49 research outputs found
Some light-traffic and heavy-traffic results for the GI/G/n/0 queue using the GM Heuristic
ΠΡΠΎΠ°Π½Π°Π»ΡΠ·ΠΎΠ²Π°Π½ΠΎ ΠΉΠΌΠΎΠ²ΡΡΠ½ΠΎΡΡΡ Π²ΡΡΠ°ΡΠΈ Π²ΠΈΠΌΠΎΠ³ΠΈ Π² Π±Π°Π³Π°ΡΠΎΠΊΠ°Π½Π°Π»ΡΠ½ΡΠΉ ΡΠΈΡΡΠ΅ΠΌΡ ΠΎΠ±ΡΠ»ΡΠ³ΠΎΠ²ΡΠ²Π°Π½Π½Ρ Π· Π²ΡΠ΄ΠΌΠΎΠ²Π°ΠΌΠΈ GI/G/n/0 ΡΠΊ Ρ Π²ΠΈΠΏΠ°Π΄ΠΊΡ ΠΌΠ°Π»ΠΎΠ³ΠΎ Π½Π°Π²Π°Π½ΡΠ°ΠΆΠ΅Π½Π½Ρ, ΡΠ°ΠΊ Ρ Π²Π΅Π»ΠΈΠΊΠΎΠ³ΠΎ. ΠΠ½Π°Π»ΡΠ· ΠΎΡΠ½ΠΎΠ²Π°Π½ΠΈΠΉ Π½Π° Π΅Π²ΡΠΈΡΡΠΈΡΡ GM , Π΄Π»Ρ ΡΠΊΠΎΡ Π²ΠΈΠΏΠ°Π΄ΠΎΠΊ ΠΏΠΎΠΌΡΡΠ½ΠΎΠ³ΠΎ Π½Π°Π²Π°Π½ΡΠ°ΠΆΠ΅Π½Π½Ρ Π΄Π΅ΡΠ°Π»ΡΠ½ΠΎ Π²ΠΈΠ²ΡΠ΅Π½ΠΎ ΡΠ°Π½ΡΡΠ΅. ΠΠ½Π°ΠΉΠ΄Π΅Π½ΠΎ Π΄ΠΎΡΡΠ°ΡΠ½Ρ ΡΠΌΠΎΠ²ΠΈ Π΄Π»Ρ Π°ΡΠΈΠΌΠΏΡΠΎΡΠΈΡΠ½ΠΎΡ ΡΠΎΡΠ½ΠΎΡΡΡ Π΅Π²ΡΠΈΡΡΠΈΠΊΠΈ GM Ρ Π²ΠΈΠΏΠ°Π΄ΠΊΡ ΠΌΠ°Π»ΠΎΠ³ΠΎ Π½Π°Π²Π°Π½ΡΠ°ΠΆΠ΅Π½Π½Ρ. Π¦Ρ Π΅Π²ΡΠΈΡΡΠΈΠΊΠ° ΠΌΠ°Ρ Π²ΠΊΠ°Π·Π°Π½Ρ Π²Π»Π°ΡΡΠΈΠ²ΡΡΡΡ ΡΠ°ΠΊΠΎΠΆ Ρ Π²ΠΈΠΏΠ°Π΄ΠΊΡ Π²Π΅Π»ΠΈΠΊΠΎΠ³ΠΎ Π½Π°Π²Π°Π½ΡΠ°ΠΆΠ΅Π½Π½Ρ, ΡΠΊΡΠΎ ΡΠΈΡΠ»ΠΎ ΠΊΠ°Π½Π°Π»ΡΠ² n ΠΏΡΡΠΌΡΡ Π΄ΠΎ Π½Π΅ΡΠΊΡΠ½ΡΠ΅Π½Π½ΠΎΡΡΡ.In this paper we carry out both light-traffic and heavy-traffic analyses for the calculation of steady-state loss probabilities in the general multi-server queueing loss system, the GI /G/n/0 queue. The analysis makes use of a heuristic approach called the GM Heuristic, for which a detailed analysis in normal traffic has previously been published. Sufficient conditions are