scholarly journals The Orbit?Lattice Interaction for Lanthanide Ions. I. Determination of Empirical Parameters

1978 ◽  
Vol 31 (1) ◽  
pp. 79 ◽  
Author(s):  
DJ Newman
Keyword(s):  
Lanthanide Ions ◽  
Lattice Vibrations ◽  
Superposition Model ◽  
Coupling Parameters ◽  
Paramagnetic Ions ◽  
Theoretical Results

The coupling between lattice vibrations and electrons in the partly filIed shells of paramagnetic ions is normaIIy presumed to take place via a localized complex consisting of the paramagnetic ion surrounded by its ligands. In such cases the number of parameters is reduced significantly by the use of the superposition model. This model, with some related approximations, has been employed to determine coupling parameters for fluorine, chlorine and oxygen ligands using both experimental and theoretical results.

scholarly journals IV. On the dynamical theory of incompressible viscous fluids and the determination of the criterion

1895 ◽  
Vol 186 ◽  
pp. 123-164 ◽  
Keyword(s):  
Singular Solution ◽  
Physical State ◽  
Theoretical Calculations ◽  
Equations Of Motion ◽  
Dynamical Theory ◽  
Viscous Fluids ◽  
Linear Functions ◽  
Incompressible Viscous Fluids ◽  
Theoretical Results

1. The equations of motion of viscous fluid (obtained by grafting on certain terms to the abstract equations of the Eulerian form so as to adapt these equations to the case of fluids subject to stresses depending in some hypothetical manner on the rates of distortion, which equations Navier seems to have first introduced in 1822, and which were much studied by Cauchy and Poisson) were finally shown by St. Venant and Sir Gabriel Stokes, in 1845, to involve no other assumption than that the stresses, other than that of pressure uniform in all directions, are linear functions of the rates of distortion, with a co-efficient depending on the physical state of the fluid. By obtaining a singular solution of these equations as applied to the case of pendulums in steady periodic motion, Sir G. Stokes was able to compare the theoretical results with the numerous experiments that had been recorded, with the result that the theoretical calculations agreed so closely with the experimental determinations as seemingly to prove the truth of the assumption involved. This was also the result of comparing the flow of water through uniform tubes with the flow calculated from a singular solution of the equations so long as the tubes were small and the velocities slow. On the other hand, these results, both theoretical and practical, were directly at variance with common experience as to the resistance encountered by larger bodies moving with higher velocities through water, or by water moving with greater velocities through larger tubes. This discrepancy Sir G. Stokes considered as probably resulting from eddies which rendered the actual motion other than that to which the singular solution referred and not as disproving the assumption.

Analysis of Stress Concentrations in Thick Cylinders With Sideholes and Crossholes

1972 ◽  
Vol 94 (3) ◽  
pp. 815-824 ◽  
Author(s):  
J. C. Gerdeen
Keyword(s):  
Stress Concentration ◽  
Stress Concentrations ◽  
Concentration Factors ◽  
Stress Concentration Factors ◽  
Experimental Values ◽  
Pressure Stress ◽  
Shrink Fit ◽  
Outside Diameter ◽  
Theoretical Results

An approximate theoretical analysis is presented for the determination of stress concentration factors in thick walled cylinders with sideholes and crossholes. The cylinders are subjected to both internal pressure and external shrink-fit pressure. Stress concentration factors are plotted as functions of the geometrical ratios of outside diameter-to-bore diameter, and bore diameter-to-sidehole diameter. Theoretical results are compared to experimental values available in the literature and results of experiments described in a separate paper.

scholarly journals On the Semi-Local Convergence of a Traub-Type Method for Solving Equations

Foundations ◽  
2022 ◽  
Vol 2 (1) ◽  
pp. 114-127
Author(s):  
Samundra Regmi ◽  
Christopher I. Argyros ◽  
Ioannis K. Argyros ◽  
Santhosh George
Keyword(s):  
Banach Space ◽  
Local Convergence ◽  
Type Method ◽  
Lipschitz Constants ◽  
Solving Equations ◽  
Original Domain ◽  
Theoretical Results

The celebrated Traub’s method involving Banach space-defined operators is extended. The main feature in this study involves the determination of a subset of the original domain that also contains the Traub iterates. In the smaller domain, the Lipschitz constants are smaller too. Hence, a finer analysis is developed without the usage of additional conditions. This methodology applies to other methods. The examples justify the theoretical results.

scholarly journals Mathematical Modelling of Nitric Oxide Release Caused by Exocytosis and Determination of a Stellate Neuron Activity Function in Rat Brain

2007 ◽  
Vol 12 (3) ◽  
pp. 399-408 ◽  
Author(s):  
A. Oleinick ◽  
C. Amatore ◽  
O. Klymenko ◽  
I. Svir
Keyword(s):  
Mathematical Modelling ◽  
Neuron Activity ◽  
Nitric Oxide Release ◽  
Numerical Fitting ◽  
No Release ◽  
Initial Hypothesis ◽  
Gaussian Decomposition ◽  
The Brain ◽  
Theoretical Results

