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1

Oscillation conditions for difference equations with several variable delays

El-Matary Bassant M., El-Morshedy Hassan A., Benekas Vasileios, Stavroulakis Ioannis P.

Opuscula Mathematica

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2023

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Vol. 43, no. 6

789--801

EN

A technique is developed to establish a new oscillation criterion for a first-order linear difference equation with several delays and non-negative coefficients. Our result improves recent oscillation criteria and covers the cases of monotone and non-monotone delays. Moreover, the paper is concluded with an illustrative example to show the applicability and strength of our result.

2

New oscillation constraints for even-order delay differential equations

Moaaz Osama, Anis Mona, El-Deeb Ahmed A., Elshenhab Ahmed M.

Opuscula Mathematica

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2023

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Vol. 43, no. 3

455--467

EN

The purpose of this paper is to study the oscillatory properties of solutions to a class of delay differential equations of even order. We focus on criteria that exclude decreasing positive solutions. As in this paper, this type of solution emerges when considering the noncanonical case of even equations. By finding a better estimate of the ratio between the Kneser solution with and without delay, we obtain new constraints that ensure that all solutions to the considered equation oscillate. The new findings improve some previous findings in the literature.

3

Method of the environmentally friendly dry single-pass honing with use of the superimposed low frequency oscillations

Rozek Andre, Uhlmann Eckart

Journal of Machine Engineering

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2023

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Vol. 23, No. 3

116--129

EN

Single-pass honing is used as a finishing process to meet high demands regarding form and dimensional accuracy of drilled holes. The disadvantages of single-pass honing compared to the conventional long-stroke honing are high process forces and torques as well as an increased risk of chip space clogging of the abrasive stones. Following this, the oscillation-superimposed single-pass honing without cutting fluid has been conducted in this work, which is promising when it comes to the environmentally friendly improvement of machining processes. It was shown that the omitted lubrication and flushing effect of the contact zone between the tool and the workpiece could be compensated with the aid of the superimposed oscillations. The process forces of the dry honing process are up to 37% lower compared to the conventional process, the height of the surface profile Rz decreases by 33% and the form deviations decrease up to 47%. Hence, the new method allows the saving of resources, while improving the work results.

4

Low Energy Trap with Light Emitting Diode for Increased Attraction of Phthorimaea operculella Zeller

Carbajal-Morán Hipólito, Márquez-Camarena Javier F., Galván-Maldonado Carlos A., Zárate-Quiñones Rosa H., Galván-Maldonado Alberto C.

Ecological Engineering & Environmental Technology

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2023

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Vol. 24, iss. 6

270--275

EN

The Phthorimaea operculella Zeller moth is a pest that affects potato crops and is found mainly in the inter-Andean valleys of the highlands of Peru (Huancavelica). The objective of the research was to use the phenomenon of light generated by light-emitting diodes (LEDs) to attract the potato moth in storage. Every day at seven o’clock in the morning, the number of moths falling dead in the light trap on the water contained in the container was counted. Five LED lights with different light densities per square centimeter were tested for five nights with different frequencies: 3.125 Hz, 12.5 Hz, 50 Hz, 200 Hz and 400 Hz. Every five nights the operating current of the LEDs was changed: 5 mA, 10 mA and 15 mA. Every fifteen nights the color of the LEDs was changed, according to the following sequence: white, blue, green, yellow and red; the color that attracted the most was white light, while the one with the least attraction was red light. The white light trap using the 64 LED array attracted 38.73% of moths and consumed a total of 43 W of energy in seven days, so it is considered low energy consumption.

5

Studying the dynamic system “tire-suspension-body” by the resonance method

Gogiashvili Phridon, Kbilashvili David, Chogovadze Jumber, Lekveishvili Gocha, Sirbiladze Besik

Transport Problems

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2022

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T. 17, z. 1

63--72

EN

By comparing the results of a pilot study of the damping coefficient of a pneumatic tire carried out on a test bench, this study justifies the possibility of using the less time-consuming experimental resonance curve method instead of the dynamic loop method. A mathematical model of the vertical oscillations of a vehicle’s dynamic system “pneumatic wheel-suspension-sprung weight”was created on the test-bench, and an image of the amplitude-frequency characteristic of the sprung weight oscillation was obtained. The approaches and results of the pilot and analytical studies presented in the article aid the selection of the tire with the best damping properties. The use of the experimental resonance curve method to determine the damping characteristic of a vehicle’s tire is limited in the external frequency range of the resonant frequencies. In this case, we have to use the dynamic loop method.

