scholarly journals Group actions, non-Kähler complex manifolds and SKT structures

2018 ◽  
Vol 5 (1) ◽  
pp. 9-25
Author(s):  
Mainak Poddar ◽  
Ajay Singh Thakur
Keyword(s):  
Principal Bundle ◽  
Complex Structure ◽  
Total Space ◽  
Structure Group ◽  
Characteristic Classes ◽  
Complex Structures ◽  
Complex Manifolds ◽  
Compact Lie Groups ◽  
Large Classes ◽  
Torus Bundles

AbstractWe give a construction of integrable complex structures on the total space of a smooth principal bundle over a complex manifold, with an even dimensional compact Lie group as structure group, under certain conditions. This generalizes the constructions of complex structure on compact Lie groups by Samelson and Wang, and on principal torus bundles by Calabi-Eckmann and others. It also yields large classes of new examples of non-Kähler compact complex manifolds. Moreover, under suitable restrictions on the base manifold, the structure group, and characteristic classes, the total space of the principal bundle admits SKT metrics. This generalizes recent results of Grantcharov et al. We study the Picard group and the algebraic dimension of the total space in some cases. We also use a slightly generalized version of the construction to obtain (non-Kähler) complex structures on tangential frame bundles of complex orbifolds.

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

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

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

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.

scholarly journals SCATTERING, GREEN’S FUNCTIONS AND SYMMETRIES IN A TOTAL SPACE OF A DIRAC MONOPOLE FIBRE BUNDLE

1991 ◽  
Vol 06 (04) ◽  
pp. 577-598 ◽  
Author(s):  
A.G. SAVINKOV ◽  
A.B. RYZHOV
Keyword(s):  
Green's Functions ◽  
Principal Bundle ◽  
Fibre Bundle ◽  
Green’S Functions ◽  
Wave Functions ◽  
Total Space ◽  
Dirac Monopole ◽  
Hidden Symmetries ◽  
Scattering Wave ◽  
A Charge

The scattering wave functions and Green’s functions were found in a total space of a Dirac monopole principal bundle. Also, hidden symmetries of a charge-Dirac monopole system and those joining the states relating to different topological charges n=2eg were found.

scholarly journals Deformation quantization of principal bundles

2016 ◽  
Vol 13 (08) ◽  
pp. 1630010
Author(s):  
Paolo Aschieri
Keyword(s):  
Quantum Group ◽  
Deformation Quantization ◽  
Principal Bundle ◽  
Base Space ◽  
Structure Group ◽  
Galois Extensions ◽  
Principal Bundles ◽  
Group Of Automorphisms ◽  
Drinfeld Twist

We outline how Drinfeld twist deformation techniques can be applied to the deformation quantization of principal bundles into noncommutative principal bundles and, more in general, to the deformation of Hopf–Galois extensions. First, we twist deform the structure group in a quantum group, and this leads to a deformation of the fibers of the principal bundle. Next, we twist deform a subgroup of the group of automorphisms of the principal bundle, and this leads to a noncommutative base space. Considering both deformations, we obtain noncommutative principal bundles with noncommutative fiber and base space as well.

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

Fractals ◽  
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.

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

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.

Response of Complex Structures From Reed-Gage Data

1958 ◽  
Vol 25 (4) ◽  
pp. 501-508
Author(s):  
Sheldon Rubin
Keyword(s):  
Vibrational Mode ◽  
Complex Structure ◽  
Structural Response ◽  
Complex Structures ◽  
General Applicability ◽  
Single Degree Of Freedom ◽  
Peak Response ◽  
Transient Motion ◽  
Single Degree ◽  
Recorded Data

Abstract The paper considers the general applicability of the reed gage, an instrument which records the peak response to a transient motion of single-degree-of-freedom systems. These recorded data permit the calculation of peak response in each vibrational mode of a complex structure experiencing the measured excitation as a base motion. An upper bound to the maximum structural response can be obtained by summing the peak responses in each of the modes. An analysis is made of the error inherent in this superposition process. In many practical problems the distribution of mode frequencies and the form of the excitation are such that this error is not of great significance.

Basic Forms

2020 ◽  
pp. 97-102
Author(s):  
Loring W. Tu
Keyword(s):  
Lie Group ◽  
Principal Bundle ◽  
Differential Forms ◽  
Total Space ◽  
Lie Derivative ◽  
Connected Lie Group

This chapter describes basic forms. On a principal bundle π‎: P → M, the differential forms on P that are pullbacks of forms ω‎ on the base M are called basic forms. The chapter characterizes basic forms in terms of the Lie derivative and interior multiplication. It shows that basic forms on a principal bundle are invariant and horizontal. To understand basic forms better, the chapter considers a simple example. The plane ℝ2 may be viewed as the total space of a principal ℝ-bundle. A connected Lie group is generated by any neighborhood of the identity. This example shows the necessity of the connectedness hypothesis.

Homotopy Quotients and Equivariant Cohomology

2020 ◽  
pp. 29-38
Author(s):  
Loring W. Tu
Keyword(s):  
Topological Group ◽  
Fiber Bundle ◽  
Equivariant Cohomology ◽  
Principal Bundle ◽  
Total Space

This chapter investigates two candidates for equivariant cohomology and explains why it settles on the Borel construction, also called Cartan's mixing construction. Let G be a topological group and M a left G-space. The Borel construction mixes the weakly contractible total space of a principal bundle with the G-space M to produce a homotopy quotient of M. Equivariant cohomology is the cohomology of the homotopy quotient. More generally, given a G-space M, Cartan's mixing construction turns a principal bundle with fiber G into a fiber bundle with fiber M. Cartan's mixing construction fits into the Cartan's mixing diagram, a powerful tool for dealing with equivariant cohomology.

scholarly journals BRANCHED SHADOWS AND COMPLEX STRUCTURES ON 4-MANIFOLDS

2008 ◽  
Vol 17 (11) ◽  
pp. 1429-1454 ◽  
Author(s):  
FRANCESCO COSTANTINO
Keyword(s):  
Complex Structure ◽  
Complex Structures ◽  
Almost Complex Structure ◽  
Homotopy Classes ◽  
Almost Complex Structures ◽  
Almost Complex

We define and study branched shadows of 4-manifolds as a combination of branched spines of 3-manifolds and of Turaev's shadows. We use these objects to combinatorially represent 4-manifolds equipped with Spinc-structures and homotopy classes of almost complex structures. We then use branched shadows to study complex 4-manifolds and prove that each almost complex structure on a 4-dimensional handlebody is homotopic to a complex one.

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