given for the GM Heuristic to be asymptotically exact in light traffic. The heuristic is also shown to be asymptotically exact in heavy-traffic when the number of servers n tends to infinity. These results are illustrated numerically using two-phase Coxian distributions for both the inter-arrival time and service time
Goniometer control
The control unit for the goniometer has been developed and manufactured. The unit includes four independent programmable stepper motor control channels, three logical channels for analyzing the state of limit switches and a power supply. Powerful field-effect transistors of the company International Rectifier are used as controlled power switches. To generate output signals and communicate with a computer, an ATmega328 microprocessor is used in each control channel. This channel design allows you to control almost any type of stepper motors, you only need to replace the control program. The software is written using the WinAVR package which has a General Public License. Data transfer between the computer and the unit is carried out via the USB interface.Π ΠΎΠ·ΡΠΎΠ±Π»Π΅Π½ΠΎ ΡΠ° Π²ΠΈΠ³ΠΎΡΠΎΠ²Π»Π΅Π½ΠΎ Π±Π»ΠΎΠΊ ΡΠΏΡΠ°Π²Π»ΡΠ½Π½Ρ Π³ΠΎΠ½ΡΠΎΠΌΠ΅ΡΡΠΎΠΌ. ΠΠΎ ΡΠΊΠ»Π°Π΄Ρ Π±Π»ΠΎΠΊΡ Π²Ρ
ΠΎΠ΄ΡΡΡ ΡΠΎΡΠΈΡΠΈ Π½Π΅Π·Π°Π»Π΅ΠΆΠ½ΠΈΡ
