Some comments on fuzzy variables

Nahmias introduced the concept of a fuzzy variable as a possible axiomatic framework from which a rigorous theory of fuzziness may be constructed. In this paper we attempt to shed more light on fuzzy variables in analogy with random variables. In particular, we study the problem: if X₁, X₂,…,X_n are mutually unrelated fuzzy variables with common membership function μ and α₁, α₂,…,α_n are real numbers satisfying α_i ? o for every i and Σ_i=1ⁿα_i=1, when does does Z = Σ_{i = 1}ⁿα_iX_i have the same membership function μ?     

The linear response of a one-dimensional electron gas

A not widely used method is employed to calculate the static dielectric function of an electron gas. A specific calculation is presented for a one- dimensional electron system surrounded by a medium of dielectric constant ?₀. The asymptotic, oscillatory, two-body interaction decays more slowly than in the three-dimensional case.     

Some properties of an electron gas in a quantizing magnetic field

The electron gas neutralized by a rigid positive background and in a quantizing magnetic field, is studied in a ‘quasi-classical’ model previously proposed by the author and collaborators. The plasma oscillation of the electron gas shows an acoustic-type dispersion for small wave vector. The potential behind an ion moving along the direction of the magnetic field is calculated and is found to have a sinusoidal behaviour. Some consequences of this potential are pointed out. The energy loss by a moving charge in the electron gas is shown to exhibit some interesting properties. Other quantities such as light scattering and magneto-acoustic oscillations are also discussed. A derivation is given for a ‘quasi-classical’ linear response in the finite relaxation time approximation.     

Migratory insertion of [B(C6F5)2] into C-H bonds: CO promoted transfer of the boryl fragment

The reaction of (eta(5)-C5H5)Fe(CO)2B(C6F5)2 with CO has been shown to proceed via ligand substitution at the metal with accompanying transfer of the boryl fragment (via C-H insertion) to the Cp ring, thereby generating the zwitterion [eta(5)-C5H4B(C6F5)2H]Fe(CO)3 in quantitative yield.     

<Emphasis Type="Italic">In situ</Emphasis> Oxidation of phenol and <Emphasis Type="Italic">o</Emphasis>-aminophenol in the channels of 3d-supramolecular coordination polymers

The host attractive properties of supramolecular coordination polymers of the type _￥³ _\infty^3 [(R₃Sn)₃FeIII(CN)₆], where R = methyl (I), n-butyl (II), and phenyl (III), afford the ability to be used as effective oxidizing reagents for phenol and o-aminophenol forming new host-guest supramolecular coordination polymers. Phenol was oxidized to 1,4-benzoquinone while o-aminophenol was oxidized to poly-o-aminophenol by the polymers I and II and to 2-aminophenoxazin-3-one by the polymer III. The oxidation products were investigated by methods of spectroscopy and high-performance liquid chromatography. The redox reactions were characterized by first-order kinetics. Moreover, mechanisms of the oxidation processes of phenol and o-aminophenol have been proposed.     

Inverse subsemigroups of finite index in finitely generated inverse semigroups

We study some aspects of Schein’s theory of cosets for closed inverse subsemigroups of inverse semigroups. We establish an index formula for chains of subsemigroups, and an analogue of M. Hall’s Theorem on the number of cosets of a fixed finite index. We then investigate the relationships between the following properties of a closed inverse submonoid of an inverse monoid: having finite index; being a recognizable subset; being a rational subset; being finitely generated (as a closed inverse submonoid). A remarkable result of Margolis and Meakin shows that these properties are equivalent for a closed inverse submonoid of a free inverse monoid.     

