606 research outputs found
On the real linear polarization constant problem
The present paper deals with lower bounds for the norm of products of linear forms. It has been proved by J. Arias-de-Reyna [2], that the so-called n(th) linear polarization constant c(n)(C-n) is n(n/2), for arbitrary n is an element of N. The same value for c(n) (R-n) is only conjectured. In a recent work A. Pappas and S. Revesz prove that c(n) (R-n) = n(n/2) for n <= 5. Moreover, they show that if the linear forms are given as f(j)(x) = [x, a(j)),for some unit vectors a(j) (1 <= j <= n), then the product of the f(j)'s attains at least the value n(-n/2) at the normalized signed sum of the vectors having maximal length. Thus they asked whether this phenomenon remains true for arbitrary n is an element of N. We show that for vector systems {a(j)}(j=1)(n) close to an orthonormal system, the Pappas-Revesz estimate does hold true. Furthermore, among these vector systems the only system giving n(-n/2) as the norm of the product is the orthonormal system. On the other hand, for arbitrary vector systems we answer the question of A. Pappas and S. Revesz in the negative when n is an element of N is large enough. We also discuss various further examples and counterexamples that may be instructive for further research towards the determination of c(n)(R-n)
Diffuse Interstellar Bands Toward HD 62542
Diffuse interstellar bands (DIBs) have been detected for the first time along the peculiar translucent line of sight toward HD 62542, which passes through a diffuse cloud core. Although only a small fraction (18 out of more than 300) of generally weak DIB features have been shown to correlate with C_2 and C_3 (the "C_2 DIBs"), it is predominantly these DIBs that are observed toward HD 62542. The typically strong DIBs λλ5780 and 5797 are detected but are significantly weaker than toward other lines of sight with similar reddening. Other commonly observed DIBs (such as λλ4430, 6270, and 6284) remain noticeably absent. These observations further support the suggestion that the line of sight toward HD 62542 crosses only the core of a diffuse cloud and show that the correlation between the C_2 DIBs and small carbon chains is maintained in environments with very large fractions of molecular hydrogen, f_(H_2) > 0.8. A comparison of CH, CN, C_2, and C_3 column densities and C_2 DIB strengths toward HD 62542, HD 204827, and HD 172028 suggests that the line of sight toward HD 204827 passes through a diffuse cloud core similar to that seen toward HD 62542, as well as what might be referred to as a diffuse cloud envelope. This indicates that the bare core toward HD 62542 may not have significantly different relative chemical abundances from other diffuse cloud cores and that the C_2 DIBs may serve as a diagnostic of such cores
Observations of Rotationally Resolved C_3 in Translucent Sight Lines
The rotationally resolved spectrum of the A^1Î _u â X^1ÎŁ^+_g 000-000 transition of C_3, centered at 4051.6 Ă
, has been observed along 10 translucent lines of sight. To interpret these spectra, a new method for the determination of column densities and analysis of excitation profiles involving the simulation and fitting of observed spectra has been developed. The populations of lower rotational levels (J †14) in C_3 are best fitted by thermal distributions that are consistent with the kinetic temperatures determined from the excitation profile of C_2. Just as in the case of C_2, higher rotational levels (J > 14) of C_3 show increased nonthermal population distributions in clouds that have been determined to have total gas densities below ~500 cm^(-3)
On the Number of Real Zeros of Random Sparse Polynomial Systems
Consider a random system of
random real polynomials in variables, where each has a
prescribed set of exponent vectors in a set of size
. Assuming that the coefficients of the are independent
Gaussian of any variance, we prove that the expected number of zeros of the
random system in the positive orthant is bounded from above by . This result is a probabilisitc version of
Kushnirenko's conjecture; it provides a bound that only depends on the number
of terms and is independent of their degree.Comment: 26 pages. Different original titl
Certifying an irreducible 1024-dimensional photonic state using refined dimension witnesses
We report on a new class of dimension witnesses, based on quantum random
access codes, which are a function of the recorded statistics and that have
different bounds for all possible decompositions of a high-dimensional physical
system. Thus, it certifies the dimension of the system and has the new distinct
feature of identifying whether the high-dimensional system is decomposable in
terms of lower dimensional subsystems. To demonstrate the practicability of
this technique we used it to experimentally certify the generation of an
irreducible 1024-dimensional photonic quantum state. Therefore, certifying that
the state is not multipartite or encoded using non-coupled different degrees of
freedom of a single photon. Our protocol should find applications in a broad
class of modern quantum information experiments addressing the generation of
high-dimensional quantum systems, where quantum tomography may become
intractable.Comment: Journal version (except for small editorial modifications), 4+12
pages, 7 figure
High precision Y(,)Y scattering at low energies
Elastic scattering cross sections of the Y(,)Y
reaction have been measured at energies E = 15.51 and 18.63 MeV. The
high precision data for the semi-magic nucleus Y are used to
derive a local potential and to evaluate the predictions of global and regional
-nucleus potentials. The variation of the elastic alpha scattering
cross sections along the isotonic chain is investigated by a study of
the ratios of angular distributions for Y(,)Y and
Mo(,)Mo at E 15.51 and 18.63
MeV. This ratio is a very sensitive probe at energies close to the Coulomb
barrier, where scattering data alone is usually not enough to characterize the
different potentials. Furthermore, -cluster states in Nb =
Y are investigated
Investigation of alpha-nuclear potential families from elastic scattering experiments
In this work we present the continuation of the reported analysis [1] of the experimentally measured angular distributions of the reaction Cd-106(alpha, alpha)Cd-106 at several different energies around the Coulomb barrier. The difficulties that arise in the study of Cd-106-alpha-nuclear potential and the so called Family Problem are addressed
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