2,009 research outputs found
Infinite dimensional integrals beyond Monte Carlo methods: yet another approach to normalized infinite dimensional integrals
An approach to (normalized) infinite dimensional integrals, including
normalized oscillatory integrals, through a sequence of evaluations in the
spirit of the Monte Carlo method for probability measures is proposed. in this
approach the normalization through the partition function is included in the
definition. For suitable sequences of evaluations, the ("classical")
expectation values of cylinder functions are recoveredComment: Submitted as a communication in the ICMSQUARE conference, september
201
Local monotonicity of Riemannian and Finsler volume with respect to boundary distances
We show that the volume of a simple Riemannian metric on is locally
monotone with respect to its boundary distance function. Namely if is a
simple metric on and is sufficiently close to and induces
boundary distances greater or equal to those of , then . Furthermore, the same holds for Finsler metrics and the
Holmes--Thompson definition of volume. As an application, we give a new proof
of the injectivity of the geodesic ray transform for a simple Finsler metric.Comment: 13 pages, v3: minor corrections and clarifications, to appear in
Geometriae Dedicat
Filling minimality of Finslerian 2-discs
We prove that every Riemannian metric on the 2-disc such that all its
geodesics are minimal, is a minimal filling of its boundary (within the class
of fillings homeomorphic to the disc). This improves an earlier result of the
author by removing the assumption that the boundary is convex. More generally,
we prove this result for Finsler metrics with area defined as the
two-dimensional Holmes-Thompson volume. This implies a generalization of Pu's
isosystolic inequality to Finsler metrics, both for Holmes-Thompson and
Busemann definitions of Finsler area.Comment: 16 pages, v2: improved introduction and formattin
On Alternative Supermatrix Reduction
We consider a nonstandard odd reduction of supermatrices (as compared with
the standard even one) which arises in connection with possible extension of
manifold structure group reductions. The study was initiated by consideration
of the generalized noninvertible superconformal-like transformations. The
features of even- and odd-reduced supermatrices are investigated on a par. They
can be unified into some kind of "sandwich" semigroups. Also we define a
special module over even- and odd-reduced supermatrix sets, and the generalized
Cayley-Hamilton theorem is proved for them. It is shown that the odd-reduced
supermatrices represent semigroup bands and Rees matrix semigroups over a unit
group.Comment: 22 pages, Standard LaTeX with AmS font
Grafting of (3-chloropropyl)-trimethoxy silane on halloysite nanotubes surface
Modified halloysite nanotubes (HNTs-Cl) were synthesized by a coupling reaction with (3-chloropropyl) trimethoxysilane (CPTMS). The incorporation of chloro-silane onto HNTs surface creates HNTs-Cl, which has great chemical activity and is considered a good candidate as an active site that reacts with other active molecules in order to create new materials with great applications in chemical engineering and nanotechnology. The value of this work lies in the fact that improving the degree of grafting of chloro-silane onto the HNT’s surface has been accomplished by incorporation of HNTs with CPTMS under different experimental conditions. Many parameters, such as the dispersing media, the molar ratio of HNTs/CPTMS/H2O, refluxing time, and the type of catalyst were studied. The greatest degree of grafting was accomplished by using toluene as a medium for the grafting process, with a molar ratio of HNTs/CPTMS/H2O of 1:1:3, and a refluxing time of 4 h. The addition of 7.169 mmol of triethylamine (Et3N) and 25.97 mmol of ammonium hydroxide (NH4OH) led to an increase in the degree of grafting of CPTMS onto the HNT’s surface
Theory and computation of directional nematic phase ordering
A computational study of morphological instabilities of a two-dimensional
nematic front under directional growth was performed using a Landau-de Gennes
type quadrupolar tensor order parameter model for the first-order
isotropic/nematic transition of 5CB (pentyl-cyanobiphenyl). A previously
derived energy balance, taking anisotropy into account, was utilized to account
for latent heat and an imposed morphological gradient in the time-dependent
model. Simulations were performed using an initially homeotropic
isotropic/nematic interface. Thermal instabilities in both the linear and
non-linear regimes were observed and compared to past experimental and
theoretical observations. A sharp-interface model for the study of linear
morphological instabilities, taking into account additional complexity
resulting from liquid crystalline order, was derived. Results from the
sharp-interface model were compared to those from full two-dimensional
simulation identifying the specific limitations of simplified sharp-interface
models for this liquid crystal system. In the nonlinear regime, secondary
instabilities were observed to result in the formation of defects, interfacial
heterogeneities, and bulk texture dynamics.Comment: first revisio
Noise auto-correlation spectroscopy with coherent Raman scattering
Ultrafast lasers have become one of the most powerful tools in coherent
nonlinear optical spectroscopy. Short pulses enable direct observation of fast
molecular dynamics, whereas broad spectral bandwidth offers ways of controlling
nonlinear optical processes by means of quantum interferences. Special care is
usually taken to preserve the coherence of laser pulses as it determines the
accuracy of a spectroscopic measurement. Here we present a new approach to
coherent Raman spectroscopy based on deliberately introduced noise, which
increases the spectral resolution, robustness and efficiency. We probe laser
induced molecular vibrations using a broadband laser pulse with intentionally
randomized amplitude and phase. The vibrational resonances result in and are
identified through the appearance of intensity correlations in the noisy
spectrum of coherently scattered photons. Spectral resolution is neither
limited by the pulse bandwidth, nor sensitive to the quality of the temporal
and spectral profile of the pulses. This is particularly attractive for the
applications in microscopy, biological imaging and remote sensing, where
dispersion and scattering properties of the medium often undermine the
applicability of ultrafast lasers. The proposed method combines the efficiency
and resolution of a coherent process with the robustness of incoherent light.
As we demonstrate here, it can be implemented by simply destroying the
coherence of a laser pulse, and without any elaborate temporal scanning or
spectral shaping commonly required by the frequency-resolved spectroscopic
methods with ultrashort pulses.Comment: To appear in Nature Physic
Generic representations of abelian groups and extreme amenability
If is a Polish group and is a countable group, denote by
\Hom(\Gamma, G) the space of all homomorphisms . We study
properties of the group \cl{\pi(\Gamma)} for the generic \pi \in
\Hom(\Gamma, G), when is abelian and is one of the following
three groups: the unitary group of an infinite-dimensional Hilbert space, the
automorphism group of a standard probability space, and the isometry group of
the Urysohn metric space. Under mild assumptions on , we prove that in
the first case, there is (up to isomorphism of topological groups) a unique
generic \cl{\pi(\Gamma)}; in the other two, we show that the generic
\cl{\pi(\Gamma)} is extremely amenable. We also show that if is
torsion-free, the centralizer of the generic is as small as possible,
extending a result of King from ergodic theory.Comment: Version
DIRECTED DESIGN OF NOVEL ADSORBENTS BASED ON HALLOYSITE MINERA
The research work was supported by the Russian Foundation for Basic Research (Grant 18-29-12129мк)
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