1,569 research outputs found
Clarke subgradients of stratifiable functions
We establish the following result: if the graph of a (nonsmooth)
real-extended-valued function
is closed and admits a Whitney stratification, then the norm of the gradient of
at relative to the stratum containing bounds from below
all norms of Clarke subgradients of at . As a consequence, we obtain
some Morse-Sard type theorems as well as a nonsmooth Kurdyka-\L ojasiewicz
inequality for functions definable in an arbitrary o-minimal structure
Beyond happiness: Building a science of discrete positive emotions.
While trait positive emotionality and state positive-valence affect have long been the subject of intense study, the importance of differentiating among several "discrete" positive emotions has only recently begun to receive serious attention. In this article, we synthesize existing literature on positive emotion differentiation, proposing that the positive emotions are best described as branches of a "family tree" emerging from a common ancestor mediating adaptive management of fitness-critical resources (e.g., food). Examples are presented of research indicating the importance of differentiating several positive emotion constructs. We then offer a new theoretical framework, built upon a foundation of phylogenetic, neuroscience, and behavioral evidence, that accounts for core features as well as mechanisms for differentiation. We propose several directions for future research suggested by this framework and develop implications for the application of positive emotion research to translational issues in clinical psychology and the science of behavior change. (PsycINFO Database Recor
Mechanical properties of Pt monatomic chains
The mechanical properties of platinum monatomic chains were investigated by
simultaneous measurement of an effective stiffness and the conductance using
our newly developed mechanically controllable break junction (MCBJ) technique
with a tuning fork as a force sensor. When stretching a monatomic contact
(two-atom chain), the stiffness and conductance increases at the early stage of
stretching and then decreases just before breaking, which is attributed to a
transition of the chain configuration and bond weakening. A statistical
analysis was made to investigate the mechanical properties of monatomic chains.
The average stiffness shows minima at the peak positions of the
length-histogram. From this result we conclude that the peaks in the
length-histogram are a measure of the number of atoms in the chains, and that
the chains break from a strained state. Additionally, we find that the smaller
the initial stiffness of the chain is, the longer the chain becomes. This shows
that softer chains can be stretched longer.Comment: 6 pages, 5 figure
The effect of thermal annealing on the properties of Al-AlOx-Al single electron tunneling transistors
The effect of thermal annealing on the properties of Al-AlOx-Al single
electron tunneling transistors is reported. After treatment of the devices by
annealing processes in forming gas atmosphere at different temperatures and for
different times, distinct and reproducible changes of their resistance and
capacitance values were found. According to the temperature regime, we observed
different behaviors as regards the resistance changes, namely the tendency to
decrease the resistance by annealing at T = 200 degree C, but to increase the
resistance by annealing at T = 400 degree C. We attribute this behavior to
changes in the aluminum oxide barriers of the tunnel junctions. The good
reproducibility of these effects with respect to the changes observed allows
the proper annealing treatment to be used for post-process tuning of tunnel
junction parameters. Also, the influence of the annealing treatment on the
noise properties of the transistors at low frequency was investigated. In no
case did the noise figures in the 1/f-regime show significant changes.Comment: 6 pages, 7 eps-figure
Lectures on the Asymptotic Expansion of a Hermitian Matrix Integral
In these lectures three different methods of computing the asymptotic
expansion of a Hermitian matrix integral is presented. The first one is a
combinatorial method using Feynman diagrams. This leads us to the generating
function of the reciprocal of the order of the automorphism group of a tiling
of a Riemann surface. The second method is based on the classical analysis of
orthogonal polynomials. A rigorous asymptotic method is established, and a
special case of the matrix integral is computed in terms of the Riemann
-function. The third method is derived from a formula for the
-function solution to the KP equations. This method leads us to a new
class of solutions of the KP equations that are
\emph{transcendental}, in the sense that they cannot be obtained by the
celebrated Krichever construction and its generalizations based on algebraic
geometry of vector bundles on Riemann surfaces. In each case a mathematically
rigorous way of dealing with asymptotic series in an infinite number of
variables is established
Three Dimensional Structure and Energy Balance of a Coronal Mass Ejection
The Ultraviolet Coronagraph Spectrometer (UVCS) observed Doppler shifted
material of a partial Halo Coronal Mass Ejection (CME) on December 13 2001. The
observed ratio of [O V]/O V] is a reliable density diagnostic important for
assessing the state of the plasma. Earlier UVCS observations of CMEs found
evidence that the ejected plasma is heated long after the eruption. We have
investigated the heating rates, which represent a significant fraction of the
CME energy budget. The parameterized heating and radiative and adiabatic
cooling have been used to evaluate the temperature evolution of the CME
material with a time dependent ionization state model. The functional form of a
flux rope model for interplanetary magnetic clouds was also used to
parameterize the heating. We find that continuous heating is required to match
the UVCS observations. To match the O VI-bright knots, a higher heating rate is
required such that the heating energy is greater than the kinetic energy. The
temperatures for the knots bright in Ly and C III emission indicate
that smaller heating rates are required for those regions. In the context of
the flux rope model, about 75% of the magnetic energy must go into heat in
order to match the O VI observations. We derive tighter constraints on the
heating than earlier analyses, and we show that thermal conduction with the
Spitzer conductivity is not sufficient to account for the heating at large
heights.Comment: 40 pages, 16 figures, accepted for publication in ApJ For associated
mpeg file, please see https://www.cora.nwra.com/~jylee/mpg/f5.mp
Bispectral KP Solutions and Linearization of Calogero-Moser Particle Systems
A new construction using finite dimensional dual grassmannians is developed
to study rational and soliton solutions of the KP hierarchy. In the rational
case, properties of the tau function which are equivalent to bispectrality of
the associated wave function are identified. In particular, it is shown that
there exists a bound on the degree of all time variables in tau if and only if
the wave function is rank one and bispectral. The action of the bispectral
involution, beta, in the generic rational case is determined explicitly in
terms of dual grassmannian parameters. Using the correspondence between
rational solutions and particle systems, it is demonstrated that beta is a
linearizing map of the Calogero-Moser particle system and is essentially the
map sigma introduced by Airault, McKean and Moser in 1977.Comment: LaTeX, 24 page
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