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Progress in Natural Science:Materials International 2024年第2期34卷 251-262页

作者： Ritong Huang Limei Wu Xiaolong Wang Ning Tang Lili Gao Aiqin Wang Yushen Lu School of Materials Science and Engineering Shenyang Jianzhu University School of Mechanical Engineering Shenyang Jianzhu University Key Laboratory of Clay Mineral Applied Research of Gansu Province Center of Eco-material and Green Chemistry Lanzhou Institute of Chemical Physics Chinese Academy of Sciences

Clay minerals represent a class of hydrated phyllosilicates making up the fine-grained portions of rocks, sediments, and soils. Due to the advantages of abundant reserves, low prices, and wide applications, the development and utilization of clay minerals have received increasing attention in recent years. Isomorphic replacement is a common phenomenon in clay minerals, which is one of the main causes of changes in mineral chemical composition and physical and chemical properties. This article briefly describes the crystal structure of several clay minerals such as montmorillonite, vermiculite, palygorskite, kaolinite, and halloysite. It summarized the research status of the effect of isomorphic replacement on their structure and application performance. The research results can provide theoretical basis for the structural research and efficient resource utilization of clay minerals.

关键词： Clay minerals Crystal structure isomorphism Application performance

On the Infinite-Dimensional Modular Lie Superalgebras of O-Type

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Algebra Colloquium 2024年第2期31卷 347-360页

作者： Xiaoning Xu Jing Zhao Yucai Su School of Mathematics and Statistics Liaoning UniversityShenyang 110036China 不详

The natural filtrations of infinite-dimensional Lie superalgebras of O-type over a field of positive characteristic are proved to be invariant under automorphisms by studying ad-nilpotent elements.We observe that two Lie superalgebras of O-type are isomorphic if and only if the integers in the definition of these Lie superalgebras are intrinsic.Thereby,all the Lie superalgebras of O-type are classified in the sense of isomorphism.

关键词： filtration isomorphism classification

On the Proof of the Contradiction of Set Theory

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Advances in Pure Mathematics 2024年第3期14卷 139-159页

作者： Yury M. Volin Mountain View USA

The article is devoted to proving the inconsistency of set theory arising from the existence of strange trees. All steps of the proof rely on common informal set-theoretic reasoning, but they take into account the prohibitions that were introduced into axiomatic set theories in order to overcome the difficulties encountered by the naive Cantor set theory. Therefore, in fact, the article is about proving the inconsistency of existing axiomatic set theories, in particular, the ZFC theory.

关键词： Set Theory Inconsistency Tree Strange Tree Through Way Almost through Way isomorphism Almost isomorphism isomorphism Tree Place Plane Superposition of Trees on the Place Plane Disposition of Trees on the Place Plane

isomorphism analysis on generalized modules oriented to the distributed parameterized intelligent product platform

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Frontiers of Mechanical Engineering 2020年第1期15卷 12-23页

作者： Shasha ZENG Weiping PENG Tiaoyu LEI Hubei Key Laboratory of Waterjet Theory and New Technology School of Power and Mechanical EngineeringWuhan UniversityWuhan 430072China

The distributed parameterized intelligent product platform(DPIPP)contains many agents of a product minimum approximate autonomous subsystem(generalized module).These distributed agents communicate,coordinate,and cooperate using their knowledge and skills and eventually accomplish the design for mass customization in a loosely coupled environment.In this study,a new method of isomorphism analysis on generalized modules oriented to DPIPP is proposed.First,on the basis of the bill of material partition and generalized module mining,the parameters of the main characteristics are extracted to construct the main characteristic parameter matrix.Second,similarity calculation of generalized modules is realized by improving the clustering using representatives algorithm,and isomorphism model sets are obtained.Generalized modules with a similar structure are combined to complete the isomorphism analysis.The effectiveness of the proposed method is verified by taking high-and medium-pressure valve data as an example.