6

Oscillation theorems for third order neutral delay difference equation with negative coefficient in the neutral term

Jesinthaangel R., Gomathi Jawahar G.

Przegląd Elektrotechniczny

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2022

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R. 98, nr 3

36--38

EN

The article describes the new oscillation criteria which improves the existing results for the third order neutral delay difference equation with the negative coefficient in the neutral term is obtained. Where are positive sequences.

PL

W artykule opisano nowe kryteria oscylacji, które poprawiają dotychczasowe wyniki dla równania różnicy opóźnienia neutralnego trzeciego rzędu z ujemnym współczynnikiem w członie neutralnym. Gdzie są sekwencje dodatnie.

7

Fourth order qualitative inspection of nonlinear neutral delay difference equation

Jesinthaangel R., Jawahar G. Gomathi, Aruna K.

Przegląd Elektrotechniczny

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2022

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R. 98, nr 7

66--69

EN

This paper aim is to investigate the nonlinear neutral fourth order difference equation in the form. We establish some conditions to assure that all solutions to this equation are oscillatory or nonoscillatory. We derived this using summation averaging technique and comparison principle. The main outcomes are illustrated using examples.

PL

W artykule badano nieliniowe równanie różnicowe czwartego rzędu. Ustalamy pewne warunki, aby zapewnić, że wszystkie rozwiązania tego równania są oscylacyjne lub nieoscylacyjne. Wyprowadziliśmy to za pomocą techniki uśredniania sumowania i zasady porównania. Główne wyniki zilustrowano na przykładach.

8

A program design to form an oscillation curve and reduction with PID control on a heat exchanger

Cekdin Cekmas, Juniar Heni, Fadilah S.T

Przegląd Elektrotechniczny

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2022

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R. 98, nr 10

67--71

EN

A Heat Exchanger is a secondary process unit that is widely needed in the chemical process industry. This equipment is used to exchange heat between two types of fluids that have different temperatures. The existence of several physical events that change the characteristics of the process causes the stability of the system to be disturbed that necessitates to control the changes in the process parameters. PID controllers are actually conventional controllers which, due to their relatively good condition and easy operation, are still widely used. Many methods have been introduced to analyze PID control parameters, including the Rungge-Kutta method. However, the controlling operators in an industrial process, in order to get good control performance in every industrial process in the event of overshoot or oscillation, adjust the control parameters manually through the trial and error method. For this reason, we need a technique that is able to adapt to changes in process parameters that occur, and at the same time perform automatic re-tuning of controlling parameters. This paper describes a program designed to form an oscillation and reduction curve with a PID controller on a heat exchanger. The design of this program must at least be in accordance with the dynamics of the actual events in the field. the results of the oscillation curve reduction program design which are quite good are the one with the 'PI' controller type as compared to those with the 'P' and 'PID' controller types. The results of the one with the control type 'P' are not good because the process variable (process temperature) is not close to the set. o be used for operator training in industrial processes in the event of disturbances in the form of oscillations.

