scholarly journals Inequalities approach in determination of convergence of recurrence sequences

2021 ◽  
Vol 5 (1) ◽  
pp. 65-72
Author(s):  
Albert Adu-Sackey ◽  
◽  
Francis T. Oduro ◽  
Gabriel Obed Fosu ◽  
◽  
...  
Keyword(s):  
Mathematical Expression ◽  
Mathematical Induction ◽  
Recurrence Sequence ◽  
Recursive Sequences ◽  
Recursive Sequence ◽  
Leading Term ◽  
Geometric Sequence ◽  
Newton Raphson ◽  
Recurrence Sequences

The paper proves convergence for three uniquely defined recursive sequences, namely, arithmetico-geometric sequence, the Newton-Raphson recursive sequence, and the nested/composite recursive sequence. The three main hurdles for this prove processes are boundedness, monotonicity, and convergence. Oftentimes, these processes lie in the predominant use of prove by mathematical induction and also require some bit of creativity and inspiration drawn from the convergence monotone theorem. However, these techniques are not adopted here, rather, as a novelty, extensive use of basic manipulation of inequalities and useful equations are applied in illustrating convergence for these sequences. Moreover, we established a mathematical expression for the limit of the nested recurrence sequence in terms of its leading term which yields favorable results.

Determination of the Force Constants of Non-linear XY2 Molecules in the Gas-Phase by the GF Matrix Method

2004 ◽  
Vol 59 (9) ◽  
pp. 621-622 ◽  
Author(s):  
Fatih Ucun ◽  
Vesile Gūçlü
Keyword(s):  
Gas Phase ◽  
Condensed Phase ◽  
Matrix Method ◽  
Solid Phase ◽  
Force Constants ◽  
Matrix Solution ◽  
The Matrix ◽  
Newton Raphson ◽  
Raphson Method

The force constants of the internal coordinates of nonlinear XY2 molecules in the gas-phase were calculated by using the GF matrix method. The matrix solution was carried out by means a computer program built relative to the Newton-Raphson method and the calculations were listed in a table. The force constants of some molecules in the liquidand solid- phase were also found and compared with these ones, and it was seen that the force constants for more condensed phase are lower as in an agreement with having its lower frequency.

The Influence of Complex Dynamic Phenomena Caused by Wind Action on Behaviour of Transportation Pipelines

2013 ◽  
Vol 837 ◽  
pp. 170-174
Author(s):  
Gheorghe Pintilie
Keyword(s):  
Wind Speed ◽  
Aerodynamic Force ◽  
Mathematical Expression ◽  
Periodic Variation ◽  
Operating Conditions ◽  
Frequency Variation ◽  
Wind Action ◽  
Karman Vortex ◽  
Dynamic Phenomena

The main transportation pipelines are subjected to complex stresses resulting from the nature and state of the transported material, the operating conditions, and the environmental factors and so on. Thus, the stress in the pipe wall is generated and influenced by the pressure, the temperature and the mass of the transported fluid, by the weight of the pipe, the ambient temperature and in certain periods of time by the wind speed. In this paper are presented dynamic phenomena generated by wind flow and their effect on the magistrate transportation pipelines. The content of the paper presents an detailed analysis regarding the regimes in which is developing the force generated by Karman vortex and the situation when resonance phenomena are developed. The study presents a mathematical model that describes the dynamic phenomena generated by the wind action, determining the mathematical expression of the aerodynamic force that act on the normal direction to the wind speed. This force is having a periodic variation, its size and the frequency variation is dependent on the wind speed. Some methods are proposed in order to decrease the wind influence on the lifetime of transportation pipelines. The main results of the study are: determination of the speed range for which the dynamic phenomena have a high influence on the pipeline lifetime; determination of the real conditions that can lead to sharp rises of the pipe deformations; determination of the pipeline lifetime reduction under development of dynamic loads.

