scholarly journals Zhang–Zhang Polynomials of Multiple Zigzag Chains Revisited: A Connection with the John–Sachs Theorem

Molecules ◽  
2021 ◽  
Vol 26 (9) ◽  
pp. 2524
Author(s):  
Henryk A. Witek

Multiple zigzag chains Zm,n of length n and width m constitute an important class of regular graphene flakes of rectangular shape. The physical and chemical properties of these basic pericondensed benzenoids can be related to their various topological invariants, conveniently encoded as the coefficients of a combinatorial polynomial, usually referred to as the ZZ polynomial of multiple zigzag chains Zm,n. The current study reports a novel method for determination of these ZZ polynomials based on a hypothesized extension to John–Sachs theorem, used previously to enumerate Kekulé structures of various benzenoid hydrocarbons. We show that the ZZ polynomial of the Zm,n multiple zigzag chain can be conveniently expressed as a determinant of a Toeplitz (or almost Toeplitz) matrix of size m2×m2 consisting of simple hypergeometric polynomials. The presented analysis can be extended to generalized multiple zigzag chains Zkm,n, i.e., derivatives of Zm,n with a single attached polyacene chain of length k. All presented formulas are accompanied by formal proofs. The developed theoretical machinery is applied for predicting aromaticity distribution patterns in large and infinite multiple zigzag chains Zm,n and for computing the distribution of spin densities in biradical states of finite multiple zigzag chains Zm,n.

Author(s):  
O.S. Bezuglova ◽  

Rostov Region belongs to the highly protected natural territories characterized by the continuous plowing. There territories are the only reserves with the soils preserved in their natural state. However, these areas often lack detailed information about the soils quality and composition. Surveying soils on these territories is crucial for determination of their basic physical and chemical properties. The resulted compilation of soil maps could lay a foundation for creating the Red Book of Soils and the formation of a section in the soil-geographical database of the Russian Federation. Subsequently, such information can be used as a background data for the main types of soils in the region. It will be also valuable during monitoring and justification of conservation measures.


2015 ◽  
Vol 63 (1) ◽  
pp. 47-54 ◽  
Author(s):  
Karsten Schacht ◽  
Bernd Marschner

Abstract The use of treated wastewater (TWW) for agricultural irrigation becomes increasingly important in water stressed regions like the Middle East for substituting fresh water (FW) resources. Due to elevated salt concentrations and organic compounds in TWW this practice has potential adverse effects on soil quality, such as the reduction of hydraulic conductivity (HC) and soil aggregate stability (SAS). To assess the impact of TWW irrigation in comparison to FW irrigation on HC, in-situ infiltration measurements using mini disk infiltrometer were deployed in four different long-term experimental orchard test sites in Israel. Topsoil samples (0-10 cm) were collected for analyzing SAS and determination of selected soil chemical and physical characteristics. The mean HC values decreased at all TWW sites by 42.9% up to 50.8% compared to FW sites. The SAS was 11.3% to 32.4% lower at all TWW sites. Soil electrical conductivity (EC) and exchangeable sodium percentage (ESP) were generally higher at TWW sites. These results indicate the use of TWW for irrigation is a viable, but potentially deleterious option, as it influences soil physical and chemical properties.


2009 ◽  
Vol 97 (4-5) ◽  
Author(s):  
K. M. Dziewinska ◽  
A. M. Peters ◽  
J. A. La Verne ◽  
P. Martinez ◽  
J. J Dziewinski ◽  
...  

AbstractDensity measurements of plutonium metal and its alloys are performed at Los Alamos National Laboratory (LANL) using a technique based on the Archimedes principle. The goal is to find and characterize a fluid for density determination of large objects made of plutonium to replace the currently used monobromobenzene. Physical and chemical properties must be considered while selecting the fluid. Chemical properties of the fluid must ensure low corrosion rates and good resistance to radiological decomposition. The study was carried on to evaluate the corrosion rates of Pu metal cause by FC-43 and the FC-43 decomposition products of radiolysis. The results of these studies proved favourable for this application. The evaluation of the surface reactions between FC-43 and Pu metal will be conducted in the near future.


2002 ◽  
Vol 67 (7) ◽  
pp. 473-480 ◽  
Author(s):  
Hulya Çelik

In this study, monoketo and monohydroxy eicosanoic acids and their methyl esters with the position of the substituent on odd numbered carbon atoms from 3 to 13 were synthesized with high purity. Furthermore, the semicarbazone and anilide derivatives of the obtained keto acids were prepared. They were characterized by TLC, IR and 1H-NMR spectroscopy and their physical and chemical properties were established.


2014 ◽  
Vol 70 (a1) ◽  
pp. C141-C141
Author(s):  
Ozen Ozgen ◽  
Engin Kendi ◽  
Semra Koyunoglu ◽  
Akgul Yesilada ◽  
Hwo-Shuenn Sheu

A significant part of medicine is based on the discovery and development of drugs. It is very important to know the crystal structure of pharmaceutical compounds for fundamental understanding of structure, physical and chemical properties. Many of these materials are available only as powders. So any structural information must be obtained from powder diffraction. I am going to present following the stages while solving the structure of C23H19N4OBr, 2-[3-phenyl-4(m-bromophenyl)-2-pyrazolin-1-yl]-3-methyl-4(3H)-quinazolinone, from 2-pyrazolines derivatives. The compounds are known to display various biological properties such as fungicidal insecticidal, anti bacterial, anti viral activities, pharmacological properties such as antiinflammatory agents and have industral properties(1). The powder diffraction data was collected with Debye Scherrer camera at the BL01C2 beamline at room temperature in National Synchrotron Radiation Research Center(NSRRC), Taiwan. X-ray of wavelength was 1.0333Å. This compound crystallizes in orthorhombic system space group P bca, Z=8, unit cell parameters of a=25.83(1)Å, b=15.55(5)Å, c=10.63(3)Å, and V=4266.0(10)Å3. Reliability factors were reached Rwp=0.075, Rp=0.053, RB=0.086 ve S=1.31 after Rietveld refinement.


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