PL

Wymiennik ciepła jest drugorzędną jednostką procesową, która jest powszechnie potrzebna w przemyśle chemicznym. To urządzenie służy do wymiany ciepła między dwoma rodzajami płynów, które mają różne temperatury. Istnienie kilku zdarzeń fizycznych zmieniających charakterystykę procesu powoduje zaburzenie stabilności systemu, co wymusza kontrolowanie zmian parametrów procesu. Regulatory PID to właściwie regulatory konwencjonalne, które ze względu na stosunkowo dobry stan techniczny i łatwą obsługę nadal znajdują szerokie zastosowanie. Wprowadzono wiele metod analizy parametrów regulacji PID, w tym metodę Rungge-Kutty. Jednak operatorzy kontrolujący w procesie przemysłowym, w celu uzyskania dobrej wydajności sterowania w każdym procesie przemysłowym w przypadku przeregulowania lub oscylacji, dostosowują parametry sterowania ręcznie metodą prób i błędów. Z tego powodu potrzebujemy techniki, która jest w stanie dostosować się do zachodzących zmian parametrów procesu, a jednocześnie wykonać automatyczne przestrojenie parametrów sterujących. W artykule opisano program przeznaczony do tworzenia krzywej oscylacji i redukcji z regulatorem PID na wymienniku ciepła. Projekt tego programu musi być przynajmniej zgodny z dynamiką rzeczywistych wydarzeń w terenie. wyniki projektu programu redukcji krzywej oscylacji, które są dość dobre, to te z regulatorem typu „PI” w porównaniu z tymi z regulatorami typu „P” i „PID”. Wyniki tego ze sterowaniem typu „P” nie są dobre, ponieważ zmienna procesowa (temperatura procesu) nie jest zbliżona do zadanej. o być używany do szkolenia operatorów w procesach przemysłowych w przypadku zakłóceń w postaci oscylacji.

9

Properties of even order linear functional differential equations with deviating arguments of mixed type

Dzurina Jozef

Opuscula Mathematica

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2022

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Vol. 42, no. 5

659--671

EN

This paper is concerned with oscillatory behavior of linear functional differential equations of the type y(n)(t) = p(t)y(τ (t)) with mixed deviating arguments which means that its both delayed and advanced parts are unbounded subset of (0,∞). Our attention is oriented to the Euler type of equation, i.e. when p(t) ∼ a/tn.

10

Oscillation of even order linear functional differential equations with mixed deviating arguments

Baculikova Blanka

Opuscula Mathematica

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2022

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Vol. 42, no. 4

549--560

EN

In the paper, we study oscillation and asymptotic properties for even order linear functional differential equations y (n)(t) = p(t)y(τ (t)) with mixed deviating arguments, i.e. when both delayed and advanced parts of τ (t) are significant. The presented results essentially improve existing ones.

11

On oscillatory behaviour of third-order half-linear dynamic equations on time scales

Grace Said R., Chhatria Gokula Nanda

Opuscula Mathematica

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2022

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Vol. 42, no. 6

849--865

EN

In this work, we study the oscillation and asymptotic behaviour of third-order nonlinear dynamic equations on time scales. The findings are obtained using an integral criterion as well as a comparison theorem with the oscillatory properties of a first-order dynamic equation. As a consequence, we give conditions which guarantee that all solutions to the aforementioned problem are only oscillatory, different from any other result in the literature. We propose novel oscillation criteria that improve, extend, and simplify existing ones in the literature. The results are associated with a numerical example. We point out that the results are new even for the case T = R or T = Z.

12

New oscillation conditions for first-order linear retarded difference equations with non-monotone arguments

Attia Emad R., El-Matary Bassant M., Chatzarakis George E.

Opuscula Mathematica

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2022

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Vol. 42, no. 6

769--791

EN

In this paper, we study the oscillatory behavior of the solutions of a first-order difference equation with non-monotone retarded argument and nonnegative coefficients, based on an iterative procedure. We establish some oscillation criteria, involving lim sup, which achieve a marked improvement on several known conditions in the literature. Two examples, numerically solved in MAPLE software, are also given to illustrate the applicability and strength of the obtained conditions.

13

New aspects for the oscillation of first-order difference equations with deviating arguments

Attia Emad R., El-Matary Bassant M.

Opuscula Mathematica

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2022

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Vol. 42, no. 3

393--413

EN

We study the oscillation of first-order linear difference equations with non-monotone deviating arguments. Iterative oscillation criteria are obtained which essentially improve, extend, and simplify some known conditions. These results will be applied to some numerical examples.

14

Kneser-type oscillation criteria for second-order half-linear advanced difference equations

Indrajith N., Graef John R., Thandapani E.

