A Generalization of Mathieu Subspaces to Modules of Associative Algebras

We first propose a generalization of the notion of Mathieu subspaces of associative algebras $\mathcal A$, which was introduced recently in [Z4] and [Z6], to $\mathcal A$-modules $\mathcal M$. The newly introduced notion in a certain sense also generalizes the notion of submodules. Related with this new notion, we also introduce the sets $\sigma(N)$ and $\tau(N)$ of stable elements and quasi-stable elements, respectively, for all $R$-subspaces $N$ of $\mathcal A$-modules $\mathcal M$, where $R$ is the base ring of $\mathcal A$. We then prove some general properties of the sets $\sigma(N)$ and $\tau(N)$. Furthermore, examples from certain modules of the quasi-stable algebras [Z6], matrix algebras over fields and polynomial algebras are also studied.Comment: A new case has been added; some mistakes and misprints have been corrected. Latex, 31 page

Loss of mass and stability of galaxies in MOND

The self-binding energy and stability of a galaxy in MOND-based gravity are curiously decreasing functions of its center of mass acceleration towards neighbouring mass concentrations. A tentative indication of this breaking of the Strong Equivalence Principle in field galaxies is the RAVE-observed escape speed in the Milky Way. Another consequence is that satellites of field galaxies will move on nearly Keplerian orbits at large radii (100 - 500 kpc), with a declining speed below the asymptotically constant naive MOND prediction. But consequences of an environment-sensitive gravity are even more severe in clusters, where member galaxies accelerate fast: no more Dark-Halo-like potential is present to support galaxies, meaning that extended axisymmetric disks of gas and stars are likely unstable. These predicted reappearance of asymptotic Keplerian velocity curves and disappearance of "stereotypic galaxies" in clusters are falsifiable with targeted surveys.Comment: 4 pages, 2 figures, ApJ Letter

AC electrokinetic phenomena over semiconductive surfaces: effective electric boundary conditions and their applications

Electrokinetic boundary conditions are derived for AC electrokinetic (ACEK) phenomena over leaky dielectric (i.e., semiconducting) surfaces. Such boundary conditions correlate the electric potentials across the semiconductor-electrolyte interface (consisting of the electric double layer (EDL) inside the electrolyte solutions and the space charge layer (SCL) inside the semiconductors) under AC electric fields with arbitrary wave forms. The present electrokinetic boundary conditions allow for evaluation of induced zeta potential contributed by both bond charges (due to electric polarization) and free charges (due to electric conduction) from the leaky dielectric materials. Subsequently, we demonstrate the applications of these boundary conditions in analyzing the ACEK phenomena around a semiconducting cylinder. It is concluded that the flow circulations exist around the semiconducting cylinder and are shown to be stronger under an AC field with lower frequency and around a cylinder with higher conductivity.Comment: 29 pages, 4 figure

Theory of quasi-one dimensional imbalanced Fermi gases

We present a theory for a lattice array of weakly coupled one-dimensional ultracold attractive Fermi gases (1D `tubes') with spin imbalance, where strong intratube quantum fluctuations invalidate mean field theory. We first construct an effective field theory, which treats spin-charge mixing exactly, based on the Bethe ansatz solution of the 1D single tube problem. We show that the 1D Fulde-Ferrel-Larkin-Ovchinnikov (FFLO) state is a two-component Luttinger liquid, and its elementary excitations are fractional states carrying both charge and spin. We analyze the instability of the 1D FFLO state against inter-tube tunneling by renormalization group analysis, and find that it flows into either a polarized Fermi liquid or a FFLO superfluid, depending on the magnitude of interaction strength and spin imbalance. We obtain the phase diagram of the quasi-1D system and further determine the scaling of the superfluid transition temperature with intertube coupling.Comment: new expanded version, 8 pages, updated reference

