Exceptional complex structures and the hypermultiplet moduli of 5d Minkowski compactifications of M-theory

Abstract We present a detailed study of a new mathematical object in E6(6)ℝ+ generalised geometry called an ‘exceptional complex structure’ (ECS). It is the extension of a conventional complex structure to one that includes all the degrees of freedom of M-theory or type IIB supergravity in six or five dimensions, and as such characterises, in part, the geometry of generic supersymmetric compactifications to five-dimensional Minkowkski space. We define an ECS as an integrable U*(6) × ℝ+ structure and show it is equivalent to a particular form of involutive subbundle of the complexified generalised tangent bundle L1 ⊂ Eℂ. We also define a refinement, an SU*(6) structure, and show that its integrability requires in addition a vanishing moment map on the space of structures. We are able to classify all possible ECSs, showing that they are characterised by two numbers denoted ‘type’ and ‘class’. We then use the deformation theory of ECS to find the moduli of any SU*(6) structure. We relate these structures to the geometry of generic minimally supersymmetric flux backgrounds of M-theory of the form ℝ4,1 × M, where the SU*(6) moduli correspond to the hypermultiplet moduli in the lower-dimensional theory. Such geometries are of class zero or one. The former are equivalent to a choice of (non-metric-compatible) conventional SL(3, ℂ) structure and strikingly have the same space of hypermultiplet moduli as the fluxless Calabi-Yau case.

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Abelian Complex Structures and Generalizations

Complex Manifolds ◽

10.1515/coma-2020-0117 ◽

2021 ◽

Vol 8 (1) ◽

pp. 247-266

Author(s):

Yat Sun Poon

Keyword(s):

Deformation Theory ◽

Complex Structure ◽

Complex Structures ◽

Generalized Complex Structure ◽

Generalized Complex

Abstract After a review on the development of deformation theory of abelian complex structures from both the classical and generalized sense, we propose the concept of semi-abelian generalized complex structure. We present some observations on such structure and illustrate this new concept with a variety of examples.

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Duality, Quantum Mechanics and (Almost) Complex Manifolds

Modern Physics Letters A ◽

10.1142/s0217732303011873 ◽

2003 ◽

Vol 18 (28) ◽

pp. 1975-1990 ◽

Cited By ~ 5

Author(s):

José M. Isidro

Keyword(s):

Degrees Of Freedom ◽

Complex Structure ◽

Classical Mechanics ◽

Quantum Mechanical ◽

Complex Structures ◽

Analytic Manifold ◽

Duality Transformation ◽

Almost Complex Manifolds ◽

Almost Complex ◽

Complex Analytic Manifold

The classical mechanics of a finite number of degrees of freedom requires a symplectic structure on phase space [Formula: see text], but it is independent of any complex structure. On the contrary, the quantum theory is intimately linked with the choice of a complex structure on [Formula: see text]. When the latter is a complex-analytic manifold admitting just one complex structure, there is a unique quantization whose classical limit is [Formula: see text]. Then the notion of coherence is the same for all observers. However, when [Formula: see text] admits two or more nonbiholomorphic complex structures, there is one different quantization per different complex structure on [Formula: see text]. The lack of analyticity in transforming between nonbiholomorphic complex structures can be interpreted as the loss of quantum-mechanical coherence under the corresponding transformation. Observers using one complex structure perceive as coherent the states that other observers, using a different complex structure, do not perceive as such. This is the notion of a quantum-mechanical duality transformation: the relativity of the notion of a quantum.

