Wyniki wyszukiwania - BazTech

1

Analytical performance analysis of the M2M wireless link with an antenna selection system over interference limited dissimilar composite fading environments

Ðošić Danijel, Milić Dejan, Kontrec Nataša, Stefanović Časlav, Milosavljević Srðan, Stefanović Dušan M.

International Journal of Applied Mathematics and Computer Science

|

2022

|

Vol. 32, no. 4

569--582

EN

This paper considers direct mobile-to-mobile (M2M) communications with a dual antenna selection (AS) system at a destination mobile node (DMN) in interference limited, dissimilar composite fading environments. In particular, we model dissimilar interference limited signals at the inputs of the dual branch AS system as (i) the ratio of two Nakagami-m (N) random variables (RVs) at the first branch and (ii) the ratio of two Rice RVs at the second branch, in order to account for non line-of-sight (NLOS) and line-of-sight (LOS) communications, respectively. Moreover, we assume variable powers of the desired as well as interference signals at the output of the DMN in order to account for the impact of shadowing. For the proposed model, we derive probability density functions, cumulative distribution functions, outage probabilities and average level crossing rates. The derived statistical results are evaluated for all the statistical measures considered and are graphically presented in order to provide insight into the impact of composite fading severities and LOS factors for the desired signal, as well as for the interference, on the system performances.

2

Distribution of tropospheric amplitude scintillation on Ku Band earth-space link over a tropical station

Ashidi Ayodeji Gabriel, Ojo Joseph Sunday, Ajewole Moses Oludare, Adediji Adekunle Titus

Acta Geophysica

|

2022

|

Vol. 70, no 1

415--427

EN

This work utilized three years of measured satellite radio beacons to examine the statistical and temporal characteristics of tropospheric scintillation intensity and amplitude on the earth-space link over Akure, Southwest Nigeria (7.17 °N, 5.18 °E, 358 m). The signal measurement from Eutelsat W4/W7 satellite was taken between January 2016 and December 2018. The instrument used is Tektronix Y400 NetTek spectrum analyzer at a sampling rate of 1-s, downlink frequency 12.254 GHz, and path elevation of 036°E. Analysis involving cumulative distribution and probability density functions was performed over seven sampling intervals for characterizing the distribution of scintillation phenomenon on an annual and sub-annual basis. The results show scintillation intensity (σχ) to be well approximated by lognormal, Gamma, and generalized extreme value (GEV) distributions, while scintillation amplitude (χ) was suitably described by Gaussian distribution model. Also, as the sampling interval increased, the accuracy of the distribution models decreased. Analysis of mean and standard deviation equally revealed that scintillation intensities measured over longer intervals are less variable. Finally, a two-part exponential model developed for scintillation intensity prediction performed well as indicated by a least R2 value of 0.97 just as highest sum of square error (SSE) and root-mean-square error (RMSE) values of 0.192 and 0.087, respectively, were returned for both the goodness of ft and goodness of validation tests.

3

A statistical analysis of wind speed probabilistic distributions for the wind power assessment in different regions

Bay Yuly, Ruban Nikolay, Andreev Mikhail, Gusev Alexander

Przegląd Elektrotechniczny

|

2021

|

R. 97, nr 12

82--85

EN

The penetration of renewable energy sources (RES) into the electricity supply is gaining popularity all over the world, including countries that have large oil and gas reserves, since only the development of alternative energy will help avoid regression and take a green path development, reducing the damage to the environment. According to estimates of the International Energy Agency (IEA), the capacity of RES units built in China in 2016 was 34 GW, and Australia is one of the world leaders in the photovoltaic power plants installation, the share of which in the Australian electricity production exceeds 3%. It should be noted, that the final power generation capacity and stability are stochastic (probabilistic) in nature. Unlike the classical type generator, the output RES characteristics depend on the geographical features of the installation area, the season, and prevailing winds. Risks associated with inaccurate knowledge of the cumulative distribution function (CDF) describing these sources, as well as environmental uncertainties, are the reasons why it is more difficult for distribution network operators (DNO) to take RES into account in the power balance calculations. The wind speed CDF clarification can provide significant assistance in predicting the RES power production.

