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On Branched Chain Processes, the Laws of Development of Which Are Expressed by Numerical Sequences Like Fibonacci Numbers, a New Look at Their Nature
Issue:
Volume 6, Issue 4, August 2018
Pages:
30-42
Received:
23 July 2018
Accepted:
15 August 2018
Published:
11 October 2018
Abstract: Branched chain chemical reactions represent a special class of chemical transformation reactions of matter, for the discovery and experimental-theoretical development of which Semenov N. N. and Hinshelwood C. N. were awarded the Nobel Prize in 1956. In nature, such processes are widespread. Objective. To investigate the nature of various numerical sequences of the Fibonacci type and to find out under what conditions they can reflect (express) the patterns of development of branched chain processes. In this work, the state is formulated that branched chain chemical reactions are a particular case of branched chain processes of any nature in different spheres, including biological. It is shown that many branched chain processes can generate numerical sequences of Fibonacci, Lucas, Shannon and others of the same type, which reflect the dynamics of their development. For all the indicated numerical sequences, it is typical that their formation is determined by a general recurrent law, which has been the subject of research for many well-known mathematicians. For each of the indicated numerical sequences they established other laws alternative to the recurrent one, however, they were all of a private nature. They were in accordance with the recurrent law only in the case of one specific sequence. Comparative analysis of many numerical sequences allowed us to find a universal law that is common for all types of sequences and terminologically define it as the law of "doubling with subtraction." For all numerical series the formation of which follows a recurrent law, the law "doubling with subtraction" is equally valid. The opposite is not true since there are numerical sequences that obey only the law of "doubling with subtraction," and the recurrent law is not valid for them. It means that the new law is more fundamental and, in fact, is the primary law and the recurrent law is secondary. Significant differences also exist in the consequences of these two laws. For example, the increments of sequences formed according to the recurrent law and the law of "doubling with subtraction" have fundamental differences in their mathematical expression, although they lead in different ways to the same result, namely, to Ф = 1,618... with the serial numbers of the sequence terms tending to infinity. In the work for each of these laws, a branched chain biological process that was unique to it was found and put in correspondence. In the case of the law of "doubling with subtraction", the process was followed by the termination of chains with characteristic parameters: the chain length is three links, the branching factor is -2. In the case of a recurrent law, the process was without chain termination, with an infinite length and with a branching factor of -2, and with some delay limiting the branching. It seems interesting that such different branched chain processes of different character are described by the same Fibonacci sequence. The processes of branched chain character corresponding to the sequences of Lucas, Shannon, and others are discussed. Conclusions. According to our work, it follows that all formal mathematics, that is, all the mathematical features and patterns related to the Fibonacci sequence is just a description of those features and patterns that are inherent in the branched chain processes that actually produce these and other sequences.
Abstract: Branched chain chemical reactions represent a special class of chemical transformation reactions of matter, for the discovery and experimental-theoretical development of which Semenov N. N. and Hinshelwood C. N. were awarded the Nobel Prize in 1956. In nature, such processes are widespread. Objective. To investigate the nature of various numerical ...
