2,527 research outputs found
Homogenization of the elliptic Dirichlet problem: operator error estimates in
Let be a bounded domain of class . In
the Hilbert space , we consider a matrix
elliptic second order differential operator with
the Dirichlet boundary condition. Here is the small parameter.
The coefficients of the operator are periodic and depend on
. A sharp order operator error estimate
is obtained. Here is the effective
operator with constant coefficients and with the Dirichlet boundary condition.Comment: 13 page
Exploiting replication in distributed systems
Techniques are examined for replicating data and execution in directly distributed systems: systems in which multiple processes interact directly with one another while continuously respecting constraints on their joint behavior. Directly distributed systems are often required to solve difficult problems, ranging from management of replicated data to dynamic reconfiguration in response to failures. It is shown that these problems reduce to more primitive, order-based consistency problems, which can be solved using primitives such as the reliable broadcast protocols. Moreover, given a system that implements reliable broadcast primitives, a flexible set of high-level tools can be provided for building a wide variety of directly distributed application programs
Reliable broadcast protocols
A number of broadcast protocols that are reliable subject to a variety of ordering and delivery guarantees are considered. Developing applications that are distributed over a number of sites and/or must tolerate the failures of some of them becomes a considerably simpler task when such protocols are available for communication. Without such protocols the kinds of distributed applications that can reasonably be built will have a very limited scope. As the trend towards distribution and decentralization continues, it will not be surprising if reliable broadcast protocols have the same role in distributed operating systems of the future that message passing mechanisms have in the operating systems of today. On the other hand, the problems of engineering such a system remain large. For example, deciding which protocol is the most appropriate to use in a certain situation or how to balance the latency-communication-storage costs is not an easy question
Image of the Burau Representation at -th Roots of unity
We prove that the image of the Full braid group on strands
under the Burau representation, evaluated at a primitive -th root of unity
is arithmetic provided .Comment: To appear in Annals of Mathematics. arXiv admin note: text overlap
with arXiv:1204.477
On localization of pseudo-relativistic energy
We present a Kato-type inequality for bounded domain Omega \subset R^n, n>1.Comment: 17 page
Invariants of 2+1 Quantum Gravity
In [1,2] we established and discussed the algebra of observables for 2+1
gravity at both the classical and quantum level. Here our treatment broadens
and extends previous results to any genus with a systematic discussion of
the centre of the algebra. The reduction of the number of independent
observables to is treated in detail with a precise
classification for and .Comment: 10 pages, plain TEX, no figures, DFTT 46/9
Strong-coupling asymptotic expansion for Schr\"odinger operators with a singular interaction supported by a curve in
We investigate a class of generalized Schr\"{o}dinger operators in
with a singular interaction supported by a smooth curve
. We find a strong-coupling asymptotic expansion of the discrete
spectrum in case when is a loop or an infinite bent curve which is
asymptotically straight. It is given in terms of an auxiliary one-dimensional
Schr\"{o}dinger operator with a potential determined by the curvature of
. In the same way we obtain an asymptotics of spectral bands for a
periodic curve. In particular, the spectrum is shown to have open gaps in this
case if is not a straight line and the singular interaction is strong
enough.Comment: LaTeX 2e, 30 pages; minor improvements, to appear in Rev. Math. Phy
The a priori Tan Theta Theorem for spectral subspaces
Let A be a self-adjoint operator on a separable Hilbert space H. Assume that
the spectrum of A consists of two disjoint components s_0 and s_1 such that the
set s_0 lies in a finite gap of the set s_1. Let V be a bounded self-adjoint
operator on H off-diagonal with respect to the partition spec(A)=s_0 \cup s_1.
It is known that if ||V||<\sqrt{2}d, where d=\dist(s_0,s_1), then the
perturbation V does not close the gaps between s_0 and s_1 and the spectrum of
the perturbed operator L=A+V consists of two isolated components s'_0 and s'_1
grown from s_0 and s_1, respectively. Furthermore, it is known that if V
satisfies the stronger bound ||V||< d then the following sharp norm estimate
holds: ||E_L(s'_0)-E_A(s_0)|| \leq sin(arctan(||V||/d)), where E_A(s_0) and
E_L(s'_0) are the spectral projections of A and L associated with the spectral
sets s_0 and s'_0, respectively. In the present work we prove that this
estimate remains valid and sharp also for d \leq ||V||< \sqrt{2}d, which
completely settles the issue.Comment: v3: some typos fixed; Examples adde
Higher Order Terms in the Melvin-Morton Expansion of the Colored Jones Polynomial
We formulate a conjecture about the structure of `upper lines' in the
expansion of the colored Jones polynomial of a knot in powers of (q-1). The
Melvin-Morton conjecture states that the bottom line in this expansion is equal
to the inverse Alexander polynomial of the knot. We conjecture that the upper
lines are rational functions whose denominators are powers of the Alexander
polynomial. We prove this conjecture for torus knots and give experimental
evidence that it is also true for other types of knots.Comment: 21 pages, 1 figure, LaTe
Linear Parsing Expression Grammars
PEGs were formalized by Ford in 2004, and have several pragmatic operators
(such as ordered choice and unlimited lookahead) for better expressing modern
programming language syntax. Since these operators are not explicitly defined
in the classic formal language theory, it is significant and still challenging
to argue PEGs' expressiveness in the context of formal language theory.Since
PEGs are relatively new, there are several unsolved problems.One of the
problems is revealing a subclass of PEGs that is equivalent to DFAs. This
allows application of some techniques from the theory of regular grammar to
PEGs. In this paper, we define Linear PEGs (LPEGs), a subclass of PEGs that is
equivalent to DFAs. Surprisingly, LPEGs are formalized by only excluding some
patterns of recursive nonterminal in PEGs, and include the full set of ordered
choice, unlimited lookahead, and greedy repetition, which are characteristic of
PEGs. Although the conversion judgement of parsing expressions into DFAs is
undecidable in general, the formalism of LPEGs allows for a syntactical
judgement of parsing expressions.Comment: Parsing expression grammars, Boolean finite automata, Packrat parsin
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