PL

Według szacunków Międzynarodowej Agencji Energetycznej (IEA) moc jednostek OZE wybudowanych w Chinach w 2016 roku wyniosła 34 GW, a Australia jest jednym ze światowych liderów w instalacji elektrowni fotowoltaicznych, której udział w australijskiej produkcji energii elektrycznej przekracza 3%. Należy zauważyć, że końcowa moc i stabilność wytwarzania energii ma charakter stochastyczny (probabilistyczny). W przeciwieństwie do generatora typu klasycznego, charakterystyka wyjściowa OZE zależy od cech geograficznych obszaru instalacji, pory roku i dominujących wiatrów. Ryzyko związane z niedokładną znajomością skumulowanej funkcji dystrybucji (CDF) opisującej te źródła, a także niepewności środowiskowe powodują, że operatorom sieci dystrybucyjnych (DNO) trudniej jest uwzględnić OZE w obliczeniach bilansu mocy. Wyjaśnienie prędkości wiatru CDF może zapewnić znaczącą pomoc w przewidywaniu produkcji energii z OZE.

4

Derivation of Equations for a Size Distribution of Spherical Particles in Non-Transparent Materials

Gurgul Daniel, Burbelko Andriy, Wiktor Tomasz

Journal of Casting & Materials Engineering

|

2021

|

Vol. 5, no. 4

53--60

EN

This paper presents a new proposition on how to derive mathematical formulas that describe an unknown Probability Density Function (PDF3) of the spherical radii (r3) of particles randomly placed in non-transparent materials. We have presented two attempts here, both of which are based on data collected from a random planar cross-section passed through space containing three-dimensional nodules. The first attempt uses a Probability Density Function (PDF2) the form of which is experimentally obtained on the basis of a set containing two-dimensional radii (r2). These radii are produced by an intersection of the space by a random plane. In turn, the second solution also uses an experimentally obtained Probability Density Function (PDF1). But the form of PDF1 has been created on the basis of a set containing chord lengths collected from a cross-section. The most important finding presented in this paper is the conclusion that if the PDF1 has proportional scopes, the PDF3 must have a constant value in these scopes. This fact allows stating that there are no nodules in the sample space that have particular radii belonging to the proportional ranges the PDF1.

5

Stochastic Simulation of Production Processes - selected issues

Snopkowski Ryszard, Sukiennik Marta, Napieraj Aneta

Inżynieria Mineralna

|

2021

|

no. 1

137--146

EN

The article presents selected issues in the field of stochastic simulation of production processes. Attention was drawn to the possibility of including, in this type of models, the risk accompanying the implementation of processes. Probability density functions that can be used to characterize random variables present in the model are presented. The possibility of making mistakes while creating this type of models was pointed out. Two selected examples of the use of stochastic simulation in the analysis of production processes on the example of the mining process are presented.

6

Exact response probability density functions of some uncertain structural systems

Falsone G., Laudani R.

Archives of Mechanics

|

2019

|

Vol. 71, nr 4-5

315--336

EN

This paper has the goal of defining a class of uncertain structural systems for which it is possible to consider an approach able to give the exact response in terms of the probability density function (PDF). The uncertain structures have been identified in the discretized statically determined ones and the approach has been identified in the coupling of the approximated principal deformation modes method (APDM) and of the probability transformation method (PTM). The first one gives the explicit relationships between the response variables and the uncertainty ones, that are exact when the structures are statically determined. The second method allows to determine the explicit relationship between the PDFs of the response and of the uncertainty variables. The results of some applications have confirmed the goodness of these choices and that the proposed approach gives always exact results for both correlated and uncorrelated uncertainty random variables.

