Characteristic Polynomial in Assessment of Carbon-Nano Structures

2017 ◽  
pp. 122-147
Author(s):  
Sorana D. Bolboacă ◽  
Lorentz Jäntschi
Keyword(s):  
Characteristic Polynomial ◽  
Chemical Structure ◽  
Chair Conformation ◽  
Point Of View ◽  
Characteristic Polynomials ◽  
Graph Invariant ◽  
Real Roots ◽  
Nano Structures ◽  
Central Form ◽  
Number Of Real Roots

Six dodecahedrane assemblies as multiple of five and respectively six structures were constructed and investigated from the topological point of view. The investigation was conducted using characteristic polynomials, graph invariant encoding important properties of the graph of the chemical structure. The assemblies of 5, 6, 15 and 25 dodecahedranes proved to have the center in the same plane while the assemblies of 12 and 24 dodecahedranes degenerated from the planar central form to a chair conformation. Generally, the number of real roots of characteristic polynomials is equal to the number of atoms in the assembly. The obtained roots of the characteristic polynomial were split into intervals and the frequency apparition spectra were simulated. The obtained spectra were used to investigate the behavior of investigated assembly.

scholarly journals Differences in PARP Inhibitors for the Treatment of Ovarian Cancer: Mechanisms of Action, Pharmacology, Safety, and Efficacy

2021 ◽  
Vol 22 (8) ◽  
pp. 4203
Author(s):  
Giorgio Valabrega ◽  
Giulia Scotto ◽  
Valentina Tuninetti ◽  
Arianna Pani ◽  
Francesco Scaglione
Keyword(s):  
Ovarian Cancer ◽  
Signal Transduction ◽  
Dna Damage ◽  
Chemical Structure ◽  
Parp Inhibitors ◽  
Mechanisms Of Action ◽  
Point Of View ◽  
Safety And Efficacy ◽  
Damage Repair ◽  
Pharmacokinetic Properties

Poly(ADP-ribose) polymerases (PARP) are proteins responsible for DNA damage detection and signal transduction. PARP inhibitors (PARPi) are able to interact with the binding site for PARP cofactor (NAD+) and trapping PARP on the DNA. In this way, they inhibit single-strand DNA damage repair. These drugs have been approved in recent years for the treatment of ovarian cancer. Although they share some similarities, from the point of view of the chemical structure and pharmacodynamic, pharmacokinetic properties, these drugs also have some substantial differences. These differences may underlie the different safety profiles and activity of PARPi.

Detection of psychotropic substances in the blood by LC/MS/MS

2014 ◽  
Vol 284 ◽  
pp. 60-69
Author(s):  
Mariola Wicka ◽  
◽  
Piotr Chołbiński ◽  
Dorota Kwiatkowska ◽  
Andrzej Pokrywka ◽  
...  
Keyword(s):  
Human Body ◽  
Chemical Structure ◽  
Drugs Of Abuse ◽  
Point Of View ◽  
The Body ◽  
Psychoactive Substances ◽  
Psychotropic Substances ◽  
Road Users ◽  
Conducting Research ◽  
Proper Interpretation

Year on year, one can observe an increase in the use of addictive substances. This leads to occurring the problem of addiction as well as the use of psychoactive substances as a serious hazard to road users. The Regulation of the Minister of Health on agents acting similarly to alcohol and the conditions and manner of conducting research on their presence in the human body, requires adequate benchmarks for performing these tests. An importantfactor, from consultative point of view, is the knowledge of the chemical structure of substances belonging to different groups of drugs of abuse, their metabolic transformations that occur in the body as well as their influence on the body. This is to aid in the proper interpretation of the results of the analytical tests.

Intestinal absorption of coprostanol (coprosterol) in the rat

1960 ◽  
Vol 199 (6) ◽  
pp. 1008-1010 ◽  
Author(s):  
C.S. Narayana Setty ◽  
A. C. Ivy
Keyword(s):  
Oleic Acid ◽  
Intestinal Absorption ◽  
Chemical Structure ◽  
Control Period ◽  
Chair Conformation ◽  
Color Reaction ◽  
Salt Mixture ◽  
Streptomycin Sulfate

A basal sterol-free diet consisting of casein, 18%; dextrin, 57%; oleic acid, 9%; U.S.P. salt mixture, 2%; yeast, 5%; and cellulose, 9%; along with 1% sulfasuxidine and 0.2% streptomycin sulfate was fed to eight rats during a control period of 12 days, the feces being collected under alcohol the last 4 days and assayed for digitonide sterol. The experiment was repeated with the addition of 28 mg of coprostanol to the diet. It was found that from 41 to 61% (average 48%) of the coprostanol was absorbed. The relation of chemical structure to the absorbability of cholesterol derivatives is discussed with the finding that all absorbable cholesterol derivatives have the ‘chair’ conformation, but are not alike in digitonide formation and Liebermann-Burchard color reaction.

