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1

Mathematical analysis of a MERS-Cov coronavirus model

DarAssi Mahmoud H., Shatnawi Taqi A. M., Safi Mohammad A.

Demonstratio Mathematica

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2022

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Vol. 55, nr 1

265--276

EN

In this study, we have proposed a mathematical model to describe the dynamics of the spread of Middle East Respiratory Syndrome disease. The model consists of six-coupled ordinary differential equations. The existence of the corona-free equilibrium and endemic equilibrium points has been proved. The threshold condition for which the disease will die out or becomes permanent has been computed. That is the corona-free equilibrium point is locally asymptotically stable whenever the reproduction number is less than unity, and it is globally asymptotically stable (GAS) whenever the reproduction number is greater than unity. Moreover, we have proved that the endemic equilibrium point is GAS whenever the reproduction number is greater than unity. The results of the model analysis have been illustrated by numerical simulations.

2

Determination of sorption properties of heavy metals in various biosorbents

Kłos A.

Ecological Chemistry and Engineering. S

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2018

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Vol. 25, nr 2

201--216

EN

Various techniques of determination of properties of physicochemical processes of heavy metal sorption in biosorbents were analysed. The methods of preparing and storing samples, conditions of experiment performance, as well as the methods of data interpretation were discussed. Two procedures of study were analysed: (1) in the static system of biosorbent-solution contact and (2) in the system of dynamic flow of solution. Copper cation sorption was studied. The effect of consecutive stages of the study on the quality of final results was shown. A high degree of uncertainty of the sorption capacity assessment was reported, which was dependent on the manner of conducting the study. The application of the pseudo-second order reaction model was substantiated to describe kinetics of cation-exchange sorption and the model of Langmuir isotherm to describe equilibria. The study conducted reveals that in order to perform comparative analyses, it is necessary to establish a joint concept of conducting studies and the interpretation of results.

3

Badania potencjometryczne, ESI-MS i NMR nad kompleksowaniem magnezu(II) i wapnia(II) wybranymi kwasami bisfosfonowymi w roztworze wodnym

Szpak M., Matczak-Jon E., Kurzak B.

Chemik

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2014

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Vol. 68, nr 4

321--328

PL

Przeprowadzono badania nad równowagami w roztworze układów Mg(II)/Ca(II)-L (L= kwas (cykloheksylo)aminometano-1,1-difosfonowy (1), kwas azepan-1-ylo-metano-1,1-difosfonowy (2), kwas azekan-1-ylo-metano-1,1-difosfonowy (3)) metodami pH-potencjometrii, NMR i ESI-MS. Uzyskane wyniki wskazują, że we wszystkich badanych układach preferowane jest tworzenie kompleksów jednordzeniowych o stechiometrii 1:1. Rozpatrywane związki wiążą koordynacyjnie Mg(II) i Ca(II) poprzez atomy tlenu grup fosfonianowych w szerokim zakresie wartości pH.

EN

Solution equilibrium studies on the Mg(II)/Ca(II)-L systems (L= (cyclohexyl)aminomethane-1,1-diphosphonic acid (1), azepan-1-yl-methane-1,1-diphosphonic acid (2), azecan-1-yl-methane-1,1-diphosphonic acid (3) have been performed by pH-potentiometry, NMR and ESI-MS methods. The obtained results suggest preference for the formation of mononuclear complexes of 1:1 stoichiometry in all studied systems. Compounds under consideration coordinate Mg(II) and Ca(II) through oxygen atoms of the phosphonate groups over a broad pH range.

4

An unconditionally stable nonstandard finite difference method applied to a mathematical model of HIV infection

Obaid H. A., Ouifki R., Patidar K. C.

International Journal of Applied Mathematics and Computer Science

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2013

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Vol. 23, no. 2

357--372

EN

We formulate and analyze an unconditionally stable nonstandard finite difference method for a mathematical model of HIV transmission dynamics. The dynamics of this model are studied using the qualitative theory of dynamical systems. These qualitative features of the continuous model are preserved by the numerical method that we propose in this paper. This method also preserves the positivity of the solution, which is one of the essential requirements when modeling epidemic diseases. Robust numerical results confirming theoretical investigations are provided. Comparisons are also made with the other conventional approaches that are routinely used for such problems.

5

Strontium Isopoly Tung states: Synthesis and Properties

Rozantsev G. M., Radio S. V., Gumerova N. I.

Polish Journal of Chemistry

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2008

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Vol. 82, nr 11

2067-2080

EN

By single-point pH-metric titration method we investigated the interactions in the system of Na2WO4 - HNO3 - KNO3 - H2O in the conditions that are close to equilibrium. We also showed by mathematical modeling of the processes (Newton's method, CLINP 2.1 software) that interconvertion between particular isopoly tungstate anions (ITA) takes place and this leads to the decrease in concentration of hexatungstate W6O20(OH)2 6- and hydroheptatungstate HW7O24 5- anions with simultaneous increase of quantity of paratungstate B HxW12O40(OH)2 (10-x) - and metatungstate W12O38(OH)2 6- anions in the system. The results of the modeling were proven by the successful synthesis of strontium salts with ITA. From non-equilibrium solution with different acidity Z = n(H+) / n(WO42-) we isolated strontium paratungstate B Sr5[W12O40(OH)2]ź27H2O (Z = 1.14-1.17) and strontium hydroheptatungstate Sr5[HW7O24]2ź30H2O (Z = 1.29). From the equilibrium solution the only strontium paratungstate B Sr5[W12O40(OH)2]ź27H2O (Z = 1.17-1.33) precipitates. All the salts synthesized were characterized by elemental analysis, FTIR spectroscopy, X-ray diffraction, and DTA.

6

Polarography in investigation of equilibria and kinetics of some reactions of organic compounds

Zuman P.

Chemia Analityczna

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2007

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Vol. 52, No. 6

875-896

EN

Reasons lor the current limited use of DC polarography. using the dropping mercury electrode, are discussed. One area, in which DC polarography is useful and promising, involves applications in physical organic chemistry. In this area polarography offers information about equilibria and rates, both ofslow and fast reactions. For slowly established equilibria and for kinetics of slower reactions, diffusion controlled limiting currents are measured. Equilibrium constants of rapidly established acid-base equilibria are determined from shifts of half-wave potentials with pH. Values of rate constants of the orders between 105 to 1010 L mol-1 s-1 can be obtained for reactions occurring in the vicinity of the electrode surface by measuring limiting kinetic currents. Examples of applications of DC polarography of each of the four categories in physical organic chemistry are given.

PL

Przedyskutowano ograniczenia w użyciu polarografii staloprądowej z kapiącą elektroda rtęciową. Polem, na którym polarografia stalą się użyteczna I obiecująca jest fizyczna chemia organiczna. W tej dziedzinie daje ona możliwość otrzymania informacji na temat równowag reakcji i szybkości reakcji -zarówno wolnych jak i szybkich, Piv.y badaniu wolno ustalających się równowag i wyznaczaniu parametrów kinetycznych wolnych reakcji mierzy się wysokość dyfuzjnych prądów granicznych. Stale równowagi szybko ustalających się równowag kwasowo-zasadowych można wyznaczyć z przesunięć potencjałów pólial w funkcji pH. Stale szybkości rzędu 105 L molmol-1 s-1, w przypadku reakcji przebiegających w pobliżu powierzchni elektrody, można wyznaczyć z pomiarów granicznych prądów kinetycznych. Podano przykłady zastosowania polarografii stałoprądowej dla każdego z wyżej wymienionych przypadków.