scholarly journals Complex geometry of nuclei and atoms

2018 ◽  
Vol 33 (24) ◽  
pp. 1830022
Author(s):  
M. F. Atiyah ◽  
N. S. Manton
Keyword(s):  
Complex Geometry ◽  
Betti Numbers ◽  
Geometrical Model ◽  
Algebraic Surfaces ◽  
Finite Range ◽  
Neutral Atoms ◽  
Proton Number ◽  
Chern Numbers ◽  
Geometrical Constraints ◽  
Hodge Numbers

We propose a new geometrical model of matter, in which neutral atoms are modelled by compact, complex algebraic surfaces. Proton and neutron numbers are determined by a surface’s Chern numbers. Equivalently, they are determined by combinations of the Hodge numbers, or the Betti numbers. Geometrical constraints on algebraic surfaces allow just a finite range of neutron numbers for a given proton number. This range encompasses the known isotopes.

scholarly journals On Algebraic Surfaces Associated with Line Arrangements

2019 ◽  
Vol 71 (2) ◽  
pp. 471-499
Author(s):  
Zhenjian Wang
Keyword(s):  
General Type ◽  
Algebraic Surfaces ◽  
Minimal Resolution ◽  
Complex Projective Plane ◽  
Line Arrangement ◽  
Milnor Fiber ◽  
Chern Numbers ◽  
Hodge Numbers ◽  
Triple Points ◽  
Complex Projective

AbstractFor a line arrangement ${\mathcal{A}}$ in the complex projective plane $\mathbb{P}^{2}$, we investigate the compactification $\overline{F}$ in $\mathbb{P}^{3}$ of the affine Milnor fiber $F$ and its minimal resolution $\tilde{F}$. We compute the Chern numbers of $\tilde{F}$ in terms of the combinatorics of the line arrangement ${\mathcal{A}}$. As applications of the computation of the Chern numbers, we show that the minimal resolution is never a quotient of a ball; in addition, we also prove that $\tilde{F}$ is of general type when the arrangement has only nodes or triple points as singularities. Finally, we compute all the Hodge numbers of some $\tilde{F}$ by using some knowledge about the Milnor fiber monodromy of the arrangement.

scholarly journals Dimensional Structural Mass Optimization of a Welded I-Profile Bridge Crane Girder

2020 ◽  
Vol 14 (2) ◽  
pp. 186-193
Author(s):  
Nedim Pervan ◽  
Adis J. Muminovic ◽  
Elmedin Mesic ◽  
Mirsad Colic ◽  
Vahidin Hadziabdic
Keyword(s):  
Optimization Model ◽  
Geometrical Model ◽  
Optimization Process ◽  
Design Parameters ◽  
Minimal Amount ◽  
Bridge Crane ◽  
Analysis Model ◽  
Geometrical Constraints ◽  
Minimal Mass ◽  
Structural Mass

This paper presents the methodology for the development of an optimization model for the optimization of the cross-section dimensions of a bridge crane girder designed as a welded I-profile. To carry out this optimization, the CAD/CAE software package CATIA V5 was used. In order to develop an optimization model, a CAD geometrical model and structural analysis model were developed. Optimization was carried out by the iterative method using a simulated hardening algorithm. Additionally, the optimization process is carried out by using the PEO (Product Engineering Optimization) CATIA module that contains tools for setting the optimization criteria, design parameters, constraints, and algorithms. The goal of the optimization is to achieve the minimal mass of the girder, while satisfying all functional and geometrical constraints. As a result of the optimization process, minimal girder dimensions were obtained and due to that, a minimal amount of material can be used for the manufacturing of the girder.

scholarly journals Chern numbers of algebraic surfaces

1984 ◽  
Vol 266 (3) ◽  
pp. 351-356 ◽  
Author(s):  
F. Hirzebruch
Keyword(s):  
Algebraic Surfaces ◽  
Chern Numbers

scholarly journals Hodge polynomials of the SL(2, ℂ)-character variety of an elliptic curve with two marked points

2014 ◽  
Vol 25 (14) ◽  
pp. 1450125 ◽  
Author(s):  
Marina Logares ◽  
Vicente Muñoz
Keyword(s):  
Elliptic Curve ◽  
Moduli Space ◽  
Betti Numbers ◽  
Conjugacy Classes ◽  
Character Variety ◽  
Higgs Bundles ◽  
Hodge Numbers ◽  
Hodge Polynomials ◽  
Marked Points

We compute the Hodge polynomials for the moduli space of representations of an elliptic curve with two marked points into SL(2, ℂ). When we fix the conjugacy classes of the representations around the marked points to be diagonal and of modulus one, the character variety is diffeomorphic to the moduli space of strongly parabolic Higgs bundles, whose Betti numbers are known. In that case we can recover some of the Hodge numbers of the character variety. We extend this result to the moduli space of doubly periodic instantons.

scholarly journals PRELAUNCH PHOTOGRAMMETRIC CALIBRATION OF RUSSIAN SATELLITE ELEKTRO-L IMAGERY INSTRUMENTS

2016 ◽  
Vol XLI-B6 ◽  
pp. 161-163
Author(s):  
U. M. Gektin ◽  
N. A. Egoshkin ◽  
V. V. Eremeev ◽  
A. E. Kuznetcov ◽  
A. M. Kochergin
Keyword(s):  
Complex Geometry ◽  
Control Point ◽  
Geometrical Model ◽  
Design Parameters ◽  
Test Field ◽  
Control Points ◽  
Geometric Calibration ◽  
Multiple Observations ◽  
Point Detection ◽  
Mirror Motion

Technology of prelaunch geometric calibration of multispectral imagery instruments of Russian geostationary satellites “Elektro-L” No.1 and No.2 is considered. Circular control points are used as a test field. Its geometrical model is developed to take distortions in the collimator optical system into account. Multiple observations of a test field at different angles is used to cover the full visual field of a geostationary sensor. New algorithm of circular control point detection is developed and adapted to complex geometry of geostationary imagery. It is capable of processing images formed as a set of separate scans. Under calibration, sensor design parameters and also the law of scanning mirror motion are specified. The paper contains results of the technology approval under prelaunch calibration of MSU-GS sensors for geostationary operational meteorological satellites (GOMS) “Elektro-L” No.1 and No.2.

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