Smoothing of time series by the methods of Discrete Mathematical Analysis

2010 ◽  
Vol 11 (4) ◽  
pp. 1-5 ◽  
Author(s):  
S. M. Agayan ◽  
Sh. R. Bogoutdinov ◽  
A. D. Gvishiani ◽  
A. I. Kagan
Keyword(s):  
Time Series ◽  
Mathematical Analysis

Regression derivatives and their application for registration of a tsunami wave arrival by sea-level records

2019 ◽  
pp. 28-41
Author(s):  
Сергей Мартикович Агаян ◽  
Шамиль Рафекович Богоутдинов ◽  
Ольга Васильевна Иванченко ◽  
Дмитрий Альфредович Камаев
Keyword(s):  
Time Series ◽  
Data Processing ◽  
Sea Level ◽  
Discrete Time ◽  
Mathematical Analysis ◽  
Visual Analysis ◽  
Tsunami Wave ◽  
Information Support ◽  
Discrete Time Series ◽  
Wave Arrival

Структура дискретного временного ряда тесно связана со свойствами процесса, который он описывает. В рамках дискретного математического анализа имеется несколько подходов к анализу структуры дискретных рядов: геометрические меры, динамические коридоры и концепция тренда. Для дискретного временного ряда, заданного в общем случае на нерегулярной сетке, с характером тренда тесным образом связана регрессионная производная: области ее положительного (отрицательного) значения соответствуют возрастающим (убывающим) трендам, а границы между ними - экстремумам. В настоящей работе исследуются возможности применения методов дискретного математического анализа для разработки процедуры регистрации вступления волны цунами по оперативным данным измерения уровня моря. The research addresses the possibility of application of the methods of discrete mathematical analysis to develop a procedure for recording tsunami wave arrival on the base of the operational data for measuring sea level. As a basis for constructing a tsunami wave registration procedure, this research uses a schematization of the actions of the oceanographer on-duty during visual analysis of the sea level records. The task of automatic registration of a tsunami wave by sea level recording arises in various situations of information support of the oceanographer on duty. Requirements for the processing of sea level records depend on the situation. The structure of a discrete time series is closely related to the properties of the described process. As part of the discrete mathematical analysis, there are several approaches to the analysis of the structure of discrete series: geometric measures, dynamic corridors and the trend concept. For a discrete time series, given in the general case on an irregular grid, the regression derivative is closely related to the nature of the trend: the areas of its positive (negative) values correspond to the increasing (decreasing) trends, and the boundaries between them are extremes. The content of this research is a presentation of data processing techniques using regression derivatives, constructing data processing procedures based on derivatives, as well as a demonstration of their applicability to the problem of recording tsunami wave arrival according to the measuring of sea level.

Density waves in disk galaxies

1967 ◽  
Vol 31 ◽  
pp. 313-317 ◽  
Author(s):  
C. C. Lin ◽  
F. H. Shu
Keyword(s):  
Mathematical Analysis ◽  
Spiral Structure ◽  
Stellar System ◽  
Collective Modes ◽  
Disk Galaxies ◽  
Spiral Pattern ◽  
Density Waves ◽  
The Galaxy ◽  
Detailed Mathematical Analysis

Density waves in the nature of those proposed by B. Lindblad are described by detailed mathematical analysis of collective modes in a disk-like stellar system. The treatment is centered around a hypothesis of quasi-stationary spiral structure. We examine (a) the mechanism for the maintenance of this spiral pattern, and (b) its consequences on the observable features of the galaxy.

The LDE-Type Flare Occurrence (1969-1993)

1994 ◽  
Vol 144 ◽  
pp. 279-282
Author(s):  
A. Antalová
Keyword(s):  
Time Series ◽  
Fourier Analysis ◽  
Sunspot Cycle ◽  
List Type ◽  
Type Number ◽  
Solar Cycles ◽  
Type Iv ◽  
Long Duration ◽  
Cycle Maximum ◽  
Flare Index

AbstractThe occurrence of LDE-type flares in the last three cycles has been investigated. The Fourier analysis spectrum was calculated for the time series of the LDE-type flare occurrence during the 20-th, the 21-st and the rising part of the 22-nd cycle. LDE-type flares (Long Duration Events in SXR) are associated with the interplanetary protons (SEP and STIP as well), energized coronal archs and radio type IV emission. Generally, in all the cycles considered, LDE-type flares mainly originated during a 6-year interval of the respective cycle (2 years before and 4 years after the sunspot cycle maximum). The following significant periodicities were found:• in the 20-th cycle: 1.4, 2.1, 2.9, 4.0, 10.7 and 54.2 of month,• in the 21-st cycle: 1.2, 1.6, 2.8, 4.9, 7.8 and 44.5 of month,• in the 22-nd cycle, till March 1992: 1.4, 1.8, 2.4, 7.2, 8.7, 11.8 and 29.1 of month,• in all interval (1969-1992):a)the longer periodicities: 232.1, 121.1 (the dominant at 10.1 of year), 80.7, 61.9 and 25.6 of month,b)the shorter periodicities: 4.7, 5.0, 6.8, 7.9, 9.1, 15.8 and 20.4 of month.Fourier analysis of the LDE-type flare index (FI) yields significant peaks at 2.3 - 2.9 months and 4.2 - 4.9 months. These short periodicities correspond remarkably in the all three last solar cycles. The larger periodicities are different in respective cycles.

Computing cell tractions from particle displacements on silicone rubber substrata

1994 ◽  
Vol 52 ◽  
pp. 162-163
Author(s):  
Tim Oliver ◽  
Akira Ishihara ◽  
Ken Jacobsen ◽  
Micah Dembo
Keyword(s):  
Plane Stress ◽  
Linear Elasticity ◽  
Silicone Rubber ◽  
Mathematical Analysis ◽  
Elastic Recovery ◽  
Video Images ◽  
Cell Traction Forces ◽  
Latex Beads ◽  
Cell Traction ◽  
Better Than

In order to better understand the distribution of cell traction forces generated by rapidly locomoting cells, we have applied a mathematical analysis to our modified silicone rubber traction assay, based on the plane stress Green’s function of linear elasticity. To achieve this, we made crosslinked silicone rubber films into which we incorporated many more latex beads than previously possible (Figs. 1 and 6), using a modified airbrush. These films could be deformed by fish keratocytes, were virtually drift-free, and showed better than a 90% elastic recovery to micromanipulation (data not shown). Video images of cells locomoting on these films were recorded. From a pair of images representing the undisturbed and stressed states of the film, we recorded the cell’s outline and the associated displacements of bead centroids using Image-1 (Fig. 1). Next, using our own software, a mesh of quadrilaterals was plotted (Fig. 2) to represent the cell outline and to superimpose on the outline a traction density distribution. The net displacement of each bead in the film was calculated from centroid data and displayed with the mesh outline (Fig. 3).

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