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This paper deals with the analysis with actual mathematical tools of some structural proposals done by Leonardo in his notebooks. At difference of other subjects such as the Fly of Birds or Treatise of Painting, he never made his ...
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This paper deals with the analysis with actual mathematical tools of some structural proposals done by Leonardo in his notebooks. At difference of other subjects such as the Fly of Birds or Treatise of Painting, he never made his sketches to establish a coherent treatise on structures although he consumed a lot of pages analyzing constructional patterns to build bridges, roofs and floors a well vas beams, strings and mechanisms. May be he never constructed his proposals, but them are designed as if it would necessary to define minimal details. A particular subject contained in his notebooks are concerning to great span structures built with short elements. We try to proof the validity of these proposals.
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We study automatic equivalence and nested equivalence structures. The goal is to compare and contrast these automatic structures with computable equivalence and nested equivalence structures. Equivalence structures A may be charac...
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We study automatic equivalence and nested equivalence structures. The goal is to compare and contrast these automatic structures with computable equivalence and nested equivalence structures. Equivalence structures A may be characterized by their characters x (A) which encodes the number of equivalence classes of any given size. The characters of computably categorical, △_2~0 categorical but not computably categorical, or △_3~0 categorical but not △_2~0, categorical have been determined. We show that every computably categorical equivalence structure has an automatic copy, but not every △_2~0 categorical structure has an automatic copy. We construct an automatic equivalence structure which is △_2~0 categorical but not computably categorical and another automatic equivalence structure which is not △_2~0 categorical. We observe that the theory of an automatic equivalence structure is decidable and hence the character of any automatic equivalence structure is computable. On the other hand, there is a computable character which is not the character of any automatic equivalence structure. We show that any two automatic equivalence structures which are isomorphic are in fact computably isomorphic. Moreover, we show that for certain characters, there is always a exponential time isomorphism between two automatic equivalence structures with that character. Finally, we briefly consider nested equivalence structures and construct an automatic nested equivalence structure that is not △_3~0 categorical but △_4~0 categorical and an automatic nested equivalence structure that is not △_4~0 categorical.
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Recent advances in RNA research and the steady growth of available RNA structures call for bioinformatics methods for handling and analyzing RNA structural data. Recently, we introduced SETTER—a fast and accurate method for RNA p...
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Recent advances in RNA research and the steady growth of available RNA structures call for bioinformatics methods for handling and analyzing RNA structural data. Recently, we introduced SETTER—a fast and accurate method for RNA pairwise structure alignment. In this paper, we describe MultiSETTER, SETTER extension for multiple RNA structure alignment. MultiSETTER combines SETTER’s decomposition of RNA structures into non-overlapping structural subunits with the multiple sequence alignment algorithm ClustalW adapted for the structure alignment. The accuracy of MultiSETTER was assessed by the automatic classification of RNA structures and its comparison to SCOR annotations. In addition, MultiSETTER classification was also compared to multiple sequence alignment-based and secondary structure alignment-based classifications provided by LocARNA and RNADistance tools, respectively. MultiSETTER precompiled Windows libraries, as well as the C++ source code, are freely available from http://siret.cz/multisetter.
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The authors have been developing a large deployable mesh reflector for advanced satellite communication. This large reflector consists of a mesh membrane surface and a deployable truss structure. In this paper, analysis methods fo...
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The authors have been developing a large deployable mesh reflector for advanced satellite communication. This large reflector consists of a mesh membrane surface and a deployable truss structure. In this paper, analysis methods for a large deployable mesh reflector structure are introduced, and the theoretical basis for the analysis is explained. By using those analysis methods, we manufactured prototype reflector modules and carried out an experiment on them. The validity of the analysis methods were verified from the results of the analyses and experiments. The design procedure of mesh reflector surface and the effect of the mesh surface tension on the truss deployment are discussed.
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Databases of three-dimensional macromolecular structures became so large that fast search tools and comparison methods were needed and were actually designed. All of them employ simplified representations of the threedimensional s...
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Databases of three-dimensional macromolecular structures became so large that fast search tools and comparison methods were needed and were actually designed. All of them employ simplified representations of the threedimensional structure: strings of characters of variable length, which can be handled with procedures that were designed for sequence analysis; fixed dimension arrays that can be processed with standard statistical methods; ensembles of secondary structural elements, which are much less numerous than the atoms/residues of the protein; and continuous representations of the backbone, through stereochemical figures. Some of these computational procedures were developed long ago, when computers were too slow, and others have been designed recently, with the specific aim of handling large amount of information. The present article is focused on the algorithms that allow fast structure comparison, particularly suitable to handle large databases, and should provide a comprehensive picture, useful for the development and the assessment of novel tools.
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In the early stages of the design process, an engineer sets the geometry of the structure. The decisions made about the layout of the structure will determine the overall efficiency that can be achieved and the magnitude of the fo...
