scholarly journals Trees with Minimum Weighted Szeged Index Are of a Large Diameter

Symmetry ◽  
2020 ◽  
Vol 12 (5) ◽  
pp. 793
Author(s):  
Risto Atanasov ◽  
Boris Furtula ◽  
Riste Škrekovski
Keyword(s):  
Maximum Degree ◽  
Large Diameter ◽  
Minimal Tree ◽  
Szeged Index ◽  
Mathematical Properties ◽  
Structural Details

The weighted Szeged index ( w S z ) has gained considerable attention recently because of its unusual mathematical properties. Searching for a tree (or trees) that minimizes the w S z is still going on. Several structural details of a minimal tree were described. Here, it is shown a surprising property that these trees have maximum degree at most 16, and as a consequence, we promptly conclude that these trees are of large diameter.

scholarly journals Bounds for symmetric division deg index of graphs

Filomat ◽  
2019 ◽  
Vol 33 (3) ◽  
pp. 683-698 ◽  
Author(s):  
Kinkar Das ◽  
Marjan Matejic ◽  
Emina Milovanovic ◽  
Igor Milovanovic
Keyword(s):  
Connected Graph ◽  
Maximum Degree ◽  
Topological Index ◽  
Minimum Degree ◽  
Topological Indices ◽  
Symmetric Division ◽  
Mathematical Properties ◽  
Vertex Degrees ◽  
Additive Modeling ◽  
Simple Connected Graph

LetG = (V,E) be a simple connected graph of order n (?2) and size m, where V(G) = {1, 2,..., n}. Also let ? = d1 ? d2 ?... ? dn = ? > 0, di = d(i), be a sequence of its vertex degrees with maximum degree ? and minimum degree ?. The symmetric division deg index, SDD, was defined in [D. Vukicevic, Bond additive modeling 2. Mathematical properties of max-min rodeg index, Croat. Chem. Acta 83 (2010) 261- 273] as SDD = SDD(G) = ?i~j d2i+d2j/didj, where i~j means that vertices i and j are adjacent. In this paper we give some new bounds for this topological index. Moreover, we present a relation between topological indices of graph.

Anchoring Fibrils in Arterial Endothelium

1969 ◽  
Vol 27 ◽  
pp. 274-275
Author(s):  
A. Trillo
Keyword(s):  
Carotid Arteries ◽  
Animal Species ◽  
Cell Layer ◽  
Present Communication ◽  
Internal Elastic Lamina ◽  
Endothelial Cell Layer ◽  
Structural Details ◽  
Rats And Mice ◽  
Arterial Endothelium ◽  
Elastic Lamina

There are conflicting reports regarding some fine structural details of arteries from several animal species. Buck denied the existence of a sub-endothelial space, while Karrer and Keech described a space of variable width which separates the endothelium from the underlying internal elastic lamina in aortas of aging rats and mice respectively.The present communication deals with the ultrastrueture of the interface between the endothelial cell layer and the internal elastic lamina as observed in carotid arteries from rabbits of varying ages.

Annulate lamellae in the Sertoli cells of guinea pig testis after unilateral torsion of the spermatic cord

1984 ◽  
Vol 42 ◽  
pp. 196-197
Author(s):  
J. Chakraborty ◽  
A. P. Sinha Hikim ◽  
J. S. Jhunjhunwala
Keyword(s):  
Sertoli Cells ◽  
Guinea Pigs ◽  
Spermatic Cord ◽  
Present Report ◽  
Cell Types ◽  
Annulate Lamellae ◽  
Spermatogenic Cells ◽  
Electron Microscopic ◽  
Structural Details ◽  
First Time

Although the presence of annulate lamellae was noted in many cell types, including the rat spermatogenic cells, this structure was never reported in the Sertoli cells of any rodent species. The present report is based on a part of our project on the effect of torsion of the spermatic cord to the contralateral testis. This paper describes for the first time, the fine structural details of the annulate lamellae in the Sertoli cells of damaged testis from guinea pigs.One side of the spermatic cord of each of six Hartly strain adult guinea pigs was surgically twisted (540°) under pentobarbital anesthesia (1). Four months after induction of torsion, animals were sacrificed, testes were excised and processed for the light and electron microscopic investigations. In the damaged testis, the majority of seminiferous tubule contained a layer of Sertoli cells with occasional spermatogonia (Fig. 1). Nuclei of these Sertoli cells were highly pleomorphic and contained small chromatinic clumps adjacent to the inner aspect of the nuclear envelope (Fig. 2).

Development of a digital SEM

1991 ◽  
Vol 49 ◽  
pp. 358-359
Author(s):  
A. Yamada ◽  
A. Shibano ◽  
K. Harasawa ◽  
T. Kobayashi ◽  
H. Fukuda ◽  
...  
Keyword(s):  
Large Diameter ◽  
Objective Lens ◽  
Large Specimen ◽  
Backscattered Electrons ◽  
Digital Scanning ◽  
Junction Type ◽  
High Resolution Images ◽  
Working Distance ◽  
Type Detector ◽  
Short Working

A newly developed digital scanning electron microscope, the JSM-6300, has the following features: Equipped with a narrower conical objective lens (OL), it allows high resolution images to be obtained easily at a short working distance (WD) and a large specimen tilt angle. In addition, it is provided with automatic functions and digital image processing functions for ease of operation.Conical C-F lens: The newly developed conical C-F objective lens, having low aberration characteristics over a wide WD range, allows a large-diameter (3-inch) specimen to be tilted up to 60° at short WD, and provides images with low magnifications starting at 10*. On the bottom of the lens, a p n junction type detector is provided to detect backscattered electrons (BE) from the specimen. As the narrower conical 0L increases the secondary electron (SE) detector's field intensity on the specimen surface, high SE image quality is obtained.

