75,597 research outputs found
[Colored solutions of Yang-Baxter equation from representations of U_{q}gl(2)]
We study the Hopf algebra structure and the highest weight representation of
a multiparameter version of . The commutation relations as well as
other Hopf algebra maps are explicitly given. We show that the multiparameter
universal matrix can be constructed directly as a quantum double
intertwiner, without using Reshetikhin's transformation. An interesting feature
automatically appears in the representation theory: it can be divided into two
types, one for generic , the other for being a root of unity. When
applying the representation theory to the multiparameter universal
matrix, the so called standard and nonstandard colored solutions of the Yang-Baxter equation is obtained.Comment: [14]pages, latex, no figure
MICRO BUBBLE FORMATION AND BUBBLE DISSOLUTION IN DOMESTIC WET CENTRAL HEATING SYSTEMS
16 % of the carbon dioxide emissions in the UK are known to originate from wet domestic central heating systems. Contemporary systems make use of very efficient boilers known as condensing boilers that could result in efficiencies in the 90-100% range. However, research and development into the phenomenon of micro bubbles in such systems has been practically non-existent. In fact, such systems normally incorporate a passive deaerator that is installed as a ‘default’ feature with no real knowledge as to the micro bubble characteristics and their effect on such systems. High saturation ratios are known to occur due to the widespread use of untreated tap water in such systems and due to the inevitable leakage of air into the closed loop circulation system during the daily thermal cycling. The high temperatures at the boiler wall result in super saturation conditions which consequently lead to micro bubble nucleation and detachment, leading to bubbly two phase flow. Experiments have been done on a test rig incorporating a typical 19 kW domestic gas fired boiler to determine the expected saturation ratios and bubble production and dissolution rates in such systems
Variational formulas of higher order mean curvatures
In this paper, we establish the first variational formula and its
Euler-Lagrange equation for the total -th mean curvature functional
of a submanifold in a general Riemannian manifold
for . As an example, we prove that closed
complex submanifolds in complex projective spaces are critical points of the
functional , called relatively -minimal submanifolds,
for all . At last, we discuss the relations between relatively -minimal
submanifolds and austere submanifolds in real space forms, as well as a special
variational problem.Comment: 13 pages, to appear in SCIENCE CHINA Mathematics 201
Conservation relation of nonclassicality and entanglement for Gaussian states in a beam-splitter
We study the relation between single-mode nonclassicality and two-mode
entanglement in a beam-splitter. We show that not all of the nonclassicality
(entanglement potential) is transformed into two-mode entanglement for an
incident single-mode light. Some of the entanglement potential remains as
single-mode nonclassicality in the two entangled output modes. Two-mode
entanglement generated in the process can be equivalently quantified as the
increase in the minimum uncertainty widths (or decrease in the squeezing) of
the output states compared to the input states. We use the nonclassical depth
and logarithmic negativity as single-mode nonclassicality and entanglement
measures, respectively. We realize that a conservation relation between the two
quantities can be adopted for Gaussian states, if one works in terms of
uncertainty width. This conservation relation is extended to many sets of
beam-splitters.Comment: 10 pages, 8 figure
A rescaled method for RBF approximation
In the recent paper [8], a new method to compute stable kernel-based
interpolants has been presented. This \textit{rescaled interpolation} method
combines the standard kernel interpolation with a properly defined rescaling
operation, which smooths the oscillations of the interpolant. Although
promising, this procedure lacks a systematic theoretical investigation. Through
our analysis, this novel method can be understood as standard kernel
interpolation by means of a properly rescaled kernel. This point of view allow
us to consider its error and stability properties
A rescaled method for RBF approximation
A new method to compute stable kernel-based interpolants
has been presented by the second and third authors. This rescaled interpolation method combines the
standard kernel interpolation with a properly defined rescaling operation, which
smooths the oscillations of the interpolant. Although promising, this procedure
lacks a systematic theoretical investigation.
Through our analysis, this novel method can be understood as standard
kernel interpolation by means of a properly rescaled kernel. This point of view
allow us to consider its error and stability properties.
First, we prove that the method is an instance of the Shepard\u2019s method,
when certain weight functions are used. In particular, the method can reproduce
constant functions.
Second, it is possible to define a modified set of cardinal functions strictly
related to the ones of the not-rescaled kernel. Through these functions, we
define a Lebesgue function for the rescaled interpolation process, and study its
maximum - the Lebesgue constant - in different settings.
Also, a preliminary theoretical result on the estimation of the interpolation
error is presented.
As an application, we couple our method with a partition of unity algorithm.
This setting seems to be the most promising, and we illustrate its behavior with
some experiments
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