Assessment of health risk associated with natural gamma dose rate levels and isodose mapping of Jordan

ABSTRACT

As a pioneering study in Jordan, an extensive measurement for external gamma dose rate (GDR) was conducted. A portable gamma radiation detector was used to perform these measurements at 1?m above the soil surface. A geographical positioning system Garmin was used to record a total of 823 measured points. The GDRs’ measurement ranged from 35 to 470?nGy?h^?1 giving a mean value of 90?nGy?h^?1, which was found to be one and half times higher than the world average of 59?nGy?h^?1. The lowest mean GDR 72?nGy?h^?1 was found in the Albalqa governate, while the highest mean GDR 131?nGy?h^?1 was found to be for the Alkarak governate. The mean annual effective dose was found to be 0.551?mSv, which is higher than the world average value of 0.48?mSv. This is a pivotal study evaluating the risks associated with GDR levels in Jordan that were the relative excess lifetime cancer risk, the mean collective effective dose, the mean weighted GDR and the mean lifetime dose that are 2.24?×?10^?3, 5538manSv?y^?1, 0.531?mSv and 39?mSv, respectively. The cosmic rays mean GDR was determined to be 20?nGy?h^?1. This study focuses on constructing GDRs’ baseline data in Jordan, which will be used to determine the possible change in the natural radiation due to other human activities in the future. ArcGIS software was employed to generate an isodose map to characterise exposure rates caused by GDR in Jordan.     

Synthesis and crystal structure of bis(4-methylpiperidine-dithiocarbamato-S,S′)-palladium(II)

The complex bis(4-methylpiperidine-dithiocarbamato-S,S′)-palladium(II) was synthesized by the reaction of 4-methyl-1-piperidine dithiocarbamic acid with palladium(II) chloride. Its structure was determined by X-ray crystal diffraction analysis. It crystallizes in the monoclinic P2₁/c space group with the crystal cell parameters a=8.6491(8) ?, b=18.7305(16) ?, c=11.9933(10) ?, β=107.074(1)°, V=1857.3(3) ?³ and Z=4. The palladium (II) ion is bonded to four sulfur atoms, belonging to two dithiocarbamate ligands, in a distorted square planar geometry. The X-ray data suggest a pronounced electronic delocalization in the two NCS₂ moieties.     

Synthesis, characterization, in vitro cytotoxicity and anti-inflammatory activity of palladium(II) complexes with tertiary phosphines and heterocyclic thiolates: Crystal structure of [PdC28H19N8PS2]

The new four-coordinated mononuclear palladium(II) complexes 1-9 with chelating heterocyclic thiolates and tertiary phosphines with general formula [Pd(L)_nCl(R′R₂P)] (L = Pym2SH (pyrimidine-2-thiolate), Pur6SH (purine-6-thiolate), Py2SH (pyridine-2-thiolate), R₃P = PPh₃, P(o-tolyl)₃, PPh₂Cl), n = 1, 2) have been synthesized by the direct reaction of [PdCl₂(R′R₂P)₂] with polyfunctional heterocyclic thiolates which display a wide variety of coordinations. These compounds were characterized by elemental analysis, FT-IR and multinuclear (¹H, ¹³C and ³¹P) NMR. The X-ray diffraction study of non-ionic compound 5 showed that the thiolate acts as unidentate and that the chelating (-N,S) ligand adopts a slightly distorted square planar geometry around the palladium atom. In vitro the anti-inflammatory inhibition of compounds 1-9 was 10-15% greater than that of the standard drug Declofenac. Compounds 1 and 4 showed mostly a moderate to low cytotoxicity against seven human tumor cell lines whereas compound 3 was somewhat more active.     

Advancing MXene Electrocatalysts for Energy Conversion Reactions: Surface,Stoichiometry, and Stability

MXenes, due to their tailorable chemistry and favourable physical properties, have great promise in electrocatalytic energy conversion reactions. To exploit fully their enormous potential, further advances specific to electrocatalysis revolving around their performance, stability, compositional discovery and synthesis are required. The most recent advances in these aspects are discussed in detail: surface functional and stoichiometric modifications which can improve performance, Pourbaix stability related to their electrocatalytic operating conditions, density functional theory and advances in machine learning for their discovery, and prospects in large scale synthesis and solution processing techniques to produce membrane electrode assemblies and integrated electrodes. This Review provides a perspective that is complemented by new density functional theory calculations which show how these recent advances in MXene material design are paving the way for effective electrocatalysts required for the transition to integrated renewable energy systems.