On Weyl’s solution for space-times with two commuting Killing fields

1988 ◽  
Vol 415 (1849) ◽  
pp. 329-345 ◽  
Keyword(s):  
Wave Equation ◽  
Differential Equations ◽  
Explicit Form ◽  
Physical Problem ◽  
Frequent Occurrence ◽  
Coordinate Frame ◽  
Physical Problems ◽  
Killing Fields ◽  
Metric Functions ◽  
Selection Of

The solution of the metric coefficients for space-times with diagonal metrics and two commuting Killing fields can be reduced to a Laplace or a wave equation in two variables and to a further pair of integrable differential equations. This reduction can be achieved in a variety of ways. The choice of a coordinate frame and the selection of the combination of metric functions that satisfies the Laplace or the wave equation depend on the physical problem that is considered. The resolution of the issues that arise is illustrated in the contexts of three physical problems; and the solution of the remaining pair of equations, of most frequent occurrence in these contexts, is obtained in explicit form.

Constraints on the accuracy of messenger RNA movement

1985 ◽  
Vol 18 (4) ◽  
pp. 423-450 ◽  
Author(s):  
C. G. Kurland ◽  
Måns Ehrenberg
Keyword(s):  
Messenger Rna ◽  
Experimental Studies ◽  
Physical Problem ◽  
Translational Accuracy ◽  
Trna Species ◽  
Selection Of

SUMMARYTheoretical as well as experimental studies of translational accuracy have most often been concerned with the selection of aminoacyl-tRNA by codon-programmed ribosomes. The selection of the successive codons on the mRNA has received much less attention, probably because it represents both conceptually and experimentally, a much more demanding physical problem. Nevertheless, it would seem that errors in the selection of the codon are potentially much more destructive than errors in selection of aminoacyl-tRNA species. This can be appreciated from the following.

A method for constructing solutions of homogeneous partial differential equations: localized waves

1992 ◽  
Vol 437 (1901) ◽  
pp. 673-692 ◽  
Keyword(s):  
Wave Equation ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Gordon Equation ◽  
Partial Differential ◽  
Wave Solutions ◽  
Propagation Axis ◽  
Potential Applications ◽  
Klein Gordon ◽  
Localized Waves

We introduce a method for constructing solutions of homogeneous partial differential equations. This method can be used to construct the usual, well-known, separable solutions of the wave equation, but it also easily gives the non-separable localized wave solutions. These solutions exhibit a degree of focusing about the propagation axis that is dependent on a free parameter, and have many important potential applications. The method is based on constructing the space-time Fourier transform of a function so that it satisfies the transformed partial differential equation. We also apply the method to construct localized wave solutions of the wave equation in a lossy infinite medium, and of the Klein-Gordon equation. The localized wave solutions of these three equations differ somewhat, and we discuss these differences. A discussion of the properties of the localized waves, and of experiments to launch them, is included in the Appendix.

DIFFERENTIAL EQUATIONS FOR TRAIN STARTING WITH ELASTIC CONNECTIONS

2021 ◽  
Vol 2 ◽  
pp. 18-26
Author(s):  
I.P. POPOV
Keyword(s):  
Mathematical Model ◽  
Differential Equations ◽  
Friction Force ◽  
Static Friction ◽  
Longitudinal Vibrations ◽  
Maximum Tension ◽  
Inert Mass ◽  
The Moment ◽  
Elastic Couplings ◽  
Selection Of

The starting mode for the train is the most difficult. An effective method of pulling is the selection of coupling clearances. In this case, the cars are set in motion sequentially and the inert mass, as well as the static friction force immediately at the moment of starting, are minimal. This method has two significant drawbacks - a small fixed value of the gaps in the couplings and the shock nature of the impulse transfer. These disadvantages can be avoided by using elastically deformable couplings. The aim of this work is to construct a mathematical model of "easy" starting of a train with elastic couplings. The softening of the train start-off mode is essentially due to the replacement of the simultaneous start-off of the sections with alternate ones. To exclude longitudinal vibrations of the composition, after reaching the maximum tension of the coupling, the possibility of its harmonic compression should be mechanically blocked.

