The first example of a recursive function which is not primitive recursive

The first example of a recursive function which is not primitive recursive is usually attributed to W. Ackermann. The authors of the present paper show that such an example can also be found in a paper by G. Sudan, published concomitantly with Ackermann's paper.     

Synthesis and characterization of phenoxarsin-10-yl 2-R2N-cyclopent-1-ene-1-carbodithioate (R = H,C2H5, cyclo-C6H11CH2) and the crystal and molecular structure of the 2-amino (R = H) derivative

Phenoxarsin-10-yl derivatives of 2-amino-cyclopent-1-ene-1-carbodithioic acid, (ACDA), and its N-alkyl derivativesO(C₆H₄)₂ AsS₂C—C₅H₆— NHR-2 (R = H, CH₂CH₃, CH₂C₆H₁₁,), have been prepared by reacting O(C₆H₄)₂AsCI with the corresponding ACDA 1,1-dithioic acid. The compounds were obtained by stirring stoichiometric amounts of the reagents in ethanol, over 24 h, at room temperature. The scale of the preparations were in the order of 2 mmol and the yields of the compounds ca 75%. The reactions were carried out in absolute ethanol. The compounds were characterized by IR, mass and NMR (¹H, ¹³C) spectroscopy. The molecular structure of O(C₆H₄)₂AsS₂C—C₅H₆—NH₂-2 was determined using X-ray diffractometry, achieving an R-value of 6.3%; this compound is monomeric and contains an asymmetric monometallic biconnective 1,1-dithiolato ligand [As—S(1) 2.272(2) å, As … S(2) 3.125(2) å]. An intramolecular hydrogen bond is established between one hydrogen atom of the NH₂ group and the sulfur [S(2)] atom involved in the secondary interaction to arsenic. The dihedral angle (150.3(3)°) of the phenoxarsine moiety is practically unaffected by substitution of chlorine on arsenic by the carbodithioato ligand.     

Lagrange Inversion and Schur Functions

Macdonald defined an involution on symmetric functions by considering the Lagrange inverse of the generating function of the complete homogeneous symmetric functions. The main result we prove in this note is that the images of skew Schur functions under this involution are either Schur positive or Schur negative symmetric functions. The proof relies on the combinatorics of Lagrange inversion. We also present a q-analogue of this result, which is related to the q-Lagrange inversion formula of Andrews, Garsia, and Gessel, as well as the operator of Bergeron and Garsia.     

On the Collision between two PNG Droplets

In this article we study the interface generated by the collision between two crystals growing layer by layer on a one-dimensional substrate through random decomposition of particles. We relate this interface with the notion of β-path in an equivalent directed polymer model and, by using asymptotics results from J. Baik and E. Rains, J. Stat. Phys., 100:523–541 (2000). and some hydrodynamic tools introduced by E. Cator and P. Groeneboom, Ann. Probab., 33:879–903 (2005), we derive a law of large numbers for such a path and obtain some bounds for its fluctuations. 2000 Mathematics Subject Classification: 60C05, 60K35     

The Voice Handicap Index: Correlation Between Subjective Patient Response and Quantitative Assessment of Voice

The aim of this prospective study is to elucidate the relationship between the Voice Handicap Index (VHI) and several voice laboratory measurements in the network of the multidimensional voice assessment. Fifty-eight patients were included. Each patient replies to the questionnaire and performs a voice assessment during the same time. The following parameters were measured: minimum frequency, maximum frequency, range, minimum intensity, subglottic pressure, mean flow, maximum phonation time, jitter, and dysphonia severity index. Regarding the relationship with the scores of the VHI, poor correlations with the minimal frequency for all the scores except the emotional one (total and subscales) and with the range for only the physical one are found. Seventeen questions correlate with the voice laboratory measurements we performed, with a decreased distribution between physical, functional, and emotional subscales. We observe that acoustic parameter is correlated with the emotional subscale, the parameters of the profile range are more often involved in the emotional subscale, as is the minimal frequency, but never with the physical subscale, and all the subscales are interesting despite the smaller number of differences with the emotional one. The VHI and the laboratory measurements give independent informations in practice.     

Sister Beiter and Kloosterman: A tale of cyclotomic coefficients and modular inverses

For a fixed prime p$p$, the maximum coefficient (in absolute value) M(p)$M\left(p\right)$ of the cyclotomic polynomial _Φpqr(x)${\Phi }_{pqr}\left(x\right)$, where r$r$ and q$q$ are free primes satisfying r>q>p$r>q>p$ exists. Sister Beiter conjectured in 1968 that M(p)≤(p+1)/2$M\left(p\right)\le (p+1)/2$. In 2009 Gallot and Moree showed that M(p)≥2p(1−?)/3$M\left(p\right)\ge 2p(1-?)/3$ for every p$p$ sufficiently large. In this article Kloosterman sums (‘cloister man sums’) and other tools from the distribution of modular inverses are applied to quantify the abundancy of counter-examples to Sister Beiter’s conjecture and sharpen the above lower bound for M(p)$M\left(p\right)$.     

Radial solutions of Neumann problems involving mean extrinsic curvature and periodic nonlinearities

We show that if ${{\mathcal A} \subset \mathbb{R}^N}$ is an annulus or a ball centered at zero, the homogeneous Neumann problem on ${{\mathcal A}}$ for the equation with continuous data $$\nabla \cdot \left(\frac{\nabla v}{\sqrt{1 - |\nabla v|^2}} \right) = g(|x|,v) + h(|x|)$$ has at least one radial solution when g(|x|,·) has a periodic indefinite integral and ${\int_{\mathcal A} h(|x|)\,{\rm{d}}x = 0.}$ The proof is based upon the direct method of the calculus of variations, variational inequalities and degree theory.     

Long-time behavior of an angiogenesis model with flux at the tumor boundary

This paper deals with a nonlinear system of partial differential equations modeling a simplified tumor-induced angiogenesis taking into account only the interplay between tumor angiogenic factors and endothelial cells. Considered model assumes a nonlinear flux at the tumor boundary and a nonlinear chemotactic response. It is proved that the choice of some key parameters influences the long-time behavior of the system. More precisely, we show the convergence of solutions to different semi-trivial stationary states for different range of parameters.