scholarly journals On the Lower Bound for the Number of Real Roots of a Random Algebraic Equation

2007 ◽  
Vol 2007 ◽  
pp. 1-8
Author(s):  
Takashi Uno
Keyword(s):  
Lower Bound ◽  
Algebraic Equation ◽  
Random Variables ◽  
Real Roots ◽  
Number Of Real Roots

We estimate a lower bound for the number of real roots of a random alegebraic equation whose random coeffcients are dependent normal random variables.

scholarly journals Stellar Atmospheres: The Sources of Interstellar Molecules

1973 ◽  
Vol 52 ◽  
pp. 405-412 ◽  
Author(s):  
Mikio Shimizu
Keyword(s):  
Chemical Structure ◽  
Interstellar Dust ◽  
Solar Nebula ◽  
Stellar Atmospheres ◽  
Point Of View ◽  
H Ii Regions ◽  
Interstellar Molecules ◽  
Cometary Nuclei ◽  
Stellar Radiation ◽  
Neutral Clouds

The analysis of the abundance of interstellar molecules in compact H II regions suggests that the molecules are formed in stellar atmospheres (possibly of protostars or of late type stars), transported to the location of the neutral clouds in the cpmpact H II regions, and shielded from decomposition due to stellar radiation by the dust in the clouds. Cometary nuclei and interstellar dust are argued from the astrochemical point of view to be dirty ice of the second kind (or a sort of frozen interstellar molecules). The chemical structure of the primordial solar nebula is discussed under the assumption that long-period comets consist of the most primordial substances of the solar system.

scholarly journals Asymptotic variance of the number of real roots of random polynomial systems

2018 ◽  
Vol 146 (12) ◽  
pp. 5437-5449 ◽  
Author(s):  
D. Armentano ◽  
J-M. Azaïs ◽  
F. Dalmao ◽  
J. R. León
Keyword(s):  
Asymptotic Variance ◽  
Polynomial Systems ◽  
Random Polynomial ◽  
Real Roots ◽  
Number Of Real Roots

Laplace and Extended Adjacency Matrices for Isomorphism Detection of Kinematic Chains Using the Characteristic Polynomial Approach

2005 ◽  
Author(s):  
Rajesh Pavan Sunkari ◽  
Linda C. Schmidt
Keyword(s):  
Characteristic Polynomial ◽  
Spectral Properties ◽  
Kinematic Chain ◽  
Detection Algorithm ◽  
Isomorphism Problem ◽  
Characteristic Polynomials ◽  
Kinematic Chains ◽  
Laplace Matrix ◽  
Adjacency Matrices ◽  
Single Matrix

The kinematic chain isomorphism problem is one of the most challenging problems facing mechanism researchers. Methods using the spectral properties, characteristic polynomial and eigenvectors, of the graph related matrices were developed in literature for isomorphism detection. Detection of isomorphism using only the spectral properties corresponds to a polynomial time isomorphism detection algorithm. However, most of the methods used are either computationally inefficient or unreliable (i.e., failing to identify non-isomorphic chains). This work establishes the reliability of using the characteristic polynomial of the Laplace matrix for isomorphism detection of a kinematic chain. The Laplace matrix of a graph is used extensively in the field of algebraic graph theory for characterizing a graph using its spectral properties. The reliability in isomorphism detection of the characteristic polynomial of the Laplace matrix was comparable with that of the adjacency matrix. However, using the characteristic polynomials of both the matrices is superior to using either method alone. In search for a single matrix whose characteristic polynomial unfailingly detects isomorphism, novel matrices called the extended adjacency matrices are developed. The reliability of the characteristic polynomials of these matrices is established. One of the proposed extended adjacency matrices is shown to be the best graph matrix for isomorphism detection using the characteristic polynomial approach.

scholarly journals On the class of square Petrie matrices induced by cyclic permutations

2004 ◽  
Vol 2004 (31) ◽  
pp. 1617-1622
Author(s):  
Bau-Sen Du
Keyword(s):  
Finite Field ◽  
Zeta Function ◽  
Topological Entropy ◽  
Characteristic Polynomial ◽  
Characteristic Polynomials ◽  
Dynamical Properties

Letn≥2be an integer and letP={1,2,…,n,n+1}. LetZpdenote the finite field{0,1,2,…,p−1}, wherep≥2is a prime. Then every mapσonPdetermines a realn×nPetrie matrixAσwhich is known to contain information on the dynamical properties such as topological entropy and the Artin-Mazur zeta function of the linearization ofσ. In this paper, we show that ifσis acyclicpermutation onP, then all such matricesAσare similar to one another overZ2(but not overZpfor any primep≥3) and their characteristic polynomials overZ2are all equal to∑k=0nxk. As a consequence, we obtain that ifσis acyclicpermutation onP, then the coefficients of the characteristic polynomial ofAσare all odd integers and hence nonzero.

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