关键词： distributed parameterized intelligent product platform generalized module isomorphism analysis product family

isomorphism classes of hyperelliptic curves of genus 2 over finite fields with characteristic 2

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Science China Mathematics 2006年第2期49卷 173-184页

作者： DENG Yingpu LIU Mulan Institute of Systems Science Academy of Mathematics and Systems Science Chinese Academy of SciencesBeijing 100080 China Institute of Systems Science Academy of Mathematics and Systems Science Chinese Academy of SciencesBeijing 100080 China

In this paper we study the computation of the number of isomorphism classes of hyperelliptic curves of genus 2 over finite fields Fq with q even. We show the formula of the number of isomorphism classes, that is, for q = 2m, if 4 (|) m, then the formula is 2q3 + q2 - q;if 4 | m, then the formula is 2q3 + q2 - q + 8. These results can be used in the classification problems and the hyperelliptic curve cryptosystems.

关键词： hyperelliptic curves hyperelliptic curve cryptosystems Jacobian groups isomorphism classes.

isomorphism and Generation of Montgomery-Form Elliptic Curves Suitable for Cryptosystems

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Tsinghua Science and Technology 2005年第2期10卷 145-151页

作者：刘铎宋涛戴一奇 Department of Computer Science and Technology Tsinghua University Beijing 100084 China

Many efficient algorithms of Montgomery-form elliptic curve cryptology have been investigated recently. At present, there are no reported studies of the isomorphic class of the Montgomery-form elliptic curve over a finite field. This paper investigates the isomorphism of Montgomery-form elliptic curves via the isomorphism of Weierstrass-form elliptic curves and gives a table of (nearly) all the forms of Montgomery- form elliptic curves suitable for cryptographic usage. Then, an algorithm for generating a secure elliptic curve with Montgomery-form is presented. The most important advantages of the new algorithm are that it avoids the transformation from an elliptic curve’s Weierstrass-form to its Montgomery-form, and that it de- creases the probability of collision. So, the proposed algorithem is quicker, simpler, and more efficient than the old ones.

关键词： elliptic curve cryptography Montgomery-form isomorphism

Leaching isomorphism rare earths from phosphorite ore by sulfuric acid and phosphoric acid

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Rare Metals 2017年第10期36卷 840-850页

作者： Hui-Xin Jin Fu-Zhong Wu Xiao-Hao Mao Mei-Long Wang Hong-Yan Xie College of Materials and Metallurgy Guizhou University Guiyang 550025 China Guizhou Province Key Laboratory of Metallurgical Engineering and Process Energy Saving Guiyang 550025 China

Most of the phosphorite deposits in the world contain isomorphism rare earths （RE） which are considerably difficult to be leached into solution in the wet phos- phoric acid process. In this work, a systematic study of leaching RE using sulfuric acid, phosphoric acid, mixed acid and two-step leaching of phosphoric acid and sulfuric acid was performed. The aims are to illuminate the main factors that inhibit RE leaching and to provide insights into the further enrichment of RE in the wet phosphoric acid solution. The results indicate that H2SO4 is not an effective acid for leaching isomorphism RE from phosphorite ore. The low RE leaching efficiency attributes to the RE cocrystallized and encapsulated by phosphogypsum （PG） as well as the precipitation of RE by RE sulfates or phosphates. High concentration of H3PO4 can enhance the dissolution and diffusion of RE ions. Hence, the optimized leaching mode of improving RE leaching efficiency is to adequately dissolve phosphorite ores in high concentration of H3PO4 solution and then add H2SO4 to crystallize PG. The effect of corystallization or encapsulation of PG on RE can be decreased due to the crystallizing mode of PG in the bulk solution instead of on the interface of solid reactants. RE leaching efficiency can be high up to 65% by the optimized leaching mode.

