Experience in feeding coal into a liquefaction process development unit

A system for preparing coal slurry and feeding it into a high pressure liquefaction plant is described. The system was developed to provide supporting research and development for the Bureau of Mines coal liquefaction pilot plant. Operating experiences are included

Rational Solutions of the Painleve' VI Equation

In this paper, we classify all values of the parameters $\alpha$, $\beta$, $\gamma$ and $\delta$ of the Painlev\'e VI equation such that there are rational solutions. We give a formula for them up to the birational canonical transformations and the symmetries of the Painlev\'e VI equation.Comment: 13 pages, 1 Postscript figure Typos fixe

On the Linearization of the First and Second Painleve' Equations

We found Fuchs--Garnier pairs in 3X3 matrices for the first and second Painleve' equations which are linear in the spectral parameter. As an application of our pairs for the second Painleve' equation we use the generalized Laplace transform to derive an invertible integral transformation relating two its Fuchs--Garnier pairs in 2X2 matrices with different singularity structures, namely, the pair due to Jimbo and Miwa and the one found by Harnad, Tracy, and Widom. Together with the certain other transformations it allows us to relate all known 2X2 matrix Fuchs--Garnier pairs for the second Painleve' equation with the original Garnier pair.Comment: 17 pages, 2 figure

Existence and Uniqueness of Tri-tronqu\'ee Solutions of the second Painlev\'e hierarchy

The first five classical Painlev\'e equations are known to have solutions described by divergent asymptotic power series near infinity. Here we prove that such solutions also exist for the infinite hierarchy of equations associated with the second Painlev\'e equation. Moreover we prove that these are unique in certain sectors near infinity.Comment: 13 pages, Late

A remark on the Hankel determinant formula for solutions of the Toda equation

We consider the Hankel determinant formula of the $\tau$ functions of the Toda equation. We present a relationship between the determinant formula and the auxiliary linear problem, which is characterized by a compact formula for the $\tau$ functions in the framework of the KP theory. Similar phenomena that have been observed for the Painlev\'e II and IV equations are recovered. The case of finite lattice is also discussed.Comment: 14 pages, IOP styl

Breakup of the proton halo nucleus 8B near barrier energies

The dynamics of a nuclear open quantum system could be revealed in the correlations between the breakup fragments of halo nuclei. The breakup mechanism of a proton halo nuclear system is of particular interest as the Coulomb polarization may play an important role, which, however, remains an open question. Here we use a highly efficient silicon detector array and measure the correlations between the breakup fragments of 8B incident on 120Sn at near-barrier energies. The energy and angular correlations can be explained by a fully quantum mechanical method based on the state-of-the-art continuum discretized coupled channel calculations. The results indicate that, compared to the neutron halo nucleus 6He, 8B presents distinctive reaction dynamics: the dominance of the elastic breakup. This breakup occurs mainly via the short-lived continuum states, almost exhausts the 7Be yield, indicating the effect of Coulomb polarization on the proton halo state. The correlation information reveals that the prompt breakup mechanism dominates, occurring predominantly on the outgoing trajectory. We also show that, as a large environment, the continuum of 8B breakup may not significantly influence elastic scattering and complete fusion.National Key R&D Program of China 2018YFA0404404National Natural Science Foundation of China U2167204, 12175314, 12235020, U18672122Continuous Basic Scientific Research WDJC-2019-13Leading Innovation Project LC192209000701, LC202309000201Basic Scientific Research Program JCKY2020201C002Ministerio de Ciencia e Innovación PID2020-114687GB-I00Junta de Andalucía P20_01247Korea government (MSIT) 2013M7A1A1075764, 2018R1A5A102556

Mass measurements of very neutron-deficient Mo and Tc isotopes and their impact on rp process nucleosynthesis

The masses of ten proton-rich nuclides, including the N=Z+1 nuclides 85-Mo and 87-Tc, were measured with the Penning trap mass spectrometer SHIPTRAP. Compared to the Atomic Mass Evaluation 2003 a systematic shift of the mass surface by up to 1.6 MeV is observed causing significant abundance changes of the ashes of astrophysical X-ray bursts. Surprisingly low alpha-separation energies for neutron-deficient Mo and Tc are found, making the formation of a ZrNb cycle in the rp process possible. Such a cycle would impose an upper temperature limit for the synthesis of elements beyond Nb in the rp process.Comment: Link to online abstract: http://link.aps.org/doi/10.1103/PhysRevLett.106.12250

The Hamiltonian Structure of the Second Painleve Hierarchy

In this paper we study the Hamiltonian structure of the second Painleve hierarchy, an infinite sequence of nonlinear ordinary differential equations containing PII as its simplest equation. The n-th element of the hierarchy is a non linear ODE of order 2n in the independent variable $z$ depending on n parameters denoted by ${t}_1,...,{t}_{n-1}$ and $\alpha_n$. We introduce new canonical coordinates and obtain Hamiltonians for the $z$ and $t_1,...,t_{n-1}$ evolutions. We give explicit formulae for these Hamiltonians showing that they are polynomials in our canonical coordinates

Lattice modified KdV hierarchy from a Lax pair expansion

We produce a hierarchiy of integrable equations by systematically adding terms to the Lax pair for the lattice modified KdV equation. The equations in the hierarchy are related to one aonother by recursion relations. These recursion relations are solved explicitly so that every equation in the hierarchy along with its Lax pair is known

Mathematics difficulties in extremely preterm children : evidence of a specific deficit in basic mathematics processing

Background: Extremely preterm (EP, <26 wk gestation) children have been observed to have poor academic achievement in comparison to their term-born peers, especially in mathematics. This study investigated potential underlying causes of this difficulty. Methods: A total of 219 EP participants were compared with 153 term-born control children at 11 y of age. All children were assessed by a psychologist on a battery of standardized cognitive tests and a number estimation test assessing children’s numerical representations. Results: EP children underperformed in all tests in comparison with the term controls (the majority of Ps < 0.001). Different underlying relationships between performance on the number estimation test and mathematical achievement were found in EP as compared with control children. That is, even after controlling for cognitive ability, a relationship between number representations and mathematical performance persisted for EP children only (EP: r = 0.346, n = 186, P < 0.001; control: r = 0.095, n = 146, P = 0.256). Conclusion: Interventions for EP children may target improving children’s numerical representations in order to subsequently remediate their mathematical skills