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^1Π_u ← X^1Σ^+_g 000-000 transition of C_3, centered at 4051.6 Å, 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)

A morphometric and molecular study of the genus Pseudopodisma (Orthoptera: Acrididae)

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On the Number of Real Zeros of Random Sparse Polynomial Systems

Consider a random system $\mathfrak{f}_1(x)=0,\ldots,\mathfrak{f}_n(x)=0$ of $n$ random real polynomials in $n$ variables, where each $\mathfrak{f}_k$ has a prescribed set of exponent vectors in a set $A_k\subseteq \mathbb{Z}^n$ of size $t_k$. Assuming that the coefficients of the $\mathfrak{f}_k$ 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 $4^{-n} \prod_{k=1}^n t_k(t_k-1)$. 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 89^{89}Y(α\alpha,α\alpha)89^{89}Y scattering at low energies

Elastic scattering cross sections of the $^{89}$Y($\alpha$,$\alpha$)$^{89}$Y reaction have been measured at energies E$_{c.m.}$ = 15.51 and 18.63 MeV. The high precision data for the semi-magic $N = 50$ nucleus $^{89}$Y are used to derive a local potential and to evaluate the predictions of global and regional $\alpha$-nucleus potentials. The variation of the elastic alpha scattering cross sections along the $N = 50$ isotonic chain is investigated by a study of the ratios of angular distributions for $^{89}$Y($\alpha$,$\alpha$)$^{89}$Y and $^{92}$Mo($\alpha$,$\alpha$)$^{92}$Mo at E$_{c.m.} \approx$ 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, $\alpha$-cluster states in $^{93}$Nb = $^{89}$Y $\otimes$ $\alpha$ are investigated

OGG1 Inhibition Reduces Acinar Cell Injury in a Mouse Model of Acute Pancreatitis

Acute pancreatitis (AP) is a potentially life-threatening gastrointestinal disease with a complex pathology including oxidative stress. Oxidative stress triggers oxidative DNA lesions such as formation of 7,8-dihydro-8-oxo-2′-oxoguanine (8-oxoG) and also causes DNA strand breaks. DNA breaks can activate the nuclear enzyme poly(ADP-ribose) polymerase 1 (PARP1) which contributes to AP pathology. 8-oxoG is recognized by 8-oxoG glycosylase 1 (OGG1) resulting in the removal of 8-oxoG from DNA as an initial step of base excision repair. Since OGG1 also possesses a DNA nicking activity, OGG1 activation may also trigger PARP1 activation. In the present study we investigated the role played by OGG1 in AP. We found that the OGG1 inhibitor compound TH5487 reduced edema formation, inflammatory cell migration and necrosis in a cerulein-induced AP model in mice. Moreover, TH5487 caused 8-oxoG accumulation and reduced tissue poly(ADP-ribose) levels. Consistent with the indirect PARP inhibitory effect, TH5487 shifted necrotic cell death (LDH release and Sytox green uptake) towards apoptosis (caspase activity) in isolated pancreatic acinar cells. In the in vivo AP model, TH5487 treatment suppressed the expression of various cytokine and chemokine mRNAs such as those of TNF, IL-1β, IL1ra, IL6, IL16, IL23, CSF, CCL2, CCL4, CCL12, IL10 and TREM as measured with a cytokine array and verified by RT-qPCR. As a potential mechanism underlying the transcriptional inhibitory effect of the OGG1 inhibitor we showed that while 8-oxoG accumulation in the DNA facilitates NF-κB binding to its consensus sequence, when OGG1 is inhibited, target site occupancy of NF-κB is impaired. In summary, OGG1 inhibition provides protection from tissue injury in AP and these effects are likely due to interference with the PARP1 and NF-κB activation pathways