37,881 research outputs found
Convenient stability criteria for difference approximations of hyperbolic initial-boundary value problems
The purpose of this paper is to achieve more versatile, convenient stability criteria for a wide class of finite-difference approximations to initial boundary value problems associated with the hyperbolic system u sub t = au sub x + Bu + f in the quarter-plane x greater than or equal to 0, t greater than or equal to 0. With these criteria, stability is easily established for a large number of examples, thus incorporating and generalizing many of the cases studied in recent literature
Exact Nonperturbative Unitary Amplitudes for 1->N Transitions
I present an extension to arbitrary N of a previously proposed field
theoretic model, in which unitary amplitudes for processes were
obtained. The Born amplitude in this extension has the behavior
expected in a bosonic field theory. Unitarity
is violated when , or when Numerical
solutions of the coupled Schr\"odinger equations shows that for weak coupling
and a large range of N>\ncrit, the exact unitary amplitude is reasonably fit
by a factorized expression |A(1->N)| \sim (0.73 /N) \cdot \exp{(-0.025/\g2)}.
The very small size of the coefficient 1/\g2 , indicative of a very weak
exponential suppression, is not in accord with standard discussions based on
saddle point analysis, which give a coefficient The weak dependence
on could have experimental implications in theories where the exponential
suppression is weak (as in this model). Non-perturbative contributions to
few-point correlation functions in this theory would arise at order $K\ \simeq\
\left((0.05/\g2)+ 2\ ln{N}\right)/ \ ln{(1/\g2)}\g2.$Comment: 11 pages, 3 figures (not included
The complexity of weighted boolean #CSP*
This paper gives a dichotomy theorem for the complexity of computing the partition
function of an instance of a weighted Boolean constraint satisfaction problem. The problem
is parameterized by a finite set F of nonnegative functions that may be used to assign weights to
the configurations (feasible solutions) of a problem instance. Classical constraint satisfaction problems
correspond to the special case of 0,1-valued functions. We show that computing the partition
function, i.e., the sum of the weights of all configurations, is FP#P-complete unless either (1) every
function in F is of “product type,” or (2) every function in F is “pure affine.” In the remaining cases,
computing the partition function is in P
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Tax Implications for Same-Sex Couples
This week Americans will rush to complete their tax returns, and perhaps to write out a check to the Internal Revenue Service. For some taxpayers, the pain will be sharper, particularly for gay, lesbian, and bisexual individuals and their families. While same-sex couples in Massachusetts, Connecticut, and soon in Iowa and Vermont may marry, the federal government still does not recognize same-sex couples as married, no matter where they live. As a result, same-sex couples pay more in taxes and receive fewer benefits than do married different-sex couples
On the boundedness of wave operators for two-dimensional Schr\"odinger operators with threshold obstructions
Let be a Schr\"odinger operator on with
real-valued potential , and let . If has sufficient
pointwise decay, the wave operators are known to be bounded on for all if zero is not an eigenvalue or resonance. We show that if there is an
s-wave resonance or an eigenvalue only at zero, then the wave operators are
bounded on for . This result stands in
contrast to results in higher dimensions, where the presence of zero energy
obstructions is known to shrink the range of valid exponents .Comment: Revised according to referee's comments. 22 pages, to appear in J.
Funct. Ana
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