in BBM. Standard Cosmology cannot explain how Galaxies and Extra Solar systems obtained their substantial orbital and rotational angular momenta, and why the orbital momentum of Jupiter is considerably larger than the rotational momentum of the Sun. WUM is the only cosmological model in existence that is consistent with the Law of Conservation of Angular Momentum. To be consistent with this Fundamental Law, WUM discusses in detail the Beginning of the World. The Model introduces Dark Epoch (spanning from the Beginning of the World for 0.4 billion years) when only Dark Matter Particles (DMPs) existed, and Luminous Epoch (ever since for 13.8 billion years). Big Bang discussed in Standard Cosmology is, in our view, transition from Dark Epoch to Luminous Epoch due to Rotational Fission of Overspinning Dark Matter (DM) Supercluster’s Cores. WUM envisions Matter carried from the Universe into the World from the fourth spatial dimension by DMPs. Ordinary Matter is a byproduct of DM annihilation. WUM solves a number of physical problems in contemporary Cosmology and Astrophysics through DMPs and their interactions: Angular Momentum problem in birth and subsequent evolution of Galaxies and Extrasolar systems—how do they obtain it;Fermi Bubbles—two large structures in gamma-rays and X-rays above and below Galactic center;Diversity of Gravitationally-Rounded Objects in Solar system;some problems in Solar and Geophysics [1]. WUM reveals Inter-Connectivity of Primary Cosmological Parameters and calculates their values, which are in good agreement with the latest results of their measurements.
基金This work was supported by the National Key R&D Program of China(Grant No.2018YFB1304902)the National Natural Science Foundation of China(Grant Nos.12004034,U1813211,22005247,11904372,51502007,52072323,52122211,12174019,and 51972058)+1 种基金the Gen-eral Research Fund of Hong Kong(Project No.11217221)China Postdoctoral Science Foundation Funded Project(Grant No.2021M690386).
文摘Potassium-ion batteries(PIBs)are considered promising alternatives to lithium-ion batteries owing to cost-effective potassium resources and a suitable redox potential of-2.93 V(vs.-3.04 V for Li+/Li).However,the exploration of appro-priate electrode materials with the correct size for reversibly accommodating large K+ions presents a significant challenge.In addition,the reaction mecha-nisms and origins of enhanced performance remain elusive.Here,tetragonal FeSe nanoflakes of different sizes are designed to serve as an anode for PIBs,and their live and atomic-scale potassiation/depotassiation mechanisms are revealed for the first time through in situ high-resolution transmission electron micros-copy.We found that FeSe undergoes two distinct structural evolutions,sequen-tially characterized by intercalation and conversion reactions,and the initial intercalation behavior is size-dependent.Apparent expansion induced by the intercalation of K+ions is observed in small-sized FeSe nanoflakes,whereas unexpected cracks are formed along the direction of ionic diffusion in large-sized nanoflakes.The significant stress generation and crack extension originating from the combined effect of mechanical and electrochemical interactions are elucidated by geometric phase analysis and finite-element analysis.Despite the different intercalation behaviors,the formed products of Fe and K_(2)Se after full potassiation can be converted back into the original FeSe phase upon depotassiation.In particular,small-sized nanoflakes exhibit better cycling perfor-mance with well-maintained structural integrity.This article presents the first successful demonstration of atomic-scale visualization that can reveal size-dependent potassiation dynamics.Moreover,it provides valuable guidelines for optimizing the dimensions of electrode materials for advanced PIBs.
文摘Rumors are a type of false information, a consequence of an asymmetrical informational structure. This paper focuses on the social mechanisms of rumor fulfilling. Rumors with important contents related to people’s personal interests win acceptance through changing people’s expected payoffs, misleading people to the belief that acceptance of the rumor would beneficially outperform rejection of it. Nevertheless, it is risky to believe rumors; therefore, people make their decision whether to believe a rumor or not by referring to other people’s choices. An analysis was performed first within a game model that incorporated the variables of an individual’s expectancy and other people’s impact to predict whether the individual would accept or reject a rumor. Another analysis followed to further examine the functions of some dynamic mechanisms in rumor fulfilling when group pressure and network effects were introduced. Finally, an exploratory discussion on how to prevent rumors and erase their effects via information management strategies was presented.
基金the Beijing Natural Science Foundation(Grant Nos.JQ24010 and Z220020)the Fundamental Research Funds for the Central Universities,and the National Natural Science Foundation of China(Grant No.52273279)Project supported by the Electron Microscopy Laboratory of Peking University,China for the use of Nion U-HERMES200 scanning transmission electron microscopy.We thank Materials Processing and Analysis Center,Peking University,for assistance with TEM characterization.The electron microscopy work was through a user project at Center of Oak Ridge National Laboratory(ORNL)for Nanophase Materials Sciences(CNMS),which is a DOE Office of Science User Facility.
