Reaction Rate Theory-Based Mathematical Approximation For The Amount Of Time It Takes For Cellular Respiration To Occur

The venerable process of cellular respiration is essential for cells to produce energy from glucose molecules, in order to carry out cellular work. The process is responsible for producing molecules of ATP, a molecule which is thermodynamically coupled with other biochemical and biophysical processes in order to provide energy for such processes to occur. While the process of cellular respiration is essential to biology, one cycle of the process occurs only in a matter of milliseconds, and so, it would be impractical to measure the time it takes for the process to occur through conventional means. Therefore, using concepts from reaction rate theory, particularly Marcus Theory of electron transfer, Michaelis-Menten kinetics for enzymatic catalysis, and the hard-sphere model of collision theory, I formulate and propose a mathematical approximation for the amount of time it takes forcellular respiration to occur. Through this heuristic approach, quantitatively knowing the amount of time it takes for one cycle of cellular respiration to occur could potentially have future applications in biological research.

A MATHEMATICAL APPROXIMATION TO LEFT-SIDED TRUNCATED NORMAL DISTRIBUTION BASED ON HART’S MODEL

Left-sided truncated distributions (LSTD) have been found in different situations in the industry. For example, the life distribution of used devices is left-sided truncated distribution. Moreover, if a lower specification exists without the upper specification limit, the product distribution is truncated from the left side. Left-sided truncated normal distributions (LSTND) is a special case where the original distribution is normal. LSTND characteristics, as well as cumulative densities and probabilities can be difficult to employ manually, with most practitioners relying largely on specialized (and expensive) software. In many cases, practitioners are against purchasing software, as they are often limited in the number of estimations. The paper will provide an accurate and straightforward approximation to the cumulative density of LSTND. Hart’s normal distribution is simplified and used as a foundation of this model. The maximum absolute error for the curve at different truncation points (i.e., ZL) over the definition range (i.e., [zL: ∞]) is as follows: 0.004303 for ZL=-4, 0.00432 for ZL=-3, 0.00449 for ZL=-2, 0.005727 for ZL=-1, and 0.0106 for ZL=0. Even the maximum errors are very ignorable in probability applications. Further, it is rare to find a truncation point of higher than -2 in the industry.

Measurement Time Reduction by Means of Mathematical Modeling of Enzyme Mediated RedOx Reaction in Food Samples Biosensors

The possibility of measuring in real time the different types of analytes present in food is becoming a requirement in food industry. In this context, biosensors are presented as an alternative to traditional analytical methodologies due to their specificity, high sensitivity and ability to work in real time. It has been observed that the behavior of the analysis curves of the biosensors follow a trend that is reproducible among all the measurements and that is specific to the reaction that occurs in the electrochemical cell and the analyte being analyzed. Kinetic reaction modeling is a widely used method to model processes that occur within the sensors, and this leads to the idea that a mathematical approximation can mimic the electrochemical reaction that takes place while the analysis of the sample is ongoing. For this purpose, a novel mathematical model is proposed to approximate the enzymatic reaction within the biosensor in real time, so the output of the measurement can be estimated in advance. The proposed model is based on adjusting an exponential decay model to the response of the biosensors using a nonlinear least-square method to minimize the error. The obtained results show that our proposed approach is capable of reducing about 40% the required measurement time in the sample analysis phase, while keeping the error rate low enough to meet the accuracy standards of the food industry.

Correction of Non-Linearity of Load Cell using Adaptive Technique with Mathematical Approximation

Load Cell is used to evaluate unknown objects ' weight. It presents noise at the output due to different inner and external variables. The output deviates from the required response. This project's primary goal is to use Adaptive and Approximation methods to rectify a load cell's output reaction. Approximation is used to generate the reference or training signal at first using Approximation techniques. To generate the training signal, Least Square Approximation (LSA) and Particle Swarm Optimization (PSO) techniques are used and optimized to the desired value. This training signal is later used in an adaptive scheme as a reference signal. Adaptive methods are used to correct the load cell's output reaction. In the adaptive filter, Least Means Square Algorithms are used to remove the noisy load cell output with the adaptive filter. The noise is primarily caused by the creeping and drifting mistake at the output. The Adaptive Filter utilizes the reference signal produced by approximation methods to eliminate both creeping and drifting errors and to produce a load cell's required reaction.