7

Analysis of the distribution influence of the density of cost-forming factors on results of the LCCA calculations

Rogalska M., Żelazna-Pawlicka J.

Archives of Civil Engineering

|

2019

|

Vol. 65, nr 3

101--112

EN

The paper evaluates the relationship between the selection of the probability density function and the construction price, and the price of the building's life cycle, in relation to the deterministic cost estimate in terms of the minimum, mean, and maximum. The deterministic cost estimates were made based on the minimum, mean, and maximum prices: labor rates, indirect costs, profit, and the cost of equipment and materials. The net construction prices received were given different probability density distributions based on the minimum, mean, and maximum values. Twelve kinds of probability distributions were used: triangular, normal, lognormal, beta pert, gamma, beta, exponential, Laplace, Cauchy, Gumbel, Rayleigh, and uniform. The results of calculations with the event probability from 5 to 95% were subjected to the statistical comparative analysis. The dependencies between the results of calculations were determined, for which different probability density distributions of price factors were assumed. A certain price level was assigned to specific distributions in 6 groups based on the t-test. It was shown that each of the distributions analyzed is suitable for use, however, it has consequences in the form of a final result. The lowest final price is obtained using the gamma distribution, the highest is obtained by the beta distribution, beta pert, normal, and uniform.

PL

W artykule wykazano związek pomiędzy wyborem funkcji gęstości prawdopodobieństwa a ceną budowy i ceną cyklu życia budynku, w odniesieniu do posiadanego deterministycznego kosztorysu w ujęciu minimalnym, średnim i maksymalnym. Wykonano kosztorysy deterministyczne realizacji inwestycji bazując na cenach minimalnych, średnich i maksymalnych: stawki robocizny, kosztów pośrednich, zysku oraz ceny pracy sprzętu i materiałów. Otrzymanym cenom netto budowy nadawano różne rozkłady gęstości prawdopodobieństwa bazując na wartości minimalnej, średniej i maksymalnej. Wykorzystano 12 rodzajów rozkładów prawdopodobieństwa: trójkątny, normalny, lognormalny, beta pert, gamma, beta, exponential, Laplaca, Cauchy, Gumbel, Rayleigh, uniform. Wyniki obliczeń przy prawdopodobieństwach zdarzenia od 5 do 95 % poddano statystycznej analizie porównawczej. Określono zależności pomiędzy wynikami obliczeń dla których przyjęto rożne rozkłady gęstości prawdopodobieństwa czynników cenotwórczych. Przypisano określonym rozkładom poziom wysokości cen w 6 grupach na podstawie przeprowadzonego testu t-Studenta. Wykazano, że każdy z analizowanych rozkładów nadaje się do stosowania, powoduje to jednak konsekwencje w postaci wyniku końcowego. Najniższą cenę końcową uzyskamy stosując rozkład Gama, najwyższą rozkład Beta, Betapert, Normalny i Uniform.

8

Operation tests of an engine supplied with alternative fuels, working as a distributed generation device

Chmielewski A., Gumiński R., Mydłowski T., Małecki A., Bogdziński K.

Journal of Power Technologies

|

2017

|

Vol. 97, nr 5

437--445

EN

This works discusses the test performance of a HONDA NHX 110 engine supplied with RON 95 engine fuel and alternative fuels, including: Compressed Natural Gas (CNG) and biogas. The tests were conducted for various ignition advance angle values. Tests and analyzes were performed on the basis of several hundred work cycles at maximum engine load on the authors’ own low capacity, dynamometer testing unit at the Faculty of Automotive and Construction Machinery Engineering. To analyze the test results in their statistical rendering, use was made of measures such as kurtosis, coefficient of variation, asymmetric coefficient, probability density function among others. The research determined the repeatability of a performed experiment and how selected operation parameters (ignition advance angle, fuel type) influence the repeatability of measurements. The use of alternative fuels to power a low-power spark-ignition combustion engine was also analyzed in this work in the context of its use as a distributed generation device, particularly in a polygeneration system. The paper also presents and analyzes toxic compound emissions accompanying the work of the engine.

