scholarly journals ON EXTREME VALUES OF BIRTH AND DEATH PROCESSES

2021 ◽  
Vol 9 (1) ◽  
pp. 237-249
Author(s):  
I. Matsak
Keyword(s):  
Limit Theorem ◽  
Convergence Rate ◽  
Exponential Distribution ◽  
Queueing Theory ◽  
Extreme Values ◽  
Birth And Death Processes ◽  
Uniform Estimates ◽  
Regeneration Cycle ◽  
The Right ◽  
Right Order

We establish the convergence rate to exponential distribution in a limit theorem for extreme values of birth and death processes. Some applications of this result are given to processes specifying queue length.). We establish uniform estimates for the convergence rate in the exponential distribution in a limit theorem for extreme values of birth and death processes. This topic is closely related to the problem on the time of first intersection of some level u by a regenerating process. Of course, we assume that both time t and level u grow infinitely. The proof of our main result is based on an important estimate for general regenerating processes. Investigations of the kind are needed in different fields: mathematical theory of reliability, queueing theory, some statistical problems in physics. We also provide with examples of applications of our results to extremal queueing problems M/M/s. In particular case of queueing M/M/1, we show that the obtained estimates have the right order with respect to the probability q(u) of the exceeding of a level u at one regeneration cycle, that is, only improvement of the corresponding constants is possible.

The Approximation of Sum of Independent Distributions by the Erlang Distribution Function

2002 ◽  
Vol 7 (1) ◽  
pp. 55-60 ◽  
Author(s):  
Antanas Karoblis
Keyword(s):  
Distribution Function ◽  
Exponential Distribution ◽  
Queueing Theory ◽  
Erlang Distribution ◽  
Estimation Of Error

The exponential distribution and the Erlang distribution function are been used in numerous areas of mathematics, and specifically in the queueing theory. Such and similar applications emphasize the importance of estimation of error of approximation by the Erlang distribution function. The article gives an analysis and technique of error’s estimation of an accuracy of such approximation, especially in some specific cases.

scholarly journals Image Restoration by Learning Morphological Opening-Closing Network

2020 ◽  
Vol 4 (1) ◽  
pp. 87-107
Author(s):  
Ranjan Mondal ◽  
Moni Shankar Dey ◽  
Bhabatosh Chanda
Keyword(s):  
Neural Network ◽  
Image Restoration ◽  
State Of The Art ◽  
Source Code ◽  
Back Propagation ◽  
Image Features ◽  
Main Difficulty ◽  
The Right ◽  
Right Order ◽  
Morphological Opening

AbstractMathematical morphology is a powerful tool for image processing tasks. The main difficulty in designing mathematical morphological algorithm is deciding the order of operators/filters and the corresponding structuring elements (SEs). In this work, we develop morphological network composed of alternate sequences of dilation and erosion layers, which depending on learned SEs, may form opening or closing layers. These layers in the right order along with linear combination (of their outputs) are useful in extracting image features and processing them. Structuring elements in the network are learned by back-propagation method guided by minimization of the loss function. Efficacy of the proposed network is established by applying it to two interesting image restoration problems, namely de-raining and de-hazing. Results are comparable to that of many state-of-the-art algorithms for most of the images. It is also worth mentioning that the number of network parameters to handle is much less than that of popular convolutional neural network for similar tasks. The source code can be found here https://github.com/ranjanZ/Mophological-Opening-Closing-Net

scholarly journals Determination of the order of fractional derivative for subdiffusion equations

2020 ◽  
Vol 23 (6) ◽  
pp. 1647-1662
Author(s):  
Ravshan Ashurov ◽  
Sabir Umarov
Keyword(s):  
Fractional Derivative ◽  
Fixed Time ◽  
Time Instant ◽  
Observation Data ◽  
Additional Information ◽  
Fractional Modeling ◽  
Time Fractional Derivative ◽  
The Right ◽  
Right Order

Abstract The identification of the right order of the equation in applied fractional modeling plays an important role. In this paper we consider an inverse problem for determining the order of time fractional derivative in a subdiffusion equation with an arbitrary second order elliptic differential operator. We prove that the additional information about the solution at a fixed time instant at a monitoring location, as “the observation data”, identifies uniquely the order of the fractional derivative.

scholarly journals The thermochemistry of carbon: valence states, heats of sublimation and energies of linkage

1946 ◽  
Vol 187 (1010) ◽  
pp. 337-357 ◽  
Keyword(s):  
Ground State ◽  
Electronic Configuration ◽  
Dissociation Energies ◽  
True Value ◽  
Valence States ◽  
Chemical Combination ◽  
The Right ◽  
Right Order ◽  
Unambiguous Assignment ◽  
Apparent Conflict

The controversy which exists at the present time between the figures 125 and 170 kcal./g.- atom for the latent heat of sublimation of carbon into monatomic vapour in the ground state originates largely from the neglect to take into consideration the energy required to raise the carbon atoms from the ground ( 3 P ) state to the lowest tetravalent ( 5 S ) electronic configuration corresponding to that in which it is normally found in chemical combination. Consideration of the energies of removal of a hydrogen atom from the methane and ethane molecules and of the energies of reorganization of the resulting radicals leads to the figure 190 ± about 10 kcal. for L 2 , the heat of sublimation into free atoms in the 5 S state. This in turn leads to a satisfactory and unambiguous assignment of values to bond energies (as distinct from dissociation energies) which can now be expressed with an uncertainty of not more than a few kcal. In the light of the valency distinction there remains no sound evidence to maintain the higher value put forward for L 1 and 125 kcal. is unquestionably of the right order. There are strong indications that an earlier estimate of 100 kcal. for the energy level of the 5 S state above the 3 P (ground) state is about 50 % in excess of the true value. The necessity for establishing this branch of thermochemistry on a sound theoretical and experimental footing has long been a very obvious need. The scheme here suggested reconciles points hitherto in apparent conflict, and brings virtually all established experimental knowledge into alignment.