HISTORY AND PRACTICE OF TECHNICAL METHODS OF THE INTERNATIONAL CURRENCY MARKET

Introduction. Technical analysis is an assessment of the behavior of the international currency market over a period of time. Due to the unpredictability of the dynamics of the international currency market and the possibility of losses from the conducted transactions, the study of technical means becomes of particular importance and relevance. It is the comparative analysis that identifies the advantages and disadvantages of each of the methods in order to further formulate the most profitable trading strategy. The purpose of the article is a comparative analysis of the technical analysis methods used by analysts in today's international currency market; comparing the selected instruments of each method and determining the most effective ones. Results. Within the framework of this study three main methods of technical analysis of the international currency market were considered: graphic, method of mathematical approximation and theory of economic cycles. The individual instruments of each of the methods, such as «Japanese candlestick», simple moving average, the moving average convergence divergence (MACD), MACD histogram, Elliott waves, Fibonacci retracement levels are reviewed. A comparative analysis of the selected instruments is carried out on the basis of research of the specificity of each of them. Examples of graphs, indicators and histograms are given. It is identified that the main differences are the complexity of use (ie the use of mathematical computing and computer technology) and the type of strategy (short or long term). Common features of methods of technical analysis of the currency market are: the purpose of the analysis, the object of analysis and the influence of the factor «psychology of people». Conclusions. It is revealed that one can obtain the most accurate results in predicting the dynamics of currency quotations only by combining several methods simultaneously. Knowing the strengths and weaknesses of different technical analysis tools, you can use them to validate each other's signals. As a result of such tactics, the analyst will get more accurate indicators that will bring him a profit. The prospect of the research is to find the best strategic schemes using a wide range of technical tools for international currency market analysis.

Jackfruit as an Object of Drying: A Hygroscopic Study

Statics of drying is based on the laws of interaction between the gas medium and the dehydration facility, which seek a thermodynamically equilibrium state. Jackfruit is a wet thermolabile material. With a static equilibrium between the product and the environment, the water content in a hygroscopic state depends on the type of the product, its energy, humidity, and a number of parameters, e.g. temperature and partial pressure of the vapor on the surface. The paper introduces graphical dependences of the activity of water of jackfruit slices on humidity at various ambient temperatures. The authors also give its analogy in semilogarithmic coordinates. It helped to define a range of humidity that determined the type of connection between the moisture of the object and the dry residue. The laws of the mechanism of heat and mass transfer are relevant in determining the dynamics of the dehydration process. Their study can help to intensify the process of moisture removal with rational operating parameters. The present study featured the equilibrium states in the system, which made it possible to find the driving force of moisture transfer and to evaluate the heat carrier potential, as well as to substantiate the values of the parameters and the environment during storage and transportation of the finished dry product. The value of relative moisture content in equilibrium was determined by isothermal sorption curves. The value depends on the pre-treatment of the drying object, the conditions of its contact with the external environment, as well as by the energy and type of relationship between the dry residue and the moisture. The empirical results were arranged in the form of graphical dependences, which made it possible to theoretically obtain their mathematical approximation. The equations of dependence between the equilibrium moisture content of the material and the relative humidity of the vapor-air medium included a lot of constants, which also needed to be determined empirically. The mathematical dependences approximate the isothermal sorption curves, i.e. the relationship between the product’s moisture and water activity indices. The dependences can be used to conduct a thermodynamic analysis of the sorption process and determine the free, bound, and internal energies of the process of moisture absorption by the capillary-porous object of study. The hygroscopic examination of jackfruit is also necessary when making design decisions for the rational implementation of technological operations, including the storage and transportation of dry jackfruit slices.

Mathematical Approximation for Modeling the Photonic Crystal Fibers

In this research a mathematical approximation for modeling a PCFs is derived. The effective refractive index neff of the clad region obtained by this relation will be used to study the properties of the PCFs such as normalized frequency, effective area, group velocity dispersion and the nonlinear coefficient. All these properties are studied when the holes of the PCFs are filled with air ,or with any material like chloroform. The merit of our mathematical approximation is that, neff can be easily and directly calculated, then the dispersion profile can be controlled by fine manipulating the (d/Λ) of circular or elliptical air holes in PCF cladding. The results show good agreement with published works. The MATLAB 2010 program is used in this study, which is the most successful program to get appropriate diagrams and results

Mathematical modeling of thermal explosion with natural convection: a brief survey

Thermal (or heat) explosion occurs in a reacting medium if the heat production due to an exothermic chemical reaction exceeds the heat loss through the boundary. In the mathematical approximation heat explosion is characterized by an unbounded temperature growth. If the reaction occurs in a liquid or gaseous medium, then a nonuniform temperature distribution can lead to natural convection. The interaction of heat explosion with natural convection can result in various regimes with a bounded temperature distribution (stationary, periodic, chaotic) and to a transition to heat explosion. The latter can be accompanied by a monotonic temperature growth or by temperature oscillations (oscillating heat explosion). This paper presents a review on mathematical modelling of heat explosion with natural convection in a homogeneous fluid and in a porous medium.

A mathematical model of transition of the material from elastic to elasto-plastic state

The goal of this study is to develop a mathematical model of the transition of the structural material from elastic state to elastoplastic state upon tension. The model is based on a modified three-parameter transition operator from one mathematical function to another. A procedure of the mathematical approximation of the transition and corresponding algorithm, which provides a generalized canonical description of the transition, regardless of the form of the functions that characterize the system behavior before and after the transition are presented. The technique is used to describe the transition of two structural materials from the elastic to elastoplastic state upon tension of the samples. Initial sections of the tension diagram are described using three empirical parameters. The role of each of them — maximum permissible relative deformation, transition rate and asymmetry of the transition — are determined. Statistical interpretation of the elastoplastic transition is developed and substantiated. Mathematical expressions for the integral probability function and probability density functions that provide numerical statistical estimation of the degree of change in the state of the structural elements of the material during loading are derived. Analytical description of the initial part of the tension diagram of the material can be used to rearrange the diagrams when modeling deformation processes in conditions of reversible elastoplastic loading.