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1
Content available An iterative approach for solving fractional order Cauchy reaction-diffusion equations
Kumar Manoj
Journal of Applied Mathematics and Computational Mechanics
|
2023
|
Vol. 22, nr 3
19-32
EN
Reaction-diffusion equations are vitally important due to their role in developing sturdy models in various scientific fields. In the present work, we address an algorithm of the Daftardar-Gejji and Jafari method for solving the nonlinear functional equations of the form ψ = f +L(ψ) + N(ψ). Further, we employ this algorithm to solve Caputo derivative-based time-fractional Cauchy reaction-diffusion equations. We obtain solutions in a series form that converges to a closed form. Furthermore, we perform numerical simulations for the various values of the order of fractional derivatives. The computational procedure of the proposed algorithm is not burdensome. However, it is time-efficient and can easily be implemented using a computer algebra system.
2
Content available Explicit commutativity conditions for second-order linear time-varying systems with non-zero initial conditions
Koksal Mehmet Emir
Archives of Control Sciences
|
2019
|
Vol. 29, No. 3
529--548
EN
Although the explicit commutativitiy conditions for second-order linear time-varying systems have been appeared in some literature, these are all for initially relaxed systems. This paper presents explicit necessary and sufficient commutativity conditions for commutativity of second-order linear time-varying systems with non-zero initial conditions. It has appeared interesting that the second requirement for the commutativity of non-relaxed systems plays an important role on the commutativity conditions when non-zero initial conditions exist. Another highlight is that the commutativity of switched systems is considered and spoiling of commutativity at the switching instants is illustrated for the first time. The simulation results support the theory developed in the paper.
3
Content available Mathemathical Equations of the Influence of Molybdenum and Nitrogen in Welds
Węgrzyn T., Kamińska J., Piwnik J., Stanik Z.
Archives of Metallurgy and Materials
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2018
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Vol. 63, iss. 1
83--86
EN
The paper offers mathematical equations of the influence of micro-jet cooling on structure and impact toughness properties of metal weld deposit. Weld metal deposit (WMD) was carried out for standard MIG welding and for MIG welding with micro-jet cooling. This new method is very promising mainly due to the high amount of AF (acicular ferrite) and low amount of MAC (selftempered martensite, retained austenite, carbide) phases in WMD. That structure corresponds with very good mechanical properties ie. good impact toughness of welds at low temperature. Micro-jet cooling after welding can find serious application in automotive industry very soon. Until that moment only argon, helium, nitrogen and gas mixtures of argon were tested for micro-jet cooling after welding. The best results of mechanical properties of WMD in presented welding method correspond with micro-jet argon cooling.
4
Content available Effect of the height of the delivery water on performance of water ram
Grygo D.
Technical Sciences / University of Warmia and Mazury in Olsztyn
|
2016
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nr 19(2)
139--149
EN
The main aim of this article is to develop mathematical equations of the performance stream (Vc) of a water ram with regard to the height of water delivery (hc). The study was performed on the sample water ram of my own design mounted on a specially designed test stand. The content of the article is divided into two parts. The first part describes a generalized equation on the base formulae used historically to determine the performance of the water ram. The second part presents the results of research and summarizes the mathematical equations determining the streams performance (Vc) according to the height of water delivery (hc). In conclusion the article makes interpretations of the results. The motivation to approach these issues stems from the question: How much will the performance of the water ram has on the ability to set a receiver tank at different heights?
5
Content available Data-based method for the determination of temperature dependence of heat capacity of highly dispersed powders
Karnina A., Gyrenko A., Klymenko A., Mysov O.
ECONTECHMOD : An International Quarterly Journal on Economics of Technology and Modelling Processes
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2015
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Vol. 4, No 4
23--28
EN
Accuracy of engineering and economic calculations in different areas requires the use of accurate and prompt values of heat capacity for new or modified materials. A number of existing methods have an error in measuring the heat capacity of powder materials, and use non-standard devices and electric heaters which are not produced industrially. This work is aimed at developing the method for determining the heat capacity of the powder, accuracy evaluation of this method and mathematical processing of experimental data to determine the temperature dependence of the molar heat capacity. To solve the problem the method based on the DTA technique was developed. The measuring apparatus for determining the temperature dependence of the heat capacity includes two standard cups for DTA analysis with investigated material and MgO, heat-variable resistor of film type Pt100, multichannel recorder. The apparatus is placed in a drying oven. From the theory of heat transfer and the assumption about steady-flow heat transfer the equation for molar heat capacity was obtained. The method requires the measuring of temperature of the investigated material and MgO during the linear heat of the drying oven as well as air temperature in the oven. Empirical values of heat capacity of standard substances calculated by the equation for each temperature were compared with the values from reference data. The uncertainty of finding the heat capacity did not exceed 0,5%.
6
Content available remote On Language Equations with One-sided Concatenation
Baader F., Okhotin A.
