Sharp values for the constants in the polynomial Bohnenblust-Hille inequality

In this paper we prove that the complex polynomial Bohnenblust-Hille constant for $2$-homogeneous polynomials in ${\mathbb C}^2$ is exactly $\sqrt[4]{\frac{3}{2}}$. We also give the exact value of the real polynomial Bohnenblust-Hille constant for $2$-homogeneous polynomials in ${\mathbb R}^2$. Finally, we provide lower estimates for the real polynomial Bohnenblust-Hille constant for polynomials in ${\mathbb R}^2$ of higher degrees.Comment: 16 page

High-pressure tuning of d-d crystal-field electronic transitions and electronic band gap in Co(I O3)2

High-pressure optical-absorption measurements performed on polycrystalline Co ( I O 3 ) 2 samples were used to characterize the influence of pressure on the electronic d – d transitions associated with Co 2 + and the fundamental band gap of Co ( I O 3 ) 2 . The results shed light on the electron-lattice coupling and show that Co ( I O 3 ) 2 exhibits an unusual behavior because the compression of Co–O bond distances is not coupled to pressure-induced changes induced in the unit-cell volume. Experimental results on the internal d – d transitions of Co 2 + have been explained based on changes in the constituent Co O 6 octahedral units using the semiempirical Tanabe-Sugano diagram. Our findings support that the high-spin ground state ( 4 T 1 ) is very stable in Co ( I O 3 ) 2 . We have also determined the band-gap energy of Co ( I O 3 ) 2 and its pressure dependence which is highly nonlinear. According to density-functional theory band-structure calculations, this nonlinearity occurs because the bottom of the conduction band is dominated by I-5p orbitals and the top of the valence band by Co-3d and O-2p orbitals, and because the Co–O and I–O bond lengths exhibit different pressure dependences.This work was supported by the Generalitat Valenciana under Project No. PROMETEO 2018/123-EFIMAT and by the Spanish Research Agency (AEI) and Spanish Ministry of Science and Investigation (MCIN) under Projects No. PID2019106383GB-C41/C43 (DOI: 10.13039/501100011033) cofinanced by EU FEDER funds, No. PGC2018-101464-B-I00, and No. RED2018-102612-T. A.L. and D.E. thank the Generalitat Valenciana for the Ph.D. Fellowship No. GRISOLIAP/2019/025. R.T. acknowledges funding from the Spanish MINECO via the Juan de la Cierva Formación program (Grant No. FJC2018-036185-I).

KMOS LENsing Survey (KLENS) : morpho-kinematic analysis of star-forming galaxies at z∼2z \sim 2

We present results from the KMOS lensing survey-KLENS which is exploiting gravitational lensing to study the kinematics of 24 star forming galaxies at $1.4<z<3.5$ with a median mass of $\rm log(M_\star/M_\odot)=9.6$ and median star formation rate (SFR) of $\rm 7.5\,M_\odot\,yr^{-1}$. We find that 25% of these low-mass/low-SFR galaxies are rotation dominated, while the majority of our sample shows no velocity gradient. When combining our data with other surveys, we find that the fraction of rotation dominated galaxies increases with the stellar mass, and decreases for galaxies with a positive offset from the main sequence. We also investigate the evolution of the intrinsic velocity dispersion, $\sigma_0$, as a function of the redshift, $z$, and stellar mass, $\rm M_\star$, assuming galaxies in quasi-equilibrium (Toomre Q parameter equal to 1). From the $z-\sigma_0$ relation, we find that the redshift evolution of the velocity dispersion is mostly expected for massive galaxies ($\rm log(M_\star/M_\odot)>10$). We derive a $\rm M_\star-\sigma_0$ relation, using the Tully-Fisher relation, which highlights that a different evolution of the velocity dispersion is expected depending on the stellar mass, with lower velocity dispersions for lower masses, and an increase for higher masses, stronger at higher redshift. The observed velocity dispersions from this work and from comparison samples spanning $0<z<3.5$ appear to follow this relation, except at higher redshift ($z>2$), where we observe higher velocity dispersions for low masses ($\rm log(M_\star/M_\odot)\sim 9.6$) and lower velocity dispersions for high masses ($\rm log(M_\star/M_\odot)\sim 10.9$) than expected. This discrepancy could, for instance, suggest that galaxies at high-$z$ do not satisfy the stability criterion, or that the adopted parametrisation of the specific star formation rate and molecular properties fail at high redshift.Comment: Accepted for publication in A&A, 21 pages, 10 figure