scholarly journals Supplier selection using different metric functions

2015 ◽  
Vol 25 (3) ◽  
pp. 413-423 ◽  
Author(s):  
S.E. Omosigho ◽  
Dickson Omorogbe
Keyword(s):  
Supplier Selection ◽  
Selection Process ◽  
Fuzzy Topsis ◽  
Ideal Solution ◽  
Order Preference ◽  
Metric Functions ◽  
Metric Function ◽  
Topsis Technique ◽  
Intuitionistic Fuzzy Topsis ◽  
Selection Of

Supplier selection is an important component of supply chain management in today?s global competitive environment. Hence, the evaluation and selection of suppliers have received considerable attention in the literature. Many attributes of suppliers, other than cost, are considered in the evaluation and selection process. Therefore, the process of evaluation and selection of suppliers is a multi-criteria decision making process. The methodology adopted to solve the supplier selection problem is intuitionistic fuzzy TOPSIS (Technique for Order Preference by Similarity to the Ideal Solution). Generally, TOPSIS is based on the concept of minimum distance from the positive ideal solution and maximum distance from the negative ideal solution. We examine the deficiencies of using only one metric function in TOPSIS and propose the use of spherical metric function in addition to the commonly used metric functions. For empirical supplier selection problems, more than one metric function should be used.

scholarly journals PARENTAL PERCEPTION OF LOW IQ FACTS OR FICTION: RETROSPECTIVE DATA FROM CLINIC IN SEMI RURAL MAHARASHTRA

2019 ◽  
pp. 5-9
Author(s):  
Suchit Suresh Tamboli ◽  
Charudatt Joglekar ◽  
Vasant Desle ◽  
Anvesh Tamboli
Keyword(s):  
Behavioral Problems ◽  
Physical Problem ◽  
Psychological Problems ◽  
Parental Perception ◽  
Physical Problems ◽  
Increasing Trend ◽  
Child Development Center ◽  
Low Iq ◽  
Development Center ◽  
Problem Data

Objective: To study the association between physical and psychological problems perceived by parents and the IQ of their children. Methods: We studied 981 children in the child development center at Ahmednagar. Median age at followup was 7.8y (Q25=5.6y and Q75=10.4y, Babies underwent IQ evaluation by Binet Kamat scale (n=981); also their physical and psychological problems perceived by parents were documented. We categorized children into 4 categories using a number of problems (physical and psychological separately) viz 1 (no problem), 2 (1 problem), 3 (2 problems), 4 (>2 problems). When we looked at physical problem data, 555 (56.6%) had no problem, 251 (25.6%) had 1, 117 (11.9%) had 2, and the remaining 58 (5.9%) had more than 2. For psychological problems like not interested in studies, speech problems don't remember, don't understand, cannot concentrate, fears, etc. The distribution was 221 (22.5%), 212 (21.6%), 222 (22.6%) and 326 (33.3%) respectively. Result: The increasing trend of mean IQ for physical problem parameters from nil to >2 categories and decreasing prevalence of low IQ using the Binet Kamat scale were not significant. However, for psychological problems, the decreasing and statistically significant trend (p=0.000) was present for mean IQ, and a significant increasing trend (p=0.029) for the prevalence of low IQ was observed. Conclusion: Psychological problems were associated with IQ. Numbers of problems were inversely correlated with IQ. Keywords: Parental Perception; Low IQ; Behavioral Problems; Physical Problems.

scholarly journals The Modified Sadik Decomposition Method to Solve a System of Nonlinear Fractional Volterra Integro-Differential Equations of Convolution type

2021 ◽  
Vol 20 ◽  
pp. 335-343
Author(s):  
Prapart Pue-On
Keyword(s):  
Power Series ◽  
Differential Equations ◽  
Explicit Form ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Initial Solution ◽  
Convolution Type ◽  
Adomian Decomposition

