半模的张量积

本文引入了半模的张量积的泛性定义，给出了半模范畴中的有向正向系的上极限以及任意一个半模同态的上核，讨论了半模张量积的若干性质，主要结果是：证明了张量函子保持半模的右正合性和上积，并且上积保持半模的平坦性，半模范畴中的张量函子保持上极限和上核．     

切测度的几何分析

本文研究了Radon测度μ的切测度,给出了切测度的Rectifiability.利用对偶性原理及Blow-up 技巧证明了连续函数的微切集的存在性.另外,本文给出了切测度的平坦性特征.作为切测度的应用, 证明了Marstrand定理.     

$${\mathbb{Z}}_2^k$$ -Manifolds are isospectral on forms

We obtain a simple formula for the multiplicity of eigenvalues of the Hodge-Laplace operator, Δ _f , acting on sections of the full exterior bundle over an arbitrary compact flat Riemannian n-manifold M with holonomy group , 1 ≤ k ≤ n − 1. This formula implies that any two such manifolds having isospectral lattices of translations are isospectral with respect to Δ _f . As a consequence, we construct a large family of pairwise Δ _f -isospectral and nonhomeomorphic n-manifolds of cardinality greater than . Supported by Conicet, Secyt-UNC.     

A short proof of smooth implies flat

Proofs that a smooth morphism is flat available in the literature are long and di?cult. We give a short proof of this fact.     

Low-E probe for (19)F-(1)H NMR of dilute biological solids

Sample heating induced by radio frequency (RF) irradiation presents a significant challenge to solid state NMR experiments in proteins and other biological systems, causing the sample to dehydrate which may result in distorted spectra and a damaged sample. In this work we describe a large volume, low-E (19)F-(1)H solid state NMR probe, which we developed for the 2D (19)F CPMG studies of dilute membrane proteins in a static and electrically lossy environment at 600MHz field. In (19)FCPMG and related multi-pulse (19)F-(1)H experiments the sample is heated by the conservative electric fields E produced in the sample coil at both (19)F and (1)H frequencies. Instead of using a traditional sample solenoid, our low-E (19)F-(1)H probe utilizes two orthogonal loop-gap resonators in order to minimize the conservative electric fields responsible for sample heating. Absence of the wavelength effects in loop-gap resonators results in homogeneous RF fields and enables the study of large sample volumes, an important feature for the dilute protein preparations. The orthogonal resonators also provide intrinsic isolation between the (19)F and (1)H channels, which is another major challenge for the (19)F-(1)H circuits where Larmor frequencies are only 6% apart. We detail steps to reduce (19)F background signals from the probe, which included careful choice of capacitor lubricants and manufacture of custom non-fluorinated coaxial cables. Application of the probe for two-dimensional (19)F CPMG spectroscopy in oriented lipid membranes is demonstrated with Flufenamic acid (FFA), a non-steroidal anti-inflammatory drug.     

Flat bands and enigma of metamagnetic quantum critical regime in Sr3Ru2O7

Understanding the nature of field-tuned metamagnetic quantum criticality in the ruthenate Sr₃Ru₂O₇ has presented a significant challenge within condensed matter physics. It is known from experiments that the entropy within the ordered phase forms a peak, and is unexpectedly higher than that outside, while the magnetoresistivity experiences steep jumps near the ordered phase. We find a challenging connection between Sr₃Ru₂O₇ and heavy-fermion metals expressing universal physics that transcends microscopic details. Our construction of the T–B$T\text{–}B$ phase diagram of Sr₃Ru₂O₇ permits us to explain main features of the experimental one, and unambiguously implies an interpretation of its extraordinary low-temperature thermodynamic in terms of fermion condensation quantum phase transition leading to the formation of a flat band at the restricted range of magnetic fields B. We show that it is the flat band that generates both the entropy peak and the resistivity jumps at the QCPs.     

On Finite Maximal Chains of Weak Baer Going-Down Rings

Some recent results of Ayache on going-down domains and extensions of domains that either are residually algebraic or have DCC on intermediate rings are generalized to the context of extensions of commutative rings. Given a finite maximal chain 𝒞 of R-subalgebras of a weak Baer ring T, it is shown how a “min morphism” hypothesis can be used to transfer the “going-down ring” property from R to each member of 𝒞. The integral minimal ring extensions which are min morphisms are classified. The ring extensions satisfying FCP (i.e., for which each chain of intermediate rings is finite) are characterized as the strongly affine extensions with DCC on intermediate rings. In the relatively integrally closed case, such extensions R ? T induce open immersions Spec(S) → Spec(R) for each R-subalgebra S of T.     

On Covers and Envelopes in Some Functor Categories

We study the existence of covers and envelopes by some special functors on the category of finitely presented modules. As an application, we characterize some important rings using these functors. We also investigate homological properties of some functors on the stable module category. The relationship between phantoms and Ext-phantoms is obtained. It is shown that every left R-module M has an Ext-phantom preenvelope f: M → N with coker(f) pure-projective. Finally, we prove that, as a torsionfree class of (mod-R, Ab), (mod-R, Ab) is generated by the FP-injective objects.     

Flat Riemannian Manifolds as Torus Bundles

Vasquez showed that for any finite group G there exists a number n(G) such that for every flat Riemannian manifold M with holonomy group G there exists a fiber bundle T → M → N, where T is a flat torus and N is a flat manifold of dimension less than or equal to n(G). We show that n(H) ≤ n(G) if H Δ leftG or G = N ? H and use this result to describe groups with the Vasquez number equal to 2 or 3.