Noncrossing Partitions, Catalan Words, and the Semicircle Law

As is well known, the joint limit distribution of independent Wigner matrices is free with the marginals being semicircular. This freeness is intimately tied to noncrossing pair partitions or, equivalently what are known as Catalan words, each of which contributes one to the limit moments. We investigate the following questions. Consider a sequence of patterned matrices: (i) When do only Catalan words contribute (one), so that we get the semicircle limit? (ii) When does each Catalan word contribute one (with possible nonzero contribution from non-Catalan words)? (iii) For what matrix models do Catalan words not necessarily contribute one each and non-semicircle limits arise, even when non-Catalan words have zero contribution? In particular we show that in a general sense, the semicircle law serves as a lower bound for possible limits. Further, there is a large class of non-Wigner matrices whose limit is the semicircle. This may be viewed as robustness of the semicircle law. Similarly, there is a large class of block matrices whose limit is not semicircular.     

Chronology and characteristics of groundwater along the United Arab Emirates-Oman arid region: a guide for regional sustainability

Journal of Radioanalytical and Nuclear Chemistry - Estimating groundwater recharge rate is essential for water sustainability of the arid region of the United Arab Emirates that receives most...     

Diethyldisulfoammonium chlorometallates as heterogeneous Brønsted–Lewis acidic catalysts for one‐pot synthesis of 14‐aryl‐7‐(N‐phenyl)‐14H‐dibenzo[a,j]acridines

A new series of Brønsted–Lewis acidic diethyldisulfoammonium chlorometallates, [DEDSA][FeCl₄] and [DEDSA]₂[Zn₂Cl₆], were synthesized as solid materials from the reaction of [(Et)₂N(SO₃H)₂][Cl] ionic liquid with transition metal chlorides (FeCl₃ and ZnCl₂) at 80 °C in neat condition for 2 h. The chlorometallates were fully characterized using various spectroscopic and analytical techniques such as Fourier transform infrared, UV–visible and Raman spectroscopies, powder X‐ray diffraction, scanning electron microscopy, energy‐dispersive X‐ray and thermogravimetric analyses, Hammett acidity and elemental analyses. Their catalytic activity was studied as reusable heterogeneous catalysts for the three‐component synthesis of novel 14‐aryl‐7‐(N‐phenyl)‐14H‐dibenzo[a,j]acridines under solvent‐free conditions at 100 °C.     

Measurement of natural radioactivity concentrations and chemical composition of coal and its post-combustion residues in KSA

Journal of Radioanalytical and Nuclear Chemistry - The variable values of 226Ra, 228Ra and 40K were identified in coal and coal combustion residuals (CCR) samples to redistribute radionuclides...     

A Review on Obesity Management through Natural Compounds and a Green Nanomedicine-Based Approach

Obesity is a serious health complication in almost every corner of the world. Excessive weight gain results in the onset of several other health issues such as type II diabetes, cancer, respiratory diseases, musculoskeletal disorders (especially osteoarthritis), and cardiovascular diseases. As allopathic medications and derived pharmaceuticals are partially successful in overcoming this health complication, there is an incessant need to develop new alternative anti-obesity strategies with long term efficacy and less side effects. Plants harbor secondary metabolites such as phenolics, flavonoids, terpenoids and other specific compounds that have been shown to have effective anti-obesity properties. Nanoencapsulation of these secondary metabolites enhances the anti-obesity efficacy of these natural compounds due to their speculated property of target specificity and enhanced efficiency. These nanoencapsulated and naive secondary metabolites show anti-obesity properties mainly by inhibiting the lipid and carbohydrate metabolizing enzymes, suppression of adipogenesis and appetite, and enhancing energy metabolism. This review focuses on the plants and their secondary metabolites, along with their nanoencapsulation, that have anti-obesity effects, with their possible acting mechanisms, for better human health.     