9

Statistical Analysis of Indoor RSSI Read-outs for 433 MHz, 868 MHz, 2.4 GHz and 5 GHz ISM Bands

Chruszczyk Ł.

International Journal of Electronics and Telecommunications

|

2017

|

Vol. 63, No. 1

33--38

EN

This paper presents statistical analysis of RSSI readouts recorded in indoor environment. Many papers concerning indoor location, based on RSSI measurement, assume its normal probability density function (PDF). This is partially excused by relation to PDF of radio-receiver's noise and/or together with influence of AWGN (average white Gaussian noise) radio-channel – generally modelled by normal PDF. Unfortunately, commercial (usually unknown) methods of RSSI calculations, typically as "side-effect" function of receiver's AGC (automatic gain control), results in PDF being far different from Gaussian PDF. This paper presents results of RSSI measurements in selected ISM bands: 433/868 MHz and 2.4/5 GHz. The measurements have been recorded using low-cost integrated RF modules (at 433/868 MHz and 2.4 GHz) and 802.11 WLAN access points (at 2.4/5 GHz). Then estimated PDF of collected data is shown and compared to normal (Gaussian) PDF.

10

DHI evaluation by combining rock physics simulation and statistical techniques for fluid identification of Cambrian-to-Cretaceous clastic reservoirs in Pakistan

Ahmed N., Khalid P., Shafi H. M. B., Connolly P.

Acta Geophysica

|

2017

|

Vol. 65, no. 5

991--1007

EN

The use of seismic direct hydrocarbon indicators is very common in exploration and reservoir development to minimise exploration risk and to optimise the location of production wells. DHIs can be enhanced using AVO methods to calculate seismic attributes that approximate relative elastic properties. In this study, we analyse the sensitivity to pore fluid changes of a range of elastic properties by combining rock physics studies and statistical techniques and determine which provide the best basis for DHIs. Gassmann fluid substitution is applied to the well log data and various elastic properties are evaluated by measuring the degree of separation that they achieve between gas sands and wet sands. The method has been applied successfully to well log data from proven reservoirs in three different siliciclastic environments of Cambrian, Jurassic, and Cretaceous ages. We have quantified the sensitivity of various elastic properties such as acoustic and extended elastic (EEI) impedances, elastic moduli (Ksat and Ksat – μ), lambda–murho method (λρ and μρ), P-to-S-wave velocity ratio (VP/VS), and Poisson’s ratio (σ) at fully gas/water saturation scenarios. The results are strongly dependent on the local geo-logical settings and our modeling demonstrates that for Cambrian and Cretaceous reservoirs, Ksat – μ, EEI, VP/VS, and σ are more sensitive to pore fluids (gas/water). For the Jurassic reservoir, the sensitivity of all elastic and seismic properties to pore fluid reduces due to high overburden pressure and the resultant low porosity. Fluid indicators are evaluated using two metrics: a fluid indicator coefficient based on a Gaussian model and an overlap coefficient which makes no assumptions about a distribution model. This study will provide a potential way to identify gas sand zones in future exploration.

11

The use of kernel estimators to determine the distribution of groundwater level

Michalski A.

Meteorology Hydrology and Water Management. Research and Operational Applications

|

2016

|

Vol. 4, Iss. 1

41--46

EN

In this paper the problem of non-parametric estimation of the probability density function for hydrological data is considered. For a given random sample X1, X2, ..., Xn we define an estimator fˆ n of the density function ƒ based on a function K of a real variable – the so-called kernel of a distribution – and a properly chosen number sequence {hn} from the interval (0, ∞). This estimator of density function of a random variable X under more general assumptions is known in the statistical literature as the Parzen-Rosenblatt estimator or the kernel estimator. The method of kernel estimation presented in the paper has been applied to determine the probability distribution of the groundwater level based on long-term measurements made in the melioration research carried out at the foothill object Długopole.