ΠΏΡΠΎΠ³ΡΠ°ΠΌΠΎΠ²Π°Π½ΠΈΡ
ΠΊΠ°Π½Π°Π»ΠΈ ΠΊΠ΅ΡΡΠ²Π°Π½Π½Ρ ΠΊΡΠΎΠΊΠΎΠ²ΠΈΠΌΠΈ Π΄Π²ΠΈΠ³ΡΠ½Π°ΠΌΠΈ, ΡΡΠΈ Π»ΠΎΠ³ΡΡΠ½ΠΈΡ
ΠΊΠ°Π½Π°Π»ΠΈ Π°Π½Π°Π»ΡΠ·Ρ ΡΡΠ°Π½Ρ ΠΊΡΠ½ΡΠ΅Π²ΠΈΡ
Π²ΠΈΠΌΠΈΠΊΠ°ΡΡΠ² ΡΠ° Π΄ΠΆΠ΅ΡΠ΅Π»ΠΎ Π΅Π»Π΅ΠΊΡΡΠΎΠΆΠΈΠ²Π»Π΅Π½Π½Ρ. Π ΡΠΊΠΎΡΡΡ ΠΊΠ΅ΡΠΎΠ²Π°Π½ΠΈΡ
ΡΠΈΠ»ΠΎΠ²ΠΈΡ
ΠΊΠ»ΡΡΡΠ² Π²ΠΈΠΊΠΎΡΠΈΡΡΠΎΠ²ΡΡΡΡΡΡ ΠΏΠΎΡΡΠΆΠ½Ρ ΠΏΠΎΠ»ΡΠΎΠ²Ρ ΡΡΠ°Π½Π·ΠΈΡΡΠΎΡΠΈ ΡΡΡΠΌΠΈ International Rectifier. ΠΠ»Ρ ΡΠΎΡΠΌΡΠ²Π°Π½Π½Ρ Π²ΠΈΡ
ΡΠ΄Π½ΠΈΡ
ΡΠΈΠ³Π½Π°Π»ΡΠ² Ρ Π·Π²βΡΠ·ΠΊΡ Π· ΠΊΠΎΠΌΠΏβΡΡΠ΅ΡΠΎΠΌ Ρ ΠΊΠΎΠΆΠ½ΠΎΠΌΡ ΠΊΠ°Π½Π°Π»Ρ ΡΠΏΡΠ°Π²Π»ΡΠ½Π½Ρ Π²ΠΈΠΊΠΎΡΠΈΡΡΠΎΠ²ΡΡΡΡΡΡ ΠΌΡΠΊΡΠΎΠΏΡΠΎΡΠ΅ΡΠΎΡ ATmega328. Π’Π°ΠΊΠ° ΠΏΠΎΠ±ΡΠ΄ΠΎΠ²Π° ΠΊΠ°Π½Π°Π»Ρ Π΄ΠΎΠ·Π²ΠΎΠ»ΡΡ ΡΠΏΡΠ°Π²Π»ΡΡΠΈ ΠΏΡΠ°ΠΊΡΠΈΡΠ½ΠΎ Π±ΡΠ΄Ρ-ΡΠΊΠΈΠΌ ΡΠΈΠΏΠΎΠΌ ΠΊΡΠΎΠΊΠΎΠ²ΠΈΡ
Π΄Π²ΠΈΠ³ΡΠ½ΡΠ², ΠΏΠΎΡΡΡΠ±Π½ΠΎ ΡΡΠ»ΡΠΊΠΈ Π·Π°ΠΌΡΠ½ΠΈΡΠΈ ΠΏΡΠΎΠ³ΡΠ°ΠΌΡ ΡΠΏΡΠ°Π²Π»ΡΠ½Π½Ρ. ΠΡΠΎΠ³ΡΠ°ΠΌΠ½Π΅ Π·Π°Π±Π΅Π·ΠΏΠ΅ΡΠ΅Π½Π½Ρ Π½Π°ΠΏΠΈΡΠ°Π½ΠΎ Π· Π²ΠΈΠΊΠΎΡΠΈΡΡΠ°Π½Π½ΡΠΌ ΠΏΠ°ΠΊΠ΅ΡΠ° WinAVRΠ± ΡΠΊΠΈΠΉ ΠΌΠ°Ρ General Public License. ΠΠ΅ΡΠ΅Π΄Π°ΡΠ° Π΄Π°Π½ΠΈΡ
ΠΌΡΠΆ ΠΊΠΎΠΌΠΏβΡΡΠ΅ΡΠΎΠΌ ΡΠ° Π±Π»ΠΎΠΊΠΎΠΌ Π·Π΄ΡΠΉΡΠ½ΡΡΡΡΡΡ Π·Π° Π΄ΠΎΠΏΠΎΠΌΠΎΠ³ΠΎΡ USB-ΡΠ½ΡΠ΅ΡΡΠ΅ΠΉΡΡ.Π Π°Π·ΡΠ°Π±ΠΎΡΠ°Π½ ΠΈ ΠΈΠ·Π³ΠΎΡΠΎΠ²Π»Π΅Π½ Π±Π»ΠΎΠΊ ΡΠΏΡΠ°Π²Π»Π΅Π½ΠΈΡ Π³ΠΎΠ½ΠΈΠΎΠΌΠ΅ΡΡΠΎΠΌ. Π ΡΠΎΡΡΠ°Π² Π±Π»ΠΎΠΊΠ° Π²Ρ
ΠΎΠ΄ΡΡ ΡΠ΅ΡΡΡΠ΅ Π½Π΅Π·Π°Π²ΠΈΡΠΈΠΌΡΡ
ΠΏΡΠΎΠ³ΡΠ°ΠΌΠΌΠΈΡΡΠ΅ΠΌΡΡ