文摘Minimizing disorder and defects is crucial for realizing the full potential of two-dimensional transition metal dichalcogenides(TMDs) materials and improving device performance to desired properties. However, the methods in defect controlcurrently face challenges with overly large operational areas and a lack of precision in targeting specific defects. Therefore,we propose a new method for the precise and universal defect healing of TMD materials, integrating real-time imaging withscanning transmission electron microscopy (STEM). This method employs electron beam irradiation to stimulate the diffusionmigration of surface-adsorbed adatoms on TMD materials grown by low-temperature molecular beam epitaxy (MBE),and heal defects within the diffusion range. This approach covers defect repairs ranging from zero-dimensional vacancydefects to two-dimensional grain orientation alignment, demonstrating its universality in terms of the types of samples anddefects. These findings offer insights into the use of atomic-level focused electron beams at appropriate voltages in STEMfor defect healing, providing valuable experience for achieving atomic-level precise fabrication of TMD materials.
文摘The emergence of the middle class was closely related to the appearance of industrial society and its consequential constant changes in the social structure. Karl Marx and other theorists in the same camp were among the earliest scholars who discussed that topic. For a quite long period of time, the debate was mainly focused on the characteristics of the “new middle class.” The middle class, however, has undergone a categorical transformation from the old to the new middle-class, and furthermore, this transformation itself has signified the transition in social patterns from industrial to post-industrial society as well as economic globalization, both of which have contributed to the growth and global expansion of the middle class, having thus fundamentally renovated the middle class.
文摘In Advances in Pure Mathematics (www.scirp.org/journal/apm), Vol. 1, No. 4 (July 2011), pp. 136-154, the mathematical structure of the much discussed problem of probability known as the Monty Hall problem was mapped in detail. It is styled here as Monty Hall 1.0. The proposed analysis was then generalized to related cases involving any number of doors (d), cars (c), and opened doors (o) (Monty Hall 2.0) and 1 specific case involving more than 1 picked door (p) (Monty Hall 3.0). In cognitive terms, this analysis was interpreted in function of the presumed digital nature of rational thought and language. In the present paper, Monty Hall 1.0 and 2.0 are briefly reviewed (§§2-3). Additional generalizations of the problem are then presented in §§4-7. They concern expansions of the problem to the following items: (1) to any number of picked doors, with p denoting the number of doors initially picked and q the number of doors picked when switching doors after doors have been opened to reveal goats (Monty Hall 3.0;see §4);(3) to the precise conditions under which one’s chances increase or decrease in instances of Monty Hall 3.0 (Monty Hall 3.2;see §6);and (4) to any number of switches of doors (s) (Monty Hall 4.0;see §7). The afore-mentioned article in APM, Vol. 1, No. 4 may serve as a useful introduction to the analysis of the higher variations of the Monty Hall problem offered in the present article. The body of the article is by Leo Depuydt. An appendix by Richard D. Gill (see §8) provides additional context by building a bridge to modern probability theory in its conventional notation and by pointing to the benefits of certain interesting and relevant tools of computation now available on the Internet. The cognitive component of the earlier investigation is extended in §9 by reflections on the foundations of mathematics. It will be proposed, in the footsteps of George Boole, that the phenomenon of mathematics needs to be defined in empirical terms as something that happens to the brain or something that the brain does. It is generally assumed that mathematics is a property of nature or reality or whatever one may call it. There is not the slightest intention in this paper to falsify this assumption because it cannot be falsified, just as it cannot be empirically or positively proven. But there is no way that this assumption can be a factual observation. It can be no more than an altogether reasonable, yet fully secondary, inference derived mainly from the fact that mathematics appears to work, even if some may deem the fact of this match to constitute proof. On the deepest empirical level, mathematics can only be directly observed and therefore directly analyzed as an activity of the brain. The study of mathematics therefore becomes an essential part of the study of cognition and human intelligence. The reflections on mathematics as a phenomenon offered in the present article will serve as a prelude to planned articles on how to redefine the foundations of probability as one type of mathematics in cognitive fashion and on how exactly Boole’s theory of probability subsumes, supersedes, and completes classical probability theory. §§2-7 combined, on the one hand, and §9, on the other hand, are both self-sufficient units and can be read independently from one another. The ultimate design of the larger project of which this paper is part remains the increase of digitalization of the analysis of rational thought and language, that is, of (rational, not emotional) human intelligence. To reach out to other disciplines, an effort is made to describe the mathematics more explicitly than is usual.
文摘A novel coordination polymer of [Ca(2-OPA)2(H2O)2]n (2-OPA-=2-oxo-1(4H)-pyridineacetate anion) was synthesized and characterized by elemental analysis, IR, TG and single crystal X-ray diffraction. The title complex crystallizes in orthorhombic with space group Pna21, a=0.799 96(16) nm, b=0.823 77(16) nm, c=2.415 3(5) nm, V=1.591 6(6) nm3, Z=4, R=0.030 3, wR=0.070 0. The Ca atom is eight-coordinated by six O atoms of four 2-OPA- ligands and two water molecules, and displays a dodecahedron coordination geometry. Each 2-OPA- ligand bridges two adjacent Ca atoms, forming a infinite chain along the a direction. The Ca...Ca distance is 0.4102 2(8)nm. A two-dimensional supramolecular framework is further constructed by the hydrogen bonds and the weak π-π interactions. The results of TG analysis show the chain structure of the title complex was stable under 297.5 ℃. CCDC: 251669.