12

Differences between downhole and surface micro-seismic monitoring

Święch E., Wandycz P.

Mining Science

|

2015

|

Vol. 22

65--73

EN

The article presents usage of microseismic monitoring for location of microseismic events in polish geological conditions. For location of one synthetic microseismic event, two methods of acquisition were applied: surface and downhole monitoring array. Downhole microseismic monitoring is a technique of recording induced seismicity using receivers placed in the monitoring well near to the treatment well. In case of surface monitoring receivers are placed at the surface. For determination of hypocenter location probability density function was used. Based on provided analysis it is concluded that for polish conditions it is better to use downhole microseismic monitoring. Event located with usage of this technique was located correctly and uncertainty of this location was lower.

13

Strategia oceny pracowników w systemach śledzenia zagadnień

Jóźwiak I., Mariański A.

Zeszyty Naukowe. Organizacja i Zarządzanie / Politechnika Śląska

|

2014

|

z. 74

351--360

PL

W większości organizacji dokonuje się oceny pracowników na podstawie różnych kryteriów subiektywnych i obiektywnych. Często pracownicy czują się pokrzywdzeni oceną opisową lub ocena nie jest adekwatna do ich wyników pracy. W artykule proponujemy obiektywną metodę oceny pracowników z wykorzystaniem metod probabilistycznych, w tym funkcji gęstości prawdopodobieństwa, metod jądrowych oraz operacji arytmetycznych na zmiennych losowych. Omówiono również zastosowanie metody do budowania zespołu i jego oceny oraz wizualizacji wydajności prac zespołu oraz pracownika.

EN

In most of organizations evaluation of employees based on various criteria both subjective and objective is done. Employees feel often unfair by descriptive evaluation or the evaluation is not adequate to results of their work. In the publication we propose objective method of evaluation of employees based on probabilistic methods, including density estimation, kernel methods and arithmetic operations on random variables. In the paper we focus also on application method to build a team and evaluating it. The paper also introduces visualization of performance of both team and employee.

14

Statistical downscaling of probability density function of daily precipitation on the Polish coast

Wójcik R., Pilarski M., Miętus M.

Meteorology Hydrology and Water Management. Research and Operational Applications

|

2014

|

Vol. 2, Iss. 1

27--36

EN

The aim of this study was to recognize the possibility of downscaling probability density function (PDF) of daily precipitation by means of canonical correlation analysis (CCA). Sea level pressure (SLP) over Europe and the North Atlantic was used as a predictor. A skilful statistical model could be used to generate projections of future changes of precipitation PDF driven by GCM (General Circulation Model) simulations. Daily precipitation totals from 8 stations located on the Polish coast of the Baltic Sea covering the period 1961-2010 were used to estimate the gamma distribution parameters, and only wet days (i.e. ≥0.1mm) were taken in the analysis. The results of the Kolmogorov-Smirnov test and comparison of empirical and theoretical (gamma-distributed) quantiles proved that gamma distribution gives a reliable description of daily precipitation totals. The validation of CCA models applied to gamma parameters revealed that the reliable reconstruction of precipitation PDF is possible only for average long-term conditions. In the case of individual months/seasons the agreement between empirical and reconstructed quantiles is poor. This study shows the potential of modelling of precipitation PDF, however efforts should be made to improve model performance by establishing more reliable links between regional forcing and the variability of the gamma parameters.

15

Analytical Models for Distribution of the Envelope and Phase of Linearly Modulated Signals in AWGN Channel

Moazzeni T, Jiang Y., Selvaraj H., Chen T.

