We prove that the defining ideal of a sufficiently high Veronese subring of a toric algebra admits a quadratic Gröbner basis consisting of binomials. More generally, we prove that the defining ideal of a sufficiently high Veronese subring of a standard graded ring admits a quadratic Gröbner basis. This was proved by Eisenbud–Reeves–Totaro in the case where coordinates are generic. Our proof doe...

We describe the design, fabrication, and excellent performance of an optimized deep-etched high-density fused-silica transmission grating for use in dense wavelength division multiplexing (DWDM) systems. The fabricated optimized transmission grating exhibits an efficiency of 87.1% at a wavelength of 1550 nm. Inductively coupled plasma-etching technology was used to fabricate the grating. The de...

We note the condition 0 ≤ w(e) ≤ 1 is given since it is convenient for presenting our theoretical results, although we can define each problem without this condition. We say unweighted dense subgraph problem if w(e) = 1 for each edge. We define the density ∆ of the output subgraph H to be ∆ = 2w(F ) k(k−1) for the non-bipartite case and ∆ = w(F ) m′n′ for the bipartite case. In other words, den...

It is shown that any finitely generated subring of a global field has universal first-order definition in its fraction field. This covers Koenigsmann's result for the ring integers and subsequent extensions to rings number fields $S$-integers function odd characteristic. In this article proof presented which uniform all fields, including characteristic two case, where entirely novel. Furthermor...

Suppose D is an integral domain with quotient eld K and that L is an extension eld of K. We show in Theorem 4 that if the complete integral closure of D is an intersection of Archimedean valuation domains on K, then the complete integral closure of D in L is an intersection of Archimedean valuation domains on L; this answers a question raised by All rings considered in this paper are assumed to...

We study the relationship between fields of transseries and residue fields of convex subrings of non-standard extensions of the real numbers. This was motivated by a question of Todorov and Vernaeve, answered in this paper. In this note we answer a question by Todorov and Vernaeve (see, e.g., [35]) concerning the relationship between the field of logarithmic-exponential series from [14] and the...

The ever increasing demand for interconnect bandwidth in embedded parallel processors has motivated the development of photonic communications technologies that effectively support short-distance links. Electrooptical I/O to and from VLSI chips is one such photonic technology. A multiring architecture that exploits optical I/O on and off chip is described in [1]. At the heart of the system is a...