scholarly journals An Application of Sombor Index over a Special Class of Semigroup Graph

2021 ◽  
Vol 2021 ◽  
pp. 1-6
Author(s):  
Seda Oğuz Ünal
Keyword(s):  
Special Class ◽  
Topological Invariants ◽  
Important Class ◽  
Algebraic Structures ◽  
Monogenic Semigroup

Recently, Gutman introduced a class of novel topological invariants named Sombor index which is defined as S O G = ∑ u v ∈ E G d u 2 + d v 2 . In this study, the Sombor index of monogenic semigroup graphs, which is an important class of algebraic structures, is calculated.

scholarly journals Zhang–Zhang Polynomials of Ribbons

Symmetry ◽  
2020 ◽  
Vol 12 (12) ◽  
pp. 2060
Author(s):  
Bing-Hau He ◽  
Chien-Pin Chou ◽  
Johanna Langner ◽  
Henryk A. Witek
Keyword(s):  
Closed Form ◽  
Topological Invariants ◽  
Important Class ◽  
Kekulé Structures ◽  
Clar Number ◽  
Interface Theory ◽  
Clar Structures ◽  
Closed Form Formula ◽  
Clar Covering Polynomial

We report a closed-form formula for the Zhang–Zhang polynomial (also known as ZZ polynomial or Clar covering polynomial) of an important class of elementary peri-condensed benzenoids Rbn1,n2,m1,m2, usually referred to as ribbons. A straightforward derivation is based on the recently developed interface theory of benzenoids [Langner and Witek, MATCH Commun. Math. Comput. Chem.2020, 84, 143–176]. The discovered formula provides compact expressions for various topological invariants of Rbn1,n2,m1,m2: the number of Kekulé structures, the number of Clar covers, its Clar number, and the number of Clar structures. The last two classes of elementary benzenoids, for which closed-form ZZ polynomial formulas remain to be found, are hexagonal flakes Ok,m,n and oblate rectangles Orm,n.

The Projectively Flat Conditions of One Special Class (α, β)-Metrics

2013 ◽  
Vol 756-759 ◽  
pp. 2528-2532
Author(s):  
Wen Jing Zhao ◽  
Yan Yan ◽  
Li Nan Shi ◽  
Bo Chao Qu
Keyword(s):  
Special Class ◽  
Riemannian Metric ◽  
Class I ◽  
Flag Curvature ◽  
Finsler Metrics ◽  
Important Class ◽  
Randers Metric ◽  
New Class ◽  
Projectively Flat ◽  
Randers Metrics

The-metric is an important class of Finsler metrics including Randers metric as the simplest class, and many people research the Randers metrics. In this paper, we study a new class of Finsler metrics in the form ,Whereis a Riemannian metric, is a 1-form. Bengling Li had introduced the projective flat of the-Metric F. We find another method which is about flag curvature to prove the projective flat conditions of this kind of-metric.

scholarly journals Cohomological framework for contextual quantum computations

2019 ◽  
Vol 19 (13&14) ◽  
pp. 1141-1170
Author(s):  
Robert Raussendorf
Keyword(s):  
Quantum Computation ◽  
The Other ◽  
Topological Invariants ◽  
Algebraic Structures ◽  
Cohomology Groups ◽  
Essential Information ◽  
Quantum Computations

We describe a cohomological framework for measurement-based quantum computation in which symmetry plays a central role. Therein, the essential information about the computation is contained in either of two topological invariants, namely two cohomology groups. One of them applies only to deterministic quantum computations, and the other to general probabilistic ones. Those invariants characterize the computational output, and at the same time witness quantumness in the form of contextuality. In result, they give rise to fundamental algebraic structures underlying quantum computation.

Gold liposomes

1996 ◽  
Vol 54 ◽  
pp. 898-899
Author(s):  
James F. Hainfeld
Keyword(s):  
Direct Methods ◽  
Important Class ◽  
Double Bonds ◽  
Membrane Phospholipids ◽  
Essential Ingredient ◽  
Lipid Structures

Lipids are an important class of molecules, being found in membranes, HDL, LDL, and other natural structures, serving essential roles in structure and with varied functions such as compartmentalization and transport. Synthetic liposomes are also widely used as delivery and release vehicles for drugs, cosmetics, and other chemicals; soap is made from lipids. Lipids may form bilayer or multilammellar vesicles, micelles, sheets, tubes, and other structures. Lipid molecules may be linked to proteins, carbohydrates, or other moieties. EM study of this essential ingredient of life has lagged, due to lack of direct methods to visualize lipids without extensive alteration. OsO4 reacts with double bonds in membrane phospholipids, forming crossbridges. This has been the method of choice to both fix and stain membranes, thus far. An earlier work described the use of tungstate clusters (W11) attached to lipid moieties to form lipid structures and lipid probes.

