Monotonicity of the matrix geometric mean

An attractive candidate for the geometric mean of m positive definite matrices A ₁, . . . , A _m is their Riemannian barycentre G. One of its important operator theoretic properties, monotonicity in the m arguments, has been established recently by Lawson and Lim. We give an elementary proof of this property using standard matrix analysis and some counting arguments. We derive some new inequalities for G. One of these says that, for any unitarily invariant norm, ||| G ||| is not bigger than the geometric mean of |||A ₁|||, . . . , |||A _m |||.     

Charge transfer excitations in cofacial fullerene-porphyrin complexes

Porphyrin and fullerene donor-acceptor complexes have been extensively studied for their photo-induced charge transfer characteristics. We present the electronic structure of ground states and a few charge transfer excited states of four cofacial porphyrin-fullerene molecular constructs studied using density functional theory at the all-electron level using large polarized basis sets. The donors are base and Zn-tetraphenyl porphyrins and the acceptor molecules are C(60) and C(70). The complexes reported here are non-bonded with a face-to-face distance between the porphyrin and the fullerene of 2.7 to 3.0 A?. The energies of the low lying excited states including charge transfer states calculated using our recent excited state method are in good agreement with available experimental values. We find that replacing C(60) by C(70) in a given dyad may increase the lowest charge transfer excitation energy by about 0.27 eV. Variation of donor in these complexes has marginal effect on the lowest charge transfer excitation energy. The interfacial dipole moments and lowest charge transfer states are studied as a function of face-to-face distance.     

An economical synthesis of dibenzocyclamnickel(II) and a metal-free macrocycle with tetramethyl substituents

The cationic dibenzocyclamnickel(II) complex, [Ni(Me₄Bzo₂[14]aneN₄)]²⁺, was obtained in good yield by Fe/HCl reduction of the corresponding tetraazaannulene complex [Ni(Me₄taa)], (1) {Me₄Bzo₂[14]aneN₄ = 5,7,12,14-tetramethyldibenzo[b,i]-1,4,8,11-tetraazacyclotetradecane; Me₄taa = 5,7,12,14-tetramethyldibenzo[b,i]-1,4,8,11-tetraazaannulene(2-)}. The orange–red product was isolated as the chloride (2) and perchlorate (3) salts. Analogous reduction with Zn/HCl yielded a diprotonated silky-white product [Ni(Me₄Bzo₂[14]aneN₄-H₂)][ZnCl₄]₂, (4). In the dry state, complex (4) is stable only under an HCl atmosphere and readily dissociates to give a solution of (2) when dissolved in polar solvents. Complexes (2) and (3), upon treatment with an excess of aqueous NaCN, undergo facile demetallation yielding the metal free macrocycle Me₄Bzo₂[14]aneN₄, (5). These compounds were characterized using a combination of i.r., u.v.–vis., ¹H-n.m.r., mass spectroscopy and voltammetry techniques. Unlike the parent tetraazaannulene complex (1), the reduced macrocycle complex, [Ni(Me₄Bzo₂[14]aneN₄)]²⁺ exhibits mild catalytic activity towards electro-reduction of CO₂ in MeCN solution.     

Positive Definite Functions and Operator Inequalities

We construct several examples of positive definite functions,and use the positive definite matrices arising from them toderive several inequalities for norms of operators. 1991 MathematicsSubject Classification 42A82, 47A63, 15A45, 15A60.     

More Operator Versions of the Schwarz Inequality

Some new operator versions of the Schwarz inequality are obtained. One of them is a counterpart of the variance-covariance inequality in the context of noncommutative probability. Received: 14 April 2000 / Accepted: 10 May 2000     

Salt‐Induced Depression of Lower Critical Solution Temperature in a Surface‐Grafted Neutral Thermoresponsive Polymer

Summary: Quartz crystal microbalance with dissipation monitoring (QCM‐D) is employed to determine the effect of salt on the volume phase transition of thermoresponsive polymer brushes. Changes in mass and viscoelasticity of poly(N‐isopropylacrylamide) (PNIPAM) layers grafted from a QCM‐D crystal are measured as a function of temperature, upon contact with aqueous solutions of varying salt concentrations. The phase‐transition temperature of PNIPAM brushes, T_C,graft, quantified from the QCM‐D measurements is found to decrease as the concentration of salt is increased. This phenomenon is explained by the tendency of salt ions to affect the structure of water molecules (Hofmeister effect). However, in contrast to the linear decrease in phase‐transition temperature upon increasing salt concentration observed for free PNIPAM, the trend in T_C,graft for PNIPAM brushes is distinctively non‐linear.

