We present two complementary designs of pneumatically actuated and kinematically positioned optics mounts: one designed for vertical mounting and translation, the other designed for horizontal mounting and translation. The design and measured stabili
ty make these mounts well-suited to experiments with laser-cooled atoms.
A version of the twisted Poincar{e} duality is proved between the Poisson homology and cohomology of a polynomial Poisson algebra with values in an arbitrary Poisson module. The duality is achieved by twisting the Poisson module structure in a canoni
cal way, which is constructed from the modular derivation. In the case that the Poisson structure is unimodular, the twisted Poincar{e} duality reduces to the Poincar{e} duality in the usual sense. The main result generalizes the work of Launois-Richard cite{LR} for the quadratic Poisson structures and Zhu cite{Zhu} for the linear Poisson structures.
We present the specific heat, magnetization, optical spectroscopy measurements and the firstprinciple calculations on the Weberite structure Ca2Os2O7 single crystal/polycrystalline sample. The Ca2Os2O7 shows a Curie-Weiss nature at high temperature a
nd goes into a ferrimagnetic insulating state at 327 K on cooling. A lambda-like peak is observed at 327 K in the specific heat implying a second-order phase transition. The vanishing electronic specific heat at low temperature suggests a full energy gap. At high temperature above the transition, small amount of itinerant carriers with short life time tau are observed, which is gapped at 20 K with a direct gap of 0:24 eV . Our first principle calculations indicate that the anti-ferromagnetic (AFM) correlation with intermediate Coulomb repulsion U could effectively split Os(4b) t2g bands and push them away from Fermi level(EF). On the other hand, a non-collinear magnetic interaction is needed to push the Os(4c) bands away from EF, which could be induced by Os(4c)-Os(4c) frustration. Therefore, AFM correlation, Coulomb repulsion U and non-collinear interaction all play important roles for the insulating ground state in Ca2Os2O7.
We report magnetization, specific heat, and NMR investigations on YFe2Al10 over a wide range in temperature and magnetic field and zero field (NQR) measurements. Magnetic susceptibility, specific heat and spin-lattice relaxation rate divided by T (1/
T1T) follow a weak power law (T^-0.4) temperature dependence, which is a signature of critical fluctuations of Fe moments. The value of the Sommerfeld-Wilson ratio and linear relation between 1/T1T and chi(T) suggest the existence of ferromagnetic correlations in this system. No magnetic ordering down to 50 mK in Cp(T) and the unusual temperature and field scaling of the bulk and NMR data are associated with a magnetic instability which drives the system to quantum criticality. The magnetic properties of the system are tuned by field wherein ferromagnetic fluctuations are suppressed and a crossover from quantum critical to FL behavior is observed with increasing magnetic field.
Suppose that $E=A[x;sigma,delta]$ is an Ore extension with $sigma$ an automorphism. It is proved that if $A$ is twisted Calabi-Yau of dimension $d$, then $E$ is twisted Calabi-Yau of dimension $d+1$. The relation between their Nakayama automorphisms
is also studied. As an application, the Nakayama automorphisms of a class of 5-dimensional Artin-Schelter regular algebras are given explicitly.
We constrain parity-violating interactions to the surface of last scattering using spectra from the QUaD experiments second and third seasons of observations by searching for a possible systematic rotation of the polarization directions of CMB photon
s. We measure the rotation angle due to such a possible cosmological birefringence to be 0.55 deg. +/- 0.82 deg. (random) +/- 0.5 deg. (systematic) using QUaDs 100 and 150 GHz TB and EB spectra over the multipole range 200 < l < 2000, consistent with null, and constrain Lorentz violating interactions to < 2^-43 GeV (68% confidence limit). This is the best constraint to date on electrodynamic parity violation on cosmological scales.
We present low temperature tunneling density-of-states measurements in Al films in high parallel magnetic fields. The thickness range of the films, t=6-9 nm, was chosen so that the orbital and Zeeman contributions to their parallel critical fields we
re comparable. In this quasi-spin paramagnetically limited configuration, the field produces a significant suppression of the gap, and at high fields the gapless state is reached. By comparing measured and calculated tunneling spectra we are able to extract the value of the antisymmetric Fermi-liquid parameter G^0 and thereby deduce the quasiparticle density dependence of the effective parameter G^0_{eff} across the gapless state.
Let $A$ be a connected graded $k$-algebra with a balanced dualizing complex. We prove that $A$ is a Koszul AS-regular algebra if and only if that the Castelnuovo-Mumford regularity and the Ext-regularity coincide for all finitely generated $A$-module
s. This can be viewed as a non-commutative version of cite[Theorem 1.3]{ro}. By using Castelnuovo-Mumford regularity, we prove that any Koszul standard AS-Gorenstein algebra is AS-regular. As a preparation to prove the main result, we also prove the following statements are equivalent: (1) $A$ is AS-Gorenstein; (2) $A$ has finite left injective dimension; (3) the dualizing complex has finite left projective dimension. This generalizes cite[Corollary 5.9]{mori}.
The concept of Koszul differential graded algebra (Koszul DG algebra) is introduced. Koszul DG algebras exist extensively, and have nice properties similar to the classic Koszul algebras. A DG version of the Koszul duality is proved. When the Koszul
DG algebra $A$ is AS-regular, the Ext-algebra $E$ of $A$ is Frobenius. In this case, similar to the classical BGG correspondence, there is an equivalence between the stable category of finitely generated left $E$-modules, and the quotient triangulated category of the full triangulated subcategory of the derived category of right DG $A$-modules consisting of all compact DG modules modulo the full triangulated subcategory consisting of all the right DG modules with finite dimensional cohomology. The classical BGG correspondence can derived from the DG version.
We prove a version of Koszul duality and the induced derived equivalence for Adams connected $A_infty$-algebras that generalizes the classical Beilinson-Ginzburg-Soergel Koszul duality. As an immediate consequence, we give a version of the Bernv{s}te
{ui}n-Gelfand-Gelfand correspondence for Adams connected $A_infty$-algebras. We give various applications. For example, a connected graded algebra $A$ is Artin-Schelter regular if and only if its Ext-algebra $Ext^ast_A(k,k)$ is Frobenius. This generalizes a result of Smith in the Koszul case. If $A$ is Koszul and if both $A$ and its Koszul dual $A^!$ are noetherian satisfying a polynomial identity, then $A$ is Gorenstein if and only if $A^!$ is. The last statement implies that a certain Calabi-Yau property is preserved under Koszul duality.
