scholarly journals Determination of the number of radicals in the initial chain reactions by mathematical methods

2009 ◽  
Vol 63 (2) ◽  
pp. 121-127
Author(s):  
Branko Pejovic ◽  
Milovan Jotanovic ◽  
Vladan Micic ◽  
Milorad Tomic ◽  
Goran Tadic
Keyword(s):  
General Chemistry ◽  
Difference Equation ◽  
Analytical Form ◽  
Mathematical Methods ◽  
Linear Difference Equations ◽  
Efficient Procedure ◽  
Chain Reactions ◽  
Chemical Equation ◽  
The Difference

Starting from the fact that the real mechanism in a chemical equation takes places through a certain number of radicals which participate in simultaneous reactions and initiate chain reactions according to a particular pattern, the aim of this study is to determine their number in the first couple of steps of the reaction. Based on this, the numbers of radicals were determined in the general case, in the form of linear difference equations, which, by certain mathematical transformations, were reduced to one equation that satisfies a particular numeric series, entirely defined if its first members are known. The equation obtained was solved by a common method developed in the theory of numeric series, in which its solutions represent the number of radicals in an arbitrary step of the reaction observed, in the analytical form. In the final part of the study, the method was tested and verified using two characteristic examples from general chemistry. The study also gives a suggestion of a more efficient procedure by reducing the difference equation to a lower order.

scholarly journals Modelling of the Flow of Streams of Cohesionless and Cohesive Bulk Materials in a Conveyor Discharge Point with a Flat Conveyor Belt

2018 ◽  
Vol 23 (1) ◽  
pp. 23-35 ◽  
Author(s):  
J.A. Cyganiuk ◽  
P. Kuryło
Keyword(s):  
Mathematical Description ◽  
Conveyor Belt ◽  
Flow Conditions ◽  
Mathematical Methods ◽  
Bulk Materials ◽  
Discharge Point ◽  
Stationary Flows ◽  
The Difference ◽  
Mathematical Relations

Abstract The paper presents the analysis of flow conditions of cohesive and cohesionless bulk materials in a conveyor discharge point of a flat conveyor belt. The analysis was carried out for stationary flows at high velocities. It presents mathematical methods for the description of the velocity of a material leaving a throwing point of a flat conveyor belt as well as final equations which enable the determination of velocity of the material after it has left the throwing point (with the accuracy sufficient for practical use). Next, the velocity calculated for the proposed mathematical description (for selected material groups) has been compared with the velocity obtained from mathematical relations commonly used by engineers. The proposed equations for determining the velocity of the material beyond the point have proved useful, since they enable excluding the indirect equations. Finally, the difference between the values of the velocity obtained with the proposed and indirect equations have been determined and the relative error for the proposed method has been calculated.

FRACTIONAL DETERMINATIONS OF URINARY 17-KETOSTEROIDS IN HYPEREMESIS GRAVIDARUM

1962 ◽  
Vol 41 (1) ◽  
pp. 123-128 ◽  
Author(s):  
Pentti A. Järvinen ◽  
Sykkö Pesonen ◽  
Pirkko Väänänen
Keyword(s):  
Hyperemesis Gravidarum ◽  
First Trimester ◽  
Control Group ◽  
Before And After ◽  
Daily Urine ◽  
First Trimester Of Pregnancy ◽  
The Difference

ABSTRACT The fractional determination of 17-ketosteroids in the daily urine was performed in nine cases of hyperemesis gravidarum and in four control cases, in the first trimester of pregnancy both before and after corticotrophin administration. The excretion of total 17-KS is similar in the two groups. Only in the hyperemesis group does the excretion of total 17-KS increase significantly after corticotrophin administration. The fractional determination reveals no difference between the two groups of patients with regard to the values of the fractions U (unidentified 17-KS), A (androsterone) and Rest (11-oxygenated 17-KS). The excretion of dehydroepiandrosterone is significantly higher in the hyperemesis group than in the control group. The excretion of androstanolone seems to be lower in the hyperemesis group than in the control group, but the difference is not statistically significant. The differences in the correlation between dehydroepiandrosterone and androstanolone in the two groups is significant. The high excretion of dehydroepiandrosterone and low excretion of androstanolone in cases of hyperemesis gravidarum is a sign of adrenal dysfunction.

