100,912 research outputs found

### Surgery on links with unknotted components and three-manifolds

It is shown that any closed three-manifold M obtained by integral surgery on
a knot in the three-sphere can always be constructed from integral surgeries on
a 3-component link L with each component being an unknot in the three-sphere.
It is also interesting to notice that infinitely many different integral
surgeries on the same link L could give the same three-manifold M.Comment: 10 pages, 8 figure

### The CHSH-type inequalities for infinite-dimensional quantum systems

By establishing CHSH operators and CHSH-type inequalities, we show that any
entangled pure state in infinite-dimensional systems is entangled in a
$2\otimes2$ subspace. We find that, for infinite-dimensional systems, the
corresponding properties are similar to that of the two-qubit case: (i) The
CHSH-type inequalities provide a sufficient and necessary condition for
separability of pure states; (ii) The CHSH operators satisfy the Cirel'son
inequalities; (iii) Any state which violates one of these Bell inequalities is
distillable.Comment: 9 pages. arXiv admin note: text overlap with arXiv:1006.3557 by other
author

### Any entanglement of assistance is polygamous

We propose a condition for a measure of quantum correlation to be polygamous
without the traditional polygamy inequality. It is shown to be equivalent to
the standard polygamy inequalities for any continuous measure of quantum
correlation with the polygamy power. We then show that any entanglement of
assistance is polygamous but not monogamous and any faithful entanglement
measure is not polygamous.Comment: 5 page

### Unified view of monogamy relations for different entanglement measures

A particularly interesting feature of nonrelativistic quantum mechanics is
the monogamy laws of entanglement. Although the monogamy relation has been
explored extensively in the last decade, it is still not clear to what extent a
given entanglement measure is monogamous. We give here a conjecture on the
amount of entanglement contained in the reduced states by observing all the
known related results at first. Consequently, we propose the monogamy power of
an entanglement measure and the polygamy power for its dual quantity, the
assisted entanglement, and show that both the monogamy power and the polygamy
power exist in any multipartite systems with any dimension, from which we
formalize exactly for the first time when an entanglement measure and an
assisted entanglement obey the monogamy relation and the polygamy relation
respectively in a unified way. In addition, we show that any entanglement
measure violates the polygamy relation, which is misstated in some recent
papers. Only the existence of monogamy power is conditioned on the conjecture,
all other results are strictly proved.Comment: 6 pages. Comments are welcom

### Sharp capacity estimates in s-John domains

It is well-known that several problems related to analysis on $s$-John
domains can be unified by certain capacity lower estimates. In this paper, we
obtain general lower bounds of $p$-capacity of a compact set $E$ and the
central Whitney cube $Q_0$ in terms of the Hausdorff $q$-content of $E$ in an
$s$-John domain $\Omega$. Moreover, we construct several examples to show the
essential sharpness of our estimates.Comment: 13 pages, 3 figure

### Fractional Sobolev-Poincare inequalities in irregular domains

This paper is devoted to the study of fractional (q,p)-Sobolev-Poincare
inequalities in irregular domains. In particular, we establish (essentially)
sharp fractional (q,p)-Sobolev-Poincare inequality in s-John domains and in
domains satisfying the quasihyperbolic boundary conditions. When the order of
the fractional derivative tends to 1, our results tends to the results for the
usual derivative. Furthermore, we verified that those domains that support the
fractional (q,p)-Sobolev-Poincare inequality together with a separation
property are s-diam John domains for certain s, depending only on the
associated data. We also point out an inaccurate statement in [2]

### Rescaled range and transition matrix analysis of DNA sequences

In this paper we treat some fractal and statistical features of the DNA
sequences. First, a fractal record model of DNA sequence is proposed by mapping
DNA sequences to integer sequences, followed by R/S analysis of the model and
computation of the Hurst exponents. Second, we consider transition between the
four kinds of bases within DNA. The transition matrix analysis of DNA sequences
shows that some measures of complexity based on transition proportion matrix
are of interest. We use some measures of complexity to distinguish exon and
intron. Regarding the evolution, we find that for species of higher grade, the
transition rate among the four kinds of bases goes further from the
equilibrium.Comment: 8 pages with one figure. Communication in Theoretical Physics (2000)
(to appear

### Fuzzy L languages

In this paper we introduce some families of fuzzy L-systems and investigate
their properties. We further discuss the relationship between fuzzy L languages
and the fuzzy languages generated by fuzzy grammar proposed in Ref.[3,5]. A
measure of fuzziness for a string, called the fuzzy entropy of a string with
respect to a given fuzzy L system, will be defined. The relationship between
fuzzy L languages and the ordinary L languages is also discussed.Comment: 9 pages with no figure. International J. of Fuzzy sets and Systems
(Accepted for publ ication

### Nonlinear Optical Properties of Transition Metal Dichalcogenide MX$_2$ (M = Mo, W; X = S, Se) Monolayers and Trilayers from First-principles Calculations

Due to the absence of interlayer coupling and inversion symmetry, transition
metal dichalcogenide (MX$_2$) semiconductor monolayers exhibit novel properties
that are distinctly different from their bulk crystals such as direct optical
band gaps, large band spin splittings, spin-valley coupling, piezoelectric and
nonlinear optical responses, and thus have promising applications in, e.g.,
opto-electronic and spintronic devices. Here we have performed a systematic
first-principles study of the second-order nonlinear optical properties of
MX$_2$ (M = Mo, W; X = S, Se) monolayers and trilayers within the density
functional theory with the generalized gradient approximation plus scissors
correction. We find that all the four MX$_2$ monolayers possess large
second-order optical susceptibility $\chi^{(2)}$ in the optical frequency range
and significant linear electro-optical coefficients in low frequency limit,
thus indicating their potential applications in non-linear optical devices and
electric optical switches. The $\chi^{(2)}$ spectra of the MX$_2$ trilayers are
overall similar to the corresponding MX$_2$ monolayers, {\it albeit} with the
magnitude reduced by roughly a factor of 3. The prominent features in the
$\chi^{(2)}$ spectra of the MX$_2$ multilayers are analyzed in terms of the
underlying band structures and optical dielectric function, and also compared
with available experiments.Comment: references updated, new Figure 2, revised Figure 8 and text improve

### Constructing positive maps from block matrices

Positive maps are useful for detecting entanglement in quantum information
theory. Any entangled state can be detected by some positive map. In this
paper, the relation between positive block matrices and completely positive
trace-preserving maps is characterized. Consequently, a new method for
constructing decomposable maps from positive block matrices is derived. In
addition, a method for constructing positive but not completely positive maps
from Hermitian block matrices is also obtained.Comment: 13 page

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