Strained Configurations in Three-Dimensional Analogues of Kekulé-Type Structures for Deltahedral Boranes

2002 ◽  
Vol 67 (6) ◽  
pp. 751-768 ◽  
Author(s):  
R. Bruce King
Keyword(s):  
Symmetry Group ◽  
Three Dimensional ◽  
Wide Distribution ◽  
Kekulé Structure ◽  
Kekulé Structures ◽  
Benzenoid Hydrocarbons ◽  
Localized Structures ◽  
Minimum Number ◽  
Excessive Strain ◽  
Partial Retention

Localized structures analogous to the Kekulé structures for benzenoid hydrocarbons can be constructed for the deltahedral boranes BnHn2-. These localized structures contain exactly three two-center two-electron (2c-2e) B-B bonds and n - 2 three-center two-electron (3c-2e) B-B-B bonds. The number of equivalent such Kekulé-type structures corresponds to the index of the symmetry group of the Kekulé structure, K, in the symmetry group, D, of the deltahedron. Three-dimensional Kekulé-type structures with the following configurations exhibit excessive strain and are therefore unfavorable: (i) structures having one or more pairs of boron atoms connected simultaneously by a 2c-2e B-B bond and a 3c-2e B-B-B bond (violation of the O'Neill-Wade restrictions); (ii) structures in which the three 2c-2e B-B bonds are excessively concentrated occupying only three or four vertices (the undesirable ∆, U, and Y configurations). Computations by Lipscomb and coworkers with partial retention of diatomic differential overlap (PRDDO) suggest that wide distribution of the three 2c-2e B-B bonds throughout the deltahedron and a minimum number of empty faces are more important than maximum symmetry in leading to the most favorable Kekulé-type structure.

scholarly journals Three-dimensional assessment of the anterior and inferior loop of the inferior alveolar nerve using computed tomography images in patients with and without mandibular asymmetry

2021 ◽  
Vol 21 (1) ◽  
Author(s):  
Jae-Young Kim ◽  
Michael D. Han ◽  
Kug Jin Jeon ◽  
Jong-Ki Huh ◽  
Kwang-Ho Park
Keyword(s):  
Computed Tomography ◽  
Symmetry Group ◽  
Three Dimensional ◽  
Inferior Alveolar Nerve ◽  
Mental Foramen ◽  
3D Analysis ◽  
Mandibular Asymmetry ◽  
Computed Tomography Images ◽  
Significant Difference ◽  
Mandibular Body

Abstract Background The purpose of this study was to investigate the differences in configuration and dimensions of the anterior loop of the inferior alveolar nerve (ALIAN) in patients with and without mandibular asymmetry. Method Preoperative computed tomography images of patients who had undergone orthognathic surgery from January 2016 to December 2018 at a single institution were analyzed. Subjects were classified into two groups as “Asymmetry group” and “Symmetry group”. The distance from the most anterior and most inferior points of the ALIAN (IANant and IANinf) to the vertical and horizontal reference planes were measured (dAnt and dInf). The distance from IANant and IANinf to the mental foramen were also calculated (dAnt_MF and dInf_MF). The length of the mandibular body and symphysis area were measured. All measurements were analyzed using 3D analysis software. Results There were 57 total eligible subjects. In the Asymmetry group, dAnt and dAnt_MF on the non-deviated side were significantly longer than the deviated side (p < 0.001). dInf_MF on the non-deviated side was also significantly longer than the deviated side (p = 0.001). Mandibular body length was significantly longer on the non-deviated side (p < 0.001). There was no significant difference in length in the symphysis area (p = 0.623). In the Symmetry group, there was no difference between the left and right sides for all variables. Conclusion In asymmetric patients, there is a difference tendency in the ALIAN between the deviated and non-deviated sides. In patients with mandibular asymmetry, this should be considered during surgery in the anterior mandible.

scholarly journals Estimating tree stem diameters and volume from smartphone photogrammetric point clouds

2019 ◽  
Vol 93 (3) ◽  
pp. 411-429 ◽  
Author(s):  
Maria Immacolata Marzulli ◽  
Pasi Raumonen ◽  
Roberto Greco ◽  
Manuela Persia ◽  
Patrizia Tartarino
Keyword(s):  
Low Cost ◽  
Three Dimensional ◽  
Laser Scanner ◽  
Point Clouds ◽  
Stem Volume ◽  
Forest Plot ◽  
3D Point Clouds ◽  
Dense Point ◽  
Minimum Number ◽  
Scale Point

