Superfilters, Ramsey theory, and van der Waerden's Theorem

Superfilters are generalizations of ultrafilters, and capture the underlying concept in Ramsey-theoretic theorems such as van der Waerden's Theorem. We establish several properties of superfilters, which generalize both Ramsey's Theorem and its variants for ultrafilters on the natural numbers. We use them to confirm a conjecture of Kočinac and Di Maio, which is a generalization of a Ramsey-theoretic result of Scheepers, concerning selections from open covers. Following Bergelson and Hindman's 1989 Theorem, we present a new simultaneous generalization of the theorems of Ramsey, van der Waerden, Schur, Folkman–Rado–Sanders, Rado, and others, where the colored sets can be much smaller than the full set of natural numbers.     

Synthesis and Crystal Structure of Mixed-valence Hexanuclear Manganase Oxide Complex,Hexakis(μ<Subscript>2</Subscript>-pivalato)-tetrakis(μ<Subscript>3</Subscript>-pivalato)-mono(pyridine)-tris(pivalic acid)-bis(μ<Subscript>4</Subscript>-oxo)dimanganese(III) tetramanganase(II)

Abstract  The complex, [Mn₆O₂(OOCCMe₃)₁₀(HOOCCMe₃)₃(py)], has a hexanuclear structure with a Mn₆O₂ core. This complex crystallizes in the monoclinic space group P2₁/n with a = 17.757(5) ?, b = 27.413(5) ?, c = 22.348(5) ?, β = 90.233(5)°, V = 9,040(4) ?³ and Z = 4. It contains a [Mn₆O₂]¹⁰⁺ core that can be described as two edge-sharing Mn₄ tetrahedra at the centre of each of which tetrahedron lies a μ₄-O²⁻ ion. All Mn atoms are six-coordinate and possess distorted octahedral geometry. Mn₄ exhibits butterfly arrangement with both μ₄-O atoms on the same side of the molecule. The complex is mixed-valence , and the Mn^III centers are assigned as the two central metal ions bridged by two O²⁻ ions. Index abstract  The complex, [Mn₆O₂(OOCCMe₃)₁₀(HOOCCMe₃)₃(py)], has a hexanuclear structure with a Mn₆O₂ core. This complex crystallizes in the monoclinic space group P2₁/n with a = 17.757(5) ?, b = 27.413(5) ?, c = 22.348(5) ?, β = 90.233(5)°, V = 9040(4) ?³ and Z = 4. It contains a [Mn₆O₂]¹⁰⁺ core that can be described as two edge-sharing Mn₄ tetrahedra at the centre of each of which tetrahedron lies a μ₄-O²⁻ ion. All Mn atoms are six-coordinate and possess distorted octahedral geometry. Mn₄ exhibits butterfly arrangement with both μ₄-O atoms on the same side of the molecule. The complex is mixed-valence , and the Mn^III centers are assigned as the two central metal ions bridged by two O²⁻ ions.      