A Master Class in Dimensional Analysis: the Universal Gas Constant

2018 ◽  
Author(s):  
john andraos
Keyword(s):  
Physical Chemistry ◽  
High School ◽  
General Chemistry ◽  
Dimensional Analysis ◽  
Undergraduate Students ◽  
Microsoft Excel ◽  
Energy Unit ◽  
Spreadsheet Program ◽  
Volume Unit

We present a spreadsheet-assisted exercise using Microsoft Excel software for the<br>determination of the universal gas constant, R, in 35,712 different units. This large<br>number of units arises from a simple enumeration of possible pressure-volume unit<br>combinations and energy unit combinations covering SI (metric), Imperial (British), and<br>American units. In turn, various units for force and area used for defining pressure, and<br>various units for force and distance used for defining energy are explored. This<br>presentation serves as an excellent exercise for high school and undergraduate students to<br>master the skill of dimensional analysis, unit conversions, and basic combinatorics in<br>general chemistry and physical chemistry courses. Instructors can also use the described<br>exercise of constructing conversion matrices to train students in how to efficiently use the<br>Microsoft Excel spreadsheet program.

THE SUBJECT FIELD OF INSTITUTIONAL EDUCATION: THE SENSE AND PROSPECTS OF DEVELOPMENT IN UKRAINE

2020 ◽  
pp. 25-38
Author(s):  
Irina Mordous
Keyword(s):  
Decisive Role ◽  
Subject Field ◽  
National Education ◽  
Progressive Development ◽  
Separate Area ◽  
Economic Transformations ◽  
The Difference ◽  
The Individual ◽  
Political Economic

The development of modern civilization attests to its decisive role in the progressive development of institutions. They identified the difference between Western civilization and the rest of the world. Confirmation of the institutional advantages of the West was its early industrialization. The genesis and formation of institutionalism in its ideological and conceptualmethodological orientation occurs as a process alternative to neoclassic in the context of world heterodoxia, which quickly spread in social science. Highlighting institutional education as a separate area of sociocultural activity is determined by the factor of differentiation of institutional theory as a whole. A feature of institutional education is its orientation toward the individual and his/her transformation into a personality. The content of institutional education is revealed through the analysis of the institution, which includes a set of established customs, traditions, ways of thinking, behavioral stereotypes of individuals and social groups. The dynamics of socio-political, economic transformations in Ukraine requires a review of the foundations of national education and determination of the prospects for its development in the 21st century in the context of institutionalism.

scholarly journals Possibility of Human Gender Recognition Using Raman Spectra of Teeth

Molecules ◽  
2021 ◽  
Vol 26 (13) ◽  
pp. 3983
Author(s):  
Ozren Gamulin ◽  
Marko Škrabić ◽  
Kristina Serec ◽  
Matej Par ◽  
Marija Baković ◽  
...  
Keyword(s):  
Raman Spectra ◽  
Principal Component ◽  
Support Vector ◽  
Gender Recognition ◽  
Proof Of Concept ◽  
Male And Female ◽  
Tooth Type ◽  
Tooth Apex ◽  
The Difference

Gender determination of the human remains can be very challenging, especially in the case of incomplete ones. Herein, we report a proof-of-concept experiment where the possibility of gender recognition using Raman spectroscopy of teeth is investigated. Raman spectra were recorded from male and female molars and premolars on two distinct sites, tooth apex and anatomical neck. Recorded spectra were sorted into suitable datasets and initially analyzed with principal component analysis, which showed a distinction between spectra of male and female teeth. Then, reduced datasets with scores of the first 20 principal components were formed and two classification algorithms, support vector machine and artificial neural networks, were applied to form classification models for gender recognition. The obtained results showed that gender recognition with Raman spectra of teeth is possible but strongly depends both on the tooth type and spectrum recording site. The difference in classification accuracy between different tooth types and recording sites are discussed in terms of the molecular structure difference caused by the influence of masticatory loading or gender-dependent life events.

