Search results for "Commutative algebra"
showing 7 items of 127 documents
Non-commutative Ring Learning with Errors from Cyclic Algebras
2022
AbstractThe Learning with Errors (LWE) problem is the fundamental backbone of modern lattice-based cryptography, allowing one to establish cryptography on the hardness of well-studied computational problems. However, schemes based on LWE are often impractical, so Ring LWE was introduced as a form of ‘structured’ LWE, trading off a hard to quantify loss of security for an increase in efficiency by working over a well-chosen ring. Another popular variant, Module LWE, generalizes this exchange by implementing a module structure over a ring. In this work, we introduce a novel variant of LWE over cyclic algebras (CLWE) to replicate the addition of the ring structure taking LWE to Ring LWE by add…
Spatial Demixing of Ring and Chain Polymers in Pressure-Driven Flow
2019
We investigate mixtures of ring and linear polymers in solution at various number ratios, ranging from pure chains to pure rings, and at densities around the overlap concentration. In bulk and at r...
Scaling behavior of topologically constrained polymer rings in a melt
2014
Large scale molecular dynamics simulations on graphic processing units (GPUs) are employed to study the scaling behavior of ring polymers with various topological constraints in melts. Typical sizes of rings containing $3_1$, $5_1$ knots and catenanes made up of two unknotted rings scale like $N^{1/3}$ in the limit of large ring sizes $N$. This is consistent with the crumpled globule model and similar findings for unknotted rings. For small ring lengths knots occupy a significant fraction of the ring. The scaling of typical ring sizes for small $N$ thus depends on the particular knot type and the exponent is generally larger than 0.4.
Adsorption of Oligomers and Polymers into a Polymer Brush Formed from Grafted Ring Polymers
2013
The interaction of a ring polymer brush with a solution containing oligomers or free linear flexible macromolecules is studied by Monte Carlo simulation, varying the chain length of the free chains, and in selected cases also the lengths of the rings. Two grafting densities are studied, corresponding to semidilute and very concentrated conditions, and a comparison with the corresponding case of brushes formed from grafted linear chains is made. Although the ring polymer linear dimensions in the brushes show an anomalous scaling with ring length, similar to (noncatenated) ring polymer melts, the concentration profiles of oligomers and long macromolecules in ring polymer brushes differ only v…
"Figure 5a" of "Measurement of jet-medium interactions via direct photon-hadron correlations in Au$+$Au and $d$$+$Au collisions at $\sqrt{s_{_{NN}}}=…
2021
$I_{AA}$ vs $\xi$ for direct photon $p_{T}^{\gamma}$ of 5-7 GeV/$c$, 7-9 GeV/$c$, and 9-12 GeV/$c$.
Some remarks on Hilbert's (Weak) Nullstellensatz
2011
Certain remarks are provided related to weak nullstellensatz exploiting some problems proposed in Fulton’s book entitled “An Introduction to Algebraic Geometry” and elementary notions of Functional Analysis.
A survey on algebraic dilatations
2023
In this text, we wish to provide the reader with a short guide to recent works on the theory of dilatations in Commutative Algebra and Algebraic Geometry. These works fall naturally into two categories: one emphasises foundational and theoretical aspects and the other applications to existing theories.