Analytic number theorists usually seek to show that sequences which appear naturally in arithmetic are “well-distributed” in some appropriate sense. In various discrepancy problems, combinatorics researchers have analyzed limitations to equidistribution, as have Fourier analysts when working with the “uncertainty principle”. In this article we ﬁnd that these ideas have a natural setting in the analysis of distributions of sequences in analytic number theory, formulating a general principle, and giving several examples. ...
Classical physics breaks down to the level of atoms and molecules. This was made
possible by the invention of a new apparatus that enabled the introduction of
measurements in microscopic area of physics. There were two revolutions in the way
we viewed the physical world in the twentieth century: relativity and quantum
mechanics. Quantum mechanics was born in 1924, through the work of Einstein,
Rutherford and Bohr, Schrödinger and Heisenberg, Born, Dirac, and many others. The
principles of quantum mechanics that were discovered then are the same as we know
(BQ) Part 2 book "Principles of microeconomics" has contents: Monopoly and antitrust policy, oligopoly, monopolistic competition, uncertainty and asymmetric information, income distribution and poverty, income distribution and poverty, economic growth in developing economies,...and other contents.
All kinds of processes – those that make things or deliver services
or operate companies – can be made more productive, and society’s
continued well-being requires it. This book is for all those with a
stake in improving how companies run. It introduces the concept
of “swift, even l ow” and explains how that concept stands behind
popular business tools such as “lean” principles and Six Sigma.
More than that, it shows how swift, even l ow can lead to deep,
strategic insights and fresh ideas.
In a world of geo-political, social and economic uncertainty, strategic financial management is in a process of change, which requires a reassessment of the fundamental assumptions that cut across the traditional boundaries of the subject. Read on and you will not only appreciate the major components of contemporary finance but also find the subject much more accessible for future reference.
One of the most prominent and urgent problems in international
governance is how the different branches and norms of international
law interact, and what to do in the event of conﬂict. With no single
‘international legislator’and a multitude of states, international
organisations and tribunals making and enforcing the law, the
international legal system is decentralised.
The development of quantum mechanics has taken physics in a vastly new direction from that of classical physics from the very start. In fact, there continue at present to be many developments in the subject of a very fundamental nature, such as implications for the foundations of physics, physics of entanglement, geometric phases, gravity and cosmology and elementary particles as well. It is hoped the papers in this volume will provide a much needed resource for researchers with regard to current topics of research in this growing area....
In this chapter we discuss relations between information theory and statistical
mechanics. We show that the canonical and grand canonical distributions
can be obtained from Shannon’s principle of maximum uncertainty [1, 2, 3].
Moreover, the time evolution of the entropy of an isolated system and the H
theorem are discussed.
Calibration, Veriﬁcation, Statistical Treatment of Analytical Data, Detection Limits, and Quality Assurance/Quality Control
If you can measure that of which you speak, and can express it by a number, you know something of your subject, but if you cannot measure it, your knowledge is meager and unsatisfactory. —Lord Kelvin
CHAPTER AT A GLANCE
Good laboratory practice .........................................................................................38 Error in laboratory measurement ............................................................................
Colours! The most beautiful of buds – an apple bud in my garden changes colour
from red to rosy after a few days. Why? It then explodes into a beautiful pale rosy
ﬂower. After a few months what was once a ﬂower looks completely different: it
has become a big, round and red apple. Look at the apple skin. It is pale green,
but moving along its surface the colour changes quite abruptly to an extraordinary
vibrant red. The apple looks quite different when lit by full sunlight, or when placed
in the shade....
Non-Linear TirneFrequency Distributions
In Chapters 7 and 8 twotime-frequencydistributions were discussed: the spectrogram and the scalogram. Both distributions are the result of linear filtering and subsequent forming of the squared magnitude. In this chapter time-frequency distributions derived in a different manner will be considered. Contrary to spectrograms and scalograms, their resolution is not restricted by the uncertainty principle.
This book examines the intersection of WTO trade liberalisation rules and
domestic health protection, a subject that is of considerable interest to
those concerned that the WTO impinges on national regulatory auto-
nomy. In analysing the tension between health protection and trade liber-
alisation, the book focuses on the way in which this tension is (or is not)
resolved through the dispute resolution process.
When comparing time series models across countries, there is always a trade-off between the
need to implement the comparison as neatly as possible and the need to fit models as best as
possible to individual countries. By using different lags for different countries, we would run
the risk to lose full comparability. By running the exercise with a common specification across
countries we are running the risk of comparing Chile with other countries on the basis of a
model that is possibly misspecified for other countries.
Chapter 11 - Current liabilities. After completing this chapter you should be able to: Describe current and long-term liabilities and their characteristics, identify and describe known current liabilities, explain how to account for contingent liabilities.
298 Planning and Forecasting
later. Since the cash f low is deferred, the true value of that sale to the firm is somewhat diminished. By focusing on cash f lows and when they occur, NPV ref lects the true value of increased revenues and costs. Consequently, NPV analysis requires that accounting data be unraveled to reveal the underlying cash f lows. That is why changes in net working capital must be accounted for and why depreciation does not show up directly.
Principle No. 2: Use Expected Values
There is always going to be some uncertainty over future cash f lows. Future costs and...
Financial and insurance markets always operate under various types of uncertainties
that can affect nancial positions of companies and individuals. In nancial and
insurance theories these uncertainties are usually referred to as risks. Given certain
states of the market, and the economy in general, one can talk about risk exposure.
Any economic activities of individuals, companies and public establishments aiming
for wealth accumulation assume studying risk exposure. The sequence of the corresponding
actions over some period of time forms the process of risk management.
Fang et al. Nanoscale Research Letters 2011, 6:237 http://www.nanoscalereslett.com/content/6/1/237
Measurement of the extinction coefficients of magnetic fluids
Xiaopeng Fang, Yimin Xuan*, Qiang Li
Abstract A novel spectral transmittance approach for measuring the extinction coefficient of magnetic fluids is proposed. The measuring principle and accuracy of the approach are analysed. Experiments are conducted to measure the extinction coefficient of magnetic fluids with different particle volume fractions.
Xu et al. Nanoscale Research Letters 2011, 6:355 http://www.nanoscalereslett.com/content/6/1/355
Quantum-squeezing effects of strained multilayer graphene NEMS
Yang Xu1*, Sheping Yan1, Zhonghe Jin1* and Yuelin Wang2
Abstract Quantum squeezing can improve the ultimate measurement precision by squeezing one desired fluctuation of the two physical quantities in Heisenberg relation. We propose a scheme to obtain squeezed states through graphene nanoelectromechanical system (NEMS) taking advantage of their thin thickness in principle.