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1

A note on confidence intervals for deblurred images

Biel Michał, Szkutnik Zbigniew

Opuscula Mathematica

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2020

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Vol. 40, no. 3

361-–373

EN

We consider pointwise asymptotic confidence intervals for images that are blurred and observed in additive white noise. This amounts to solving a stochastic inverse problem with a convolution operator. Under suitably modified assumptions, we fill some apparent gaps in the proofs published in [N. Bissantz, M. Birke, Asymptotic normality and confidence intervals for inverse regression models with convolution-type operators, J. Multivariate Anal. 100 (2009), 2364-2375]. In particular, this leads to modified bootstrap confidence intervals with much better finite-sample behaviour than the original ones, the validity of which is, in our opinion, questionable. Some simulation results that support our claims and illustrate the behaviour of the confidence intervals are also presented.

2

Performance Evaluation of the Threshold Call Admission Policy in Multi-rate Loss Systems

Moscholios Ioannis D., Chousainov Iskanter-Alexandros, Panagoulias Panagiotis I., Sarigiannidis Panagiotis G., Logothetis Michael D.

Journal of Telecommunications and Information Technology

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2020

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nr 2

51--60

EN

In this paper we consider a link, characterized by speciﬁc capacity, that services multi-rate random or quasirandom traﬃc. Random traﬃc is generated by an inﬁnite number of traﬃc sources, while quasi-random traﬃc is generated by a ﬁnite population of traﬃc sources. The link is modeled as a multi-rate loss system. Handover and new calls are distinguished. New calls compete for the available bandwidth under a threshold call admission policy. In that policy, a new call of a particular service-class is not allowed to enter the system if the in-service handover and new calls of the same service-class plus the new call, exceed a predeﬁned threshold (which can be diﬀerent for each service-class). On the other hand, handover calls compete for the available bandwidth based on the complete sharing policy. We show that the steady state probabilities in the proposed models have a product form solution (PFS). The PFS leads to a convolution algorithm for accurate calculation of congestion probabilities and link utilization.

3

Active-controlled two-terminal network implementing a convolution-type immittance operator

Siwczyński M., Jaraczewski M.

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2020

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Vol. 68, nr 5

1107--1111

EN

Commonly known DC-AC switching converters are commonly used in compensator branches. One example of this is a static synchronous compensator (STATCOM). It consists of a voltage source converter (VSC) and acts as an inverter with a capacitor as a DC power source. These compensators use the PWM switching scheme or space vector modulation (SVM) method. Both methods require the desired signal to be generated. In some cases, as during the synthesis of self-excited systems or active energy-compensators, it is necessary to perform the desired branch immittance, e.g. negative capacitance, inductance, resistance or irrational impedance. In such cases, it is necessary to control the universal branch on the basis of a formula. This article presents the implementation method for the convolutional type impedance operators.

4

Application of convolutional neuron network for image processing and interpretation

Pałczyński Krzysztof

Zeszyty Naukowe. Telekomunikacja i Elektronika / Uniwersytet Technologiczno-Przyrodniczy w Bydgoszczy

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2019

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nr 23

5--12

EN

This article describes the application of Convolutional Neural Network in image processing and describes how it works. There are presented: network layers, types of activation functions, example of the AlexNet network architecture, the use of the loss function and the cross entropy method to calculate the loss during tests, L2 and Dropout methods used for weights regularization and optimization of the loss function using Stochastic Gradient Drop.

PL

Artykuł ten opisuje zastosowanie Konwolucyjnych Sieci Neuronowych w przetwarzaniu obrazów. W celu lepszego zrozumienia tematu opisano sposób działania sieci. Przedstawiono sieci wielowarstwowe, rodzaje funkcji aktywacji, przykład architektury sieci AlexNet. W artykule skupiono się na opisaniu wykorzystania funkcji straty oraz metody entropii krzyżowej do obliczenia straty w czasie testów. Opisano również sposoby normalizacji wag L2 i Dropout oraz optymalizację funkcji straty za pomocą Stochastycznego Spadku Gradientu.

5

Wpływ kwantowania współczynników na działanie filtru Gaussa dla realizacji bezpośredniej i ortogonalnej (rotatory Givensa)

Poczekajło Paweł

Przegląd Elektrotechniczny

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2019

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R. 95, nr 5

175--178

PL

W artykule przedstawiono dwie realizacje filtru Gaussa 1D. Pierwsza oparta jest na bezpośredniej implementacji splotu, druga bazuje na filtrze ortogonalnym realizowanym za pomocą rotatorów Givensa. Obie realizacje został przeanalizowane pod kątem wrażliwości na kwantowanie współczynników dla 8-, 16- i 24-bitowych rejestrów. Wyznaczono i porównano błędy średniokwadratowe charakterystyki amplitudowej oraz błędy dla odpowiedzi systemu na pobudzenie losowym szumem i deltą Kroneckera.