Fundamenta Informaticae
|
2013
|
Vol. 126, nr 1
1--35
EN
Language equations are equations where both the constants occurring in the equations and the solutions are formal languages. They have first been introduced in formal language theory, but are now also considered in other areas of computer science. In the present paper, we restrict the attention to language equations with one-sided concatenation, but in contrast to previous work on these equations, we allow not just union but all Boolean operations to be used when formulating them. In addition, we are not just interested in deciding solvability of such equations, but also in deciding other properties of the set of solutions, like its cardinality (finite, infinite, uncountable) and whether it contains least/greatest solutions. We show that all these decision problems are EXPTIME-complete.
7
Content available remote Equations for Asynchronous Message Passing
Czaja L.
Fundamenta Informaticae
|
2013
|
Vol. 128, nr 1-2
35--45
8
Content available remote Podstawowe równania modelu degradacji otuliny w wyniku korozji zbrojenia
Krykowski T.
Roczniki Inżynierii Budowlanej
|
2011
|
z. 11
81--84
EN
This paper presents the sketch of the model that can be used for the analysis of concrete cover in the corrosion conditions. The application of this model requires formulation of FEM theory equations. The presented model in the sense of idea is complete and can be used for determination of exploitation time of the cover in the case as well of chloride and the other type of corrosion.
9
Content available remote Asymtotic stability of solutions to the equations of linear elasticity and thermoelasticity in viscoporus media
Głowiński P., Łada A.
Demonstratio Mathematica
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2009
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Vol. 42, nr 4
757-779
EN
The systems of evolution equations modelling elasticity and thermoelas-ticity of viscoporous bounded media are considered. The existence of co-semigroups of contractions defining solutions to the systems is proved. The asymptotic vanishing of energies of solutions when t -> (infinity) is explained.
10
Problems of designing a logistic support system with time dependency
Werbińska S.
Systems : journal of transdisciplinary systems science
|
2007
|
Vol. 12, nr 2
37-50
EN
The paper considers the time dependent system of systems where the system total task must be executed during constrained time resource. For the developed model, general analytical equations for the evaluation of system of systems downtime, availability function, and total expected cost function are derived. Furthermore, the theoretical results with sensitivity analysis are discussed when all probability density functions are to be exponential
11
Content available remote On a problem concerning the indicator plurality function
Bahyrycz A.
Opuscula Mathematica
|
2001
|
Vol. 21
11-30
12
Content available remote Relationships between selected elements of the flood hydrographs in rivers
Ciepielowski A.
Journal of Water and Land Development
|
2001
|
no. 5
89-105
EN
Since the middle sixties, statistical analyses have been conducted in Poland on the description and identification of a hydrograph of a typical flood wave in rivers according to the concept of STRUPCZEWSKI (1964). These works have been enlarged by studies on relationships between basic elements of high waters: culmination flow [Qmax], wave volume (V), rising time (ts) and duration of high water (T). (CIEPIELOWSKI, CZECHOWICZ, 1984; CIEPIELOWSKI, 1987; 1994; CIEPIELOWSKI et al., 2001). In this paper I attempt to summarize these studies and to draw conclusions of a pure (on the mechanisms of floods) and applied (on using flood hydrographs in designing sluice and overflow devices in small retention reservoirs) character.
PL
W przypadku braku obserwacji hydrologicznych istnieje problem ustalania i przyjmowania kształtu fali i podstawowych jego elementów: czasów wznoszenia ts i trwania fali T, objętości fali V i przepływu kulminacyjnego Qmax. Dlatego przeprowadzono badania prowadzące do ustalenia związków empirycznych, które będzie można stosować w różnych warunkach fizycznogeograficznych. Do opisu fali wykorzystano koncepcję typowej fali wezbraniowej wg STRUPCZEWSKIEGO (1964). Przy ustalaniu równań związków elementów fal wezbraniowych zastosowano metodę analizy regresji wielokrotnej i korelacji, wykorzystując również statystyczne testy zgodności. Za istotne statystycznie oraz możliwe do stosowania w praktyce uznano związki w których I r I > rα i jednocześnie r > 0,5, I F I > Fα, I t I > tα przy poziomie istotności α = 0,05. Podsumowano dotychczasowe wyniki badań parametrów równań typowych fal wezbraniowych różnego pochodzenia i powstałych w zróżnicowanych warunkach fizycznogeograficznych. Stwierdzono, że ustalenie jednolitego równania typowej fali wezbraniowej dla warunków polskich nie jest możliwe ze względu na zróżnicowanie warunków tworzenia się wezbrań. Czas wznoszenia fal wezbraniowych zimowych, czyli pochodzenia roztopowego lub roztopowo-opadowego, jest większy niż w przypadku fal pochodzenia opadowego z okresu letniego i wzrasta wraz z wielkością zlewni (tab. 3). Równania związków elementów fal wezbraniowych możliwe do stosowania podano w tabeli 4. W przypadku braku danych do opisu hydrogramu fali wezbraniowej pochodzenia opadowego małej zlewni górskiej (do 12 km²) można stosować równanie: Qt = Qmaxp% [wzór] gdzie: Qt - przepływ w chwili t, w m³ ·s-¹, Qmaxp% - przepływ maksymalny letni o określonym prawdopodobieństwie występowania, w m³ ·s-¹. W przypadku braku danych należy przyjmować ze wzorów empirycznych. t - czas liczony od momentu przyjętego za początek fali wezbraniowej, w h, ts - czas wznoszenia fali, w h (w przypadku braku danych należy przyjmować ts ≅ 7 h).
