MODELING OF ATOMIC SYSTEMS AND POSITIONING OF ELEMENTS OF NOBLE GASES OF THE PERIODIC TABLE BY PROPORTIONAL DIVISION METHOD

This paper studies regularities of proportional division, on the basis of which we show the possibility of effective application of the golden section method to modeling regularities of atomic systems and positioning of elements of noble gases of the periodic table. It is illustrated that by partial reconstruction of the Mendeleev tables, the elements of noble gases can be arranged along lines whose slope tangents in the coordinate system “the atomic number – the relative atomic mass” are in close agreement with the sequence of inverse Fibonacci numbers. It was shown that given the correct slope of axes, slope tangents of the corresponding lines does not change.

PEMILIHAN PARAMETER OPTIMUM MENGGUNAKAN EXPONENTIAL SMOOTHING DENGAN METODE GOLDEN SECTION UNTUK PERAMALAN JUMLAH TITIK PANAS DI KALIMANTAN TIMUR

The exponential smoothing method is one method that can be used to predict time series data by smoothing the data. In this study, the method used was exponential smoothing with one smoothing parameter from Brown. The data used is the number of hotspots in East Kalimantan from January 2019 to September 2019. The purpose of this study is to obtain the optimum smoothing parameter values for exponential smoothing from the results of the optimization process using the golden section method to minimize the MAPE value, to obtain forecasting results for each method in exponential smoothing for the number of hotspots in East Kalimantan from October to December 2019, and obtain a good exponential smoothing method to predict data on the number of hotspots in East Kalimantan. From this analysis, the researchers chose the methods used were DES and TES. The optimum smoothing parameter obtained at DES was 0,558430 and TES was 0,376352. The results of forecasting the number of hotspots obtained in DES in October were 2.142, November was 2.707, and December was 3.271 with a MAPE value of 95%. The TES method forecasting results were obtained in October as many as 2.193, November as much as 2.975, and December as many as 3.852 with a MAPE value of 108%. Based on the comparison of the MAPE values in the two methods, the DES method is better than the TES for calculating the predicted value of the number of hotspots in East Kalimantan, although the two methods are not yet suitable for handling this case.

New One-Dimensional Search Iteration Algorithm and Engineering Application

In structural optimization design, obtaining the optimal solution of the objective function is the key to optimal design, and one-dimensional search is one of the important methods for function optimization. The Golden Section method is the main method of one-dimensional search, which has better convergence and stability. Based on the solution of the Golden Section method, this paper proposes an efficient one-dimensional search algorithm, which has the advantages of fast convergence and good stability. An objective function calculation formula is introduced to compare and analyse this method with the Golden Section method, Newton method, and Fibonacci method. It is concluded that when the accuracy is set to 0.1, the new algorithm needs 3 iterations to obtain the target value. The Golden Section method takes 11 iterations, and the Fibonacci method requires 11 iterations. The Newton method cannot obtain the target value. When the accuracy is set to 0.01, the number of iterations of the new method is still the least. The optimized design of the T-section beam is introduced for engineering application research. When the accuracy is set to 0.1, the new method needs 3 iterations to obtain the target value and the Golden Section method requires 13 iterations. When the accuracy is set to 0.01, the new method requires 4 iterations and the Golden Section method requires 18 iterations. The new method has significant advantages in the one-dimensional search optimization problem.

ON THE ACCELERATION OF OPTIMIZATION METHODS FOR THE PROBLEM OF SYNTHESIS OF MULTILAYER OPTICAL COATINGS

Five ways to speed up the multidimensional search in order to solve the problem of synthesis of multilayer optical coatings by using the methods of zero and first orders have been considered. The first way is to use an analytical derivative for the target quality function of the multilayer coating. It allows us to calculate accurately (within the computer arithmetic) the value of the gradient of a smooth objective function and generalized gradient of a non-smooth objective one. The first way requires the same number of arithmetic operations as well as finite-difference methods of calculating the gradient and the generalized gradient. The second way is to use a speedy finding of the objective function gradient using the prefix- and suffix-arrays in the analytical method of calculating the gradient. This technique allows us to reduce the number of arithmetic operations thrice for large-scale problems. The third way is the use of tabulating the values of trigonometric functions to calculate the characteristic matrices. This technique reduces the execution time of multiplication operations of characteristic matrices ten times depending on the computer’s specifications. For some computer architectures, this advantage is more than 140 times. The fourth method is the use of the golden section method for the one-dimensional optimization in the problems of synthesis of optical coatings. In particular, when solving one partial problem it is shown that the ternary search method requires approximately 40% more time than the golden section method. The fifth way is to use the effective implementation of multiplication of two matrices. It lies in changing the order of the second and third cycles for the well-known method of multiplying two matrices and fixing in a common variable value of the element of the first matrix. This allows us to speed up significantly the multiplication operation of two matrices. For matrices having 1000 x 1000 dimension the acceleration is from 2 to 15 times, depending on the computer's specifications.

Perancangan Aplikasi Peramalan untuk Metode Exponential Smoothing Menggunakan Aplikasi Lazarus (Studi Kasus: Data Konsumsi Listrik Kota Samarinda)

Exponential smoothing is forecasting method used to predict the future. Lazarus is an open source software based on free pascal compiler. at this research, program Lazarus be design used exponential smoothing method to predict electricity consumption data in Samarinda City from September to November 2018. Purposed of this researched is to determine the procedure of building an exponential smoothing forecasting application and obtained forecasting result using the built application. Procedure of built the application are designed interface, designed properties and filled coding. The optimum smoothing parameters were obtained used the golden section method. Based on the analysis, electricity consumption data in Samarinda City shows a trend pattern, then the forecasting was used double exponential smoohting (DES) method are DES Brown and DES Holt. The best forecasting method for at this researched is DES Holt, because DES Holt method produced MAPE 0,0659% less than DES Brown method produced MAPE 0,0843%.

Buckling behavior of laminated composite cylinders under external hydrostatic pressure

PurposeThe objective of this paper is to investigate numerically the buckling behavior of submersible composite cylinders.Design/methodology/approachBy means of FEM and golden section method, the search of hoop winding layers, longitudinal winding layers and helical winding layers are studied to optimize the buckling pressure. Considering the mid-strengthening cylinder, the size and distribution of stiffeners are studied systematically.FindingsThe results show that laying the hoop winding layers in the two outer sidewalls and the longitudinal winding layers in the middle of the shell is helpful to increase the buckling pressure, and the optimal helical winding angle changes with slenderness ratio.Originality/valueFor mid-strengthening cylinder, the effect of helical winding angle of stiffener on buckling pressure becomes weak gradually with the increase of stiffener thickness. With the increasing of the spacing between stiffeners, the buckling pressure increases first and decreases later. What is more, the mid-strengthening cylinder is less sensitive to the initial geometric imperfections than unstiffened shells.