EN

In the paper, two realizations of 1D Gauss filter are presented. The first realization is based on direct structure with convolution, in the second orthogonal filter with use Givens rotations is realized. Both systems are analyzed of sensitivity on coefficient quantization for 8-, 16- and 24- bits length of register. Also determined mean squared errors for amplitude characteristics, impulse responses and responses on noise excitation.

6

Bulk modulus of copper alloys in context of modern metal theory

Chrzanowski J., Bieg B.

New Trends in Production Engineering

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2018

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Vol. 1, Iss. 1

681-686

EN

The authors used a modern quantum theory allowing to determine the energy levels of electrons in real metal. Based on that analytical equations have been presented by means of which the bulk modulus for chosen metals were calculated. It should be emphasized that all values obtained directly from the derived equation are in perfect conformity with the experimental data, a few percentage differences are comparable with the potential measurement error. Subsequently a simple mathematical model has been proposed which allows to calculate the bulk modulus of copper alloys depending on their percentage composition. The authors performed numerical calculations for the typical copper alloys and the results are presented in the form of graphs.

7

Call-level Analysis of a Two-Link Multirate Loss Model based on a Convolution Algorithm

Sagkriotis S. G., Pantelis S. K., Moscholios I. D., Vassilakis V. G.

Journal of Telecommunications and Information Technology

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2018

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nr 1

3--10

EN

We consider a two-link system that accommodates Poisson arriving calls from different service-classes and propose a multirate teletraffic loss model for its analysis. Each link has two thresholds, which refer to the number of in-service calls in the link. The lowest threshold, named support threshold, defines up to which point the link can support calls offloaded from the other link. The highest threshold, named offloading threshold, defines the point where the link starts offloading calls to the other link. The adopted bandwidth sharing policy is the complete sharing policy, in which a call can be accepted in a link if there exist enough available bandwidth units. The model does not have a product form solution for the steady state probabilities. However, we propose approximate formulas, based on a convolution algorithm, for the calculation of call blocking probabilities. The accuracy of the formulas is verified through simulation and found to be quite satisfactory.

8

On the existence of solutions of a perturbed functional integral equation in the space of Lebesgue integrable functions on R+

Al Sayed W., Darwish M. A.

Journal of Mathematics and Applications

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2018

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Vol. 41

19--27

EN

In this paper, we investigate and study the existence of solutions for perturbed functional integral equations of convolution type using Darbo's fixed point theorem, which is associated with the measure of noncompactness in the space of Lebesgue integrable functions on R+. Finally, we offer an example to demonstrate that our abstract result is applicable.

9

Detailed Consideration of Graphical Calculation of Min-Plus Convolution in Deterministic Network Calculus

Borys A.

International Journal of Electronics and Telecommunications

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2018

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Vol. 64, No. 2

217--222

EN

The convolution operation used in deterministic network calculus differs from its counterpart known from the classic systems theory. A reason for this lies in the fact that the former is defined in terms of the so-called min-plus algebra. Therefore, it is oft difficult to realize how it really works. In these cases, its graphical interpretation can be very helpful. This paper is devoted to a topic of construction of the min-plus convolution curve. This is done here in a systematic way to avoid arriving at non-transparent figures that are presented in publications. Contrary to this, our procedure is very transparent and removes shortcomings of constructions known in the literature. Some examples illustrate its usefulness.

10

Digital filters: hermitian, antihermitian, unitary and their applications

Siwczyński M., Jaraczewski M.

Technical Transactions

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2017

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Vol. 1(114)

101--112

EN

The paper presents the relation between the three types of noncausal digital filters: unitary, Hermitian and antihermitian filters. A decomposition has been made of a causal filter into a Hermitian and unitary filter cascade, and the use of this decomposition to calculate the electric power quality of receivers has been highlighted. Reference has also been made to the analogy between the set of unitary filters and the unit circle in the Gaussian plane.

PL

W artykule podano związek między trzema typami nieprzyczynowych filtrów cyfrowych: filtrami unitarnymi, hermitowskimi i antyhermitowskimi. Dokonano też rozkładu filtru przyczynowego na kaskadę filtru hermitowskiego i unitarnego, oraz zwrócono uwagę na zastosowanie tego rozkładu do jakościowo-energetycznej oceny odbiorników energii elektrycznej. Nawiązano też do analogii zbioru filtrów unitarnych i okręgu jednostkowego na płaszczyźnie Gaussa.

11

Radiotracer investigation of a pulp and paper mill effl uent treatment plant

Sarkar M., Sangal V. K., Bhunia H., Bajpai P. K., Pant H. J., Sharma V. K., Kumar A., Naithani A. K.

