Using limit linear series and a result controlling degeneration from separable maps to inseparable maps, we give a formula for the number of self-maps of P1 with ramification to order ei at general points Pi, in the case that all ei are less than the characteristic. We also develop a new, more functorial construction for the basic theory of limit linear series, which works transparently in posi...

For an odd prime p and each non-empty subset S ⊂ GF (p), consider the hyperelliptic curve XS defined by y = fS(x), where fS(x) = Q a∈S(x− a). Using a connection between binary quadratic residue codes and hyperelliptic curves over GF (p), this paper investigates how coding theory bounds give rise to bounds such as the following example: for all sufficiently large primes p there exists a subset S...

Koszul algebras, introduced by Priddy in [P], are positively graded Kalgebras R whose residue field K has a linear free resolution as an R-module. Here linear means that the non-zero entries of the matrices describing the maps in the R-free resolution of K have degree 1. For example, the polynomial ring S = K[x1, . . . ,xn] over a field K (i.e the symmetric algebra SymK(V ) of a n-dimensional K...

A series of simulated maps showing the appearance in total intensity of flows computed using a recently developed relativistic hydrodynamic code (Duncan & Hughes 1994: ApJ, 436, L119) are presented. The radiation transfer calculations were performed by assuming the flow is permeated by a magnetic field and fast particle distribution in energy equipartition, with energy density proportional to t...

Let C be a curve of genus g > 2 defined over the fraction field K of a complete discrete valuation ring R with algebraically closed residue field. Suppose that char(K) = 0 and that the characteristic of the residue field is not 2. Suppose that the Jacobian Jac(C) has semi-stable reduction over R. Embed C in Jac(C) using a K-rational point. We show that the coordinates of the torsion points lyin...

NMR titration curves are reported for the 4 histidine residues of ribonuclease A in sodium acetate and for ribonuclease S in sodium acetate, phosphate, and sulfate solutions. Evidence is presented that the imidazole side chain of histidine residue 48 undergoes a conformational change, probably also involving the carboxyl side chain of aspartic acid residue 14. This group is considered to be res...

In recent years, residue-to-energy utilization has become an important energy source that can alleviate the reliability of fossil fuel, and agricultural residue (AR) transportation great potential for optimization in AR supply chain. However, various methods presented make their correct implementation difficult sustainable optimization. Therefore, four key issues bioenergy production have been ...

Let p be a prime number, Fp be a finite field, and let k ∈ Fp. In this paper, we consider the number of rational points on conics Cp,k : x − ky = 1 over Fp. We proved that the order of Cp,k over Fp is p− 1 if k is a quadratic residue mod p and is p+1 if k is not a quadratic residue mod p. Later we derive some results concerning the sums ∑ C [x] p,k(Fp) and ∑ C [y] p,k(Fp), the sum of x− and y−c...

In this paper we describe the moduli spaces of degree d branched superminimal immersions of a compact Riemann surface of genus g into S4. We prove that when d ≥ max{2g, g + 2}, such spaces have the structure of projectivized fibre products and are path-connected quasi-projective varieties of dimension 2d − g + 4. This generalizes known results for spaces of harmonic 2-spheres in S4. In the Cala...

We introduce a structured image compression scheme based on a u = v + w model, where the orignal image u is decomposed between a sketch v and a residue w. The sketch contains the main edge curves while the information carried by the residue is mostly composed by microtextures. This split of the meaningful information allows the use of a representation adapted to each structure. The edge curve g...