Fundamental Sciences Issue 1 NP (4) 2013

2013

Publication date: 2013

Description

Licence: CC BY

Editorial team

Editor-in-Chief Józef Gawlik

Issue content

Resonance phenomena in micro/nanoelectromechanical systems

Anna Foryś, Andrzej S. Foryś

Technical Transactions, Fundamental Sciences Issue 1 NP (4) 2013, 2013, pp. 3-10

https://doi.org/10.4467/2353737XCT.14.027.2610

In the paper, some aspects of nonlinearity of micro/nanoelectromechanical systems (MEMS/
NEMS) are presented. Because of great values of strains of micro/nanobeams the nonlinear
description is necessary. Particularly, the nonlinear inertia term is added to equation relating
to motion of the beam. Numerical calculations of resonance curves and instability regions
are given. Results are presented on graphs.

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On abstract nonlocal Cauchy problem

Adam Bednarz, Ludwik Byszewski

Technical Transactions, Fundamental Sciences Issue 1 NP (4) 2013, 2013, pp. 11-17

https://doi.org/10.4467/2353737XCT.14.028.2611

In this paper, we investigate the existence and uniqueness of the classical solution to an abstract
nonlocal Cauchy problem. For this purpose, we apply a notion of mild solution and the Banach
contraction theorem.

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On nonlocal evolution problem for the equation of the first order

Ludwik Byszewski, Teresa Winiarska

Technical Transactions, Fundamental Sciences Issue 1 NP (4) 2013, 2013, pp. 19-26

https://doi.org/10.4467/2353737XCT.14.029.2612

The aim of the paper is to prove theorems about the existence and uniqueness of mild
and classical solutions of a nonlocal semilinear functional-differential evolution Cauchy
problem. The method of semigroups, the Banach fixed-point theorem and theorems (see [2])
about the existence and uniqueness of the classical solutions of the first-order differential
evolution problems in a not necessarily reflexive Banach space are used to prove the existence
and uniqueness of the solutions of the problems considered. The results obtained are based
on publications [1–6].

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Continuous dependence of mild solutions, on initial nonlocal data, of the nonlocal evolution Cauchy problems

Ludwik Byszewski, Teresa Winiarska

Technical Transactions, Fundamental Sciences Issue 1 NP (4) 2013, 2013, pp. 27-32

https://doi.org/10.4467/2353737XCT.14.030.2613

The aim of the paper is to prove two theorems on continuous dependence of mild solutions,
on initial nonlocal data, of the nonlocal Cauchy problems. For this purpose, the method
of semigroups and the theory of cosine family in Banach spaces are applied. The paper is based
on publications [1–5].

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The non-existence of the Fejer‒Riesz type result for some weighted Bergman spaces in the unit disc

Piotr Jakóbczak

Technical Transactions, Fundamental Sciences Issue 1 NP (4) 2013, 2013, pp. 33-40

https://doi.org/10.4467/2353737XCT.14.031.2614

In this note, we consider the analogues of the classical Fejer‒Riesz inequality for some weighted
Hilbert spaces of analytic functions in the unit disc. We prove that for some class of such spaces,
the Fejer-Riesz inequality type results do not hold.

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Distribution-valued functions

Margareta Wiciak

Technical Transactions, Fundamental Sciences Issue 1 NP (4) 2013, 2013, pp. 41-54

https://doi.org/10.4467/2353737XCT.14.032.2615

We study continuity and differentiability of a distribution-valued function. It is understood
in a strong sense due to inductive limit topology.

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Bug Fixing Tool (BFT) for continuous integration

Przemysław Leguła, Piotr Zabawa

Technical Transactions, Fundamental Sciences Issue 1 NP (4) 2013, 2013, pp. 55-61

https://doi.org/10.4467/2353737XCT.14.033.2616

The paper is focused on the bug fixing handling business process rather then just on fixing
a bug. The tool presented here is dedicated to supporting the business process of bug fixing and
not to bug fixing itself. It is addressed especially to small teams having a common testing team.

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Słowa kluczowe: MEMS, NEMS, nonlinearities, parametric resonance, stability, abstract Cauchy problem, nonlocal conditions, mild and classical solution, evolution Cauchy problem, existence and uniqueness of the solutions, nonlocal conditions, evolution Cauchy problems, continuous dependence of solutions, nonlocal conditions, Fejer-Riesz inequality, Bergman spaces of analytic functions, distribution-valued function, inductive limit topology, continuous integration, version control server, bug fixing, bug submission, iterative software development process