An Intervention in a “Special” Class

1980 ◽  
Vol 9 (1) ◽  
pp. 99-103 ◽  
Author(s):  
Virginia Monroe ◽  
Lisa Ford
Keyword(s):  
Special Class

Flavonoids and Reduction of Cardiovascular Disease (CVD) in Chronic Obstructive Pulmonary Disease (COPD)

2019 ◽  
Vol 26 (39) ◽  
pp. 7048-7058 ◽  
Author(s):  
Patrizia Russo ◽  
Giulia Prinzi ◽  
Palma Lamonaca ◽  
Vittorio Cardaci ◽  
Massimo Fini
Keyword(s):  
Chronic Obstructive Pulmonary Disease ◽  
Pulmonary Disease ◽  
Clinical Studies ◽  
Risk Prevention ◽  
Chronic Obstructive ◽  
Low Molecular Weight ◽  
Important Class ◽  
Cvd Risk ◽  
Obstructive Pulmonary Disease ◽  
Convincing Data

Background: Chronic Obstructive Pulmonary Disease (COPD) and Cardiovascular Diseases (CV) Often Coexist. COPD and CVD are complex diseases characterized by a strict interaction between environment and genetic. The mechanisms linking these two diseases are complex, multifactorial and not entirely understood, influencing the therapeutic approach. COPD is characterized by several comorbidities, it hypothesized the treatment of cardiovascular co-morbidities that may reduce morbidity and mortality. Flavonoids are an important class of plant low molecular weight Secondary Metabolites (SMs). Convincing data from laboratory, epidemiological, and human clinical studies point the important effects on CVD risk prevention. Objective: This review aims to provide up-to-date information on the ability of Flavonoids to reduce the CVD risk. Conclusion: Current studies support the potential of Flavonoids to prevent the risk of CVD. Well-designed clinical studies are suggested to evaluate advantages and limits of Flavonoids for managing CVD comorbidity in COPD.

Novel GABAA Agonist Entities: Pharmacological Investigation and Molecular Modeling Study of Thiazolo- and Thiadiazolo-[3,2-a][1,3] diazepine Analogs

2020 ◽  
Vol 21 ◽  
Author(s):  
Hussein I. El-Subbagh
Keyword(s):  
Molecular Modeling ◽  
Drug Development ◽  
Biological Evaluation ◽  
Neuromuscular Blocking ◽  
Present Review ◽  
Pharmacological Investigation ◽  
Important Class ◽  
Pharmacological Activities ◽  
Short Acting ◽  
New Drug Development

Abstract:: Thiazolo- and thiadiazolo-[3,2-a][1,3]diazepines and their patented derivatives, tested with diverse CNS pharmacological activities, constitute an important class of compounds for new drug development. Therefore, research efforts were continued to design, synthesize, and evaluate compounds for their ultra-short, short-acting hypnotic, anticonvulsant, and neuromuscular blocking activities. The present review provides a summary of the work accomplished by these heterocycles and their biological evaluation.

Synthesis and Biological Properties of some New Lead Sulphonamide and Carboxamide Scaffolds Bearing Coumarin Moiety (Mini Review)

2020 ◽  
Vol 20 ◽  
Author(s):  
Cosmas Chinweike Eze ◽  
Mercy Amarachukwu Ezeokonkwo ◽  
Benjamin Ebere Ezema ◽  
Abraham Efeturi Onoabedje ◽  
David Izuchukwu Ugwu
Keyword(s):  
Biological Properties ◽  
Therapeutic Agents ◽  
Amide Group ◽  
Pharmacological Properties ◽  
Important Class ◽  
Synthetic Route ◽  
Therapeutic Activities

: Coumarin, sulphonamide and amide scaffolds exhibit diverse pharmacological features and constitute an important class of therapeutic agents. In this review, we have discussed the synthesis, biological properties, and SAR of coumarins containing sulphonamide or amide group in the last seven years. Many reviews on the therapeutic activities of coumarins, sulphonamides, and amides have been published, hence the authors focused on coumarin-linked sulphonamide or amide scaffolds. The review provides information on the synthetic route to new coumarins containing sulphonamide or amide groups with improved pharmacological properties.

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