The 13-C(p,d) Reaction at 120 MeV

This research was sponsored by the National Science Foundation Grant NSF PHY 87-1440

Directed routes or chosen pathways? : teachers' views of continuing professional development within a group of rural primary schools

This research project examines teachers' Continuing Professional Development (C. P. D. ) within two clusters of rural primary schools in the north of England. The research considers teachers' attitudes to, and their understanding of, the meaning and purpose of C. P. D., and how it affects themselves and the pupils they teach. The research, which is set within its historical context with particular reference to the impact of the Education Reform Act (1988) and the raft of initiatives that have influenced the direction of teachers' C. P. D., reflects on teachers as professionals. Through a combination of survey and case study, quantitative and qualitative approaches to data collection were used and the initial questionnaires were followed up by semi-structured interviews in the two case study schools. Using Bolam's (1993) tripartite definition as an analytical framework C. P. D. is subdivided into the areas of training, education and support. The data analysis showed that across both clusters teachers' C. P. D. was driven by national government initiatives and, in some cases, the national initiatives became the schools' priorities, leaving little opportunity for an individual school based approach to C. P. D. Across the clusters there was an established relationship between the School Development Plan (S. D. P. ), performance management and C. P. D. The one year performance management cycle appeared to dictate the length of the C. P. D. cycle and promoted short term development, reducing opportunities for longer courses, such as advanced diplomas and higher degrees. The constraints of the cycle, along with the emphasis on the deficit model of C. P. D., is viewed as contributing to the general deprofessionalisation of teachers

Spectroscopy of η′\eta'-nucleus bound states at GSI and FAIR --- very preliminary results and future prospects ---

The possible existence of \eta'-nucleus bound states has been put forward through theoretical and experimental studies. It is strongly related to the \eta' mass at finite density, which is expected to be reduced because of the interplay between the $U_A(1)$ anomaly and partial restoration of chiral symmetry. The investigation of the C(p,d) reaction at GSI and FAIR, as well as an overview of the experimental program at GSI and future plans at FAIR are discussed.Comment: 7 pages, 3 figures; talk at the International Conference on Exotic Atoms and Related Topics (EXA2014), Vienna, Austria, 15-19 September 2014. in Hyperfine Interactions (2015

Parity-Affected Superconductivity in Ultrasmall Metallic Grains

We investigate the breakdown of BCS superconductivity in {\em ultra}\/small metallic grains as a function of particle size (characterized by the mean spacing $d$ between discrete electronic eigenstates), and the parity ($P$ = even/odd) of the number of electrons on the island. Assuming equally spaced levels, we solve the parity-dependent BCS gap equation for the order parameter $\Delta_P (d,T)$. Both the $T=0$ critical level spacing $d_{c,P}$ and the critical temperature $T_{c,P} (d)$ at which $\Delta_P = 0$ are parity dependent, and both are so much smaller in the odd than the even case that these differences should be measurable in current experiments.Comment: 4 pages RevTeX, 1 encapsulated postscript figure, submitted to Physical Review Letter

