scholarly journals Extending the Characteristic Polynomial for Characterization of C20 Fullerene Congeners

Mathematics ◽  
2017 ◽  
Vol 5 (4) ◽  
pp. 84 ◽  
Author(s):  
Dan-Marian Joiţa ◽  
Lorentz Jäntschi
Keyword(s):  
Characteristic Polynomial ◽  
C20 Fullerene

scholarly journals From Fibonacci Sequence to the Golden Ratio

2013 ◽  
Vol 2013 ◽  
pp. 1-3 ◽  
Author(s):  
Alberto Fiorenza ◽  
Giovanni Vincenzi
Keyword(s):  
Characteristic Polynomial ◽  
Golden Ratio ◽  
Fibonacci Sequence ◽  
Maximum Modulus ◽  
Point Of View ◽  
General Point ◽  
Constant Coefficients ◽  
The Difference ◽  
New Perspective

We consider the well-known characterization of the Golden ratio as limit of the ratio of consecutive terms of the Fibonacci sequence, and we give an explanation of this property in the framework of the Difference Equations Theory. We show that the Golden ratio coincides with this limit not because it is the root with maximum modulus and multiplicity of the characteristic polynomial, but, from a more general point of view, because it is the root with maximum modulus and multiplicity of a restricted set of roots, which in this special case coincides with the two roots of the characteristic polynomial. This new perspective is the heart of the characterization of the limit of ratio of consecutive terms of all linear homogeneous recurrences with constant coefficients, without any assumption on the roots of the characteristic polynomial, which may be, in particular, also complex and not real.

scholarly journals Nonderogatory Unicyclic Digraphs

2007 ◽  
Vol 2007 ◽  
pp. 1-8 ◽  
Author(s):  
Diego Bravo ◽  
Juan Rada
Keyword(s):  
Characteristic Polynomial ◽  
Minimal Polynomial ◽  
Complete Product

A digraph is nonderogatory if its characteristic polynomial and minimal polynomial are equal. We find a characterization of nonderogatory unicyclic digraphs in terms of Hamiltonicity conditions. An immediate consequence of this characterization ia that the complete product of difans and diwheels is nonderogatory.

Signless Laplacian spectral characterization of some joins

2015 ◽  
Vol 30 ◽  
Author(s):  
Xiaogang Liu ◽  
Pengli Lu
Keyword(s):  
Lower Bound ◽  
Characteristic Polynomial ◽  
Regular Graph ◽  
Spectral Characterization ◽  
Laplacian Eigenvalue ◽  
Laplacian Spectra ◽  
Signless Laplacian

The join of two disjoint graphs G and H, denoted by G ∨ H, is the graph obtained by joining each vertex of G to each vertex of H. In this paper, the signless Laplacian characteristic polynomial of the join of two graphs is first formulated. And then, a lower bound for the i-th largest signless Laplacian eigenvalue of a graph is given. Finally, it is proved that G ∨ K_m, where G is an (n − 2)-regular graph on n vertices, and K_n ∨ K_2 except for n = 3, are determined by their signless Laplacian spectra.

Morphological Characterization of Mycobacteriophage R1

1974 ◽  
Vol 32 ◽  
pp. 254-255
Author(s):  
B. L. Soloff ◽  
T. A. Rado
Keyword(s):  
Carbon Source ◽  
Stationary Phase ◽  
Growth Phase ◽  
Minimal Medium ◽  
Morphological Characterization ◽  
Logarithmic Growth Phase ◽  
Complete Lysis ◽  
Lysogenic Culture ◽  
Logarithmic Growth

Mycobacteriophage R1 was originally isolated from a lysogenic culture of M. butyricum. The virus was propagated on a leucine-requiring derivative of M. smegmatis, 607 leu−, isolated by nitrosoguanidine mutagenesis of typestrain ATCC 607. Growth was accomplished in a minimal medium containing glycerol and glucose as carbon source and enriched by the addition of 80 μg/ ml L-leucine. Bacteria in early logarithmic growth phase were infected with virus at a multiplicity of 5, and incubated with aeration for 8 hours. The partially lysed suspension was diluted 1:10 in growth medium and incubated for a further 8 hours. This permitted stationary phase cells to re-enter logarithmic growth and resulted in complete lysis of the culture.