文摘new coordination polymer {[Zn(CF3COO)2(C5H5ON)]·H2O}n was synthesized based on the reaction of zinc(Ⅱ) trifluoroacetate and 3-hydroxypyridine(C5H5ON) in methanol medium for the first time. The structure of the coordination polymer was confirmed by IR, 1H NMR, elemental analysis and thermal analysis. The crystal structure of the coordination polymer was also determined by X-ray single crystal diffraction. The crystal belongs to monoclinic system with space group P21/m, and crystallographic data of the coordination polymer are: a= 0.863 1(4) nm, b=0.717 7(3) nm, c=1.116 4(5) nm, α=γ=90°, β=107.542(6)°, V=0.659 4(5) nm3; Dc=2.037 g·cm-3; Z=2; F(000)=400; μ=1.969 mm-1. Zinc(Ⅱ) atom lies at the center of an octahedron formed by the coordination of zinc atom and six O atoms which come from four different trifluoroacetate ions and two different 3-hydroxypyridine molecules where each trifluoroacetate ion and 3-hydroxypyridine are coordinated to two different zinc ions to form coordination polymer. CCDC: 253909.
文摘s: Ultrafine A2La2Ti3O10 (A=K, Na) powders with laminar structure were successfully synthesized by citric acid sol-gel method using ANO3(A=K, Na)?La(NO3)3?Ti(OBu)4 and citric acid as starting precursors. The crystalline phase of A2La2Ti3O10 can be obtained by thermal decomposition of citrate complex precursors at a relatively low temperature of 800 ℃ (600 ℃ for A=Na), about 300 ℃(500 ℃ for A=Na) lower than that of conventional solid state reaction process. The properties of the citrate precursors and the calcined powders were characterized by Infrared spectroscopy (IR), X-ray diffraction (XRD), transmission electron microscopy (TEM), thermal-gravimetric-differential thermal analysis (TG-DTA), inductively coupled plasma (ICP) and Brunauer-Emmett-Teller (BET) techniques. Results show that the average size of A2La2Ti3O10 powders obtained by citric acid sol-gel route was reduced to 200 nm×250 nm and the specific surface area was up to 19 m2·g-1. At the same time, the product was with more regular morphological characteristics. The synthesis process and the formation of A2La2Ti3O10 were also discussed. The obtained A2La2Ti3O10 was found to be transformed from A2La2Ti3O9.5 during the formation process.
文摘A new binuclear copper(Ⅱ) complex, [Cu2(phen)2(H2O)2( μ2-C2O4)](NO3)2, has been synthesized and characterized by elemental analysis, IR and UV-Vis spectrum. Its crystal structure was determined by single crystal X-ray diffraction techniques. Crystal data: monoclinic, space group P21/c, a=0.712 21(8) nm, b=1.170 93(14) nm, c=1.783 7(2) nm, β=111.828(2)°, and V=1.380 8(3) nm3, Dc=1.769 Mg·m-3, Z=2, F(000)=744, R1=0.025 4, wR2=0.069 5, Gof=1.077, Δρ=328^-455 e·nm-3. The complex is packed by one centrosymmetry binuclear copper(Ⅱ) unit, oxalate dianion and NO3- anion. In the molecule structure of the title complex, two Cu(Ⅱ) ions are bridged by oxalate dianion and each Cu(Ⅱ) ions coordinates with two nitrogen atoms from 1,10-phenanthroline ligand and one oxygen atom from water to form a five-coordinate distorted square-pyramidal configuration. The hydrogen bonds are observed between coordinated water molecules and NO3- anions. The analysis of the crystal structure indicates that the complex has a two-dimensional stacking network structure, which is formed by intramolecular hydrogen bonds, intermolecular hydrogen bonds and stacking effect of aromatic ring. CCDC: 255345.
文摘A one-dimensional double-chain coordination polymer [Mn(phen)(tsgluo)] was synthesized in a mixed solution and its crystal structure was determined by X-ray diffraction method. It crystallizes in orthorhombic system with space group P212121. The crystal data are: a=0.530 78(17) nm, b=1.723 9(5) nm, c=2.456 9(8) nm, Z=4, μ=0.729 mm-1, Dc=1.579 g·cm-3, V=2.248 1(12) nm3, R1=0.033 1, ωR2=0.078 9. In the title complex, each Mn(Ⅱ) ion presents a octahedral geometry with the coordination of two nitrogen atoms from 1,10-phenanthroline and four oxygen atoms from three different tsgluo2- ligands. The γ-carboxyl coordinates to Mn(Ⅱ) in the mode of bidentate chelate, while the α-carboxyl coordinates in a bidentate bridging mode. CCDC: 253910.