ΠΊΠ°Π½Π°Π»Π° ΡΠΏΡΠ°Π²Π»Π΅Π½ΠΈΡ ΡΠ°Π³ΠΎΠ²ΡΠΌΠΈ Π΄Π²ΠΈΠ³Π°ΡΠ΅Π»ΡΠΌΠΈ, ΡΡΠΈ Π»ΠΎΠ³ΠΈΡΠ΅ΡΠΊΠΈΡ
ΠΊΠ°Π½Π°Π»Π° Π°Π½Π°Π»ΠΈΠ·Π° ΡΠΎΡΡΠΎΡΠ½ΠΈΡ ΠΊΠΎΠ½Π΅ΡΠ½ΡΡ
Π²ΡΠΊΠ»ΡΡΠ°ΡΠ΅Π»Π΅ΠΉ ΠΈ ΠΈΡΡΠΎΡΠ½ΠΈΠΊ ΡΠ»Π΅ΠΊΡΡΠΎΠΏΠΈΡΠ°Π½ΠΈΡ. Π ΠΊΠ°ΡΠ΅ΡΡΠ²Π΅ ΡΠΏΡΠ°Π²Π»ΡΠ΅ΠΌΡΡ
ΡΠΈΠ»ΠΎΠ²ΡΡ
ΠΊΠ»ΡΡΠ΅ΠΉ ΠΈΡΠΏΠΎΠ»ΡΠ·ΡΡΡΡΡ ΠΌΠΎΡΠ½ΡΠ΅ ΠΏΠΎΠ»Π΅Π²ΡΠ΅ ΡΡΠ°Π½Π·ΠΈΡΡΠΎΡΡ ΡΠΈΡΠΌΡ International Rectifier. ΠΠ»Ρ ΡΠΎΡΠΌΠΈΡΠΎΠ²Π°Π½ΠΈΡ Π²ΡΡ
ΠΎΠ΄Π½ΡΡ
ΡΠΈΠ³Π½Π°Π»ΠΎΠ² ΠΈ ΡΠ²ΡΠ·ΠΈ Ρ ΠΊΠΎΠΌΠΏΡΡΡΠ΅ΡΠΎΠΌ Π² ΠΊΠ°ΠΆΠ΄ΠΎΠΌ ΠΊΠ°Π½Π°Π»Π΅ ΡΠΏΡΠ°Π²Π»Π΅Π½ΠΈΡ ΠΈΡΠΏΠΎΠ»ΡΠ·ΡΠ΅ΡΡΡ ΠΌΠΈΠΊΡΠΎΠΏΡΠΎΡΠ΅ΡΡΠΎΡ ATmega328. Π’Π°ΠΊΠΎΠ΅ ΠΏΠΎΡΡΡΠΎΠ΅Π½ΠΈΠ΅ ΠΊΠ°Π½Π°Π»Π° ΠΏΠΎΠ·Π²ΠΎΠ»ΡΠ΅Ρ ΡΠΏΡΠ°Π²Π»ΡΡΡ ΠΏΡΠ°ΠΊΡΠΈΡΠ΅ΡΠΊΠΈ Π»ΡΠ±ΡΠΌ ΡΠΈΠΏΠΎΠΌ ΡΠ°Π³ΠΎΠ²ΡΡ
Π΄Π²ΠΈΠ³Π°ΡΠ΅Π»Π΅ΠΉ, ΡΡΠ΅Π±ΡΠ΅ΡΡΡ ΡΠΎΠ»ΡΠΊΠΎ Π·Π°ΠΌΠ΅Π½ΠΈΡΡ ΠΏΡΠΎΠ³ΡΠ°ΠΌΠΌΡ ΡΠΏΡΠ°Π²Π»Π΅Π½ΠΈΡ. ΠΡΠΎΠ³ΡΠ°ΠΌΠΌΠ½ΠΎΠ΅ ΠΎΠ±Π΅ΡΠΏΠ΅ΡΠ΅Π½ΠΈΠ΅ Π½Π°ΠΏΠΈΡΠ°Π½ΠΎ Ρ ΠΈΡΠΏΠΎΠ»ΡΠ·ΠΎΠ²Π°Π½ΠΈΠ΅ΠΌ ΠΏΠ°ΠΊΠ΅ΡΠ° WinAVR, ΠΈΠΌΠ΅ΡΡΠ΅Π³ΠΎ General Public License. ΠΠ΅ΡΠ΅Π΄Π°ΡΠ° Π΄Π°Π½Π½ΡΡ
ΠΌΠ΅ΠΆΠ΄Ρ ΠΊΠΎΠΌΠΏΡΡΡΠ΅ΡΠΎΠΌ ΠΈ Π±Π»ΠΎΠΊΠΎΠΌ ΠΎΡΡΡΠ΅ΡΡΠ²Π»ΡΠ΅ΡΡΡ ΠΏΠΎ USB-ΠΈΠ½ΡΠ΅ΡΡΠ΅ΠΉΡΡ
Random line tessellations of the plane: statistical properties of many-sided cells
We consider a family of random line tessellations of the Euclidean plane
introduced in a much more formal context by Hug and Schneider [Geom. Funct.