EELS study of interfaces in magnetoresistive LSMO/STO/LSMO tunnel junctions

A magnetic tunnel junction consists of two ferromagnetic conducting electrodes separated by an insulating thin layer. The performance of such a system strikingly depends on the last conducting atomic layers in contact with the insulator. Consequently, the present paper reports a nanoscale electron energy loss spectroscopy (EELS) study, which has been performed across a couple of La_0.66Sr_0.33MnO₃,/SrTiO₃/La_0.66Sr_0.33MnO₃ tunnel junctions with different barrier thickness es (1.5 nm and 5 nm respectively). It aims at determining not only the chemical composition in the interface areas, but also the effect of the neighbouring atoms on their electronic structure. Using recent improvements in the STEM-EELS data acquisition and processing techniques (systematic use of spectrum-line and spectrum-image modes, multivariate statistical analysis, 2D energy deconvolution schemes, etc.), the local chemical information is better extracted with shorter acquisition times, while the large increase of the data set contributes to validate the results. Within the accuracy level of these measurements, the elemental composition of the different phases remains stable up to the interfaces with no evidence of extra doping. Furthermore, weak changes on the Mn-2p edge fine structures (weak shift to lower energy loss values and extra splitting on the top of the Mn L₃ line are observed on all the interfaces. They are interpreted as a consequence of a slight reduction of the local Mn valence likely accompanied by a strain induced change in local symmetry. The discussion is focussed on all spectral changes identified at a (sub)nanometer scale and their potential effects on the degradation of magnetic and transport properties measured, close to room temperature, at a macroscopic level.Received: 14 April 2003, Published online: 4 August 2003PACS: 75.45.+j Macroscopic quantum phenomena in magnetic systems - 82.80.Pv Electron spectroscopy (X-ray photoelectron (XPS), Auger electron spectroscopy (AES), etc.) - 68.37.Lp Transmission electron microscopy (TEM) (including STEM, HRTEM, etc.) - 85.30.Mn Junction breakdown and tunneling devices (including resonance tunneling devices)     

Lightlike Hypersurfaces of a Golden Semi-Riemannian Manifold

We introduce lightlike hypersurfaces of a golden semi-Riemannian manifold. We investigate several properties of lightlike hypersurfaces of a golden semi-Riemannian manifold. We prove that there is no radical anti-invariant lightlike hypersurface of a golden semi-Riemannian manifold. In particular, we obtain some results for screen semi-invariant lightlike hypersurfaces of a golden semi-Riemannian manifold. Moreover, we study screen conformal screen semi-invariant lightlike hypersurfaces.     

$$\varvec{\varphi }$$-admissibility results via extended simulation functions

We introduce the class of extended simulation functions, which is more large than the class of simulation functions, recently introduced in (Khojasteh et al. Filomat 29(6):1189–1194, 2015). We obtain a \(\varphi \)-admissibility result involving extended simulation functions, for a new class of mappings \(T: X\rightarrow X\), with respect to a lower semi-continuous function \(\varphi : X\rightarrow [0,\infty )\), where X is a set equipped with a certain metric d. The main theorem in this paper generalizes a recent \(\varphi \)-admissibility result obtained in (Karap?nar et al. Fixed Point Theory Appl 2015:152, 2015), and many other related results.     

HESI-MS/MS Analysis of Phenolic Compounds from Calendula aegyptiaca Fruits Extracts and Evaluation of Their Antioxidant Activities

Considering medicinal plants as an inexhaustible source of active ingredients that may be easily isolated using simple and inexpensive techniques, phytotherapy is becoming increasingly popular. Various experimental approaches and analytical methods have been used to demonstrate that the genus Calendula (Asteraceae) has a particular richness in active ingredients, especially phenolic compounds, which justifies the growing interest in scientific studies on this genus’ species. From a chemical and biological viewpoint, Calendula aegyptiaca is a little-studied plant. For the first time, high-performance liquid chromatography combined with negative electrospray ionization mass spectrometry (HPLC-HESI-MS) was used to analyze methanolic extracts of Calendula aegyptiaca (C. aegyptiaca) fruits. Thirty-five molecules were identified. Flavonoids (47.87%), phenolic acids (5.18%), and saponins (6.47%) formed the majority of these chemicals. Rutin, caffeic acid hexoside, and Soyasaponin βg’ were the most abundant molecules in the fruit methanolic extract, accounting for 17.49% of total flavonoids, 2.32 % of total phenolic acids, and 0.95% of total saponins, respectively. The antioxidant activity of the fruit extracts of C. aegyptiaca was investigated using FRAP, TAC, and DPPH as well as flavonoids and total phenols content. Because the phenolic components were more extractable using polar solvents, the antioxidant activity of the methanolic extract was found to be higher than that of the dichloromethane and hexane extracts. The IC50 value for DPPH of methanolic extract was found to be 0.041 mg·mL⁻¹. Our findings showed that C. aegyptiaca is an important source of physiologically active compounds.     