Abstract Methods for the three-dimensional (3D) reconstruction of forest trees have been suggested for data from active and passive sensors. Laser scanner technologies have become popular in the last few years, despite their high costs. Since the improvements in photogrammetric algorithms (e.g. structure from motion—SfM), photographs have become a new low-cost source of 3D point clouds. In this study, we use images captured by a smartphone camera to calculate dense point clouds of a forest plot using SfM. Eighteen point clouds were produced by changing the densification parameters (Image scale, Point density, Minimum number of matches) in order to investigate their influence on the quality of the point clouds produced. In order to estimate diameter at breast height (d.b.h.) and stem volumes, we developed an automatic method that extracts the stems from the point cloud and then models them with cylinders. The results show that Image scale is the most influential parameter in terms of identifying and extracting trees from the point clouds. The best performance with cylinder modelling from point clouds compared to field data had an RMSE of 1.9 cm and 0.094 m3, for d.b.h. and volume, respectively. Thus, for forest management and planning purposes, it is possible to use our photogrammetric and modelling methods to measure d.b.h., stem volume and possibly other forest inventory metrics, rapidly and without felling trees. The proposed methodology significantly reduces working time in the field, using ‘non-professional’ instruments and automating estimates of dendrometric parameters.

Truss and Beam Finite Elements Revisited: A Derivation Based on Displacement-Field Decomposition

1996 ◽  
Vol 11 (4) ◽  
pp. 371-380 ◽  
Author(s):  
Alphose Zingoni
Keyword(s):  
Finite Element ◽  
Finite Elements ◽  
Symmetry Group ◽  
Displacement Field ◽  
Three Dimensional ◽  
Beam Elements ◽  
Symmetry Properties ◽  
Mass Matrices ◽  
General Displacement

Where a finite element possesses symmetry properties, derivation of fundamental element matrices can be achieved more efficiently by decomposing the general displacement field into subspaces of the symmetry group describing the configuration of the element. In this paper, the procedure is illustrated by reference to the simple truss and beam elements, whose well-known consistent-mass matrices are obtained via the proposed method. However, the procedure is applicable to all one-, two- and three-dimensional finite elements, as long as the shape and node configuration of the element can be described by a specific symmetry group.

scholarly journals Three dimensional pure gravity and generalized Hecke operators

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
M. Ashrafi
Keyword(s):  
Symmetry Group ◽  
Central Charge ◽  
Three Dimensional ◽  
Gravitational Theory ◽  
Hecke Operators ◽  
Simons Theory ◽  
Partition Functions ◽  
Integer Multiple ◽  
Pure Gravity ◽  
Modular Covariance

Abstract In this paper, we study mathematical functions of relevance to pure gravity in AdS3. Modular covariance places stringent constraints on the space of such functions; modular invariance places even stronger constraints on how they may be combined into physically viable candidate partition functions. We explicitly detail the list of holomorphic and anti-holomorphic functions that serve as candidates for chiral and anti-chiral partition functions and note that modular covariance is only consistent with such functions when the left (resp. right) central charge is an integer multiple of 8, c ∈ 8ℕ. We then find related constraints on the symmetry group of the corresponding topological, Chern-Simons, theory in the bulk of AdS. The symmetry group of the theory can be one of two choices: either SO(2; 1) × SO(2; 1) or its three-fold diagonal cover. We introduce the generalized Hecke operators which map the modular covariant functions to the modular covariant functions. With these mathematical results, we obtain conjectural partition functions for extremal CFT2s, and the corresponding microcanonical entropies, when the chiral central charges are multiples of eight. Finally, we compute subleading corrections to the Beckenstein-Hawking entropy in the bulk gravitational theory with these conjectural partition functions.

scholarly journals Adenine DNA methylation, 3D genome organization, and gene expression in the parasiteTrichomonas vaginalis

2020 ◽  
Vol 117 (23) ◽  
pp. 13033-13043
Author(s):  
Ayelen Lizarraga ◽  
Zach Klapholz O’Brown ◽  
Konstantinos Boulias ◽  
Lara Roach ◽  
Eric Lieberman Greer ◽  
...  
Keyword(s):  
Gene Expression ◽  
Dna Methylation ◽  
Trichomonas Vaginalis ◽  
Three Dimensional ◽  
Wide Distribution ◽  
Spatial Proximity ◽  
Regulation Of Transcription ◽  
3D Genome ◽  
Intergenic Regions ◽  
Close Spatial Proximity