Nukleonika

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2017

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Vol. 62, No. 4

289--294

EN

The pulp and paper industry is highly dependent on water for most of its processes, producing a significant amount of wastewater that should be treated to comply with environmental standards before its discharge into surface-water reservoirs. The wastewater generated primarily consists of substantial amounts of organic, inorganic, toxic and pathogenic compounds in addition to nutrients, which are treated in an effluent treatment plant that often combines primary, secondary, tertiary and advanced treatments. However, the treatment methods vary from industry to industry according to the process utilized. The effective performance of effluent treatment plants is crucial from both environmental and economic points of view. Radiotracer techniques can be effectively used to optimize performance and detect anomalies like dead zones, bypassing, channelling, etc. in wastewater treatment plants. Experiments on the distribution of residence time were performed on the aeration tank and secondary clarifier of a full-scale pulp and paper mill to study the flow behaviour as well as locate system anomalies and hence evaluate the performance of the treatment plants using the radiotracer I-131. The convolution method was applied to model the system with an imperfect impulse radiotracer input. The aeration tank was working efficiently in the absence of any dead zones or bypassing. Various hydrodynamic models available in the literature were applied on the aeration tank and secondary clarifier to obtain the hydraulic representation of the systems.

12

About a class of analytic functions defined by Noor-Sǎlǎgean integral operator

Engel O., Chung Y. L.

Journal of Mathematics and Applications

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2016

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Vol. 39

59--67

EN

In this paper we intoduce a new integral operator as the convolution of the Noor and Salagean integral operators. With this integral operator we define the class CNS(α), where α ϵ [0,1) and we study some properties of this class.

13

Starlikeness and convexity of certain integral operators defined by convolution

Aggarwal J., Mathur R.

Journal of Mathematics and Applications

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2015

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Vol. 38

5--13

EN

We define two new general integral operators for certain analytic functions in the unit disc U and give some sufficient conditions for these integral operators on some subclasses of analytic functions.

14

On a class of meromorphic functions defined by the convolution

Dziok J., Sokół J., Stankiewicz J.

Journal of Mathematics and Applications

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2015

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Vol. 38

59--70

EN

In the present paper we define some classes of meromorphic functions with fixed argument of coefficients. Next we obtain coefficient estimates, distortion theorems, integral means inequalities, the radii of convexity and starlikeness and convolution properties for the defined class of functions.

15

Certain subordination results on the convolution of analytic functions

Sharma P., Maurya R. K.

Journal of Mathematics and Applications

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2014

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Vol. 37

111--118

EN

In this paper, certain subordination results on the convolution of finite number of analytic functions are derived. Our results include a sufficiency condition for convexity of the convolution of analytic functions fi satisfying [wzór].

16

Convolutions of generalized white noise functionals

Ji U. C., Kim Y. Y., Park Y. J.

Probability and Mathematical Statistics

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2013

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Vol. 33, Fasc. 2

435--450

EN

We study a general definition of convolution products of test white noise functionals, of which the consistency property is examined. As an application of the consistency property of the convolution product we study an extension of the convolution to generalized white noise functionals. We also study relations between the convolution and generalized Fourier-Gauss and generalized Fourier-Mehler transforms.

17

Some properties of generalized convolution of harmonic univalent functions

Porwal S., Dixit K. K.

Demonstratio Mathematica

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2013

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Vol. 46, nr 1

63--74

EN

The purpose of the present paper is to investigate some interesting properties on generalized convolutions of functions for the classes HP∗(α), HS(α) and HC(α). Further, an application of the convolution on certain integral operator are mentioned.

18

Applications of convolution properties

Trojnar-Spelina L.

Demonstratio Mathematica

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2013

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Vol. 46, nr 3

513--523

EN

K. I. Noor (2007 Appl. Math. Comput. 188, 814–823) has defined the classes Qk(a, b, λ, γ) and Tk(a, b, λ, γ) of analytic functions by means of linear operator connected with incomplete beta function. In this paper, we have extended some of the results and have given other properties concerning these classes.

19

A class of univalent functions involving a differentio-integral operator

Jain P. K., Sharma P., Jain V.

Demonstratio Mathematica

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2013

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Vol. 46, nr 2

283--297

EN

This paper focuses on a generalized linear operator Im which is a combination of both differential and integral operators. Involving this operator, a class Tsk(...) with respect to k-symmetric points is defined. Results based on coefficient inequalities and bounds for this class are obtained. Various integral representations and some consequent results for TS(...) class are also determined. Further, results on partial sums are discussed.

20

Convolutions, integral transforms and integral equations by means of the theory of reproducing kernels

Castro L. P., Saitoh S., Tuan N. M.

Opuscula Mathematica

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2012

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Vol. 32, no. 4

633-646

EN

This paper introduces a general concept of convolutions by means of the theory of reproducing kernels which turns out to be useful for several concrete examples and applications. Consequent properties are exposed (including, in particular, associated norm inequalities).