scholarly journals Note on some representations of general solutions to homogeneous linear difference equations

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Stevo Stević ◽  
Bratislav Iričanin ◽  
Witold Kosmala ◽  
Zdeněk Šmarda
Keyword(s):  
General Solution ◽  
Difference Equation ◽  
Difference Equations ◽  
Fibonacci Sequence ◽  
Linear Difference Equation ◽  
Linear Difference Equations ◽  
Second Order Difference Equation ◽  
Constant Coefficients ◽  
Order Difference Equation ◽  
Homogeneous Linear

Abstract It is known that every solution to the second-order difference equation $x_{n}=x_{n-1}+x_{n-2}=0$ x n = x n − 1 + x n − 2 = 0 , $n\ge 2$ n ≥ 2 , can be written in the following form $x_{n}=x_{0}f_{n-1}+x_{1}f_{n}$ x n = x 0 f n − 1 + x 1 f n , where $f_{n}$ f n is the Fibonacci sequence. Here we find all the homogeneous linear difference equations with constant coefficients of any order whose general solution have a representation of a related form. We also present an interesting elementary procedure for finding a representation of general solution to any homogeneous linear difference equation with constant coefficients in terms of the coefficients of the equation, initial values, and an extension of the Fibonacci sequence. This is done for the case when all the roots of the characteristic polynomial associated with the equation are mutually different, and then it is shown that such obtained representation also holds in other cases. It is also shown that during application of the procedure the extension of the Fibonacci sequence appears naturally.

scholarly journals Sharp Lyapunov-type inequalities for second-order half-linear difference equations with different kinds of boundary conditions

2021 ◽  
Vol 115 (3) ◽  
Author(s):  
Robert Stegliński
Keyword(s):  
Difference Equation ◽  
Boundary Conditions ◽  
Difference Equations ◽  
Periodic Boundary ◽  
Periodic Boundary Conditions ◽  
Second Order ◽  
Linear Difference Equations ◽  
Order Difference ◽  
Second Order Difference Equation ◽  
Order Difference Equation

AbstractIn this work, we establish optimal Lyapunov-type inequalities for the second-order difference equation with p-Laplacian $$\begin{aligned} \Delta (\left| \Delta u(k-1)\right| ^{p-2}\Delta u(k-1))+a(k)\left| u(k)\right| ^{p-2}u(k)=0 \end{aligned}$$ Δ ( Δ u ( k - 1 ) p - 2 Δ u ( k - 1 ) ) + a ( k ) u ( k ) p - 2 u ( k ) = 0 with Dirichlet, Neumann, mixed, periodic and anti-periodic boundary conditions.

scholarly journals Influence of Erythrocytes on Direct Potentiometric Determination of Sodium and Potassium

1983 ◽  
Vol 20 (2) ◽  
pp. 116-120 ◽  
Author(s):  
P Bijster ◽  
H L Vader ◽  
C L J Vink
Keyword(s):  
Whole Blood ◽  
Potassium Concentration ◽  
Reference Electrode ◽  
Sodium Concentration ◽  
General Phenomenon ◽  
Liquid Junction ◽  
Direct Potentiometry ◽  
The Difference ◽  
Sodium And Potassium

We have shown that the sodium concentration in whole blood measured by direct potentiometry is higher than in plasma. The ‘erythrocyte-effect’, already described by Siggaard Andersen, is most pronounced for instruments equipped with a reference electrode with an open static liquid junction and is thus a general phenomenon. Instruments with a modified liquid junction show less interference. The same phenomenon appears for the determination of the potassium concentration, although the difference between whole blood and plasma, when measured with instruments equipped with a modified liquid junction, can be neglected in practice.

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