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STRUKTUR KOMPLEKS DALAM BAHASA INDONESIA ILMIAH DAN MASALAH PENERJEMAHANNYA KE DALAM BAHASA INGGRIS

PARAFRASE Jurnal Kajian Kebahasaan & Kesastraan ◽

10.30996/parafrase.v17i1.1359 ◽

2018 ◽

Vol 17 (1) ◽

Author(s):

Ni Ketut Mirahayuni ◽

Susie Chrismalia Garnida ◽

Mateus Rudi Supsiadji

Keyword(s):

Complex Structure ◽

General Concept ◽

Target Language ◽

Complex Structures ◽

Scientific Language ◽

Logical Relation ◽

Information Packaging ◽

Weight Structure ◽

The Difference ◽

Target Languages

Abstract. Translating complex structures have always been a challenge for a translator since the structures can be densed with ideas and particular logical relations. The purpose of translation is reproducing texts into another language to make them available to wider readerships. Since language is not merely classification of a set of universal and general concept, that each language articulates or organizes the world differently, the concepts in one language can be radically different from another. One issue in translation is the difference among languages, that the wider gaps between the source and target languages may bring greater problems of transfer of message from the source into the target languages (Culler, 1976). Problematic factors involved in translation include meaning, style, proverbs, idioms and others. A number of translation procedures and strategies have been discussed to solve translation problems. This article presents analysis of complex structures in scientific Indonesian, the problems and effects on translation into English. The study involves data taken from two research article papers in Indonesian to be translated into English. The results of the analysis show seven (7) problems of Indonesian complex structures, whose effect on translation process can be grouped into two: complex structures related to grammar (including: complex structure with incomplete information, run-on sentences, redundancy , sentence elements with inequal semantic relation, and logical relation and choice of conjunctor) and complex structures related to information processing in discourse (including: front-weight- structure and thematic structure with changes of Theme element). Problems related to grammar may be solved with language economy and accuracy while those related to discourse may be solved with understanding information packaging patterns in the target language discourse. Keywords: scientific language, complex structures, translation

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A Multiple and Multi-Level Substructure Method for the Dynamics of Complex Structures

Applied Sciences ◽

10.3390/app11125570 ◽

2021 ◽

Vol 11 (12) ◽

pp. 5570

Author(s):

Binbin Wang ◽

Jingze Liu ◽

Zhifu Cao ◽

Dahai Zhang ◽

Dong Jiang

Keyword(s):

Structural Characteristics ◽

Complex Structure ◽

Complex Structures ◽

System Matrix ◽

Substructure Method ◽

Residual Structure ◽

The Matrix ◽

Multi Level ◽

Fixed Interface ◽

Selection Of

Based on the fixed interface component mode synthesis, a multiple and multi-level substructure method for the modeling of complex structures is proposed in this paper. Firstly, the residual structure is selected according to the structural characteristics of the assembled complex structure. Secondly, according to the assembly relationship, the parts assembled with the residual structure are divided into a group of substructures, which are named the first-level substructure, the parts assembled with the first-level substructure are divided into a second-level substructure, and consequently the multi-level substructure model is established. Next, the substructures are dynamically condensed and assembled on the boundary of the residual structure. Finally, the substructure system matrix, which is replicated from the matrix of repeated physical geometry, is obtained by preserving the main modes and the constrained modes and the system matrix of the last level of the substructure is assembled to the upper level of the substructure, one level up, until it is assembled in the residual structure. In this paper, an assembly structure with three panels and a gear box is adopted to verify the method by simulation and a rotor is used to experimentally verify the method. The results show that the proposed multiple and multi-level substructure modeling method is not unique to the selection of residual structures, and different classification methods do not affect the calculation accuracy. The selection of 50% external nodes can further improve the analysis efficiency while ensuring the calculation accuracy.

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Selection of Degrees of Freedom for Dynamic Analysis

Journal of Pressure Vessel Technology ◽

10.1115/1.3264857 ◽

1987 ◽

Vol 109 (1) ◽

pp. 65-69 ◽

Cited By ~ 26

Author(s):

K. W. Matta

Keyword(s):

