Let T (x, ε) denote the ﬁrst hitting time of the disc of radius ε centered at x for Brownian motion on the two dimensional torus T2 . We prove that supx∈T2 T (x, ε)/| log ε|2 → 2/π as ε → 0. The same applies to Brownian motion on any smooth, compact connected, two-dimensional, Riemannian manifold with unit area and no boundary. As a consequence, we prove a conjecture, due to Aldous (1989), that the number of steps it takes a simple random walk to cover all points of the lattice torus Z2 is asymptotic to 4n2 (log...
Baby didn't cry all day, because he had a monster for a playmate. But I didn't know he had a playmate, and much less did I know it was a monster. The honest truth is that for the first time since baby was born, I had my nerves under control, and I didn't dare investigate why he wasn't crying. I got all the ironing done—all of it, mind you—and I got Harry's work-clothes mended and I also read three installments of a Saturday Evening Post serial I'd been saving. And besides this Mabel, my neighbor, and I had a couple...
During the last thirty years of his life, Albert Einstein sought relentlessly for a so-called unified field theory—a theory capable of
describing nature's forces within a single, all-encompassing, coherent framework. Einstein was not motivated by the things we
often associate with scientific undertakings, such as trying to explain this or that piece of experimental data. Instead, he was driven
by a passionate belief that the deepest understanding of the universe would reveal its truest wonder: the simplicity and power of the
principles on which it is based.
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accessible to all of our customers.
CHAPTER 16 Futures Contracts
Trading in futures contracts adds a time dimension to commodity markets. A futures contract separates the date of the agreement - when a delivery price is specified - from the date when delivery and payment actually occur. By separating these dates, buyers and sellers achieve an important and flexible tool for risk management.
Bowen’s formula relates the Hausdorﬀ dimension of a conformal repeller to the zero of a ‘pressure’ function. We present an elementary, self-contained proof to show that Bowen’s formula holds for C 1 conformal repellers. We consider time-dependent conformal repellers obtained as invariant subsets for sequences of conformally expanding maps within a suitable class.
At the global level, the relationship between population and environ-
mental impact is not easy to test in a way that leads to reliable and non-
spurious estimates. This is because of the lack of data on environmental
degradation covering a sufficiently large number of countries over a suffi-
ciently large period of time. It is for this reason that studies have tended to
focus on CO2 emissions and energy use, for which cross-country and time-
series data are available.
This book by Graham Thornicroft and Michele Tansella has a very clear objective:
how better care could achieve better outcomes for people suffering from mental
disorders. The preoccupation of the book is to derive bettermental health care from
the best ethical, evidence-based and experience-based practices available. These two
propositions, improving outcomes and framing interventions upon ethics, evidence
and experience, are so clearly defined by the authors that this book represents a
challenge to psychiatrists who sometimes forget the key link between ‘treatment’
Preface 1 The Wave Function 2 Time-Independent Schrödinger Equation 3 Formalism 4 Quantum Mechanics in Three Dimensions 5 Identical Particles 6 Time-Independent Perturbation Theory 7 The Variational Principle 8 The WKB Approximation 9 Time-Dependent Perturbation Theory 10 The Adiabatic Approximation 11 Scattering 12 Afterword Appendix Linear Algebra 2nd Edition – 1st Edition Problem Correlation Grid 2 3 14 62 87 132 154 196 219 236 254 268 282 283 299
These are my own solutions to the problems in Introduction to Quantum Mechanics, 2nd ed.
Nothing prevents an enterprising young designer from going to the local art-and-craft supply
store and buying a sheet of basswood, and cutting out a model of his or her own design. However,
the step from purchase-and-assemble to building-from-raw-materials is large: The designer must
decide and draw the parts, determine how they will join, then carefully cut them from the sheet.
Tolerance errors have severe consequences; a small mismatch between notch size or position and
material thickness means the model won’t assemble correctly.
Dualism is a dominant theory of life that considers
reality to be a balance between two independent and
fundamental principles: good and evil, mind and
matter, nature and nurture. In the same manner we
see the thread of dualism run through the ecology of
parasitism: they can generate diversity but cause
extinction, they may castrate a host but increase its
growth rate, and they can stimulate an immune
response but at the same time encourage a secondary
Identify the components of the internal environment and discuss their impact on organisations.
•Discuss the primary charateristics and determinants of an organisation’s culture and how the culture can be managed.
•Identify the main dimensions, cause and impacts of workforce diversity and discuss the strategies and approaches to diversity management.
•Describe managerial ethics and CSR and discuss how they can be managed in organisations.
External environment: Everything outside an organisation that might affect it.
–General environment: Broad dimensions/forces in an organisation’s surroundings, creating its overall context.
–Task environment: Specific organisations or groups that affect the organisation.
•Internal environment: The conditions and forces within an organisation.Political-legal dimension
•Impacts are vague, imprecise and long term.
•Cannot be influenced by organisations....
Traditional financial approaches, on the other hand, measure financial dimensions, and
provide quantitative data on which real estate investment decisions can be based. The most
widely used of all financial ratios - in real estate or any other investment - is 'return on
investment' (ROI). In attempting to define and quantify the investor's required rate of return, this
area of the literature provides a more analytical approach than the 'how to' authors. Typically,
the ROI approach is used to measure performance ‘ex poste’ - after the event.
This book examines how professionals practising in various health and welfare
settings go about the ordinary, but complicated, business of making sense
of the symptoms and troubles with which their patients or clients present.
Our motivations for writing the book are varied, but are the result of our
conversations with each other about the problem of judgement in clinical
practice, which have taken place over many years of professional, academic
and research collaboration.
The impetus to write a book on the riverine ecosystem synthesis emerged at the 2005 annual
meeting of the North American Benthological Society in New Orleans, and barely 2 months
later, we signed a contract with Academic Press. This book was to be an expansion of a
manuscript that was In Press at that time in River Research and Applications (Thorp et al.,
The concept of the division of labour in production has a long
genealogy stretching back to the seventeenth century and before,
and it recurs repeatedly in the writings of economists and other
social theorists down to the present time. In economics, the
concept plays a major role in studies of industrial organization,
productivity, and trade. In sociology, it has been of major signiWcance
as the linchpin of the distinction Wrst proposed by Durkheim
(1893) between mechanical and organic solidarity in society....
CHAPTER FOCUS Estimation Problem
This is the problem of estimating the state of a linear stochastic system by using measurements that are linear functions of the state. We suppose that stochastic systems can be represented by the types of plant and measurement models (for continuous and discrete time) shown as Equations 4.1±4.5 in Table 4.1, with dimensions of the vector and matrix quantities as shown in Table 4.2.
Solar electric plants shall be understood to be photovoltaic energy converters that are able to self-sufﬁciently satisfy a mean energy demand over a signiﬁcant period of time, be it an appliance that is permanently hooked up or just for sporadic power supply of appliances. Such plants have in common that their input and output quantities ﬂuctuate widely. They can therefore only be dimensioned on the basis of a mean value and are not able to satisfy this demand without the possibility to store energy. ...