Radiation (60Co)-Induced Graft Copolymerization of Acrylamide on Jute Fiber

The radiation induced graft copolymerization of acrylamide onto jute fibers was studied following preirradiation of jute in air using a⁶⁰Co source of γ-radiation and subsequent polymerization of acrylamide in a limited aqueous system under nitrogen at 607°C. An increase of the time of preirradiation (at a fixed dose rate) increased the percent grafting measurably and the grafting efficiency marginall Grafting effects showed further improvement on addition of Fe²⁺ or Co²⁺ ions to the system prior to the polymerization step. Increasing the concentration of Fe²⁺ or Co²⁺ ion led to an increase in the grafting parameters with a leveling off effect in the higher concentration range, however. An increase in the polymer (jute) content for a fixed monomer content produced a significant increase in the efficiency of grafting, while % grafting followed a slowly decreasing trend.     

Mechanistic aspects of ligand substitution on <Emphasis Type="Italic">cis</Emphasis>-diaqua(<Emphasis Type="Italic">cis</Emphasis>-1,2-diaminocyclohexane)platinum(II) by Glycine-<Emphasis Type="SmallCaps">l</Emphasis>-Leucine

The kinetics of the interaction of glycine-l-leucine (Glyleu) with cis-[Pt(cis-dach)(OH₂)₂]²⁺ (dach = 1,2-diaminocyclohexane) has been studied spectrophotometrically as a function of [cis-[Pt(cis-dach)(OH₂)₂]²⁺], [Glyleu] and temperature at pH 4.0, where the complex exists predominantly as the diaqua species and Glyleu as a zwitterion. The substitution reaction shows two consecutive steps: the first is the ligand-assisted anation and the second is the chelation step. The activation parameters for both the steps were evaluated using Eyring’s equation. The low ∆H₁^≠ (51.9 ± 2.8 kJmol⁻¹) and large negative value of ∆S₁^≠ (−152 ± 8 JK⁻¹mol⁻¹) as well as ∆H₂^≠ (54.4 ± 1.7 kJmol⁻¹) and ∆S₂^≠ (−162 ± 5 JK⁻¹mol⁻¹) indicate an associative mode of activation for both the aqua ligand substitution processes.     

Kinetics and mechanism of the reaction of hydroxopentaaquarhodium(III) ion with <Emphasis Type="SmallCaps">l</Emphasis>-Arginine in aqueous solution

The kinetics of the aqua ligand substitution from hydroxopentaaquarhodium(III) ion, [Rh(H₂O)₅(OH)]²⁺, by l-Arginine has been studied spectrophotometrically as a function of Arginine concentration, and temperature, at pH 4.3. The reaction proceeds via a rapid outer sphere association complex formation step followed by two consecutive steps. The first of these involves ligand-assisted anation, while the second involves chelation as the second aqua ligand is displaced. The association equilibrium constant for the outer sphere complex formation has been evaluated together with the rate constants for the two subsequent steps. The activation parameters for both steps have been evaluated using Eyring’s equation. Thermodynamic parameters calculated from the temperature dependence of the outer sphere association equilibrium constants are also consistent with an associative mode of activation. The product of the reaction has been characterized by conductivity measurement and IR spectroscopic analysis.     

Kinetic and mechanistic studies on the reaction of thiosemicarbazide with [(H<Subscript>2</Subscript>O)(tap)<Subscript>2</Subscript>RuORu(tap)<Subscript>2</Subscript>(H<Subscript>2</Subscript>O)]<Superscript>2+</Superscript> {tap = 2-(m-tolylazo)pyridine}