Anal. 17, 156 (2007)] and described by a parameter \alpha\geq 1. For \alpha=1
the zero-cell (that is, the cell containing the origin) coincides with the
Crofton cell of a Poisson line tessellation, and for \alpha=2 it coincides with
the typical Poisson-Voronoi cell. Let p_n(\alpha) be the probability for the
zero-cell to have n sides. By the methods of statistical mechanics we construct
the asymptotic expansion of \log p_n(\alpha) up to terms that vanish as
n\to\infty. In the large-n limit the cell is shown to become circular. The
circle is centered at the origin when \alpha>1, but gets delocalized for the
Crofton cell, \alpha=1, which is a singular point of the parameter range. The
large-n expansion of \log p_n(1) is therefore different from that of the
general case and we show how to carry it out. As a corollary we obtain the
analogous expansion for the {\it typical} n-sided cell of a Poisson line
tessellation.Comment: 26 pages, 3 figure
Secondary electron emission from thin aluminum foils produced by high-energy electron beams
The description of the experimental equipment and technique for measuring the secondary emission of electrons (SEE) with application of accelerated electrons at the linear accelerator of the IHEPNP NSC KIPT with energies up to 30 MeV and a standard secondary emission monitor [1] are presented. Experimental data of secondary electron emission yields from thin aluminum targets (8 and 50 ΞΌm) for primary electron beam energies of 16 and 25 MeV have been experimentally measured. The analysis of the experimental data and their comparison with the theory are carried out. It is shown that the proposed technique for measuring the yields of secondary electron emission is useful and applied for study of low-energy and Ξ΄-electrons yields from thin foils, as well as to research the effect of the density effect depending on the energy of the primary electron beam.