Non-orientable surface-plus-one-relation groups

Recently Dicks–Linnell determined the L2-Betti numbers of the orientable surface-plus-one-relation groups, and their arguments involved some results that were obtained topologically by Hempel and Howie. Using algebraic arguments, we now extend all these results of Hempel and Howie to a larger class of two-relator groups, and we then apply the extended results to determine the L2-Betti numbers of the non-orientable surface-plus-one-relation group

Foreign Bond Markets and Financial Market Development: International Perspectives

The domestic bond markets of the Asia and Pacific region have grown considerably since the Asian financial crisis of 1997, although they remain undeveloped relative to the region's weight in the world economy. This paper proposes that in order to encourage further development of these markets, regulators should make them more accessible to foreign borrowers. To that end we offer insights into the nature and mechanics of foreign bond issuance by investigating the key characteristics of 3,132 foreign bonds issued in 14 countries (other than the United States) between July 1928 and June 2009. We found that the foreign borrowers that tap domestic markets are overwhelmingly of high credit quality and comprise sovereigns, supranationals, and major financial institutions. There is a preference for simple fixed-rate payment structures, which can then be swapped into the currency and coupon type of choice using currency and interest rate derivatives. On the whole, the long-term viability of foreign bond markets appears linked to the presence of highly liquid foreign exchange and derivatives markets that facilitate risk management and transformation, enabling regulation that facilitates cooperation with market participants, the presence of benchmark issues, and competitive pricing between alternate market segments.bond markets; financial market development; foreign bonds

On the local-indicability cohen–lyndon theorem

For a group H and a subset X of H, we let HX denote the set {hxh?1 | h ? H, x ? X}, and when X is a free-generating set of H, we say that the set HX is a Whitehead subset of H. For a group F and an element r of F, we say that r is Cohen–Lyndon aspherical in F if F{r} is a Whitehead subset of the subgroup of F that is generated by F{r}. In 1963, Cohen and Lyndon (D. E. Cohen and R. C. Lyndon, Free bases for normal subgroups of free groups, Trans. Amer. Math. Soc. 108 (1963), 526–537) independently showed that in each free group each non-trivial element is Cohen–Lyndon aspherical. Their proof used the celebrated induction method devised by Magnus in 1930 to study one-relator groups. In 1987, Edjvet and Howie (M. Edjvet and J. Howie, A Cohen–Lyndon theorem for free products of locally indicable groups, J. Pure Appl. Algebra 45 (1987), 41–44) showed that if A and B are locally indicable groups, then each cyclically reduced element of A*B that does not lie in A ? B is Cohen–Lyndon aspherical in A*B. Their proof used the original Cohen–Lyndon theorem. Using Bass–Serre theory, the original Cohen–Lyndon theorem and the Edjvet–Howie theorem, one can deduce the local-indicability Cohen–Lyndon theorem: if F is a locally indicable group and T is an F-tree with trivial edge stabilisers, then each element of F that fixes no vertex of T is Cohen–Lyndon aspherical in F. Conversely, by Bass–Serre theory, the original Cohen–Lyndon theorem and the Edjvet–Howie theorem are immediate consequences of the local-indicability Cohen–Lyndon theorem. In this paper we give a detailed review of a Bass–Serre theoretical form of Howie induction and arrange the arguments of Edjvet and Howie into a Howie-inductive proof of the local-indicability Cohen–Lyndon theorem that uses neither Magnus induction nor the original Cohen–Lyndon theorem. We conclude with a review of some standard applications of Cohen–Lyndon asphericit

The local universes model: an overlooked coherence construction for dependent type theories

We present a new coherence theorem for comprehension categories, providing strict models of dependent type theory with all standard constructors, including dependent products, dependent sums, identity types, and other inductive types. Precisely, we take as input a "weak model": a comprehension category, equipped with structure corresponding to the desired logical constructions. We assume throughout that the base category is close to locally Cartesian closed: specifically, that products and certain exponentials exist. Beyond this, we require only that the logical structure should be *weakly stable* --- a pure existence statement, not involving any specific choice of structure, weaker than standard categorical Beck--Chevalley conditions, and holding in the now standard homotopy-theoretic models of type theory. Given such a comprehension category, we construct an equivalent split one, whose logical structure is strictly stable under reindexing. This yields an interpretation of type theory with the chosen constructors. The model is adapted from Voevodsky's use of universes for coherence, and at the level of fibrations is a classical construction of Giraud. It may be viewed in terms of local universes or delayed substitutions.Comment: 36 pages. Definition of "pseudo-stable" corrected from earlier version. To appear in ACM Transactions on Computational Logi

A quantitative variational phase field framework

The finite solid-liquid interface width in phase field models results in non-equilibrium effects, including solute trapping. Prior phase field modeling has shown that this extra degree of freedom, when compared to sharp-interface models, results in solute trapping that is well captured when realistic parameters, such as interface width, are employed. However, increasing the interface width, which is desirable for computational reasons, leads to artificially enhanced trapping thus making it difficult to model departure from equilibrium quantitatively. In the present work, we develop a variational phase field model with independent kinetic equations for the solid and liquid phases. Separate kinetic equations for the phase concentrations obviate the assumption of point wise equality of diffusion potentials, as is done in previous works. Non-equilibrium effects such as solute trapping, drag and interface kinetics can be introduced in a controlled manner in the present model. In addition, the model parameters can be tuned to obtain ``experimentally-relevant" trapping while using significantly larger interface widths than prior efforts. A comparison with these other phase field models suggests that interface width of about three to twenty-five times larger than current best-in-class models can be employed depending upon the material system at hand leading to a speed-up by a factor of $W^{(d+2)}$, where $W$ and $d$ denote the interface width and spatial dimension, respectively. Finally the capacity to model non-equilibrium phenomena is demonstrated by simulating oscillatory instability leading to the formation of solute bands.Comment: 51 pages, 9 figures, supplemental material