Detection of viruses by electron microscopy: Increased sensitivity by direct micro-ultracentrifugation of samples

1987 ◽  
Vol 45 ◽  
pp. 908-909
Author(s):  
Alain R. Trudel ◽  
M. Trudel
Keyword(s):  
Electron Microscopy ◽  
Fold Increase ◽  
Observation Time ◽  
Clinical Samples ◽  
Maximum Speed ◽  
Viral Particles ◽  
Structural Details ◽  
Latex Spheres ◽  
Increased Sensitivity ◽  
Size Of Particles

AirfugeR (Beckman) direct ultracentrifugation of viral samples on electron microscopy grids offers a rapid way to concentrate viral particles or subunits and facilitate their detection and study. Using the A-100 fixed angle rotor (30°) with a K factor of 19 at maximum speed (95 000 rpm), samples up to 240 μl can be prepared for electron microscopy observation in a few minutes: observation time is decreased and structural details are highlighted. Using latex spheres to calculate the increase in sensitivity compared to the inverted drop procedure, we obtained a 10 to 40 fold increase in sensitivity depending on the size of particles. This technique also permits quantification of viral particles in samples if an aliquot is mixed with latex spheres of known concentration.Direct ultracentrifugation for electron microscopy can be performed on laboratory samples such as gradient or column fractions, infected cell supernatant, or on clinical samples such as urine, tears, cephalo-rachidian liquid, etc..

The restoration of blurred electron micrographs

1986 ◽  
Vol 44 ◽  
pp. 180-181
Author(s):  
Bridget Carragher ◽  
David A. Bluemke ◽  
Michael J. Potel ◽  
Robert Josephs
Keyword(s):  
Cross Section ◽  
Electron Micrographs ◽  
Relative Motion ◽  
Finite Thickness ◽  
Image Plane ◽  
Helical Axis ◽  
Thin Sections ◽  
Structural Details

We have investigated the feasibility of restoring blurred electron micrographs. Two related problems have been considered; the restoration of images blurred as a result of relative motion between the specimen and the image plane, and the restoration of images which are rotationally blurred about an axis. Micrographs taken while the specimen is drifting result in images which are blurred in the direction of motion. An example of rotational blurring arises in micrographs of thin sections of helical particles viewed in cross section. The twist of the particle within the finite thickness of the section causes the image to appear rotationally blurred about the helical axis. As a result, structural details, particularly at large distances from the helical axis, will be obscured.

Three dimensional deblurring of transmitted-light brightfield micrographs

1993 ◽  
Vol 51 ◽  
pp. 564-565
Author(s):  
Santosh Bhattacharyya
Keyword(s):  
Image Reconstruction ◽  
Three Dimensional ◽  
Transmitted Light ◽  
Reconstruction Algorithms ◽  
3D Image Reconstruction ◽  
Structural Details ◽  
Spread Function ◽  
Early Testing ◽  
Linearized Model ◽  
Image Reconstruction Algorithms

Three dimensional microscopic structures play an important role in the understanding of various biological and physiological phenomena. Structural details of neurons, such as the density, caliber and volumes of dendrites, are important in understanding physiological and pathological functioning of nervous systems. Even so, many of the widely used stains in biology and neurophysiology are absorbing stains, such as horseradish peroxidase (HRP), and yet most of the iterative, constrained 3D optical image reconstruction research has concentrated on fluorescence microscopy. It is clear that iterative, constrained 3D image reconstruction methodologies are needed for transmitted light brightfield (TLB) imaging as well. One of the difficulties in doing so, in the past, has been in determining the point spread function of the system.We have been developing several variations of iterative, constrained image reconstruction algorithms for TLB imaging. Some of our early testing with one of them was reported previously. These algorithms are based on a linearized model of TLB imaging.

Role of the Small (40S) Subunits in the Structure of the Interface of Eukaryotic Ribosomes

1980 ◽  
Vol 38 ◽  
pp. 548-549
Author(s):  
M. Boublik ◽  
N. Robakis ◽  
W. Hellmann ◽  
F. Jenkins
Keyword(s):  
Structural Similarity ◽  
High Resolution Electron Microscopy ◽  
Peptide Bond ◽  
Uranyl Acetate ◽  
Mutual Orientation ◽  
Mutual Position ◽  
Peptide Bond Formation ◽  
Resolution Electron ◽  
Direct Technique ◽  
Structural Details

Ribosomes are ribonucleoprotein particles which process the genetic information coded in mRNA into protein synthesis. The analogy in function and composition of ribosomes from various sources, both prokaryotic and eukaryo-tic, imply a structural similarity. At present, high resolution electron microscopy is the most direct technique with a potential to resolve the extent of the structural homology of ribosomal particles at a macromolecular level. The structure of ribosomes is highly complex as a result of the large number of their constituents. In general, 80S eukaryotic monosomes consist of two uneven subunits - large (60S) and small (40S) - accomodating four different RNAs and approximately 80 different proteins. Mutual orientation of both subunits on the monosome is of particular interest because it determines the interface, the supposed site of interactions of ribosomes with other macro-molecules involved in peptide bond formation. Since entrapping of the contrasting solution (0.5% aqueous uranyl acetate) obscures all structural details in the interface, information on its architecture is limited to an indirect reconstruction based on the established 3-D structure of both sub-units and their mutual position after association.

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