Effect of nanostructuration on compressibility of cubic BN

Compressibility of high-purity nanostructured cBN has been studied under quasi-hydrostatic conditions at 300 K up to 35 GPa using diamond anvil cell and angle-dispersive synchrotron X-ray powder diffraction. A data fit to the Vinet equation of state yields the values of the bulk modulus B0 of 375(4) GPa with its first pressure derivative B0' of 2.3(3). The nanometer grain size (\sim20 nm) results in decrease of the bulk modulus by ~9%

Structure and magnetism of Cr2BP3O12: Towards the quantum-classical crossover in a spin-3/2 alternating chain

Magnetic properties of the spin-3/2 Heisenberg system Cr2BP3O12 are investigated by magnetic susceptibility chi(T) measurements, electron spin resonance, neutron diffraction, and density functional theory (DFT) calculations, as well as classical and quantum Monte Carlo (MC) simulations. The broad maximum of chi(T) at 85K and the antiferromagnetic Weiss temperature of 139 K indicate low-dimensional magnetic behavior. Below TN = 28 K, Cr2BP3O12 is antiferromagnetically ordered with the k = 0 propagation vector and an ordered moment of 2.5 muB/Cr. DFT calculations, including DFT+U and hybrid functionals, yield a microscopic model of spin chains with alternating nearest-neighbor couplings J1 and J1' . The chains are coupled by two inequivalent interchain exchanges of similar strength (~1-2 K), but different sign (antiferromagnetic and ferromagnetic). The resulting spin lattice is quasi-one-dimensional and not frustrated. Quantum MC simulations show excellent agreement with the experimental data for the parameters J1 ~= 50 K and J1'/J1 ~= 0.5. Therefore, Cr2BP3O12 is close to the gapless critical point (J1'/J1 = 0.41) of the spin-3/2 bond-alternating Heisenberg chain. The applicability limits of the classical approximation are addressed by quantum and classical MC simulations. Implications for a wide range of low-dimensional S = 3/2 materials are discussed.Comment: Published version: 13 pages, 7 figures, 5 tables + Supplementary informatio

Molecular outflow launched beyond the disk edge

One of the long-standing problems of star formation is the excess of angular momentum of the parent molecular cloud. In the classical picture, a fraction of angular momentum of the circumstellar material is removed by the magneto-centrifugally driven disk wind that is launched from a wide region throughout the disk. In this work, we investigate the kinematics in the envelope-disk transition zone of the Class I object BHB07-11, in the B59 core. For this purpose, we used the Atacama Large Millimeter/submillimeter Array in extended configuration to observe the thermal dust continuum emission ($\lambda_0 \sim$ 1.3 mm) and molecular lines (CO, C$^{18}$O and H$_2$CO), which are suitable tracers of disk, envelope, and outflow dynamics at a spatial resolution of $\sim 30$ AU. We report a bipolar outflow that was launched at symmetric positions with respect to the disk ($\sim$80~AU in radius), but was concentrated at a distance of 90--130~AU from the disk center. The two outflow lobes had a conical shape and the gas inside was accelerating. The large offset of the launching position coincided with the landing site of the infall material from the extended spiral structure (seen in dust) onto the disk. This indicates that bipolar outflows are efficiently launched within a narrow region outside the disk edge. We also identify a sharp transition in the gas kinematics across the tip of the spiral structure, which pinpoints the location of the so-called centrifugal barrier.Comment: 5 pages, 5 figures, Accepted for publication in A&A Letter

TWO DIFFERENT TYPES OF PHOTOCHEMISTRY IN PHYCOERYTHROCYANIN α-SUBUNIT

The photochemical activities of phycoerythrocyanin α-subunits from Mastigocladus laminosus separated by isoelectric focusing were tested by irradiating at 500, 550, 577 and 600 nm. Two types of photoreversible photochromic responses have been characterized by absorption and absorption difference spectroscopy. Type I is the well-known absorption shift from 571 to 506 nm. Type II is a new response characterized by a line-broadening of the 570 nm absorption