Multiplicative order convergence in ff-algebras

A net $(x_\alpha)$ in an $f$-algebra $E$ is said to be multiplicative order convergent to $x\in E$ if \x_\alpha-x\u\oc 0 for all $u\in E_+$. In this paper, we introduce the notions $mo$-convergence, $mo$-Cauchy, $mo$-complete, $mo$-continuous and $mo$-KB-space. Moreover, we study the basic properties of these notions.Comment:

Influence of temperature on the magnetic oscillations in graphene with spin splitting: a new approach

We analyze the magnetic oscillations (MO) in pristine graphene, under a perpendicular magnetic field, taking into account the Zeeman effect. We consider a constant Fermi energy, such that the valence band is always full and only the conduction band is available. At zero temperature the MO consist of two sawtooth peaks, one for each spin. Both peaks have the same frequency, but different amplitude and phase. We show that, in order to observe the spin splitting in the MO, Fermi energy of about 0.1 eV is required. At low temperatures we obtain that the MO can be expressed as the MO at zero temperature, plus small Fermi-Dirac like functions, each centered around the MO peaks. Using this expression, we show that the spin splitting is observable in the MO only when the thermal energy is smaller than the Zeeman energy. We also analyze the shift of the MO extrema as the temperature increases. We show that it depends on the magnetic field, which implies a broken periodicity at nonzero temperature. Finally, we obtain an analytical expression for the MO envelope.Comment: 22 pages, 9 figures. Published versio

‘User-friendly’ primary phosphines and an arsine: synthesis and characterization of new air-stable ligands incorporating the ferrocenyl group

Reaction of FcCH₂CH₂P(O)(OH)₂ or FcCH₂P(O)(OH)(OEt) [Fc=Fe(η⁵-C₅H₄)(η⁵-C₅H₅)] with excess CH₂N₂ followed by reduction with Me₃SiCl–LiAlH₄ gives the air-stable primary phosphines FcCH₂CH₂PH₂ and the previously reported analogue FcCH₂PH₂ in high yields. Reduction of 1,1′-Fc′[CH₂P(O)(OEt)₂] [Fc′=Fe(η⁵-C₅H₄)₂] and 1,2-Fc″[CH₂P(O)(OEt)₂] [Fc″=Fe(η⁵-C₅H₅)(η⁵-C₅H₃)] similarly gives the new primary phosphines 1,1′-Fc′(CH₂PH₂)₂ and 1,2-Fc″(CH₂PH₂)₂, respectively. The arsine FcCH₂CH₂AsH₂, which is also air-stable, has been prepared by reduction of the arsonic acid FcCH₂CH₂As(O)(OH)₂ using Zn/HCl. An X-ray structure has been carried out on the arsine, which is only the second structure determination of a free primary arsine. The molybdenum carbonyl complex [1,2-Fc″(CH₂PH₂)₂Mo(CO)₄] was prepared by reaction of the phosphine with [Mo(CO)₄(pip)₂] (pip=piperidine), and characterized by a preliminary X-ray structure determination. However, the same reaction of 1,1′-Fc′(CH₂PH₂)₂with [Mo(CO)₄(pip)₂] gave [1,1′-Fc′(CH₂PH₂)₂Mo(CO)₄] and the dimer [1,1′-Fc′(CH₂PH₂)₂Mo(CO)₄]₂, characterized by electrospray mass spectrometry. 1,1′-Fc′[CH₂PH₂Mo(CO)₅]₂ and 1,2-Fc″[CH₂PH₂Mo(CO)₅]₂ were likewise prepared from the phosphines and excess [Mo(CO)₅(THF)]

Fast Reachable Set Approximations via State Decoupling Disturbances

With the recent surge of interest in using robotics and automation for civil purposes, providing safety and performance guarantees has become extremely important. In the past, differential games have been successfully used for the analysis of safety-critical systems. In particular, the Hamilton-Jacobi (HJ) formulation of differential games provides a flexible way to compute the reachable set, which can characterize the set of states which lead to either desirable or undesirable configurations, depending on the application. While HJ reachability is applicable to many small practical systems, the curse of dimensionality prevents the direct application of HJ reachability to many larger systems. To address computation complexity issues, various efficient computation methods in the literature have been developed for approximating or exactly computing the solution to HJ partial differential equations, but only when the system dynamics are of specific forms. In this paper, we propose a flexible method to trade off optimality with computation complexity in HJ reachability analysis. To achieve this, we propose to simplify system dynamics by treating state variables as disturbances. We prove that the resulting approximation is conservative in the desired direction, and demonstrate our method using a four-dimensional plane model.Comment: in Proceedings of the IEE Conference on Decision and Control, 201

Minkowski's Object: A Starburst Triggered by a Radio Jet, Revisited

We present neutral hydrogen, ultraviolet, optical and near-infrared imaging, and optical spectroscopy, of Minkowski's Object (MO), a star forming peculiar galaxy near NGC 541. The observations strengthen evidence that star formation in MO was triggered by the radio jet from NGC 541. Key new results are the discovery of a 4.9E8 solar mass double HI cloud straddling the radio jet downstream from MO, where the jet changes direction and decollimates; strong detections of MO, also showing double structure, in UV and H-alpha; and numerous HII regions and associated clusters in MO. In UV, MO resembles the radio-aligned, rest-frame UV morphologies in many high redshift radio galaxies (HzRGs), also thought to be caused by jet-induced star formation. MO's stellar population is dominated by a 7.5 Myr-old, 1.9E7 solar mass instantaneous burst, with current star formation rate 0.52 solar masses per year (concentrated upstream from where the HI column density is high). This is unlike the jet-induced star formation in Centaurus A, where the jet interacts with pre-existing cold gas; in MO the HI may have cooled out of a warmer, clumpy intergalactic or interstellar medium as a result of jet interaction, followed by collapse of the cooling clouds and subsequent star formation (consistent with numerical simulations). Since the radio source that triggered star formation in MO is much less luminous, and therefore more common, than powerful HzRGs, and because the environment around MO is not particularly special in terms of abundant dense, cold gas, jet-induced star formation in the early universe might be even more prevalent than previously thought.Comment: 52 pages, 15 figures, accepted for publication in Ap

Concentration dependence of thermal isomerization process of methyl orange in ethanol

The thermal isomerization (TI) rates of methyl orange (MO) and 4-dimethylaminoazobenzene (DMAAB) in ethanol (EtOH) are measured. Usually TI rates of azobenzene dyes are known to be concentration independent. However, the TI rate of MO showed a concentration dependence whereas that of DMAAB did not. The TI rate of DMAAB in EtOH became larger by the addition of alkali halide. This phenomenon is caused mainly by the interaction between DMAAB and cation. MO is a derivative of DMAAB in which one end of the azobenzene is substituted by a SO3-Na+ group. The interaction with the dissociated Na+ ion is considered to be an origin of the concentration dependence of the TI rate of MO

A Utility Proportional Fairness Radio Resource Block Allocation in Cellular Networks

This paper presents a radio resource block allocation optimization problem for cellular communications systems with users running delay-tolerant and real-time applications, generating elastic and inelastic traffic on the network and being modelled as logarithmic and sigmoidal utilities respectively. The optimization is cast under a utility proportional fairness framework aiming at maximizing the cellular systems utility whilst allocating users the resource blocks with an eye on application quality of service requirements and on the procedural temporal and computational efficiency. Ultimately, the sensitivity of the proposed modus operandi to the resource variations is investigated