International Journal of Electronics and Telecommunications

|

2014

|

Vol. 60, No. 1

79-82

EN

In this paper, analytical expressions for the distribution of the envelope and phase of linearly modulated signals such as BPSK, M-PSK, and M-QAM in AWGN are presented. We perform numerical simulations for different orders of signal constellations. The results show that the proposed theoretical models are in excellent agreement with the estimated distributions from various numerical experiments.

16

Graphics processing units in acceleration of bandwidth selection for kernel density estimation

Andrzejewski W., Gramacki A., Gramacki J.

International Journal of Applied Mathematics and Computer Science

|

2013

|

Vol. 23, no. 4

869--885

EN

The Probability Density Function (PDF) is a key concept in statistics. Constructing the most adequate PDF from the observed data is still an important and interesting scientific problem, especially for large datasets. PDFs are often estimated using nonparametric data-driven methods. One of the most popular nonparametric method is the Kernel Density Estimator (KDE). However, a very serious drawback of using KDEs is the large number of calculations required to compute them, especially to find the optimal bandwidth parameter. In this paper we investigate the possibility of utilizing Graphics Processing Units (GPUs) to accelerate the finding of the bandwidth. The contribution of this paper is threefold: (a) we propose algorithmic optimization to one of bandwidth finding algorithms, (b) we propose efficient GPU versions of three bandwidth finding algorithms and (c) we experimentally compare three of our GPU implementations with the ones which utilize only CPUs. Our experiments show orders of magnitude improvements over CPU implementations of classical algorithms.

17

Asymptotically error - optimal shape of sampling zone for query selectivity estimation method based on discrete cosine transform

Augustyn D. R.

Theoretical and Applied Informatics

|

2012

|

Vol. 24, No. 1

3-22

EN

The problem of query selectivity estimation for database queries is critical for efficient query execution by database management systems. A query execution method strongly depends on early estimated size of a query result. This estimation determines a data access method used later during the query execution. The selectivity parameter is a fraction of table rows that satisfy a single-table query condition. For a selection condition of a range query where an attribute has a continuous domain, the selectivity is equivalent to a definite integral form probability density function (PDF) of attribute values distribution. For a compound selection condition based on many attributes we need a multidimensional space-efficient non-parametric estimator of multivariate PDF of attribute values distribution. A known approach based on Discrete Cosine Transform (DCT) spectrum as an representation of multidimensional PDF is considered. The energy compaction property of DCT lets omit a region of spectrum coefficients with small absolute values without significant losing an accuracy of selectivity estimation. An area of relevant spectrum coefficients is called a sampling zone. Results of experiments from previous works shows that applying the reciprocal shape of the sampling zone gives the least selectivity estimation error subject to a predetermined size of the zone. The main result of this work is a theoretical confirmation of only experimental results from previous works. The paper presents the proof of the theorem that the reciprocal shape of the sampling zone is asymptotically error-optimal. The proof is based on calculus of variations and the isoperimetric problem.

PL

Szacowanie selektywności zapytań jest krytyczne dla efektywnej realizacji zapytań w systemach zarządzania bazami danych. Sposób realizacji zapytania zależy od wstępnego oszacowania rozmiaru danych spełniających kryteria zapytania. Takie oszacowanie pozwala wybrać metodę dostępu do danych użytą później podczas realizacji zapytania. Selektywność dla zapytań jednotablicowych to stosunek liczby wierszy spełniających kryteria zapytania do liczby wszystkich wierszy tablicy. Dla zakresowych warunków zapytania, określonych na atrybutach z ciągła dziedziną, selektywność jest całką oznaczoną z funkcji gęstości prawdopodobieństwa (PDF), określającej rozkład wartości tego atrybutu. Dla złożonych warunków zapytania, opartych na kilku atrybutach, istnieje potrzeba użycia nieparametrycznego estymatora wielowymiarowej PDF, którego reprezentacja powinna być oszczędna pod względem zajętości pamięci. Jedno ze znanych podejść do konstrukcji takiego estymatora oparte jest na dyskretnej transformacie kosinusowej (DCT) - tzn. widmie z histogramu wielowymiarowego. Własność kompakcji energii pozwala na pominięcie nieznaczących współczynników widma DCT bez istotnej utraty oszacowania selektywności. Obszar znaczących współczynników widma nazywany jest strefą próbkowania. Wyniki prac eksperymentalnych innych autorów wskazują, że dla zadanego rozmiaru reprezentacji widma, optymalną strefą próbkowania (kształtem strefy o najmniejszym błędzie oszacowania selektywności) jest tzw. strefa odwrotnie proporcjonalna. Głównym wynikiem tego opracowania jest teoretyczne potwierdzenie tych eksperymentów. Artykuł przedstawia dowód twierdzenia o asymptotycznej optymalności strefy odwrotnie proporcjonalnej dla przypadku dwuwymiarowego. Dowód opiera się na elementach rachunku wariacyjnego i zagadnieniu izoperymetrycznym.