ΠΠ°Π΄Π°Π½ΠΎ ΠΎΠΏΠΈΡ Π΅ΠΊΡΠΏΠ΅ΡΠΈΠΌΠ΅Π½ΡΠ°Π»ΡΠ½ΠΎΠ³ΠΎ ΠΎΠ±Π»Π°Π΄Π½Π°Π½Π½Ρ ΡΠ° ΠΌΠ΅ΡΠΎΠ΄ΠΈΠΊΠΈ Π²ΠΈΠΌΡΡΡΠ²Π°Π½Π½Ρ Π²ΠΈΡ
ΠΎΠ΄ΡΠ² Π²ΡΠΎΡΠΈΠ½Π½ΠΎΡ Π΅ΠΌΡΡΡΡ Π΅Π»Π΅ΠΊΡΡΠΎΠ½ΡΠ² (ΠΠΠ) ΠΏΡΠΈ Π²ΠΈΠΊΠΎΡΠΈΡΡΠ°Π½Π½Ρ ΠΏΡΡΠΊΠ° ΠΏΡΠΈΡΠΊΠΎΡΠ΅Π½ΠΈΡ
Π΅Π»Π΅ΠΊΡΡΠΎΠ½ΡΠ² Π½Π° Π»ΡΠ½ΡΠΉΠ½ΠΎΠΌΡ ΠΏΡΠΈΡΠΊΠΎΡΡΠ²Π°ΡΡ ΠΠ€ΠΠΠ―Π€ ΠΠΠ¦ Π₯Π€Π’Π Π· Π΅Π½Π΅ΡΠ³ΡΡΡ Π΄ΠΎ 30 ΠΠ΅Π Ρ ΡΡΠ°Π½Π΄Π°ΡΡΠ½ΠΎΠ³ΠΎ ΠΌΠΎΠ½ΡΡΠΎΡΠ° Π²ΡΠΎΡΠΈΠ½Π½ΠΎΡ Π΅ΠΌΡΡΡΡ [1]. ΠΡΡΠΈΠΌΠ°Π½ΠΎ Π΅ΠΊΡΠΏΠ΅ΡΠΈΠΌΠ΅Π½ΡΠ°Π»ΡΠ½Ρ Π΄Π°Π½Ρ ΠΏΠΎ Π²ΠΈΡ
ΠΎΠ΄Π°Ρ
Π²ΡΠΎΡΠΈΠ½Π½ΠΎΡ Π΅ΠΌΡΡΡΡ Π΅Π»Π΅ΠΊΡΡΠΎΠ½ΡΠ² Π· ΡΠΎΠ½ΠΊΠΈΡ
ΠΌΡΡΠ΅Π½Π΅ΠΉ Π°Π»ΡΠΌΡΠ½ΡΡ (8 Ρ 50 ΠΌΠΊΠΌ) Π΄Π»Ρ Π΅Π½Π΅ΡΠ³ΡΡ ΠΏΠ΅ΡΠ²ΠΈΠ½Π½ΠΎΠ³ΠΎ ΠΏΡΡΠΊΠ° Π΅Π»Π΅ΠΊΡΡΠΎΠ½ΡΠ² 16 Ρ 25 ΠΠ΅Π. ΠΡΠΎΠ²Π΅Π΄Π΅Π½ΠΎ Π°Π½Π°Π»ΡΠ· Π΅ΠΊΡΠΏΠ΅ΡΠΈΠΌΠ΅Π½ΡΠ°Π»ΡΠ½ΠΈΡ
Π΄Π°Π½ΠΈΡ
Ρ ΠΏΠΎΡΡΠ²Π½ΡΠ½Π½Ρ ΡΡ
Π· ΡΠ΅ΠΎΡΡΡΡ. ΠΠΎΠΊΠ°Π·Π°Π½ΠΎ, ΡΠΎ Π·Π°ΠΏΡΠΎΠΏΠΎΠ½ΠΎΠ²Π°Π½Π° ΠΌΠ΅ΡΠΎΠ΄ΠΈΠΊΠ° Π²ΠΈΠΌΡΡΡΠ²Π°Π½Π½Ρ Π²ΠΈΡ
ΠΎΠ΄ΡΠ² Π²ΡΠΎΡΠΈΠ½Π½ΠΎΡ Π΅ΠΌΡΡΡΡ Π΅Π»Π΅ΠΊΡΡΠΎΠ½ΡΠ² Π΄ΠΎΠ·Π²ΠΎΠ»ΡΡ ΠΎΡΡΠΈΠΌΡΠ²Π°ΡΠΈ Π΄Π°Π½Ρ ΠΏΠΎ Π²ΠΈΡ
ΠΎΠ΄Π°Ρ
Π½ΠΈΠ·ΡΠΊΠΎΠ΅Π½Π΅ΡΠ³Π΅ΡΠΈΡΠ½ΠΈΡ
Ρ Ξ΄-Π΅Π»Π΅ΠΊΡΡΠΎΠ½ΡΠ², Π° ΡΠ°ΠΊΠΎΠΆ Π΄ΠΎΡΠ»ΡΠ΄ΠΈΡΠΈ Π²ΠΏΠ»ΠΈΠ² Π΅ΡΠ΅ΠΊΡΡ Π³ΡΡΡΠΈΠ½ΠΈ Π² Π·Π°Π»Π΅ΠΆΠ½ΠΎΡΡΡ Π²ΡΠ΄ Π΅Π½Π΅ΡΠ³ΡΡ ΠΏΠ΅ΡΠ²ΠΈΠ½Π½ΠΎΠ³ΠΎ ΠΏΡΡΠΊΠ° Π΅Π»Π΅ΠΊΡΡΠΎΠ½ΡΠ².ΠΡΠΈΠ²Π΅Π΄Π΅Π½ΠΎ ΠΎΠΏΠΈΡΠ°Π½ΠΈΠ΅ ΡΠΊΡΠΏΠ΅ΡΠΈΠΌΠ΅Π½ΡΠ°Π»ΡΠ½ΠΎΠ³ΠΎ ΠΎΠ±ΠΎΡΡΠ΄ΠΎΠ²Π°Π½ΠΈΡ ΠΈ ΠΌΠ΅ΡΠΎΠ΄ΠΈΠΊΠΈ ΠΈΠ·ΠΌΠ΅ΡΠ΅Π½ΠΈΡ Π²ΡΠΎΡΠΈΡΠ½ΠΎΠΉ ΡΠΌΠΈΡΡΠΈΠΈ ΡΠ»Π΅ΠΊΡΡΠΎΠ½ΠΎΠ² (ΠΠΠ) Ρ ΠΈΡΠΏΠΎΠ»ΡΠ·ΠΎΠ²Π°Π½ΠΈΠ΅ΠΌ ΡΡΠΊΠΎΡΠ΅Π½Π½ΡΡ
ΡΠ»Π΅ΠΊΡΡΠΎΠ½ΠΎΠ² Π½Π° Π»ΠΈΠ½Π΅ΠΉΠ½ΠΎΠΌ ΡΡΠΊΠΎΡΠΈΡΠ΅Π»Π΅ ΠΠ€ΠΠΠ―Π ΠΠΠ¦ Π₯Π€Π’Π Ρ ΡΠ½Π΅ΡΠ³ΠΈΡΠΌΠΈ Π΄ΠΎ 30 ΠΡΠ ΠΈ ΡΡΠ°Π½Π΄Π°ΡΡΠ½ΠΎΠΌ ΠΌΠΎΠ½ΠΈΡΠΎΡΠ΅ Π²ΡΠΎΡΠΈΡΠ½ΠΎΠΉ ΡΠΌΠΈΡΡΠΈΠΈ [1]. ΠΠΊΡΠΏΠ΅ΡΠΈΠΌΠ΅Π½ΡΠ°Π»ΡΠ½ΠΎ ΠΈΠ·ΠΌΠ΅ΡΠ΅Π½Ρ Π²ΡΡ