Berezin-type quantization on even-dimensional compact manifolds

In this article we show that a Berezin-type quantization can be achieved on a compact even dimensional manifold $M^{2d}$ by removing a skeleton $M_0$ of lower dimension such that what remains is diffeomorphic to ${\mathbb R}^{2d}$ which we identify with ${\mathbb C}^d$ and embed in ${\mathbb C}P^d$. A local Poisson structure and Berezin-type quantization are induced from ${\mathbb C}P^d$. We have a Hilbert space with a reproducing kernel. The symbols of bounded linear operators on the Hilbert space have a star product which satisfies the correspondence principle outside a set of measure zero. This construction depends on the diffeomorphism. However, suppose $X= M \setminus M_0$ has a complex structure and we have from $X \setminus X_0$, ($X_0$ a set of measure zero or empty) a biholomorphism from it to ${\mathbb C}^d \setminus N_0$, (where $N_0$ is of measure zero or empty). As before we embed ${\mathbb C}^d \setminus N_0$ in ${\mathbb C}^d$ and then into ${\mathbb C}P^d$ and we have a Berezin-type quantization induced from ${\mathbb C}P^d$. If we use another biholomorphism, we have a map of the two Hilbert spaces under consideration such that the reproducing kernel of one maps to the reproducing kernel of the other and we have an equivalent quantization. We have a similar construction where we consider an arbitrary complex manifold and use local coordinates to induce the quantization from ${\mathbb C}P^d$. We study the possibility of defining a global Berezin quantization on compact complex manifolds. We give a defintion of pullback Toeplitz operators and exhibit Toeplitz quantization of compact even dimensional manifolds after removing a set of measure zero. Next we give a simple construction of pullback coherent states on compact smooth manifolds which are simplified versions of those defined in an earlier work by the authors

List decoding Reed-Muller codes over small fields

The list decoding problem for a code asks for the maximal radius up to which any ball of that radius contains only a constant number of codewords. The list decoding radius is not well understood even for well studied codes, like Reed-Solomon or Reed-Muller codes. Fix a finite field $\mathbb{F}$. The Reed-Muller code $\mathrm{RM}_{\mathbb{F}}(n,d)$ is defined by $n$-variate degree-$d$ polynomials over $\mathbb{F}$. In this work, we study the list decoding radius of Reed-Muller codes over a constant prime field $\mathbb{F}=\mathbb{F}_p$, constant degree $d$ and large $n$. We show that the list decoding radius is equal to the minimal distance of the code. That is, if we denote by $\delta(d)$ the normalized minimal distance of $\mathrm{RM}_{\mathbb{F}}(n,d)$, then the number of codewords in any ball of radius $\delta(d)-\varepsilon$ is bounded by $c=c(p,d,\varepsilon)$ independent of $n$. This resolves a conjecture of Gopalan-Klivans-Zuckerman [STOC 2008], who among other results proved it in the special case of $\mathbb{F}=\mathbb{F}_2$; and extends the work of Gopalan [FOCS 2010] who proved the conjecture in the case of $d=2$. We also analyse the number of codewords in balls of radius exceeding the minimal distance of the code. For $e \leq d$, we show that the number of codewords of $\mathrm{RM}_{\mathbb{F}}(n,d)$ in a ball of radius $\delta(e) - \varepsilon$ is bounded by $\exp(c \cdot n^{d-e})$, where $c=c(p,d,\varepsilon)$ is independent of $n$. The dependence on $n$ is tight. This extends the work of Kaufman-Lovett-Porat [IEEE Inf. Theory 2012] who proved similar bounds over $\mathbb{F}_2$. The proof relies on several new ingredients: an extension of the Frieze-Kannan weak regularity to general function spaces, higher-order Fourier analysis, and an extension of the Schwartz-Zippel lemma to compositions of polynomials.Comment: fixed a bug in the proof of claim 5.6 (now lemma 5.5

Theoretical studies in the molecular Platonic solids: Pure and mixed carbon, nitrogen, phosphorus, and silicon tetrahedranes

Calculations were conducted at the G4MP2 and G4 composite method levels of theory on the 35 potential carbon, nitrogen, silicon, and phosphorus tetrahedrane derivatives with the general form C~a~N~b~Si~c~P~d~H~(4-b-d)~ (where a+b+c+d=4). At both levels of theory, optimized electronic ground state neutral singlet gas phase (298.15 K, 1 atm) geometries were obtained for 24 of the 35 possible C/N/Si/P tetrahedrane derivatives. Corresponding enthalpies of formation were calculated using the atomization method. Triplet state neutral tetrahedron starting geometries for all compounds either resulted in cage opening or failed to converge. Only 9 cationic and 3 anionic forms converged to stable geometries that retained the tetrahedron cage and were absent imaginary frequencies, thereby allowing the calculation of adiabatic ionization energies and electron affinities