Trichomonas vaginalisis a common sexually transmitted parasite that colonizes the human urogenital tract causing infections that range from asymptomatic to highly inflammatory. Recent works have highlighted the importance of histone modifications in the regulation of transcription and parasite pathogenesis. However, the nature of DNA methylation in the parasite remains unexplored. Using a combination of immunological techniques and ultrahigh-performance liquid chromatography (UHPLC), we analyzed the abundance of DNA methylation in strains with differential pathogenicity demonstrating that N6-methyladenine (6mA), and not 5‐methylcytosine (5mC), is the main DNA methylation mark inT. vaginalis. Genome-wide distribution of 6mA reveals that this mark is enriched at intergenic regions, with a preference for certain superfamilies of DNA transposable elements. We show that 6mA inT. vaginalisis associated with silencing when present on genes. Interestingly, bioinformatics analysis revealed the presence of transcriptionally active or repressive intervals flanked by 6mA-enriched regions, and results from chromatin conformation capture (3C) experiments suggest these 6mA flanked regions are in close spatial proximity. These associations were disrupted when parasites were treated with the demethylation activator ascorbic acid. This finding revealed a role for 6mA in modulating three-dimensional (3D) chromatin structure and gene expression in this divergent member of the Excavata.

scholarly journals Analysis of the three dimensional structure of the kidney glomerulus capillary network

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Mark Terasaki ◽  
Jason Cory Brunson ◽  
Justin Sardi
Keyword(s):  
3D Structure ◽  
Three Dimensional ◽  
The Body ◽  
Capillary Network ◽  
Dimensional Structure ◽  
Pixel Resolution ◽  
Longitudinal Splitting ◽  
Kidney Glomerulus ◽  
Minimum Number ◽  
Glomerular Size

AbstractThe capillary network of the kidney glomerulus filters small molecules from the blood. The glomerular 3D structure should help to understand its function, but it is poorly characterized. We therefore devised a new approach in which an automated tape collecting microtome (ATUM) was used to collect 0.5 μm thick serial sections from fixed mouse kidneys. The sections were imaged by scanning electron microscopy at ~ 50 nm/pixel resolution. With this approach, 12 glomeruli were reconstructed at an x–y–z resolution ~ 10 × higher than that of paraffin sections. We found a previously undescribed no-cross zone between afferent and efferent branches on the vascular pole side; connections here would allow blood to exit without being adequately filtered. The capillary diameters throughout the glomerulus appeared to correspond with the amount of blood flow within them. The shortest path (minimum number of branches to travel from afferent to efferent arterioles) is relatively independent of glomerular size and is present primarily on the vascular pole size. This suggests that new branches and longer paths form on the urinary pole side. Network analysis indicates that the glomerular network does not form by repetitive longitudinal splitting of capillaries. Thus the 3D structure of the glomerular capillary network provides useful information with which to understand glomerular function. Other tissue structures in the body may benefit from this new three dimensional approach.

Enumeration of branched catacondensed benzenoid hydrocarbons and their numbers of kekulé structures

Tetrahedron ◽  
1988 ◽  
Vol 44 (1) ◽  
pp. 221-228 ◽  
Author(s):  
A.T. Balaban ◽  
J. Brunvoll ◽  
B.N. Cyvin ◽  
S.J. Cyvin
Keyword(s):  
Kekulé Structures ◽  
Benzenoid Hydrocarbons

Calculating the Determinant of the Adjacency Matrix and Counting Kekulé Structures in Circulenes

1994 ◽  
Vol 49 (11) ◽  
pp. 1053-1058
Author(s):  
I. Gutman ◽  
Y.-N. Yeh ◽  
S.-L. Lee ◽  
H. Hosoya ◽  
S. J. Cyvin
Keyword(s):  
Algebraic Structure ◽  
Adjacency Matrix ◽  
Fibonacci Numbers ◽  
Kekulé Structure ◽  
Kekulé Structures ◽  
Structure Count

Abstract The determinant of the adjacentcy matrix, the algebraic structure count and the Kekulé structure count of circulenes are shown to conform to simple expressions containing Fibonacci numbers.

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