The interaction of thiosemicarbazide with the title complex has been studied spectrophotometrically in aqueous medium as a function of [complex], [thiosemicarbazide], pH and temperature at constant ionic strength. At pH 7.4, the reaction shows two distinct paths; both of which are [thiosemicarbazide] dependent. A parallel reaction scheme fits well with the experimental findings. An associative interchange mechanism is proposed for both the paths; the activation parameters calculated from Eyring plots are ΔH₁^≠ = 14.2 ± 0.8 kJ mol⁻¹, ΔS₁^≠ = −241 ± 2 JK⁻¹ mol⁻¹, ΔH₂^≠ = 30.8 ± 1.4 kJ mol⁻¹ and ΔS₂^≠ = −236 ± 4 JK⁻¹ mol⁻¹. From the temperature dependence of the outer sphere association complex equilibrium constants, the thermodynamic parameters calculated are ΔH₁^° = 34.25 ± 1.9 kJ mol⁻¹, ΔS₁^° = 146 ± 6 J K⁻¹ mol⁻¹ and ΔH₂^° = 9.4 ± 1.1 kJ mol⁻¹, ΔS₂^° = 71 ± 3 JK⁻¹ mol⁻¹, which gives a negative ΔG° at all temperatures studied, supporting the spontaneous formation of an outer sphere association complex.     

Mapping the Transformation [{RuII(CO)3Cl2}2]→[RuI2(CO)4]2+: Implications in Binuclear Water–Gas Shift Chemistry

The complete sequence of reactions in the base‐promoted reduction of [{Ru^II(CO)₃Cl₂}₂] to [Ru^I₂(CO)₄]²⁺ has been unraveled. Several μ‐OH, μ:κ²‐CO₂H‐bridged diruthenium(II) complexes have been synthesized; they are the direct results of the nucleophilic activation of metal‐coordinated carbonyls by hydroxides. The isolated compounds are [Ru₂(CO)₄(μ:κ²‐C,O‐CO₂H)₂(μ‐OH)(NP^F‐Am)₂][PF₆] ( 1 ; NP^F‐Am=2‐amino‐5,7‐trifluoromethyl‐1,8‐naphthyridine) and [Ru₂(CO)₄(μ:κ²‐C,O‐CO₂H)(μ‐OH)(NP‐Me₂)₂][BF₄]₂ ( 2 ), secured by the applications of naphthyridine derivatives. In the absence of any capping ligand, a tetranuclear complex [Ru₄(CO)₈(H₂O)₂(μ³‐OH)₂(μ:κ²‐C,O‐CO₂H)₄][CF₃SO₃]₂ ( 3 ) is isolated. The bridging hydroxido ligand in 1 is readily replaced by a π‐donor chlorido ligand, which results in [Ru₂(CO)₄(μ:κ²‐C,O‐CO₂H)₂(μ‐Cl)(NP‐PhOMe)₂][BF₄] ( 4 ). The production of [Ru₂(CO)₄]²⁺ has been attributed to the thermally induced decarboxylation of a bis(hydroxycarbonyl)–diruthenium(II) complex to a dihydrido–diruthenium(II) species, followed by dinuclear reductive elimination of molecular hydrogen with the concomitant formation of the Ru^I? Ru^I single bond. This work was originally instituted to find a reliable synthetic protocol for the [Ru₂(CO)₄(CH₃CN)₆]²⁺ precursor. It is herein prescribed that at least four equivalents of base, complete removal of chlorido ligands by Tl^I salts, and heating at reflux in acetonitrile for a period of four hours are the conditions for the optimal conversion. Premature quenching of the reaction resulted in the isolation of a trinuclear Ru^I₂Ru^II complex [{Ru(NP‐Am)₂(CO)}{Ru₂(NP‐Am)₂(CO)₂(μ‐CO)₂}(μ₃:κ³‐C,O,O′‐CO₂)][BF₄]₂ ( 6 ). These unprecedented diruthenium compounds are the dinuclear congeners of the water–gas shift (WGS) intermediates. The possibility of a dinuclear pathway eliminates the inherent contradiction of pH demands in the WGS catalytic cycle in an alkaline medium. A cooperative binuclear elimination could be a viable route for hydrogen production in WGS chemistry.