scholarly journals Uncertain Chemical Langevin Equation

2020 ◽  
Author(s):  
Han Tang ◽  
Xiangfeng Yang
Keyword(s):  
Differential Equation ◽  
Chemical Kinetics ◽  
Langevin Equation ◽  
Half Life ◽  
Reaction Rate ◽  
Rate Of Change ◽  
Uncertain Differential Equation ◽  
Important Research ◽  
Chemical Langevin Equation

Reaction rate is a particularly important research object in chemical kinetics, and it is a measure of the rate of change of reactants. In order to illustrate and clarify the evolution of number of a substance involved in the reaction, this paper derives the uncertain chemical Langevin equation based on uncertain differential equation. Using the actual observations, one can estimate the parameters presented in the uncertain chemical Langevin equation. As an application, half-life of reaction is investigated. Finally, a paradox for the stochastic chemical Langevin equation is given.

Multifactor Uncertain Chemical Reaction Equation

2022 ◽  
Author(s):  
Han Tang
Keyword(s):  
Differential Equation ◽  
Chemical Reaction ◽  
Half Life ◽  
Reaction Pathways ◽  
Uncertain Differential Equation ◽  
Reaction Equation ◽  
Moment Estimation ◽  
Multiple Reactions ◽  
Parallel Reactions ◽  
Generalized Moment

The previous uncertain chemical reaction equation describes the time evolution of single reactions. But in many practical cases, a substance is consumed by several different reaction pathways. For the above considerations, this paper extends the discussion to multiple reactions. Specifically, by taking the decomposition of C2H5OH as an example, parallel reactions with one reactant are analyzed with the multifactor uncertain differential equation. The derived equation is called the multifactor uncertain chemical reaction equation. Following that, the parameters in the multifactor uncertain chemical reaction equation are estimated by the generalized moment estimation. Based on the multifactor uncertain chemical reaction equation, half-life of reaction is investigated. Finally, a numerical example is presented to illustrate the usefulness of the multifactor uncertain chemical reaction equation.

Pricing Convertible Bond in Uncertain Financial Market

2021 ◽  
pp. 2150007
Author(s):  
Zhiqiang Zhang ◽  
Zhenfang Wang ◽  
Xiaowei Chen
Keyword(s):  
Differential Equation ◽  
Financial Market ◽  
Stock Price ◽  
Uncertainty Theory ◽  
Convertible Bonds ◽  
Convertible Bond ◽  
Uncertain Differential Equation ◽  
Numerical Examples ◽  
Liu Process ◽  
Uncertain Calculus

This paper is devoted to evaluating the convertible bonds within the framework of uncertainty theory. Under the assumption that the underlying stock price follows an uncertain differential equation driven by Liu process, the price formulas of convertible bonds and the callable convertible bonds are derived by using the method of uncertain calculus. Finally, two numerical examples are discussed.

scholarly journals A Flexible Synthesis of 68Ga-Labeled Carbonic Anhydrase IX (CAIX)-Targeted Molecules via CBT/1,2-Aminothiol Click Reaction

Molecules ◽  
2018 ◽  
Vol 24 (1) ◽  
pp. 23 ◽  
Author(s):  
Kuo-Ting Chen ◽  
Kevin Nguyen ◽  
Christian Ieritano ◽  
Feng Gao ◽  
Yann Seimbille
Keyword(s):  
Carbonic Anhydrase ◽  
Half Life ◽  
Reaction Rate ◽  
Click Reaction ◽  
Tumor Hypoxia ◽  
Carbonic Anhydrase Ix ◽  
Reaction Conditions ◽  
Positron Emitter ◽  
Radiochemical Yields ◽  
Gallium 68

We herein describe a flexible synthesis of a small library of 68Ga-labeled CAIX-targeted molecules via an orthogonal 2-cyanobenzothiazole (CBT)/1,2-aminothiol click reaction. Three novel CBT-functionalized chelators (1–3) were successfully synthesized and labeled with the positron emitter gallium-68. Cross-ligation between the pre-labeled bifunctional chelators (BFCs) and the 1,2-aminothiol-acetazolamide derivatives (8 and 9) yielded six new 68Ga-labeled CAIX ligands with high radiochemical yields. The click reaction conditions were optimized to improve the reaction rate for applications with short half-life radionuclides. Overall, our methodology allows for a simple and efficient radiosynthetic route to produce a variety of 68Ga-labeled imaging agents for tumor hypoxia.