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Synthesis of n-Butyl Lactate by Transition-Metal-Substituted Phosphotungstic Acid Salt
Ke Wu,
Li Xu,
Ling Xu,
Lijuan Xie,
Zongrui Liu
Issue:
Volume 6, Issue 4, August 2018
Pages:
43-49
Received:
16 September 2018
Published:
18 October 2018
Abstract: Fatty acid ester perfume occupied an important position in food industry. The characteristics of them were variety, easy synthesis and low price. They were widely used in daily flavor, edible flavor and industrial flavor. POMs were a kind of stong acid bifunctional mild environment-friendly catalysts, their drawback was excellent solubility and could not be reused. Here, series of transition-metal-substituted phosphotungstate K6 [PW11O39MⅡ (H2O)] (M = Cu, Co, Ni) Lewis acid heterogeneous phase catalysts based on mono-lacunary-Keggin type K7 [PW11O39] were prepared by stereoselect-eve method, K6 [PW11O39MⅡ (H2O)] (M = Cu, Co, Ni) were abbreviated as PW11MⅡ (H2O) (M = Cu, Co, Ni). They were characterized by FT-IR, PXRD and element analysis. The coordinating water of transition metal was Lewis acid catalytic sites after activated. When mole ratio of butanol and lactic acid was 2: 1, amount of PW11MⅡ (H2O) (M = Cu, Co, Ni) was 0.125 g, volume of cyclohexane was 15 mL, the reaction temperature was 105°C, reaction time was 2 h, conversion rate of n-butyl lactate were in order: 85.9%, 79.6%, 66.3%. Activity of PW11X (X = Cu, Co, Ni) had no obvious changes after three times recycling. In addition, magnetic studies indicate that antiferromagnetic interactions exist in the three compounds.
Abstract: Fatty acid ester perfume occupied an important position in food industry. The characteristics of them were variety, easy synthesis and low price. They were widely used in daily flavor, edible flavor and industrial flavor. POMs were a kind of stong acid bifunctional mild environment-friendly catalysts, their drawback was excellent solubility and cou...
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Syntheses, Geometrical and Electronic Structure of Alkyladamantanes and Their Thermodynamic Characteristic According to the Density Functional Theory
Amanzhan Saginayev,
Marina Kursina,
Altynai Kalauova
Issue:
Volume 6, Issue 4, August 2018
Pages:
50-55
Received:
3 September 2018
Accepted:
26 September 2018
Published:
22 October 2018
Abstract: Propyladamantanes synthesized by of alkylation adamantane with isopropyl alcohol temperature range from 5 to 40°C in the presence of 96% sulfuric acid. Tetramethyl- and Dimethylethyladamantanes synthesized by of isomerization of Perhydroanthracene in the presence of aluminium oxide catalyst on the setting of the flow type. Isomers Butyladamantanes was obtained by the reaction of alkylation of the adamantane with n-butane and isobutane. Adamantane and its derivatives have been the subject of many experimental and theoretical studies. The molecular structure of adamantane was studied by gasphase electron diffraction, Penning ionization electron spectroscopy, photoelectron spectroscopy, electron spin resonance, and quantum calculations of ionization potentials (IP) and electron affinity (SE). The structure 1-n-propyladamantane (1), 1-isopropyladamantane (2), 2-n-propyladamantane (3), 1,2-di-n-propyladamantane (4), 1,3-dimethyl-5-ethyladamantane (5), 1,3,5,6-tetramethyladamantane (6), 1,3,5,7-tetramethyladamantane (7), perhydroanthracene (8), 1-n-butyladamantane (9), 1-isobutyladamantane (10), 1-sec-butyladamantane (11) has been studied using the Becke–Lee–Yang–Parr (B3LYP) hybrid energy functional of electron density with the 6-31G* basis set. The geometric and electronic characteristics of the compounds and their total energy, normal vibration frequencies have been calculated. It has been shown that the calculated Gibb free energies of formation for the perhydroanthracene isomerization products are in qualitative agreement with the experimental product composition of the isomerate and alkylation of adamantane with isopropyl alcohol are in qualitative agreement with the experimental composition of the products. Obtained good agreement of calculated and experimental data on the composition of equilibrium mixtures.
Abstract: Propyladamantanes synthesized by of alkylation adamantane with isopropyl alcohol temperature range from 5 to 40°C in the presence of 96% sulfuric acid. Tetramethyl- and Dimethylethyladamantanes synthesized by of isomerization of Perhydroanthracene in the presence of aluminium oxide catalyst on the setting of the flow type. Isomers Butyladamantanes ...