AEM analysis of crystallization in Ti-based amorphous alloys

1983 ◽  
Vol 41 ◽  
pp. 270-271
Author(s):  
A.R. Pelton ◽  
A.F. Marshall ◽  
Y.S. Lee
Keyword(s):  
Magnetic Properties ◽  
Amorphous Alloys ◽  
Amorphous Materials ◽  
Isothermal Annealing ◽  
Amorphous Matrix ◽  
Nucleation And Growth ◽  
Current Interest ◽  
Amorphous Films ◽  
Electrical And Magnetic Properties

Amorphous materials are of current interest due to their desirable mechanical, electrical and magnetic properties. Furthermore, crystallizing amorphous alloys provides an avenue for discerning sequential and competitive phases thus allowing access to otherwise inaccessible crystalline structures. Previous studies have shown the benefits of using AEM to determine crystal structures and compositions of partially crystallized alloys. The present paper will discuss the AEM characterization of crystallized Cu-Ti and Ni-Ti amorphous films.Cu60Ti40: The amorphous alloy Cu60Ti40, when continuously heated, forms a simple intermediate, macrocrystalline phase which then transforms to the ordered, equilibrium Cu3Ti2 phase. However, contrary to what one would expect from kinetic considerations, isothermal annealing below the isochronal crystallization temperature results in direct nucleation and growth of Cu3Ti2 from the amorphous matrix.

Characterization of Coherent, Ordered Precipitates in Nickel-Base Alloys

1973 ◽  
Vol 31 ◽  
pp. 144-145
Author(s):  
B. H. Kear ◽  
J. M. Oblak
Keyword(s):  
Stable Phase ◽  
Nickel Base Superalloy ◽  
Alloy 718 ◽  
Commercial Alloy ◽  
Precipitate Morphology ◽  
Continuous Precipitation ◽  
Nickel Base ◽  
Base Superalloy ◽  
Strengthening Precipitate

A nickel-base superalloy is essentially a Ni/Cr solid solution hardened by additions of Al (Ti, Nb, etc.) to precipitate a coherent, ordered phase. In most commercial alloy systems, e.g. B-1900, IN-100 and Mar-M200, the stable precipitate is Ni3 (Al,Ti) γ′, with an LI2structure. In A lloy 901 the normal precipitate is metastable Nis Ti3 γ′ ; the stable phase is a hexagonal Do2 4 structure. In Alloy 718 the strengthening precipitate is metastable γ″, which has a body-centered tetragonal D022 structure.Precipitate MorphologyIn most systems the ordered γ′ phase forms by a continuous precipitation re-action, which gives rise to a uniform intragranular dispersion of precipitate particles. For zero γ/γ′ misfit, the γ′ precipitates assume a spheroidal.

The Use of Advanced Analytical Techniques for Characterization of the Chemical, Physical, and Crystallographic Nature of a Surface

1973 ◽  
Vol 31 ◽  
pp. 132-133 ◽  
Author(s):  
R. E. Herfert
Keyword(s):  
Surface Characterization ◽  
Analytical Techniques ◽  
X Ray Diffraction ◽  
Depth Of Penetration ◽  
X Ray ◽  
The Past ◽  
Transmission Electron ◽  
Scanning Electron

Studies of the nature of a surface, either metallic or nonmetallic, in the past, have been limited to the instrumentation available for these measurements. In the past, optical microscopy, replica transmission electron microscopy, electron or X-ray diffraction and optical or X-ray spectroscopy have provided the means of surface characterization. Actually, some of these techniques are not purely surface; the depth of penetration may be a few thousands of an inch. Within the last five years, instrumentation has been made available which now makes it practical for use to study the outer few 100A of layers and characterize it completely from a chemical, physical, and crystallographic standpoint. The scanning electron microscope (SEM) provides a means of viewing the surface of a material in situ to magnifications as high as 250,000X.

Skeletal elements of crinoid echinoderms: High-resolution structural and microanalytical results

1983 ◽  
Vol 41 ◽  
pp. 194-195
Author(s):  
D. F. Blake ◽  
L. F. Allard ◽  
D. R. Peacor
Keyword(s):  
High Resolution ◽  
Marine Invertebrates ◽  
Sea Urchins ◽  
Structural Features ◽  
Sea Stars ◽  
High Resolution Tem ◽  
Relationship Of ◽  
The Relationship ◽  
Insight Into

Echinodermata is a phylum of marine invertebrates which has been extant since Cambrian time (c.a. 500 m.y. before the present). Modern examples of echinoderms include sea urchins, sea stars, and sea lilies (crinoids). The endoskeletons of echinoderms are composed of plates or ossicles (Fig. 1) which are with few exceptions, porous, single crystals of high-magnesian calcite. Despite their single crystal nature, fracture surfaces do not exhibit the near-perfect {10.4} cleavage characteristic of inorganic calcite. This paradoxical mix of biogenic and inorganic features has prompted much recent work on echinoderm skeletal crystallography. Furthermore, fossil echinoderm hard parts comprise a volumetrically significant portion of some marine limestones sequences. The ultrastructural and microchemical characterization of modern skeletal material should lend insight into: 1). The nature of the biogenic processes involved, for example, the relationship of Mg heterogeneity to morphological and structural features in modern echinoderm material, and 2). The nature of the diagenetic changes undergone by their ancient, fossilized counterparts. In this study, high resolution TEM (HRTEM), high voltage TEM (HVTEM), and STEM microanalysis are used to characterize tha ultrastructural and microchemical composition of skeletal elements of the modern crinoid Neocrinus blakei.

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