Degrees-Of-Freedom in Multi-Cloud Based Sectored Cellular Networks

This paper investigates the achievable per-user degrees-of-freedom (DoF) in multi-cloud based sectored hexagonal cellular networks (M-CRAN) at uplink. The network consists of N base stations (BS) and K≤N base band unit pools (BBUP), which function as independent cloud centers. The communication between BSs and BBUPs occurs by means of finite-capacity fronthaul links of capacities CF=μF·12log(1+P) with P denoting transmit power. In the system model, BBUPs have limited processing capacity CBBU=μBBU·12log(1+P). We propose two different achievability schemes based on dividing the network into non-interfering parallelogram and hexagonal clusters, respectively. The minimum number of users in a cluster is determined by the ratio of BBUPs to BSs, r=K/N. Both of the parallelogram and hexagonal schemes are based on practically implementable beamforming and adapt the way of forming clusters to the sectorization of the cells. Proposed coding schemes improve the sum-rate over naive approaches that ignore cell sectorization, both at finite signal-to-noise ratio (SNR) and in the high-SNR limit. We derive a lower bound on per-user DoF which is a function of μBBU, μF, and r. We show that cut-set bound are attained for several cases, the achievability gap between lower and cut-set bounds decreases with the inverse of BBUP-BS ratio 1r for μF≤2M irrespective of μBBU, and that per-user DoF achieved through hexagonal clustering can not exceed the per-user DoF of parallelogram clustering for any value of μBBU and r as long as μF≤2M. Since the achievability gap decreases with inverse of the BBUP-BS ratio for small and moderate fronthaul capacities, the cut-set bound is almost achieved even for small cluster sizes for this range of fronthaul capacities. For higher fronthaul capacities, the achievability gap is not always tight but decreases with processing capacity. However, the cut-set bound, e.g., at 5M6, can be achieved with a moderate clustering size.     

Synthetic utilization of polynitroaromatic compounds. 2. Synthesis Of 4,6-dinitro-1,2-benzisothiazol-3-ones and 4,6-dinitro-1, 2-benzisothiazoles from 2-benzylthio-4,6-dinitrobenzamides

Cyclization of 2-benzylthio-4,6-dinitrobenzamides to 4,6-dinitro-1, 2-benzisothiazol-3-ones was achieved using SO(2)Cl(2) in CH(2)Cl(2) at room temperature. Alkylation of these heterocycles proceeded in a nonregioselective manner to yield a mixture of corresponding O- and N-alkylated products. Oxidation of 4,6-dinitro-1,2-benzisothiazoles (50% H(2)O(2) in AcOH) afforded the corresponding S-oxides and S, S-dioxides, depending on oxidation conditions. Unexpectedly, oxidation of a 3-methoxy derivative resulted in ring opening with the formation of the corresponding sulfamide. Chlorination of these 4,6-dinitro-1,2-benzisothiazol-3-ones (PCl(5)-POCl(3)) gave the expected 3-chloroisothiazoles.     

An Extension of Polyak’s Theorem in a Hilbert Space

Let H be an infinite-dimensional real Hilbert space equipped with the scalar product (⋅,⋅) _H . Let us consider three linear bounded operators,

Synthesis of chiral chromenes from levoglucosenone

Levoglucosenone, an optically active α,β-unsaturated ketone available from cellulose, undergoes a stereoselective oxa-Michael-aldol domino reaction with 2-hydroxybenzaldehydes with the formation of optically active oxepino[4,5-b]chromen-1-ones. These compounds attacked by nucleophiles undergo recyclization to 4-substituted oxepino[3,4-b]chromen-11a-ols, while their oximes treated with SOCl₂ are converted to 3-cyano-2H-chromenes through the Beckmann fragmentation.