Divisor Sums of Generalised Exponential Polynomials

1996 ◽  
Vol 39 (1) ◽  
pp. 35-46 ◽  
Author(s):  
G. R. Everest ◽  
I. E. Shparlinski
Keyword(s):  
Prime Ideal ◽  
Algebraic Integer ◽  
Linear Recurrence ◽  
Exponential Polynomial ◽  
Exponential Polynomials ◽  
Recurrence Sequence ◽  
Special Cases ◽  
Divisor Sums ◽  
Recurrence Sequences

AbstractA study is made of sums of reciprocal norms of integral and prime ideal divisors of algebraic integer values of a generalised exponential polynomial. This includes the important special cases of linear recurrence sequences and general sums of S-units. In the case of an integral binary recurrence sequence, similar (but stronger) results were obtained by P. Erdős, P. Kiss and C. Pomerance.

scholarly journals Determination of Diffusion Coefficients of Selected Long Chain Hydrocarbons using Reversed- Flow Gas Chromatographic Technique

2011 ◽  
Vol 8 (4) ◽  
pp. 1916-1924 ◽  
Author(s):  
Khalisanni Khalid ◽  
Rashid Atta Khan ◽  
Sharifuddin Mohd Zain
Keyword(s):  
Gas Chromatography ◽  
Diffusion Coefficients ◽  
Elution Curve ◽  
Mathematical Expression ◽  
Chromatographic Technique ◽  
Reversed Flow ◽  
Future Studies ◽  
And Diffusion ◽  
Long Chain

The reversed-flow gas chromatography (RF-GC) technique was used to study the evaporation rate and estimating the diffusion coefficient of samples. The RF-GC system comprises of six-port valve, sampling and diffusion column, detector and modified commercial gas chromatography machine. Selected long chain of hydrocarbons (99.99% purity) was used as samples. The solute (stationary phase) were carried out by carrier gas (mobile phase) to the detector. The data obtained from the RF-GC analysis were analysed by deriving the elution curve of the sample peaks using mathematical expression to find the diffusion coefficients values of respective liquids. The values obtained were compared with theoretical values to ensure the accuracy of readings. The interesting findings of the research showed the theoretical values of equilibrium at liquid-gas interphase lead to profound an agreement with the experimental evidence, which contributes for the references of future studies.

Determination of AGMA Geometry Factor J for Slotted External Spur Gears

1983 ◽  
Vol 105 (3) ◽  
pp. 305-311
Author(s):  
Y. P. Singh
Keyword(s):  
Direct Method ◽  
Mining Industry ◽  
Spur Gears ◽  
Input Output ◽  
Typical Application ◽  
Geometry Factor ◽  
Newton Raphson ◽  
A Direct Method ◽  
Raphson Method

This paper presents a direct method for determining the geometry factor J for slotted external spur gears. The location of maximum stressed point on the tooth profile where the stress parabola is tangent to the fillet curve has been determined by solving the resulting nonlinear equations using the sophisticated Newton-Raphson method. The semi-graphical procedure given in AGMA Standard [1] is not convenient for determining the geometry factory J of large gears used in grinding mill and kiln drives in the mining industry. Listing of the computer program and input-output point out for a typical application are presented.

Calculation of the blank twist angle at processing with planetary turning

2016 ◽  
Vol 230 (18) ◽  
pp. 3298-3303 ◽  
Author(s):  
Mikhail S Razumov ◽  
Aleksandr N Grechukhin ◽  
Alexey O Gladyshkin
Keyword(s):  
Mathematical Model ◽  
Cross Section ◽  
Cutting Forces ◽  
Twist Angle ◽  
Mathematical Expression ◽  
Research Problem ◽  
Calculation Scheme ◽  
Technological System ◽  
Test Calculation

The work deals with consideration of the technology of forming many-sided outer surfaces with the variable profile of planetary turning. The peculiarities of this technology were detected and the actuality of the research problem was specified. The essence of study lies in the determination of the cutting force’s effect on the blank rigidity. The calculation scheme and mathematical model, which allow studying the cutting forces effect on the rigidity of technological system during processing, were stated. The dependence of blank rigidity on the form of cross section processing with multiple-blade instrument with planetary movement was determined. The mathematical expression of the allowable twist angle under effect of cutting forces on the blank was offered. This study can be applied as the test calculation at projecting of technological rigging and setting modes of cutting at forming of many-sided outer surfaces with variable profile of planetary turning.

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