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Consideration of Contamination Status of Soils within the Vicinity of Automobile Workshops in Warri, Delta State, Nigeria
Doris Fovwe Ogeleka,
Oghenekohwiroro Edjere,
Ogechi Okokon-Ndem Nmai,
Prisca Ezeogu,
Felix Ebodaghe Okieimen
Issue:
Volume 6, Issue 4, August 2018
Pages:
56-65
Received:
17 July 2018
Accepted:
20 August 2018
Published:
26 October 2018
Abstract: This research appraised the extent of contamination in soils within the vicinity of automobile workshops in Warri, Delta State, Nigeria. This was with the view of ascertaining the effects of the estimated contamination would have on the quality of soils and terrestrial organisms in the impacted soils. The soils were moderate to slightly acidic with a range from 5.42 ± 0.04 to 6.41 ± 0.13. Zinc contamination in the soils was very severely contaminated (C/P index 0.85), lead had very slight contamination index of 0.11 while copper was moderated polluted with a C/P index value of 2.57. The soils had contamination factor (CF) greater than 6 in all the metals, indicating very high contamination. The degree of contamination was 163.25, implying very high degree of contamination. The pollution load index value of 5.47 obtained for n=3 (metals) showed that the soils had very intense perturbation. Iron being relatively abundant in nature has no C/P value as the lists of standards formulated by Department of Petroleum Resources (DPR) excludes iron. Contamination factor obtained for TPH varied from 41.88 to 47.27. The soils were rated to be excessively contaminated with petroleum hydrocarbons. There was significant variations between the controls and the contaminated soils at levels of P =.05. The impacted soils could have detrimental effects on the quality of soils and terrestrial organisms within and around automobile workshops.
Abstract: This research appraised the extent of contamination in soils within the vicinity of automobile workshops in Warri, Delta State, Nigeria. This was with the view of ascertaining the effects of the estimated contamination would have on the quality of soils and terrestrial organisms in the impacted soils. The soils were moderate to slightly acidic with...
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Oxidation State of 229Th Recoils Implanted into MgF2 Crystals
Beau J. Barker,
Edmund R. Meyer,
Michael H. Schacht,
Lee A. Collins,
Marianne P. Wilkerson,
Jason K. Ellis,
Richard L. Martin,
Xinxin Zhao
Issue:
Volume 6, Issue 4, August 2018
Pages:
66-76
Received:
31 August 2018
Accepted:
25 September 2018
Published:
31 October 2018
Abstract: A solid-state nuclear clock based on the low-lying isomeric state in 229Th has attracted growing interest. One potential problem for the solid-state nuclear clock approach is the suitability of the doped environment for photon emission of the nuclear isomeric state. Specifically, Thn+ n < 4 ions could open non-radiative decay routes for deexcitation, hindering the photon emission. Here we have used time-resolved photoluminescence (TRPL) and density functional theory (DFT) calculations to characterize MgF2 crystals that have been implanted with 229Th recoils via a-decay from a 233U source with the goal of determining the charge state of the implanted thorium atoms. The DFT calculations predicted Th4+ to be the lowest energy oxidation state with Th3+ the next lowest in the MgF2 crystal environment. The DFT calculations also show Th4+:MgF2 system has a band gap large enough so that the internal electron conversion decay channel is suppressed. Experimentally, we found no evidence for thorium in oxidations state other than +4 using TRPL spectroscopy that has a detection limit for Thn+ n < 4 ions several orders of magnitude smaller than the number of implanted 229Th recoils. This work shows that the solid-state approach is a viable option for a nuclear clock.
Abstract: A solid-state nuclear clock based on the low-lying isomeric state in 229Th has attracted growing interest. One potential problem for the solid-state nuclear clock approach is the suitability of the doped environment for photon emission of the nuclear isomeric state. Specifically, Thn+ n < 4 ions could open non-radiative decay routes for deexcitation, hindering the photon emission. Here we have used time-resolved photoluminescence (TRPL) and density functional theory (DFT) calculations to characterize MgF2 crystals that have been implanted with 229Th recoils via a-d...
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