In this work we report the results of the mathematical modelling of NO◦ -release by neurons considering a series of Gaussian bursts, together with its transport in the brain by diffusion. Our analysis relies on the NO◦ -release from a neuron monitored before, during and after its patch-clamp stimulation as detected by an ultramicroelectrode introduced into a slice of living rat’s brain. The parameters of the neuron activity function have been obtained by numerical fitting of experimental data with simulated theoretical results. Within our initial hypothesis about the Gaussian decomposition of NO◦ -release that allowed drawing qualitative and quantitative conclusions about the considered neuron activity function. It is noted that since the activity function can be readily modified this signal processing may be adapted to the treatment of other and maybe more physiologically relevant hypotheses.

scholarly journals Multi-city modeling of epidemics using spatial networks: Application to 2019-nCov (COVID-19) coronavirus in India

2020 ◽  
Author(s):  
Bhalchandra S. Pujari ◽  
Snehal Shekatkar
Keyword(s):  
Hybrid Approach ◽  
Coarse Grained ◽  
Spatial Networks ◽  
Computationally Efficient ◽  
Transport Networks ◽  
Epidemiological Modeling ◽  
Fine Grained ◽  
City Modeling ◽  
Coupling Parameters

The ongoing pandemic of 2019-nCov (COVID-19) coronavirus has made reliable epidemiological modeling an urgent necessity. Unfortunately, most of the existing models are either too fine-grained to be efficient or too coarse-grained to be reliable. Here we propose a computationally efficient hybrid approach that uses SIR model for individual cities which are in turn coupled via empirical transportation networks that facilitate migration among them. The treatment presented here differs from existing models in two crucial ways: first, self-consistent determination of coupling parameters so as to maintain the populations of individual cities, and second, the incorporation of distance dependent temporal delays in migration. We apply our model to Indian aviation as well as railway networks taking into account populations of more than 300 cities. Our results project that through the domestic transportation, the significant population is poised to be exposed within 90 days of the onset of epidemic. Thus, serious supervision of domestic transport networks is warranted even after restricting international migration.

scholarly journals Research Results of the Potato Digger Technological Process

2018 ◽  
Vol 12 (5) ◽  
pp. 14-19 ◽  
Author(s):  
V. M. Alakin ◽  
G. S. Nikitin
Keyword(s):  
Design Parameters ◽  
Operating Speed ◽  
Working Process ◽  
Projectile Motion ◽  
Operating Process ◽  
Cutoff Angle ◽  
The Stability ◽  
Theoretical Results ◽  
Optimum Working

A potato digger equipped with a four­bladed beater operating in connection with rotary separating surface has low material and energy consumption, higher separating efficiency, as well as lower degree of tuber damaging. The potato digger design should include a four­bladed intake­and­feed beater to prevent potato heap transportation faults in front of the first section. (Research purpose) Increasing the technological and economic efficiency of a potato digging­and­ separating unit through the determination of the optimum values of the design parameters and operating process of the intake­and­feed beater. (Materials and methods) the authors have made an overview of general principles of ensuring the stability of the potato heap movement provided by the four­bladed intake­and­feed beater. The dependency of the minimum beater speed on the operating speed of the potato digger has been found to exclude a probability of its overloading. The methodology of calculating the potato heap velocity and the cutoff angle between the material and the beater blades has been worked out by analyzing potato heap lifting to the upper points of the working units of the rotary separator’s first section. Operating speed of the beater has been determined through the differential equation for the speed of a potato heap moving along the blade surface. (Results and discussion) Preliminary potato heap speed and cutoff angle have been found through the equation of dynamics describing the projectile motion of an object thrown at an angle. The operating values of the angles are dependent on the potato digger working speed and can be selected from the triangle of speeds. The authors have determined the dependence of the optimal beater speed on the working speed of a potato digger. Its value should exceed the minimum speed of the beater. (Conclusions) Theoretical results allow proposing the best design features and optimum working process parameters of a four­bladed beater receiving a potato heap, transporting it and lifting on the rotary separating surface.

Methemoglobin in blood as determined by double-wavelength spectrophotometry.

1982 ◽  
Vol 28 (3) ◽  
pp. 508-511 ◽  
Author(s):  
M Sakata ◽  
A Yoshida ◽  
M Haga
Keyword(s):  
Carbon Monoxide ◽  
Spectrophotometric Determination ◽  
Potassium Ferricyanide ◽  
Hemoglobin Derivatives ◽  
Theoretical Results

Abstract We describe spectrophotometric determination of methemoglobin (Met-Hb) in blood by absorbance differences at two wavelengths (characteristic of the instrument used) in the 500-600 nm region. Blood is diluted 100- to 200-fold with a solution containing KCN and carbon monoxide to convert hemoglobin to carboxyhemoglobin and Met-Hb to cyanomethemoglobin (CN-Met-Hb). Carboxyhemoglobin has the same absorbance at the two wavelengths used, so that the differences in absorbance reflect only the CN-Met-Hb component. After measurement of absorbance differences, potassium ferricyanide is added to convert all hemoglobin derivatives to CN-Met-Hb; samples are then remeasured at the same wavelengths. The percentage of Met-Hb is determined from the ratio of the absorbance differences. Results agree satisfactorily with currently accepted procedures and with calculated theoretical results for mixtures of oxyhemoglobin, carboxyhemoglobin, and Met-Hb.

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