13
Modelowanie wspomaganego termicznie procesu desorpcji próżniowej zanieczyszczeń z gruntu
Dakiniewicz P., Kawala Z.
Inżynieria Chemiczna i Procesowa
|
2001
|
T. 22, z. 3B
361--366
PL
W pracy przedstawiono równania bilansowe masy, pędu i ciepła opisujące proces desorpcji próżniowej zanieczyszczeń z gruntu. Zaprezentowano przykładowe obliczenia numeryczne przeprowadzone na podstawie powyższych równań, które porównano z wynikami badań eksperymentalnych.
EN
In article were presented equations of mass, motion and heat transfer describing process of soil vapour extraction. Results of calculations were compared with experimental measurements.
14
Content available remote Elements of the theory of spherical particle motion on a rotating cone with rectilinear blades
Mieszkalski L., Torebko A.
Technical Sciences / University of Warmia and Mazury in Olsztyn
|
2000
|
nr 3
77-92
EN
The paper presents theoretical bases of spherical particle motion inside a rotating vertical cone with blades radially. An equation deseribing the of a spherical particle was formulated. The condition of starting the particle motion was defined. The position of a spherical particle in the state of equilibrium, as well the velocity and time of its movement on the working surface, were determined. Symbols are in the txt.
PL
W pracy przedstawiono podstawy teoretyczne ruchu cząstki kulistej poruszającej się wewnątrz wirującego pionowego stożka, mającego promieniwo rozmieszczone łopatki. Sformułowano równanie opisujące ruch cząstki kulistej określono warunek rozpoczęcia ruchu przez cząstkę kulistą. Wyznaczono położenie cząstki kulistej będącej w stanie równowagi, prędkość i czas jej przemieszczania po powierzchni roboczej. Wykaz oznaczeń znajduje się w tekście.
15
Content available remote Analysis of adsorption isotherms of water vapor on unmodified and strongly oxidized active carbons
Choma J., Jaroniec M.
Biuletyn Wojskowej Akademii Technicznej
|
1998
|
Vol. 47, nr 7-8
17-31
EN
Adsorption isotherms of water vapor measured on unmodified and strongly oxidized active carbons at 298 K were analyzed by using different isotherm equations. It was shown that the wellknown Dubinin-Serpinsky equations fail to describe adsorption isotherms of water vapor on strongly oxidized active carbons. However these isotherms can be well described by equations of the theory of the micropore volume filling such as Dubinin-Astakhov and Jaroniec-Choma equations. This suggests that water vapor adsorption on strongly oxidized active carbons resembles more the volume filling of micropores than a molecular clustering mechanism typical for unoxidized carbons. A strong oxidation of active carbons leads to the formation of surface oxygen groups, which significantly enhance adsorption of water molecules at low pressure range in comparison to that unoxidized carbons.
PL
Analizowano izotermy adsorpcji pary wodnej zmierzone na niemodyfikowanych i silnie utlenionych węglach aktywnych w temp. 298 K przy użyciu różnych równań adsorpcji. Pokazano, że znane równania Dubinina-Sierpińskiego zawodzą w opisie izoterm adsorpcji pary wodnej na silnie utlenionych węglach aktywnych. Natomiast, te izotermy mogą być dobrze opisane za pomocą równań teorii objętościowego zapełniania mikroporów takich jak równania Dubinina-Astachowa i Jarońca-Chomy. To sugeruje, że adsorpcja pary wodnej na silnie utlenionych węglach aktywnych przypomina raczej objętościowe zapełnianie mikroporów niż mechanizm tworzenia kompleksów cząsteczkowych typowy dla nieutlenionych węgli. Silne utlenianie węgli aktywnych prowadzi do utworzenia tlenowych grup powierzchniowych, które znacznie zwiększają adsorpcję cząsteczek wody w obszarze niskich ciśnień w porównaniu z adsorpcją na nieutlenionych węglach.
16
Content available remote Coercive limits for a subclass of monotonne constitutive equations in the theory of inelastic material behaviour of metals
Chełmiński Krzysztof
Matematyka Stosowana : matematyka dla społeczeństwa
|
1997
|
Nr 40
41--81
EN
We prove existence and uniqueness of strong global in tme solution for a subclass of monotone constitutive equations in the theory of inelastic material behaviour of metals without the coercivity assumption for the free energy function. We approximate noncoercive models by a sequence of coercive problems and prove the convergence result.
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