scholarly journals Transient Analysis of Thermal Treatment Processes Carburizing and Nitriding of Steel Components by Numerical Modeling and Simulation

2019 ◽  
Vol 9 (2) ◽  
pp. 2584-2593
Keyword(s):  
Differential Equation ◽  
Numerical Modeling ◽  
Ambient Temperature ◽  
Modeling And Simulation ◽  
Geometric Dimension ◽  
Rate Of Change ◽  
Critical Parameters ◽  
Numerical Modeling And Simulation ◽  
Linear Differential ◽  
Energy Balance Approach

The purpose of carburizing, nitriding and carbonitriding is to increase the strength of components. Elements such as carbon, nitrogen and carbon-nitride are diffused into the components at high temperature convective environment. The amount of diffusion is to be regulated by controlling the temperature and time of diffusion. Time and temperature of process govern diffusion rate and strength of the component. Numerical modeling is applied by energy balance approach i.e., equating rate of change of energy is equal to energy transferred by conduction, convection and radiation. By non dimensionalising relations for the mentioned critical parameters were obtained. The phenomenon of convection, radiation and conduction are taken together for the purpose of numerical modeling. Variation of temperature and depth of diffusion of component for the taken components i.e., sphere and cube was plotted in transient state. For both numerical analysis and simulation the boundary conditions i.e., for carburization the ambient temperature is 9500C with carbon monoxide as the carburizing agent and for nitriding the ambient temperature is 5300C with nitrogen as nitriding agent and the component taken is of steel which is initially at room temperature were taken. Results obtained from numerical modeling and simulation were compared with each other and observed that in both analyses the variation of temperature with time and depth of diffusion is almost linear. Final differential equation obtained in numerical modeling is a single order non linear differential equation which is solved in MATLAB using finite difference approach. Data obtained from MATLAB were plotted for variation of surface temperature and geometric dimension with respect to time.

scholarly journals SOLVING INVERSE PROBLEM OF CHEMICAL KINETICS WITH USE OF CUBIC SPLINES

2020 ◽  
Vol 63 (7) ◽  
pp. 61-66
Author(s):  
Nikolay I. Kol'tsov
Keyword(s):  
Experimental Data ◽  
Inverse Problem ◽  
Chemical Kinetics ◽  
Good Accuracy ◽  
Cubic Splines ◽  
Rate Of Change ◽  
Reference Points ◽  
Additional Advantage ◽  
Instantaneous Rate ◽  
Relaxation Curves

A simple effective method for solving the inverse problem of chemical kinetics based on non-stationary experiments for multistage reactions occurring in an isothermal reactor of ideal mixing is described. The idea of the method is based on taking into account the distinctive features (informativeness) of different fragments of relaxation curves for chemical reactions with arbitrary (non-monotonic) kinetics and their as accurate approximation as possible. For this purpose, non-linear (cubic) splines are used to describe different informative fragments of relaxation curves, which allow to approximate and interpolate experimental data as accurately as possible. An additional advantage of cubic splines, from the point of view of the implementation of the described method, is their continuity at all given points up to and including second-order derivatives (smoothness). This allows us to calculate with good accuracy not only the concentration of reagents, but also the instantaneous rate of change at any time. The consequence of this is the possibility of a sufficiently accurate solution of the inverse problem based on the data of non-stationary experiments. The correctness of the mathematical model used and the stability of the method were tested using variations of the original data. An example of using the method for determining the intervals of physical values of the rate constants of the stages of a two-stage reaction is given. The influence of the method of selecting the reference points (structure) of the spline and measurement errors (noise) of experimental data on the error of determining the speed constants of the stages is estimated. The efficiency of application and good accuracy of the method for solving the inverse problem of chemical kinetics of multistage reactions occurring in non-gradient systems with taking into account of noise is shown.

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