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In the early stages of the design process, an engineer sets the geometry of the structure. The decisions made about the layout of the structure will determine the overall efficiency that can be achieved and the magnitude of the forces that must be accommodated. For example, the deflection of a truss can actually be decreased by removing material if a geometry is created that has a shorter total load path. This paper presents concepts and methodologies for creating and understanding efficient geometries. It starts with a review of the 19th- and 20th-century load path theories of Rankine, Maxwell, Cremona and Michell. It then combines their insights with current topology optimization and shape-finding tools as a means of exploring how engineers can create structural geometries that improve the behavior and reduce the tonnage of their designs. Several examples of classical theoretical solutions are explored along with their application to new designs.
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Compliant multistable structures are presented which exhibit a large geometric change when actuated between their stable states. It is demonstrated how asymmetric-bistability is achieved through the combination of linear and nonli...
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Compliant multistable structures are presented which exhibit a large geometric change when actuated between their stable states. It is demonstrated how asymmetric-bistability is achieved through the combination of linear and nonlinear springs. Finite element analytical techniques are provided which enable the design of such structures, and which illustrate how the presence of imperfections can substantially alter their structural performance. A multistable structure is developed which consists of four connected bistable tetrahedral units. The validity of the analytical techniques is confirmed through observation of several physical models. (C) 2008 Elsevier Ltd. All rights reserved.
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In BS5950. Part 1, Structural use of steelwork in building. British Standards Insti- tution, 1990), it is recommended that in order to analyse a structure by plastic methods the section classification of its members must be "plast...
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In BS5950. Part 1, Structural use of steelwork in building. British Standards Insti- tution, 1990), it is recommended that in order to analyse a structure by plastic methods the section classification of its members must be "plastic". This condition is necessary so that ";large" rotations can be attained without local buckling of the member. For tubular members of circular hollow section the ratio of D/t must be ≤40ε2 for plastic classification.
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A generalized F-structure is a complex, isotropic subbundle E of TcM ÅT*cM{T_cM \oplus T^*_cM} ( TcM = TM Ä\mathbbR \mathbbCT_cM = TM \otimes_{{\mathbb{R}}} {\mathbb{C}} and the metric is defined by pairing) such that E Ç[`(E)]...
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A generalized F-structure is a complex, isotropic subbundle E of TcM ÅT*cM{T_cM \oplus T^*_cM} ( TcM = TM Ä\mathbbR \mathbbCT_cM = TM \otimes_{{\mathbb{R}}} {\mathbb{C}} and the metric is defined by pairing) such that E Ç[`(E)]^ = 0E \cap \bar{E}^{\perp} = 0. If E is also closed by the Courant bracket, E is a generalized CRF-structure. We show that a generalized F-structure is equivalent with a skew-symmetric endomorphism Φ of TM ÅT*MTM \oplus T^*M that satisfies the condition Φ3 + Φ = 0 and we express the CRF-condition by means of the Courant-Nijenhuis torsion of Φ. The structures that we consider are generalizations of the F-structures defined by Yano and of the CR (Cauchy-Riemann) structures. We construct generalized CRF-structures from: a classical F-structure, a pair (V, s)({\mathcal{V}}, \sigma) where V{\mathcal{V}} is an integrable subbundle of TM and σ is a 2-form on M, a generalized, normal, almost contact structure of codimension h. We show that a generalized complex structure on a manifold M̃ induces generalized CRF-structures into some submanifolds M Í [(M)\tilde]M \subseteq \tilde{M} . Finally, we consider compatible, generalized, Riemannian metrics and we define generalized CRFK-structures that extend the generalized Kähler structures and are equivalent with quadruples (γ, F +, F −, ψ), where (γ, F ±) are classical, metric CRF-structures, ψ is a 2-form and some conditions expressible in terms of the exterior differential d ψ and the γ-Levi-Civita covariant derivatives ∇ F ± hold. If d ψ = 0, the conditions reduce to the existence of two partially Kähler reductions of the metric γ. The paper ends by an Appendix where we define and characterize generalized Sasakian structures.
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In this paper, first we introduce the notion of a phase space of a 3-Lie algebra and show that a 3-Lie algebra has a phase space if and only if it is sub-adjacent to a 3-pre Lie algebra. Then we introduce the notion of a product s...
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In this paper, first we introduce the notion of a phase space of a 3-Lie algebra and show that a 3-Lie algebra has a phase space if and only if it is sub-adjacent to a 3-pre Lie algebra. Then we introduce the notion of a product structure on a 3-Lie algebra using the Nijenhuis condition as the integrability condition. A 3-Lie algebra enjoys a product structure if and only if it is the direct sum (as vector spaces) of two subalgebras. We find that there are four types special integrability conditions, and each of them gives rise to a special decomposition of the original 3-Lie algebra. They are also related to 0-operators, Rota Baxter operators and matched pairs of 3-Lie algebras. Parallelly, we introduce the notion of a complex structure on a 3-Lie algebra and there are also four types special integrability conditions. Finally, we add compatibility conditions between a complex structure and a product structure, between a symplectic structure and a paracomplex structure, between a symplectic structure and a complex structure, to introduce the notions of a complex product structure, a para-Kahler structure and a pseudoKahler structure on a 3-Lie algebra. We use 3-pre-Lie algebras to construct these structures. Furthermore, a Levi-Civita product is introduced associated to a pseudo-Riemannian 3-Lie algebra and deeply studied. (C) 2018 Elsevier Inc. All rights reserved.
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