Finite Element ◽

Dynamic Analysis ◽

Degrees Of Freedom ◽

General Purpose ◽

Component Mode Synthesis ◽

Complex Structures ◽

Large Complex ◽

Static Condensation ◽

Basis Vectors ◽

Selection Of

A technique for the selection of dynamic degrees of freedom (DDOF) of large, complex structures for dynamic analysis is described and the formulation of Ritz basis vectors for static condensation and component mode synthesis is presented. Generally, the selection of DDOF is left to the judgment of engineers. For large, complex structures, however, a danger of poor or improper selection of DDOF exists. An improper selection may result in singularity of the eigenvalue problem, or in missing some of the lower frequencies. This technique can be used to select the DDOF to reduce the size of large eigenproblems and to select the DDOF to eliminate the singularities of the assembled eigenproblem of component mode synthesis. The execution of this technique is discussed in this paper. Examples are given for using this technique in conjunction with a general purpose finite element computer program GENSAM[1].

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An Efficient Sparse Finite Element Solver for the Radiative Transfer Equation

Volume 1: Heat Transfer in Energy Systems; Thermophysical Properties; Heat Transfer Equipment; Heat Transfer in Electronic Equipment ◽

10.1115/ht2009-88140 ◽

2009 ◽

Author(s):

Gisela Widmer

Keyword(s):

Linear System ◽

Radiative Transfer ◽

Transfer Equation ◽

Degrees Of Freedom ◽

Radiative Transfer Equation ◽

Three Dimensional ◽

Discrete Ordinates ◽

Five Dimensions ◽

Computational Costs ◽

Dimensional Domain

The stationary monochromatic radiative transfer equation (RTE) is posed in five dimensions, with the intensity depending on both a position in a three-dimensional domain as well as a direction. For non-scattering radiative transfer, sparse finite elements [1, 2] have been shown to be an efficient discretization strategy if the intensity function is sufficiently smooth. Compared to the discrete ordinates method, they make it possible to significantly reduce the number of degrees of freedom N in the discretization with almost no loss of accuracy. However, using a direct solver to solve the resulting linear system requires O(N3) operations. In this paper, an efficient solver based on the conjugate gradient method (CG) with a subspace correction preconditioner is presented. Numerical experiments show that the linear system can be solved at computational costs that are nearly proportional to the number of degrees of freedom N in the discretization.

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Characteristic Constraint Modes for Component Mode Synthesis

Volume 7B: 17th Biennial Conference on Mechanical Vibration and Noise ◽

10.1115/detc99/vib-8187 ◽

1999 ◽

Author(s):

Matthew P. Castanier ◽

Yung-Chang Tan ◽

Christophe Pierre

Keyword(s):

Degrees Of Freedom ◽

Natural Frequencies ◽

Component Mode Synthesis ◽

Complex Structures ◽

Cantilever Plate ◽

Vibration Transmission ◽

Stiffness Matrices ◽

Physical Insight ◽

Insight Into

Abstract In this paper, a technique is presented for improving the efficiency of the Craig-Bampton method of Component Mode Synthesis (CMS). An eigenanalysis is performed on the partitions of the CMS mass and stiffness matrices that correspond to the so-called constraint modes. The resultant eigenvectors are referred to as “characteristic constraint modes,” since they represent the characteristic motion of the interface between the component structures. By truncating the characteristic constraint modes, a CMS model with a highly-reduced number of degrees of freedom may be obtained. An example of a cantilever plate is considered. It is shown that relatively few characteristic constraint modes are needed to yield accurate approximations of the lower natural frequencies. This method also provides physical insight into the mechanisms of vibration transmission in complex structures.

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COMPLEXITY-BASED ANALYSIS OF THE ALTERATIONS IN THE STRUCTURE OF CORONAVIRUSES

Fractals ◽

10.1142/s0218348x21501231 ◽

2021 ◽

Vol 29 (02) ◽

pp. 2150123

Author(s):

HAMIDREZA NAMAZI ◽

ALI SELAMAT ◽

ONDREJ KREJCAR

Keyword(s):

