4,442 research outputs found
Loss of energy concentration in nonlinear evolution beam equations
Motivated by the oscillations that were seen at the Tacoma Narrows Bridge, we
introduce the notion of solutions with a prevailing mode for the nonlinear
evolution beam equation in bounded
space-time intervals. We give a new definition of instability for these
particular solutions, based on the loss of energy concentration on their
prevailing mode. We distinguish between two different forms of energy transfer,
one physiological (unavoidable and depending on the nonlinearity) and one due
to the insurgence of instability. We then prove a theoretical result allowing
to reduce the study of this kind of infinite-dimensional stability to that of a
finite-dimensional approximation. With this background, we study the occurrence
of instability for three different kinds of nonlinearities and for some
forcing terms , highlighting some of their structural properties and
performing some numerical simulations
Thresholds for hanger slackening and cable shortening in the Melan equation for suspension bridges
The Melan equation for suspension bridges is derived by assuming small
displacements of the deck and inextensible hangers. We determine the thresholds
for the validity of the Melan equation when the hangers slacken, thereby
violating the inextensibility assumption. To this end, we preliminarily study
the possible shortening of the cables: it turns out that there is a striking
difference between even and odd vibrating modes since the former never shorten
the cables. These problems are studied both on beams and plates
One or Two Statement Approach for the Income Statement of Czech Companies?
Purpose of the article: The article examines the IAS 1 revised that allows the company to choose between a
reclassification of items by nature or by function (destination), it also provides two alternative presentations
of the income statement: a single statement of comprehensive income or two statements, the first containing
the components of net income, and the second that, starting from net income, shows the other components of
expanded income.
Methodology/methods: First we outline the principal theories of the statement of comprehensive income,
secondly we concentrate the research to obtain the empirical data. The research is developed in the following
steps: selection of the companies surveyed; selection of the documents to be analysed; election of the empirical
aspects to be studied.
Scientific aim: The aim of the research is to define which format has been adopted by companies listed on the
Czech Republic Stock Exchange for the new Income Statement to be prepared according to the International
Accounting Standards – IAS 1 revised in 2007. In particular, we examine the Consolidated Financial Statements
2010 published online.
Findings: This article illustrates the two choices that have the companies to present items of net income, items
of other comprehensive income and total comprehensive income: they can create one continuous statement of
comprehensive income or two separate consecutive statements.
Conclusions: The results show that the Czech financial statements have not a firms’ propensity to separate
the section of the income statement in two statements rather than to integrate it into a single one, while the
reclassification of the income statements privileges the reclassification by nature
THE DRIVERS OF PRODUCTIVITY
This paper will try to demonstrate that productivity is the basis of all productive systems, which are viewed as transformers of utility and value, since the search for maximum productive efficiency is necessary to reduce production costs and thus produce value. After presenting a coherent frame of reference, we shall examine the drivers of productivity and then move on to discuss the consequences of the continual growth in productivity and the non-economic aspects linked to the gradual improvement in productivit
Resonance tongues for the Hill equation with Duffing coefficients and instabilities in a nonlinear beam equation
We consider a class of Hill equations where the periodic coefficient is the
squared solution of some Duffing equation plus a constant. We study the
stability of the trivial solution of this Hill equation and we show that a
criterion due to Burdina (V.I. Burdina, Boundedness of solutions of a system of
differential equations) is very helpful for this analysis. In some cases, we
are also able to determine exact solutions in terms of Jacobi elliptic
functions. Overall, we obtain a fairly complete picture of the stability and
instability regions. These results are then used to study the stability of
nonlinear modes in some beam equations.Comment: Communications in contemporary mathematics. Print ISSN: 0219-1997.
Online ISSN: 1793-668
Higher order linear parabolic equations
We first highlight the main differences between second order and higher order
linear parabolic equations. Then we survey existing results for the latter, in
particular by analyzing the behavior of the convolution kernels. We illustrate
the updated state of art and we suggest several open problems.Comment: Dedicated to Patrizia Pucci. To appear in the the Contemporary
Mathematics series of the AM
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