scholarly journals A Simple Mathematical Model of Cyclic Circadian Learning

2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
J. Šimon ◽  
M. Bulko
Keyword(s):  
Mathematical Model ◽  
Differential Equations ◽  
Learning Process ◽  
Memory Retention ◽  
Simple Mathematical Model ◽  
Prior Learning ◽  
Mnemonic Devices ◽  
Concurrent Processes ◽  
Mathematical Operations ◽  
Good Agreement

This paper deals with the derivation of a simple mathematical model of cyclic learning with a period of 24 hours. Various requirements are met with an emphasis and approach which relies on simple mathematical operations, the prediction of measurable quantities, and the creation of uncomplicated processes of calibration. The presented model can be used to answer questions such as the following.Will I be able to memorize a given set of information? How long will it take to memorize information? How long will I remember the information that was memorized?The model is based on known memory retention functions that are in good agreement with experimental results. By the use of these functions and by formalism of differential equations, the concurrent processes of learning and forgetting are described mathematically. The usability of this model is limited to scenarios where logical bonds (connections to prior learning) are not created and mnemonic devices cannot be utilized during the learning process.

Statistical Energy Analysis for Electronic Equipment

1991 ◽  
Vol 113 (3) ◽  
pp. 322-325
Author(s):  
L. Lu
Keyword(s):  
Mathematical Model ◽  
High Frequency ◽  
Vibration Analysis ◽  
Energy Analysis ◽  
Element Model ◽  
Electronic Equipment ◽  
System Response ◽  
Statistical Energy Analysis ◽  
Simple Mathematical Model ◽  
Good Agreement

Vibration response of electronic equipment analyzed by a simple mathematical model or a finite element model can only provide a limited system response calculation. Application of the Statistical Energy Analysis (SEA) was extended to the calculation of the vibrations of individual components. In order to demonstrate the applicability of SEA to instrumentation vibration analysis at high frequency ranges, an 8-component electronic box was chosen for test and analysis. There was good agreement between tested and analytical results in the frequency averaged sense.

The flow in industrial cyclones

1987 ◽  
Vol 178 ◽  
pp. 507-519 ◽  
Author(s):  
M. I. G. Bloor ◽  
D. B. Ingham
Keyword(s):  
Mathematical Model ◽  
Closed Form ◽  
Secondary Flows ◽  
Experimental Investigations ◽  
Main Body ◽  
Simple Mathematical Model ◽  
Good Agreement

A simple mathematical model for the flow in a conical cyclone is developed which allows solutions to be obtained in closed form. The flow in the main body of the cyclone is regarded as inviscid but the nature of the fluid entry to the device and the conical geometry ensure that secondary flows develop which make the flow highly rotational. The results of the theory are compared with data from two quite different experimental investigations, and good agreement is obtained.

Numerical Simulation of Spray Cooling Pond Performance

1987 ◽  
Vol 109 (2) ◽  
pp. 179-185 ◽  
Author(s):  
N. Moussiopoulos
Keyword(s):  
Mathematical Model ◽  
Differential Equations ◽  
Present Model ◽  
Field Measurements ◽  
Equation System ◽  
Spray Cooling ◽  
Cooling Pond ◽  
Dependent Variables ◽  
Model Temperature ◽  
Good Agreement

A mathematical model for predictions of the performance of spray cooling ponds is presented. In contrast to previous methods, the present model requires neither empirical information from field measurements nor an adaptation of model constants. The airflow is described by partial differential equations for the vorticity and the stream function. Turbulence is taken into account by a modified version of the k-ε model. Temperature and humidity of air are obtained by solving appropriate transport differential equations. The equation system is solved by means of a finite difference method. The utilized numerical algorithm has been proved to be reasonably accurate. Predicted distributions for the dependent variables are presented for a circular spray cooling pond and the case of zero wind velocity. Results for the thermal performance of this pond are in good agreement with observations.

Theoretical and experimental research on slip and uplift of the timber-concrete composite beam

BioResources ◽  
2020 ◽  
Vol 15 (3) ◽  
pp. 7079-7099
Author(s):  
Jianying Chen ◽  
Guojing He ◽  
Xiaodong (Alice) Wang ◽  
Jiejun Wang ◽  
Jin Yi ◽  
...  
Keyword(s):  
Differential Equations ◽  
Deformation Theory ◽  
Concrete Slab ◽  
Theoretical Calculations ◽  
Structural Element ◽  
Structural Efficiency ◽  
Theoretical Investigations ◽  
New Type ◽  
Interlayer Slip ◽  
Good Agreement

Timber-concrete composite beams are a new type of structural element that is environmentally friendly. The structural efficiency of this kind of beam highly depends on the stiffness of the interlayer connection. The structural efficiency of the composite was evaluated by experimental and theoretical investigations performed on the relative horizontal slip and vertical uplift along the interlayer between composite’s timber and concrete slab. Differential equations were established based on a theoretical analysis of combination effects of interlayer slip and vertical uplift, by using deformation theory of elastics. Subsequently, the differential equations were solved and the magnitude of uplift force at the interlayer was obtained. It was concluded that the theoretical calculations were in good agreement with the results of experimentation.

Glycemia monitoring

1998 ◽  
Vol 2 ◽  
pp. 23-30
Author(s):  
Igor Basov ◽  
Donatas Švitra
Keyword(s):  
Diabetes Mellitus ◽  
Mathematical Model ◽  
Numerical Methods ◽  
Differential Equations ◽  
Blood Sugar ◽  
Self Regulation ◽  
Physiological System ◽  
Non Linear ◽  
The Mathematical Model

Here a system of two non-linear difference-differential equations, which is mathematical model of self-regulation of the sugar level in blood, is investigated. The analysis carried out by qualitative and numerical methods allows us to conclude that the mathematical model explains the functioning of the physiological system "insulin-blood sugar" in both normal and pathological cases, i.e. diabetes mellitus and hyperinsulinism.

scholarly journals Ultrasonic Waves in Bubbly Liquids: An Analytic Approach

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1309
Author(s):  
P. R. Gordoa ◽  
A. Pickering
Keyword(s):  
Mathematical Model ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Acoustic Waves ◽  
Elliptic Functions ◽  
Coupled System ◽  
Ultrasonic Waves ◽  
Partial Differential ◽  
Special Cases ◽  
Spherical Bubbles

We consider the problem of the propagation of high-intensity acoustic waves in a bubble layer consisting of spherical bubbles of identical size with a uniform distribution. The mathematical model is a coupled system of partial differential equations for the acoustic pressure and the instantaneous radius of the bubbles consisting of the wave equation coupled with the Rayleigh–Plesset equation. We perform an analytic analysis based on the study of Lie symmetries for this system of equations, concentrating our attention on the traveling wave case. We then consider mappings of the resulting reductions onto equations defining elliptic functions, and special cases thereof, for example, solvable in terms of hyperbolic functions. In this way, we construct exact solutions of the system of partial differential equations under consideration. We believe this to be the first analytic study of this particular mathematical model.

Sign in / Sign up

Export Citation Format

Share Document