18

On the instantaneous frequency of Gaussian stochastic processes

Wahlberg P., Schreier P. J.

Probability and Mathematical Statistics

|

2012

|

Vol. 32, Fasc. 1

69--92

EN

We study the instantaneous frequency (IF) of continuoustime, complex-valued, zero-mean, proper, mean-square differentiable, nonstationary Gaussian stochastic processes. We compute the probability density function for the IF for fixed time, which generalizes a result known for wide-sense stationary processes to nonstationary processes. For a fixed point in time, the IF has either zero or infinite variance. For harmonizable processes, we obtain as a consequence the result that the mean of the IF, for fixed time, is the normalized first-order frequency moment of the Wigner spectrum.

19

Metoda funkcji gęstości prawdopodobieństwa w problemie turbulencji

Icha A.

Modelowanie Inżynierskie

|

2012

|

T. 12, nr 43

69-76

PL

W pracy rozważono statystyczny opis przepływów turbulentnych przy wykorzystaniu metody funkcji gęstości rozkładu prawdopodobieństwa charakterystyk przepływu. W szczególności otrzymano równanie ewolucyjne dla jednopunktowej funkcji gęstości prawdopodobieństwa pulsacji koncentracji dyfundującej substancji w zadanym polu prędkości cieczy. Rozważono bliżej przypadek statystycznie stacjonarnego i horyzontalnie jednorodnego przepływu turbulentnego, dla którego znaleziono ścisłe, zależne od dwóch parametrów, rozwiązanie zagadnienia dyfuzji, wyrażone przez 3-konfluentną funkcję Heuna.

EN

In the paper the use of probabiiity density functions metod to the statistical description of turbulent flows is considered. This formulation is less generał than the characteristic functionals approach, but primary in the relation to the Friedmann-Keller hierarchy equations. An evolution equation for single-point probability density function of pulsation of concentration of the diffusing substance in prescribed fluid velocity field, is derived. The case of statistical stationary and horizontal homogeneous turbulent flow is considered, for which an exact, new, two-parameter solution of diffusion problem in terms of Triconfluent Heun function, is obtained.

20

Analysis of a Simple Method of CMOS IC Design for Yield Optimization

Tomaszewski D., Yakupov M.

International Journal of Microelectronics and Computer Science

|

2012

|

Vol. 3, nr 3

81-87

EN

A simple approach for CMOS integrated circuit (IC) design taking into account a process variability and oriented towards optimization of a parametric yield has been presented. Its concept is based on cumulative distribution functions of random variables representing IC performances subject to process variations. In the method it has been assumed that CMOS process statistical data are expressed in terms of so-called process parameter distributions. Thus the design centering is done via layout parameter tuning. The approach relies on maximizing the probability that random variables corresponding to IC performances remain within the performance boundaries. Also, a methodology for statistical characterization of CMOS process has been briefly described. Finally, the method operation has been illustrated using analytical and SPICE models of CMOS inverter, operational amplifier and ring oscillator.