Maximum crosswind integrated ground level concentration in two stability classes

bl 'kks/k i= esa fu"izHkkoh vkSj vfLFkj fLFkfr;ksa esa ØkWliou lekdfyr lkanz.k ysus ds fy, nks fn’kkvksa esa vfHkogu folj.k lehdj.k ¼ADE½ dks gy fd;k x;k gSA ykIykl :ikarj.k rduhd dk mi;ksx rFkk m/okZ/kj Å¡pkbZ ij vk/kkfjr iou xfr vkSj Hkaoj folj.k’khyrk dh leh{kk djrs gq, ;g gy fudkyk x;k gSA blds lkFk gh Hkw&Lrj vkSj vf/kdre lkanz.kksa dk Hkh vkdyu fd;k x;k gSA geus bl ekWMy esa iwokZuqekfur vkSj izsf{kr lkanz.k vk¡dM+ksa ds e/; rqyuk djus ds fy, dksiugsxu ¼MsuekdZ½ ls fy, x, vkuqHkfod vk¡dM+ksa dk mi;ksx fd;k gSA The advection diffusion equation (ADE) is solved in two directions to obtain the crosswind integrated concentration in neutral and unstable conditions. The solution is solved using Laplace transformation technique and considering the wind speed and eddy diffusivity depending on the vertical height. Also the ground level and maximum concentrations are estimated. We use in this model empirical data from Copenhagen (Denmark) to compare between predicted and observed concentration data.

TASKS TAKING INTO ACCOUNT THE PROFESSIONAL ORIENTATION WHEN CONSIDERING THE TOPIC «LAPLACE TRANSFORMATION» FOR STUDENTS OF THE TRAINING DIRECTION «13.03.02 - ELECTRIC POWER INDUSTRY AND ELECTRICAL ENGINEERING»

Рассматривается специфика преподавания некоторых тем по дисциплине математика в контексте профессиональной направленности обучающихся. The article considers the specifics of teaching some topics in the discipline of mathematics in the context of the professional orientation of students.

Concentrated matrix exponential distributions with real eigenvalues

Concentrated random variables are frequently used in representing deterministic delays in stochastic models. The squared coefficient of variation ( $\mathrm {SCV}$ ) of the most concentrated phase-type distribution of order $N$ is $1/N$ . To further reduce the $\mathrm {SCV}$ , concentrated matrix exponential (CME) distributions with complex eigenvalues were investigated recently. It was obtained that the $\mathrm {SCV}$ of an order $N$ CME distribution can be less than $n^{-2.1}$ for odd $N=2n+1$ orders, and the matrix exponential distribution, which exhibits such a low $\mathrm {SCV}$ has complex eigenvalues. In this paper, we consider CME distributions with real eigenvalues (CME-R). We present efficient numerical methods for identifying a CME-R distribution with smallest SCV for a given order $n$ . Our investigations show that the $\mathrm {SCV}$ of the most concentrated CME-R of order $N=2n+1$ is less than $n^{-1.85}$ . We also discuss how CME-R can be used for numerical inverse Laplace transformation, which is beneficial when the Laplace transform function is impossible to evaluate at complex points.

A Study on the Applications of Laplace Transformation

Mathematics plays an important role in our everyday life. Laplace transform is one of the important tools which is used by researchers to find the solutions of various real life problems modeled into differential equations or simultaneous differential equations or Integral equations. In this paper, we are going to study the details on lapace transform, its properties and “Applications of Laplace Transform in Various Fields”. Various uses of Laplace Transforms in the research problems have been highlighted. Detailed applications of Laplace Transform have been discussed.

Determination of CRLB and Minimum Variance Unbiased Estimator of a DC Signal in AWGN Using Laplace Transform

This paper presents an alternative approach for the determination of Cramer-Rao Lower Bound (CRLB) and Minimum Variance Unbiased Estimator (MVUE) using Laplace transformation. In this work, a DC signal in Additive White Gaussian Noise (AWGN) was considered. During the investigation, a number of experiments were conducted to analyze different possible outputs under different conditions, and then the patterns of the outcomes were studied. Finally closed-form expressions for the CRLB and MVUE were deduced employing the Laplace transformation. The resulting expressions show that the proposed method has almost the same number of steps as the existing method. However, the later requires only the knowledge of algebra to arrive at the CRLB expressions contrary to the existing approach where a strong mathematical background is required and hence making it superior over the existing method, in that sense.