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2. A Pettis-type integral and applications to transition semigroups
- Creator:
- Kunze, Markus
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- Pettis-type integral, dual pairs, Laplace transform, and transition semigroup
- Language:
- English
- Description:
- Motivated by applications to transition semigroups, we introduce the notion of a norming dual pair and study a Pettis-type integral on such pairs. In particular, we establish a sufficient condition for integrability. We also introduce and study a class of semigroups on such dual pairs which are an abstract version of transition semigroups. Using our results, we give conditions ensuring that a semigroup consisting of kernel operators has a Laplace transform which also consists of kernel operators. We also provide conditions under which a semigroup is uniquely determined by its Laplace transform.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
3. An analysis of the stability boundary for a linear fractional difference system
- Creator:
- Kisela, Tomáš
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- fractional difference system, stability, and Laplace transform
- Language:
- English
- Description:
- This paper deals with basic stability properties of a two-term linear autonomous fractional difference system involving the Riemann-Liouville difference. In particular, we focus on the case when eigenvalues of the system matrix lie on a boundary curve separating asymptotic stability and unstability regions. This issue was posed as an open problem in the paper J. Čermák, T. Kisela, and L. Nechvátal (2013). Thus, the paper completes the stability analysis of the corresponding fractional difference system.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
4. Analytical solution for transient hydraulic head, flow rate and volumetric exchange in an aquifer under recharge condition
- Creator:
- Bansal, Rajeev Kumar and Das, Samir Kumar
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- piezometric head, flow rate, volumetric exchange, confined aquifer, analytical solution, Laplace transform, piezometrická výška, rýchlosť prúdenia, prítok do podzemných vôd, ohraničený zvodnený kolektor, analytické riešenia, and Laplaceova transformácia
- Language:
- Slovak
- Description:
- This paper presents closed form solution for unsteady flow equation corresponding to the transient hydraulic head, flow rate and volumetric exchange of a confined aquifer which is in contact with a constant piezometric head at one end and a stream whose water level is rising at a constant rate at the other end. The aquifer is also subjected to receive constant inflow due to rain infiltration. The unsteady groundwater flow equation is solved using Laplace transform to get analytical expressions for the transient hydraulic head and flow rate at the left and right interfaces and the net volumetric exchange of water at the aquifer-stream interface. The analytical results presented here show the effect of recharge due to rain infiltration on the net volumetric exchange and reveal the conditions for which net inflow in the aquifer could be positive, negative or zero. The results obtained have the capability to determine transient hydraulic head for two extreme scenarios: (i) very slow rise and (ii) very fast rise in the stream water. Analytical result show that the net volumetric exchange could be positive, zero or negative depending on the surface infiltration and stream water rise rate. and Príspevok obsahuje analytické riešenie rovnice neustáleného prúdenia vzhľadom na neustálenú hydraulickú výšku, rýchlosť prúdenia a objemové toky vo zvodnenom kolektore s napätou hladinou, ktorý je v kontakte s konštantnou piezometrickou výškou na jednej strane a s tokom s konštantne sa zvyšujúcou hladinou vody na strane druhej. Zvodnený kolektor je tiež napájaný konštantnou rýchlosťou infiltrovanou vodou zo zrážok. Rovnica neustáleného prúdenia podzemnej vody je riešená s použitím Laplaceovej transformácie, aby sme získali neustálenú tlakovú výšku na ľavej aj pravej strane a objemový prítok vody na rozhraní zvodnený kolektor - tok. Výsledky analytického riešenia, ktoré predkladáme, ukazujú vplyv infiltrácie zrážok na doplňovanie podzemnej vody a odhaľujú podmienky, za ktorých prítok do zvodneného kolektora môže byť kladný, negatívny, alebo nulový. Získané výsledky umožňujú určiť neustálené hydraulické výšky pre dva extrémne scenáre: (i) veľmi pomalé a (ii) veľmi rýchle zvýšenie hladiny vody v toku. Analytické riešenie ukazuje, že objem vody, ktorou je zvodnený kolektor doplňovaný, môže byť kladný, záporný, alebo nulový, v závislosti na intenzite infiltrácie a rýchlosti zvyšovania sa hladiny vody v toku.
- Rights:
- http://creativecommons.org/licenses/by-nc-sa/4.0/ and policy:public
5. Distributional versions of Littlewood's Tauberian theorem
- Creator:
- Estrada, Ricardo and Vindas, Jasson
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- Tauberian theorem, Laplace transform, the converse of Abel's theorem, Littlewood's Tauberian theorem, Abel and Cesàro summability, distributional Tauberian theorem, and asymptotic behavior of generalized function
- Language:
- English
- Description:
- We provide several general versions of Littlewood's Tauberian theorem. These versions are applicable to Laplace transforms of Schwartz distributions. We employ two types of Tauberian hypotheses; the first kind involves distributional boundedness, while the second type imposes a one-sided assumption on the Cesàro behavior of the distribution. We apply these Tauberian results to deduce a number of Tauberian theorems for power series and Stieltjes integrals where Cesàro summability follows from Abel summability. We also use our general results to give a new simple proof of the classical Littlewood one-sided Tauberian theorem for power series.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public