Differences and similarities of stellar populations in LAEs and LBGs at z~3.4-6.8

Lyman alpha emitters (LAEs) and Lyman break galaxies (LBGs) represent the most common groups of star-forming galaxies at high z, and the differences between their inherent stellar populations (SPs) are a key factor in understanding early galaxy formation and evolution. We have run a set of SP burst-like models for a sample of 1558 sources at 3.4 < z < 6.8 from the Survey for High-z Absorption Red and Dead Sources (SHARDS) over the GOODS-N field. This work focuses on the differences between the three different observational subfamilies of our sample: LAE–LBGs, no-Ly α LBGs, and pure LAEs. Single and double SP synthetic spectra were used to model the spectral energy distributions, adopting a Bayesian information criterion to analyze under which situations a second SP is required. We find that the sources are well modelled using a single SP in ∼79 per cent of the cases. The best models suggest that pure LAEs are typically young low-mass galaxies (⁠t∼26+41−25 Myr; Mstar∼5.6+12.0−5.5×108 M⊙⁠), undergoing one of their first bursts of star formation. On the other hand, no-Ly α LBGs require older SPs (t ∼ 71 ± 12 Myr), and they are substantially more massive (Mstar ∼ 3.5 ± 1.1 × 109 M⊙). LAE–LBGs appear as the subgroup that more frequently needs the addition of a second SP, representing an old and massive galaxy caught in a strong recent star-forming episode. The relative number of sources found from each subfamily at each z supports an evolutionary scenario from pure LAEs and single SP LAE–LBGs to more massive LBGs. Stellar mass functions are also derived, finding an increase of M* with cosmic time and a possible steepening of the low-mass slope from z ∼ 6 to z ∼ 5 with no significant change to z ∼ 4. Additionally, we have derived the SFR–Mstar relation, finding an SFR∝Mβstar behaviour with negligible evolution from z ∼ 4 to z ∼ 6

Polynomial Inequalities on the π/4-Circle Sector

A number of sharp inequalities are proved for the space P (2D (π/4)) of 2-homogeneous polynomials on ℝ2 endowed with the supremum norm on the sector D (π/4) := {eiθ : θ ∈ [0, π/4]}. Among the main results we can find sharp Bernstein and Markov inequalities and the calculation of the polarization constant and the unconditional constant of the canonical basis of the space P (2D (π/4))

Anomalous Raman Modes in Tellurides

Two broad bands are usually found in the Raman spectrum of many Te-based chalcogenides, which include binary compounds, like ZnTe, CdTe, HgTe, GaTe, GeTe, SnTe, PbTe, GeTe2, As2Te3, Sb2Te3, Bi2Te3, NiTe2, IrTe2, TiTe2, as well as ternary compounds, like GaGeTe, SnSb2Te4, SnBi2Te4, and GeSb2Te5. Many different explanations have been proposed in the literature for the origin of these two anomalous broad bands in tellurides, usually located between 119 and 145 cm-1. They have been attributed to the own sample, to oxidation, to the folding of Brillouin-edge modes onto the zone center, to the existence of a double resonance, like that of graphene, or to the formation of Te precipitates. In this paper, we provide arguments to demonstrate that such bands correspond to clusters or precipitates of trigonal Te in form of nanosize or microsize grains or layers that are segregated either inside or at the surface of the samples. Several mechanisms for Te segregation are discussed and sample heating caused by excessive laser power during Raman scattering measurements is emphasized. Finally, we show that anomalous Raman modes related to Se precipitates also occur in selenides, thus providing a general vision for a better characterization of selenides and tellurides by means of Raman scattering measurements and for a better understanding of chalcogenides in general.Comment: 45 pages, 8 figure