ΠΎΠ΄Ρ Π²ΡΠΎΡΠΈΡΠ½ΠΎΠΉ ΡΠ»Π΅ΠΊΡΡΠΎΠ½Π½ΠΎΠΉ ΡΠΌΠΈΡΡΠΈΠΈ ΠΈΠ· ΡΠΎΠ½ΠΊΠΈΡ
Π°Π»ΡΠΌΠΈΠ½ΠΈΠ΅Π²ΡΡ
ΠΌΠΈΡΠ΅Π½Π΅ΠΉ (8 ΠΈ 50 ΠΌΠΊΠΌ) ΠΏΡΠΈ ΡΠ½Π΅ΡΠ³ΠΈΡΡ
ΠΏΠ΅ΡΠ²ΠΈΡΠ½ΠΎΠ³ΠΎ ΡΠ»Π΅ΠΊΡΡΠΎΠ½Π½ΠΎΠ³ΠΎ ΠΏΡΡΠΊΠ° 16 ΠΈ 25 ΠΡΠ. ΠΡΠΎΠ²Π΅Π΄Π΅Π½ Π°Π½Π°Π»ΠΈΠ· ΡΠΊΡΠΏΠ΅ΡΠΈΠΌΠ΅Π½ΡΠ°Π»ΡΠ½ΡΡ
Π΄Π°Π½Π½ΡΡ
ΠΈ ΠΈΡ
ΡΡΠ°Π²Π½Π΅Π½ΠΈΠ΅ Ρ ΡΠ΅ΠΎΡΠΈΠ΅ΠΉ. ΠΠΎΠΊΠ°Π·Π°Π½ΠΎ, ΡΡΠΎ ΠΏΡΠ΅Π΄Π»ΠΎΠΆΠ΅Π½Π½Π°Ρ ΠΌΠ΅ΡΠΎΠ΄ΠΈΠΊΠ° ΠΈΠ·ΠΌΠ΅ΡΠ΅Π½ΠΈΡ Π²ΡΡ
ΠΎΠ΄ΠΎΠ² Π²ΡΠΎΡΠΈΡΠ½ΠΎΠΉ ΡΠΌΠΈΡΡΠΈΠΈ ΡΠ»Π΅ΠΊΡΡΠΎΠ½ΠΎΠ² ΠΏΠΎΠ·Π²ΠΎΠ»ΡΠ΅Ρ ΠΏΠΎΠ»ΡΡΠ°ΡΡ Π΄Π°Π½Π½ΡΠ΅ ΠΏΠΎ Π²ΡΡ
ΠΎΠ΄Π°ΠΌ Π½ΠΈΠ·ΠΊΠΎΡΠ½Π΅ΡΠ³Π΅ΡΠΈΡΠ΅ΡΠΊΠΈΡ
ΠΈ Ξ΄-ΡΠ»Π΅ΠΊΡΡΠΎΠ½ΠΎΠ², Π° ΡΠ°ΠΊΠΆΠ΅ ΠΈΡΡΠ»Π΅Π΄ΠΎΠ²Π°ΡΡ Π²Π»ΠΈΡΠ½ΠΈΠ΅ ΡΡΡΠ΅ΠΊΡΠ° ΠΏΠ»ΠΎΡΠ½ΠΎΡΡΠΈ Π² Π·Π°Π²ΠΈΡΠΈΠΌΠΎΡΡΠΈ ΠΎΡ ΡΠ½Π΅ΡΠ³ΠΈΠΈ ΠΏΠ΅ΡΠ²ΠΈΡΠ½ΠΎΠ³ΠΎ ΠΏΡΡΠΊΠ° ΡΠ»Π΅ΠΊΡΡΠΎΠ½ΠΎΠ²
Asymptotic Expansions for Stationary Distributions of Perturbed Semi-Markov Processes
New algorithms for computing of asymptotic expansions for stationary
distributions of nonlinearly perturbed semi-Markov processes are presented. The
algorithms are based on special techniques of sequential phase space reduction,
which can be applied to processes with asymptotically coupled and uncoupled
finite phase spaces.Comment: 83 page
Three-dimensional random Voronoi tessellations: From cubic crystal lattices to Poisson point processes
We perturb the SC, BCC, and FCC crystal structures with a spatial Gaussian noise whose adimensional strength is controlled by the parameter a, and analyze the topological and metrical properties of the resulting Voronoi Tessellations (VT). The topological properties of the VT of the SC and FCC crystals are unstable with respect to the introduction of noise, because the corresponding polyhedra are geometrically degenerate, whereas the