In this work, an incorporated form of Sadik transform and Adomian decomposition method which is called the Sadik decomposition method is presented. The method is applied to solve a system of nonlinear fractional Volterra integro-differential equations in the convolution form. To avoid collecting the noise terms that lead the method to fail for seeking the solution, the proposed method is modified by selecting a suitable initial solution. The obtained results are expressed in the explicit form of a power series with easily computable terms. In addition, illustrative examples are shown to demonstrate the effectiveness of the method.

scholarly journals Measuring the Pollutants in a System of Three Interconnecting Lakes by the Semianalytical Method

2021 ◽  
Vol 2021 ◽  
pp. 1-16
Author(s):  
Indranil Ghosh ◽  
M. S. H. Chowdhury ◽  
Suazlan Mt Aznam ◽  
M. M. Rashid
Keyword(s):  
Differential Equations ◽  
Three Dimensional ◽  
Adomian Decomposition Method ◽  
Dimensional System ◽  
Physical Problems ◽  
Runge Kutta Method ◽  
Adomian Decomposition ◽  
Sinusoidal Input ◽  
Semianalytical Method ◽  
Lagrange’S Multipliers

Pollution has become an intense danger to our environment. The lake pollution model is formulated into the three-dimensional system of differential equations with three instances of input. In the present study, the new iterative method (NIM) was applied to the lake pollution model with three cases called impulse input, step input, and sinusoidal input for a longer time span. The main feature of the NIM is that the procedure is very simple, and it does not need to calculate any special type of polynomial or multipliers such as Adomian polynomials and Lagrange’s multipliers. Comparisons with the Adomian decomposition method (ADM) and the well-known purely numerical fourth-order Runge-Kutta method (RK4) suggest that the NIM is a powerful alternative for differential equations providing more realistic series solutions that converge very rapidly in real physical problems.

Design of a Thermostat for Precise Temperature Control From −190 Deg to +650 Deg C

1969 ◽  
Vol 91 (2) ◽  
pp. 168-172
Author(s):  
J. Ansari ◽  
W. Leidenfrost ◽  
R. Oldenburger
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Temperature Control ◽  
Hypothetical Case ◽  
Heat Transfer Medium ◽  
System Parameters ◽  
Set Up ◽  
Proportional Controller ◽  
Cylindrical Block ◽  
Selection Of

A proposed apparatus for controlling temperatures from −190 deg to +650 deg with an estimated accuracy of 0.001 deg C is described. The apparatus utilizes helium as the heat transfer medium. The selection of the gain constants of the controller depends upon the system parameters. The hypothetical case of a solid cylindrical block with an integral plus proportional controller is considered, the differential equations are set up, and a graphical scheme is presented for the selection of the controller constants.

scholarly journals Backstepping-based output regulation of ordinary differential equations cascaded by wave equation with in-domain anti-damping

2018 ◽  
Vol 41 (1) ◽  
pp. 246-262 ◽  
Author(s):  
Jianjun Gu ◽  
Chunqiu Wei ◽  
Junmin Wang
Keyword(s):  
Wave Equation ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
State Feedback ◽  
Solvability Condition ◽  
Reference Signal ◽  
Output Regulation ◽  
The Body ◽  
Output Regulation Problem ◽  
Feedback Regulator

Output regulation is considered in this paper for ordinary differential equations cascaded by a wave equation, in which both the body equations and the uncontrolled end are subject to disturbances. The disturbances are generated by an exosystem. A backstepping state-feedback regulator is first designed to force the output to track the reference signal. The design is based on solving cascaded regulator equations, and the solvability condition of the equations is characterized in terms of a transfer function and the eigenvalues of the exosystem. An observer-based output-feedback regulator is then designed to solve the output regulation problem. Finally, the regulator tracking performance is illustrated through numerical simulations.

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