scholarly journals ANALISIS JENIS LAYANAN PENDIDIKAN DAN NON PENDIDIKAN YANG PENTING BAGI PENINGKATAN KEPUASAN MAHASISWA (STUDI KASUS: FAKULTAS TEKNIK UNIVERSITAS DIPONEGORO)

2018 ◽  
Vol 13 (1) ◽  
pp. 7
Author(s):  
Aries Susanty ◽  
Haryo Santoso ◽  
Pramudiastuti Nursyachbani
Keyword(s):  
Taguchi Method ◽  
Student Satisfaction ◽  
Educational Services ◽  
Optimal Result ◽  
One Dimensional ◽  
The Right ◽  
Right Order ◽  
Item Item

AbstrakPenelitian ini memiliki dua tujuan. Pertama, penelitian ini bertujuan untuk mengindentifikasi item layanan pendidikan dan non pendidikan yang dianggap penting untuk peningkatan kepuasan mahasiswa Fakultas Teknik Univesitas Diponegoro (UNDIP). Kedua, penelitian ini bertujuan untuk menyusun sejumlah rekomendasi untuk perbaikan atas item layanan pendidikan  dan non pendidikan yang dianggap penting tersebut. Terdapat 7 dimensi dan 28 item layanan yang digunakan untuk mengindentifikasi jenis layanan pendidikan dan non Pendidikan yang diterima oleh mahasiswa Fakultas Teknik UNDIP. Penelitian ini menggunakan Metode Kano dan Taguchi untuk mengindentifikasi item layanan pendidikan dan non pendidikan yang dianggap paling penting. Dalam hal ini, Metode Kano digunakan untuk memilih sejumlah item layanan pendidikan dan non pendidikan yang termasuk dalam kelompok attractive dan one-dimentional. Adapun Metode Taguchi digunakan untuk dua hal, yang pertama yaitu memverifikasi hasil pengelompokan dari Metode Kano sehingga diperoleh hasil yang lebih optimal dan mengurutkan  prioritas perbaikan dari item-item layanan yang termasuk dalam kelompok  attractive dan one-dimentional. Data untuk penelitian ini diperoleh dari hasil pengisian kuesioner oleh 120 responden untuk kuesioner Kano dan 60 responden untuk kuesioner Taguchi. Hasil pengolahan data dengan menggunakan Metode Kano menunjukkan bahwa terdapat 6 item layanan yang termasuk dalam kategori one-dimensional dan terdapat 2 item layanan .yang termasuk dalam kategori attractive. Selanjutnya, pengolahan data dengan menggunakan  Metode Taguchi diperoleh bahwa terdapat 2 item layanan yang perpindah dari one-dimensional ke attractive dan 1 item layanan yangberpindah dari attractive ke one-dimensional. AbstractAnalysis of the type of educational and non-educational services that are important for the enhancement of student satisfaction (case study Faculty of Engineering, Diponegoro University)] This research has two objective. First this study aims to identify the type of educational and non-educational services that are important for the satisfaction’s enhancement of the student of Faculty Engineering, Diponegoro University. Second, this study aims to formulate some recommendation for improving the type of educational and non-educational services that are important for the satisfaction’s enhancement of the student of Faculty Engineering. There are 7 dimensions and 28 indicators used to identify the type of educational and non-educational received by the student. This research uses the Kano and Taguchi method to identify the type of educational and non-educational services that are important for student. In this case, the Kano method is used to identify educational and non-educational services that are include attractive and one-dimensional categories. Whereas the Taguchi method is used to verify Kano’s categorize result for getting more optimal result than Kano method and to put priorities in the right order of those services that are include attractive and one-dimensional categories. Data for this research is got from questionnaires that were distributed to 120 respondents for Kano method and 60 respondents for Taguchi method. Kano method’s result showed that there are 6 type of services that are include in one-dimensional category and 2 type of services that are include in attractive category.  However, based on validation result that is using Taguchi method showed that there are 5 type of services that are include in one-dimensional category and 3 type of services that are include in attractive category.Keywords: Educational and Non-educational Services; Satisfaction’s Enhancement of Student; Faculty of Engineering Diponegoro Univesity; Kano Method; Taguchi Method.

scholarly journals Berechnung der Oberfläche von Kernmaterie mit Hilfe spezieller Einteilchen-Wellenfunktionen

1962 ◽  
Vol 17 (8) ◽  
pp. 640-649
Author(s):  
Franz Lanzl
Keyword(s):  
Surface Energy ◽  
Plane Waves ◽  
Yukawa Interaction ◽  
Range Interaction ◽  
Zero Range ◽  
Volume Energy ◽  
Order Of Magnitude ◽  
The Right ◽  
Right Order ◽  
Surface Thickness

Using a YUKAWA interaction between the nucleons the volume energy per particle and the specific surface energy are calculated. These expressions assume a very simple form for a zero range interaction. The space parts of the applied orthogonal single particle wave functions are products of plane waves and a momentum independent function which brings about the decrease in density within the surface layer. First the volume energy per particle as a function of the density in the interior of nuclear matter is minimized. The interaction parameters are so selected that the values of the volume energy per particle and the density at the minimum agree with the experimental data. Then the surface energy as a function of the surface thickness is minimized. The values of the surface energy and the surface thickness in the minimum are compared with the empirical data. They are found to be of the right order of magnitude

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