Schematic representation of the effect of salt concentration on the phase transition behavior of thermoresponsive polymer brushes.     

Additive-free Aqueous Dispersions of Two-Dimensional Materials with Glial Cell Compatibility and Enzymatic Degradability

Water-dispersible two-dimensional (2D) materials are desirable for diverse applications. Aqueous dispersions make processing safer and greener and enable evaluation of these materials on biological and environmental fronts. To evaluate the effects of 2D materials with biological systems, obtaining dispersions without additives is critical and has been a challenge. Herein, a method was developed for obtaining additive-free aqueous dispersions of 2D materials like transition metal dichalcogenides and hexagonal boron nitride (h-BN). The nanosheet dispersions were investigated through spectroscopic and microscopic methods, along with the role of size on stability. The aqueous media enabled investigations on cytocompatibility and enzymatic degradation of molybdenum disulphide (MoS₂) and h-BN. Cytocompatibility with mixed glial cells was observed up to concentrations of 100 μg mL⁻¹, suggesting their plausible usage in bioelectronics. Besides, biodegradation using human myeloperoxidase (hMPO) mediated catalysis was investigated through Raman spectroscopy and electron microscopy. The findings suggested that additive-free 2H-MoS₂ and h-BN were degradable by hMPO, with 2H-phase exhibiting better resistance to degradation than the 1T-phase, while h-BN exhibited slower degradation. The findings pave a path for incorporating 2D materials in the burgeoning field of transient bioelectronics.     

Novel Inhibitors of Nicotinamide-N-Methyltransferase for the Treatment of Metabolic Disorders

Nicotinamide-N-methyltransferase (NNMT) is a cytosolic enzyme catalyzing the transfer of a methyl group from S-adenosyl-methionine (SAM) to nicotinamide (Nam). It is expressed in many tissues including the liver, adipose tissue, and skeletal muscle. Its expression in several cancer cell lines has been widely discussed in the literature, and recent work established a link between NNMT expression and metabolic diseases. Here we describe our approach to identify potent small molecule inhibitors of NNMT featuring different binding modes as elucidated by X-ray crystallographic studies.     

A meglumine catalyst–based synthesis,molecular docking,and antioxidant studies of dihydropyrano[3, 2-b]chromenedione derivatives

A simple method was employed for the synthesis of dihydropyrano[3, 2-b]chromenedione derivatives ( 4a-o) in high yields by condensation of 5, 5-dimethylcyclohexane-1, 3-dione( 1 ), different aromatic aldehydes ( 2a-o ), and 5-hydroxy-2-(hydroxymethyl)-4H-pyran-4-one( 3 ), using meglumine as a stable and reusable catalyst. Meglumine, an amino sugar, was employed as an environmentally benign catalyst, due to its splendid properties such as being inexpensive, recyclable, and biodegradable. The accomplished protocol employs low catalyst loading and easy work-up for the synthesis of 5-hydroxy-2-(hydroxymethyl)-4H-pyran-4-one derivatives. A great asset is that without any significant loss, the catalyst could be recovered and reused for extended synthetic steps. This offer huge advantage to overcome recyclability issues. Our synthesized compounds were analyzed by IR, ¹H, ¹³C NMR, mass spectra and evaluated for their antioxidant properties by 1, 1-diphenyl-2-picryl hydrazyl radical (DPPH), hydrogen peroxide(H₂O₂), and nitric oxide (NO) scavenging methods. The correlation in exhibition of antioxidant activity was effective at all doses. The binding interactions and molecular docking studies for entitled compounds were studied against 3MNG protein; 4k exhibited marked binding affinity with excellent docking score of −7.6 Kcal/mol and emerged as a lead compound.