关键词： Phosphorite isomorphism Rare earths Leaching Sulfuric acid Phosphoric acid

On Hom-groups and Hom-group Actions

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Acta Mathematica Sinica,English Series 2023年第10期39卷 1887-1906页

作者： Liang Yun CHEN Tian Qi FENG Yao MA Ripan SAHA Hong Yi ZHANG School of Mathematics and Statistics Northeast Normal UniversityChangchun 130024P.R.China Department of Mathematics Raiganj UniversityRaiganj 733134West BengalIndia School of Mathematical Sciences Nankai UniversityTianjin 300071P.R.China

A Hom-group is the non-associative generalization of a group whose associativity and unitality are twisted by a compatible bijective map.In this paper,we give some new examples of Hom-groups,and show the first,second and third isomorphism theorems of Hom-groups.We also introduce the notion of Hom-group action,and as an application,we prove the first Sylow theorem for Hom-groups along the line of group actions.

关键词： Hom-groups Hom-subgroups Hom-quotient groups isomorphism Hom-group actions first Sylow theorem

Pythagorean Neutrosophic Planar Graphs with an Application in Decision-Making

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Computers, Materials & Continua 2023年第6期75卷 4935-4953页

作者： P.Chellamani D.Ajay Mohammed M.Al-Shamiri Rashad Ismail Department of Mathematics Sacred Heart College(Autonomous)Tirupattur635601TamilnaduIndia Department of Mathematics St.Joseph’s College of EngineeringOMRChennai600119TamilnaduIndia Department of Mathematics Faculty of Science and ArtsKing Khalid UniversityMuhayl AssirSaudi Arabia Department of Mathematics and Computer Faculty of ScienceIbb UniversityIbbYemen

Graph theory has a significant impact and is crucial in the structure of many real-life situations.To simulate uncertainty and ambiguity,many extensions of graph theoretical notions were created.Planar graphs play a vital role in modelling which has the property of non-crossing edges.Although crossing edges benefit,they have some drawbacks,which paved the way for the introduction of planar graphs.The overall purpose of the study is to contribute to the conceptual development of the Pythagorean Neutrosophic graph.The basic methodology of our research is the incorporation of the analogous concepts of planar graphs in the Pythagorean Neutrosophic graphs.The significant finding of our research is the introduction of Pythagorean Neutrosophic Planar graphs,a conceptual blending of Pythagorean Neutro-sophic and Planar graphs.The idea of Pythagorean Neutrosophic multigraphs and dual graphs are also introduced to deal with the ambiguous situations.This paper investigates the Pythagorean Neutrosophic planar values,which form the edges of the Pythagorean neutrosophic graphs.The concept of Pythagorean Neutrosophic dual graphs,isomorphism,co-weak and weak isomorphism have also been explored for Pythagorean Neutrosophic planar graphs.A decision-making algorithm was proposed with a numerical illustra-tion by using the Pythagorean Neutrosophic fuzzy graph.

关键词： Pythagorean neutrosophic planar graph planarity value isomorphism dual graphs multigraph

Complexities of Homomorphism and isomorphism for Definite Logic Programs

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Journal of Computer Science & Technology 2005年第6期20卷 758-762页

作者：许道云陶志红 Department of Computer Science Guizhou University Guiyang 550025 P.R. China Department of Computer Science Peking University Beijing 100871 P.R. China

A homomorphism φ of logic programs from P to P＇ is a function mapping Atoms（P） to Atoms（P＇） and it preserves complements and program clauses. For each definite program clause a ← a1,...,an ∈ P it implies that φ（a） ←- φ（a1）,...,φ（an） is a program clause of P＇. A homomorphism φis an isomorphism if φ is a bijection. In this paper, the complexity of the decision problems on homomorphism and isomorphism for definite logic programs is studied. It is shown that the homomorphism problem （HOM-LP） for definite logic programs is NP-complete, and the isomorphism problem （ISO-LP） is equivalent to the graph isomorphism problem （GI）.

关键词： logic program homomorphism isomorphism decision problem complexity