Opuscula Mathematica

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2022

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Vol. 42, no. 1

55--64

EN

The authors present Kneser-type oscillation criteria for a class of advanced type second-order difference equations. The results obtained are new and they improve and complement known results in the literature. Two examples are provided to illustrate the importance of the main results.

15

Determination of the optimal frequency of the primary measuring transducer of the thickness of dielectric coatings of metal surfaces

Ovchynnykov Kostyantyn V., Vasilevskyi Oleksandr M., Sevastianov Volodymyr M., Polievoda Yurii A., Kalizhanova Aliya, Yeraliyeva Bakhyt

Informatyka, Automatyka, Pomiary w Gospodarce i Ochronie Środowiska

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2022

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T. 12, nr 2

56--59

EN

The article provides an analysis of the physical processes underlying the operation of the measuring transducer, with a time based information presentation. A mathematical model is developed that describes the process of free oscillation attenuation excited in the LC-contour of primary measuring transducer, and analyzes and evaluates the influence of external factors that influence the measurement results. The ways of elimination of their influence on the results of measuring control are offered.

PL

Artykuł zawiera analizę procesów fizycznych leżących u podstaw pracy przetwornika pomiarowego wraz z prezentacją informacji w czasie. Opracowano model matematyczny opisujący proces tłumienia drgań swobodnych wzbudzanych w obwodzie LC głównego przetwornika pomiarowego, analizujący i oceniający wpływ czynników zewnętrznych na wyniki pomiarów. Proponowane są sposoby wyeliminowania ich wpływu na wyniki kontroli pomiarów.

16

Oscillation criteria for linear difference equations with several variable delays

Benekas Vasileios, Garab Abel, Kashkynbayev Ardak, Stavroulakis Ioannis P.

Opuscula Mathematica

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2021

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Vol. 41, no. 5

613--627

EN

We obtain new sufficient criteria for the oscillation of all solutions of linear delay difference equations with several (variable) finite delays. Our results relax numerous well-known limes inferior-type oscillation criteria from the literature by letting the limes inferior be replaced by the limes superior under some additional assumptions related to slow variation. On the other hand, our findings generalize an oscillation criterion recently given for the case of a constant, single delay.

17

Limit states of steel supporting structure for bridge cranes

Mantič Martin, Kuľka Jozef, Kopas Melichar, Faltinová Eva, Hrabovský Leopold

Zeszyty Naukowe. Transport / Politechnika Śląska

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2020

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z. 108

141--158

EN

This paper describes a question of evaluation necessity of bridge cranes using the method of limit deformation state and oscillation damping. The solution was performed by means of theoretical analysis and an experimental verification at the selected bridge crane. The final result sounds that in the case of a correct strength computing of given bridge crane, it is not necessary to also check deformation and damping of oscillation as well.

18

Oscillatory criteria via linearization of half-linear second order delay differential equations

Baculikova Blanka, Dzurina Jozef

Opuscula Mathematica

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2020

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Vol. 40, no. 5

523--536

EN

In the paper, we study oscillation of the half-linear second order delay differential equations of the form [formula]. We introduce new monotonic properties of its nonoscillatory solutions and use them for linearization of considered equation which leads to new oscillatory criteria. The presented results essentially improve existing ones.

19

Oscillatory behavior of second-order damped differential equations with a superlinear neutral term

Tunc Ercan, Ozdemir Osman

Opuscula Mathematica

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2020

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Vol. 40, no. 5

629--639

EN

. This article concerns the oscillatory behavior of solutions to second-order damped nonlinear differential equations with a superlinear neutral term. The results are obtained by a Riccati type transformation as well as by an integral criterion. Examples illustrating the results are provided and some suggestions for further research are indicated.

20

On the qualitative behavior of the solutions to second-order neutral delay differential equations

Chatzarakis George E., Santra Shyam S.

Fasciculi Mathematici

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2020

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nr 64

43--56

EN

In this paper, we study the qualitative behavior of the solutions to second-order neutral delay differential equations of the form (r(t) ((x(t) + p(t)x(τ (t)))′)γ)′ + q(t)f (x(σ(t))) = 0. Our main tool is Lebesgue’s dominated convergence theorem. Examples illustrating the applicability of the results are also given.