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1

Flood risk analysis based on nested copula structure in Armand Basin, Iran

Amini Sasan, Bidaki Rafat Zare, Mirabbasi Rasoul, Shafaei Maryam

Acta Geophysica

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2022

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Vol. 70, no 3

1385--1399

EN

Merging different food characteristics in a distribution function is provided by copula structures. In this study, the nested copula structure was used to construct a triradiate distribution of food duration (D), peak (P), and volume (V). The required data were obtained by screening the food events recorded at Armand Gauging Station, Iran. The characteristics of selected 63 food events (1993–2018) were extracted and the best marginal distribution function of each was determined by Kolmogorov–Smirnov test. Then the fitness of six different copula functions (Frank, Clayton, Joe, Gumbel–Hougaard, Gaussian and Student’s t were examined for creating the joint distribution function. The best fitted marginal distribution is Johnson SB, for food duration, and Lognormal (3p), for food peak and food volume. The best-fitted function for creating bivariate and trivariate distributions of food characteristics in Armand Basin is Frank copula. In the next phase, the bivariate and trivariate joint return periods (at two states of AND, OR), Kendall return period and conditional return periods were calculated. The results revealed that the conditional return period of one food variable given two other food variables is greater than the corresponding values for the conditional return period of two food variables given the third food variable.

2

Bivariate food distribution analysis under parametric copula framework: a case study for Kelantan River basin in Malaysia

Latif Shahid, Mustafa Firuza

Acta Geophysica

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2020

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Vol. 68, no. 3

821--859

EN

Flood is becoming an intensive hydro-climatic issue at the Kelantan River basin in Malaysia. Univariate frequency analysis would be unreliable due to multidimensional behaviour of food, which often demands multivariate fow exceedance probabilities. The joint distribution analysis of multiple interacting food characteristics, i.e. food peak, volume and duration, is very useful for understanding critical hydrologic behaviour at a river basin scale. In this paper, a copula-based methodology is incorporated for multivariate food frequency analysis for the 50-year annual basis food characteristics of Kelantan River basin at Guillemard bridge station in Malaysia. Investigation reveals that the Lognormal (2P), Johnson SB-4P and Gamma-3P are selected as marginal distributions for the food peak fow, volume and duration series. Several bivariate families such as mono-parametric, bi-parametric (i.e. mixed version) and rotated version of Archimedean copulas and also the elliptical copula are introduced to cover a large dependence pattern of food characteristics. The dependence parameter of bivariate copulas is estimated by the method of moments (MOM) based on the inversion of Kendall’s tau and maximum pseudo-likelihood estimator. To analytically validate and recognize most parsimonious copulas, GOF test and Cramer–von Mises distance statistics (Sn) with the parametric bootstrap method are employed. The Gaussian copula is identifed as the most justifable model for joint modelling of the food peak–volume and peak–duration combination for MOM-based parameter estimation procedure. Similarly, the Frank copula is selected as the best-ftted structure for modelling peak–duration combination based on MPL estimators, but the MOM estimator recognized Gaussian copula as most suitable for peak–volume pair. Furthermore, the best-ftted copulas are used for obtaining the joint and conditional return periods of the food characteristics

3

Estimation of Network Disordering Effects by In-depth Analysis of the Resequencing Buffer Contents in Steady-state

Pechinkin A., Razumchik R.

Journal of Telecommunications and Information Technology

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2016

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nr 1

53--41

EN

The paper is devoted to the analytic analysis of resequencing issue, which is common in packet networks, using queueing-theoretic approach. The authors propose the mathematical model, which describes the simplest setting of packet resequencing, but which allows one to make the first step in the in-depth-analysis of the queues dynamics in the resequencing buffer. Specifically consideration is given to N-server queueing system (N > 3) with single infinite capacity buffer and resequencing, which may serve as a model of packet reordering in packet networks. Customers arrive at the system according to Poisson flow, occupy one place in the buffer and receive service from one of the servers, which is exponentially distributed with the same parameter. The order of customers upon arrival has to be preserved upon departure. Customers, which violated the order are kept in resequencing buffer which also has infinite capacity. It is shown that the resequencing buffer can be considered as consisting of n, 1 ≤ n ≤ N −1, interconnected queues, depending on the number of busy servers, with i-th queue containing customers, which have to wait for i service completions before they can leave the system. Recursive algorithm for computation of the joint stationary distribution of the number of customers in the buffer and servers, and each queue in resequencing buffer are being obtained. Numerical examples, which show the dynamics of the characteristics of the queues in resequencing buffer are given.

4

Orientacja ciosu w utworach węglanowych triasu obszaru pomiędzy Brudzowicami a Olkuszem

Król M.

Przegląd Geologiczny

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2002

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Vol. 50, nr 5

415-423

PL

Badany obszar obejmował odsłonięcia usytuowane pomiędzy Brudzowicami (okolice Siewierza) a Starym Olkuszem i jest częścią monokliny śląsko - Krakowskiej. Badaniami objęto utwory węglanowe należące głównie do dolnego i środkowego wapienia muszlowego. Celem było przeprowadzenie szczegółowej analizy kierunkowej występujących spękań ciosowych i wydzielenie poszczególnych zespołów spękań. Wyniki przedstawiono w postaci trójwymiarowych diagramów konturowych oraz dwuwymiarowych diagramów rozetowych biegu spękań. Na podstawie zebranych informacji wydzielono zespoły spękań, określając ich parametry rozkładu sferycznego, oraz wyznaczono niektóre parametry szczelinowatości masywu skalnego. Dokonano także porównania rozkładów spękań z poszczególnych odkrywek testem D Kołmogorowa-Smirnowa. W skali regionalnej najbardziej zaznaczają się zespoły ciosu o biegach NE-SW i NW-SE. W części półnono-wschodniej badanego obszaru bardziej widoczne stają się zespoły ciosu o kierunku biegów WNE-ESE i NNW-SSE.

EN

The examined area is a part of the Silesia-Krakow monocline with outcrops distributed between Brudzowice (near Siewierz) and Olkusz. The monocline sediments cover the lower Paleozoic basement and mask the basement's main tectonic lines of regional importance. The measurements were mainly carried out in carbonate rocks of middle and lower mushelcalk. The aim of this paper is to carry out detailed direction analysis of systematic joints and to distinguish individual joint sets of the Triassic sediments. The results are presented on a 3-dimentional stereonet diagrams and 2-dimentional rose diagrams of joints strike. Based on collected information joint sets were set apart. Parameters of spherical distribution and basic fracturing parameters of rock mass were calculated. A comparison of joints distribution between individual outcrops was carried out using a Kolmogorow-Smirnow test. The jointing is vertical or almost vertical. Very seldom there occur joints with dip angle 30-50°. The frequency relations among joint sets are different in each outcrop of studied area. On the regional scale the most remarkable joint sets have the strike directions NE-SW and XW-SE. In the NW part of the studied area joint sets strikes of WNW-ESE and NNW-SSE directions become more apparent.