Hurst Exponent ◽

Complex Structure ◽

Approximate Entropy ◽

Sample Entropy ◽

Long Term Memory ◽

Complex Structures ◽

Term Memory ◽

The World ◽

First Time

The coronavirus has influenced the lives of many people since its identification in 1960. In general, there are seven types of coronavirus. Although some types of this virus, including 229E, NL63, OC43, and HKU1, cause mild to moderate illness, SARS-CoV, MERS-CoV, and SARS-CoV-2 have shown to have severer effects on the human body. Specifically, the recent known type of coronavirus, SARS-CoV-2, has affected the lives of many people around the world since late 2019 with the disease named COVID-19. In this paper, for the first time, we investigated the variations among the complex structures of coronaviruses. We employed the fractal dimension, approximate entropy, and sample entropy as the measures of complexity. Based on the obtained results, SARS-CoV-2 has a significantly different complex structure than SARS-CoV and MERS-CoV. To study the high mutation rate of SARS-CoV-2, we also analyzed the long-term memory of genome walks for different coronaviruses using the Hurst exponent. The results demonstrated that the SARS-CoV-2 shows the lowest memory in its genome walk, explaining the errors in copying the sequences along the genome that results in the virus mutation.

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Dissimilar Ligands Bind in a Similar Fashion: A Guide to Ligand Binding-Mode Prediction with Application to CELPP Studies

International Journal of Molecular Sciences ◽

10.3390/ijms222212320 ◽

2021 ◽

Vol 22 (22) ◽

pp. 12320

Author(s):

Xianjin Xu ◽

Xiaoqin Zou

Keyword(s):

Molecular Similarity ◽

Complex Structure ◽

Binding Mode ◽

Molecular Structures ◽

Complex Structures ◽

Binding Modes ◽

Ligand Complex ◽

Systematic Analysis ◽

Binding Mode Prediction ◽

Similarity Principle

The molecular similarity principle has achieved great successes in the field of drug design/discovery. Existing studies have focused on similar ligands, while the behaviors of dissimilar ligands remain unknown. In this study, we developed an intercomparison strategy in order to compare the binding modes of ligands with different molecular structures. A systematic analysis of a newly constructed protein–ligand complex structure dataset showed that ligands with similar structures tended to share a similar binding mode, which is consistent with the Molecular Similarity Principle. More importantly, the results revealed that dissimilar ligands can also bind in a similar fashion. This finding may open another avenue for drug discovery. Furthermore, a template-guiding method was introduced for predicting protein–ligand complex structures. With the use of dissimilar ligands as templates, our method significantly outperformed the traditional molecular docking methods. The newly developed template-guiding method was further applied to recent CELPP studies.

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Kinetic electronics: Monolithic processing of a layered flexible robotic actuator film for simple film microrobot fabrication

10.21203/rs.3.rs-546958/v1 ◽

2021 ◽

Author(s):

Shiyi Zhang ◽

Joseph Wang ◽

Kenshi Hayashi ◽

Fumihiro Sassa

Keyword(s):

Mass Production ◽

Degrees Of Freedom ◽

Complex Structure ◽

Robotic Systems ◽

Durability Test ◽

Electrical Circuits ◽

Multiple Degrees Of Freedom ◽

The Past ◽

Cmos Compatible ◽

Simple Film

Abstract Low-invasive soft robotic techniques can potentially be used for developing next-generation body–machine interfaces. Most soft robots require complicated fabrication processes involving 3D printing and bonding/assembling. In this letter, we describe a monolithic soft microrobot fabrication process for the mass production of soft film robots with a complex structure by simple 2D processing of a robotic actuator film. The 45 μg/mm^2 lightweight film robot can be driven at a voltage of CMOS compatible 5 V with 0.15 mm^-1 large curvature changes; it can generate a force 5.7 times greater than its self-weight. In a durability test, actuation could be carried out over 8000 times without degradation. To further demonstrate this technique, three types of film robots with multiple degrees of freedom and moving illuminator robot were fabricated. This technique can easily integrate various electrical circuits developed in the past to robotic systems and can be used for developing advanced wearable sensing devices; It can be called “Kinetic electronics.”

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