共找到 29 条结果
We describe the structure of the Grothendieck ring of projective modules of basic Hopf algebras using a positive integer determined by the composition series of the principal indecomposable projective module.
We show that the Fourier-Laplace transform of an irreducible regular differential system on the Riemann sphere underlies, when one only considers the part at finite distance, a polarizable regular twistor $\mathcal{D}$-module. The associated holomorphic bundle out of the origin is therefore equipped with a natural harmonic metric with a tame behaviour near the origin.
We give an explicit description of the canonical Frobenius structure attached (by the results of the first part of this article) to the polynomial f(u_0,...,u_n)=w_0u_0+...+w_nu_n restricted to the torus u_0^{w_0}...u_n^{w_n}=1, for any family of positive integers w_0,...,w_n such that gcd(w_0,...,w_n)=1.
We consider associative algebras L over a field provided with a direct sum decomposition of a two-sided ideal M and a sub-algebra A - examples are provided by trivial extensions or triangular type matrix algebras. In this relative and split setting we describe a long exact sequence computing the Hochschild cohomology of L. We study the connecting homomorphism using the cup-product and we infer several results, in particular the first Hochschild cohomology group of a trivial extension never vanishes.
The CFHT Large Area U-band Deep Survey (CLAUDS) uses data taken with the MegaCam mosaic imager on CFHT to produce images of 18.60 deg2 with median seeing of FWHM=0.92 arcsec and to a median depth of U = 27.1 AB (5 sigma in 2 arcsec apertures), with selected areas that total 1.36 deg2 reaching a median depth of U=27.7 AB. These are the deepest U-band images assembled to date over this large an area. These data are located in four fields also imaged to comparably faint levels in grizy and several narrowband filters as part of the Hyper Suprime-Cam (HSC) Subaru Strategic Program (HSC-SSP). These CFHT and Subaru datasets will remain unmatched in their combination of area and depth until the advent of the Large Synoptic Survey Telescope (LSST). This paper provides an overview of the scientific motivation for CLAUDS and gives details of the observing strategy, observations, data reduction, and data merging with the HSC-SSP. Three early applications of these deep data are used to illustrate the potential of the dataset: deep U-band galaxy number counts, z~3 Lyman break galaxy (LBG) selection, and photometric redshifts improved by adding CLAUDS U to the Subaru HSC grizy photometry.
We review some aspects of the renormalization group method for interacting fermions. Special emphasis is placed on the application of scaling theory to quasi-one-dimensional systems at non zero temperature. We begin by introducing the scaling ansatz for purely one-dimensional fermion systems and its extension when interchain coupling and dimensionality crossovers are present at finite temperature. Next, we review the application of the renormalization group technique to the one-dimensional electron gas model and clarify some peculiarities of the method at the two-loop level. The influence of interchain coupling is then included and results for the crossover phenomenology and the multiplicity of characteristic energy scales are summarized. The emergence of the Kohn-Luttinger mechanism in quasi-one-dimensional electronic structures is discussed fo both superconducting and density-wave channels.
The electrophoretic mobility of a spherical particle is well understood, yet how particle shape modifies this mobility at arbitrary Debye length remains an open question. Here, we compute the electrophoretic mobility of a nearly spherical particle whose surface is described by $r_s(θ) = a[1 + \varepsilon f(θ)]$, with $\varepsilon \ll 1$, at arbitrary ratio of particle size to Debye length $κa$. Using a volume-integral formulation combined with domain perturbation techniques, we derive a universal shape correction coefficient $σ_2(κa)$ such that the mobility takes the compact form $C_\parallel = f_H(κa)\,[1 + \varepsilon\,c_2\,σ_2(κa)]$, where $f_H$ is Henry's function. We show that $σ_2$ interpolates between $+1/5$ in the thick-double-layer (Hückel) limit, governed solely by the Stokes drag correction, and zero in the thin-double-layer (Smoluchowski) limit, recovering the classical shape-independence theorem. The perturbation theory agrees quantitatively with exact spheroid solutions for both prolate and oblate orientations. A key finding is that only the $P_2$ (quadrupolar) component of the particle shape affects the mobility at leading order; higher harmonics are electrophoretica
In a quantum system having a finite number $N$ of orthogonal states, two orthonormal bases $\{a_i\}$ and $\{b_j\}$ are called mutually unbiased if all inner products $<a_i|b_j>$ have the same modulus $1/\sqrt{N}$. This concept appears in several quantum information problems. The number of pairwise mutually unbiased bases is at most $N+1$ and various constructions of $N+1$ such bases have been found when $N$ is a power of a prime number. We study families of formulas that generalize these constructions to arbitrary dimensions using finite rings.We then prove that there exists a set of $N+1$ mutually unbiased bases described by such formulas, if and only if $N$ is a power of a prime number.
We introduce the first grammar-compressed representation of a sequence that supports searches in time that depends only logarithmically on the size of the grammar. Given a text $T[1..u]$ that is represented by a (context-free) grammar of $n$ (terminal and nonterminal) symbols and size $N$ (measured as the sum of the lengths of the right hands of the rules), a basic grammar-based representation of $T$ takes $N\lg n$ bits of space. Our representation requires $2N\lg n + N\lg u + ε\, n\lg n + o(N\lg n)$ bits of space, for any $0<ε\le 1$. It can find the positions of the $occ$ occurrences of a pattern of length $m$ in $T$ in $O((m^2/ε)\lg (\frac{\lg u}{\lg n}) +occ\lg n)$ time, and extract any substring of length $\ell$ of $T$ in time $O(\ell+h\lg(N/h))$, where $h$ is the height of the grammar tree.