tessellation of the BCC crystal is topologically stable even against noise of small but finite intensity. For weak noise, the mean area of the perturbed BCC and FCC crystals VT increases quadratically with a. In the case of perturbed SCC crystals, there is an optimal amount of noise that minimizes the mean area of the cells. Already for a moderate noise (a>0.5), the properties of the three perturbed VT are indistinguishable, and for intense noise (a>2), results converge to the Poisson-VT limit. Notably, 2-parameter gamma distributions are an excellent model for the empirical of of all considered properties. The VT of the perturbed BCC and FCC structures are local maxima for the isoperimetric quotient, which measures the degre of sphericity of the cells, among space filling VT. In the BCC case, this suggests a weaker form of the recentluy disproved Kelvin conjecture. Due to the fluctuations of the shape of the cells, anomalous scalings with exponents >3/2 is observed between the area and the volumes of the cells, and, except for the FCC case, also for a->0. In the Poisson-VT limit, the exponent is about 1.67. As the number of faces is positively correlated with the sphericity of the cells, the anomalous scaling is heavily reduced when we perform powerlaw fits separately on cells with a specific number of faces
The Main Symptoms and Syndromes in Diseases of the Digestive System
The article presents the main clinical symptoms and syndromes that occur in various diseases of the abdominal cavity. Both widely known and rare symptoms of gastroenterological diseΒases are presented. Described symptoms and syndromes confirm the importance of the application of physical methods in the diagnosis of digestive system diseases