(Non-)expansivity in functional envelopes

We study expansivity in functional envelopes of dynamical systems. Our main result is that if the phase space of the original system contains an arc or if it contains a free infinite zero dimensional set, then the expansivity in the functional envelope with Hausdorff metric is impossible. This is in contrast with the fact that, when considering the uniform metric in functional envelopes, the expansivity of a system is equivalent with the expansivity of its functional envelope.     

Ab initio calculations of B<Subscript>2</Subscript> type RHg (R = Ce,Pr, Eu and Gd) intermetallic compounds

Spin polarized ab initio calculations have been carried out to study the structural, electronic, elastic and thermal properties of RHg (R = Ce, Pr, Eu and Gd) intermetallic compounds in B₂ structure. The calculations have been performed by using both generalized gradient approximation (GGA) and local spin density approximation (LSDA). The calculated value of lattice constant (a ₀) for these compounds with GGA is in better agreement with the experimental data than those with LSDA. Bulk modulus (B), first-order pressure derivative of bulk modulus and magnetic moment (μ _B ) are also presented. The energy band structure and electron density of states show the occupancy of 4f states for light as well as heavy rare earth atom. The elastic constants are predicted from which all the related mechanical properties like Poisson’s ratio (σ), Young’s modulus (E), shear modulus (G _H ) and anisotropy factor (A) are calculated. The ductility or brittleness of these compounds is predicted from Pugh’s rule (B/G _H ) and Cauchy pressure (C ₁₂ ? C ₄₄). The Debye temperature (θ _D ) is estimated from the average sound velocity, which have not been calculated and measured yet.     

A novel amino acid functionalized ionic liquid promoted one-pot solvent-free synthesis of 3,4-dihydropyrimidin-2-(1H)-thiones

An environmentally benign, cheap and reusable L-amino acid functionalized ionic liquid [L-AAIL]/AlCl₃ was found to be an effective catalyst for the synthesis of 3,4-dihydropyrimidine-2-(1H)-thione derivatives in good to excellent yield under solvent-free condition. Compared with the classical Biginelli reactions, this method consistently enjoys the advantages of mild reaction conditions, easy work-up, and short reaction time. These one-pot three-component Biginelli products could be separated easily from the catalyst–water system, and the catalyst could be reused at least five times without noticeably reducing catalytic activity.     

A “One Pot,” Environmentally Friendly,Multicomponent Synthesis of 2‐Amino‐5‐cyano‐4‐[(2‐aryl)‐1H‐indol‐3‐yl]‐6‐hydroxypyrimidines and Their Antimicrobial Activity

A series of multifunctional 2‐amino‐5‐cyano‐4‐[(2‐aryl)‐1H‐indol‐3‐yl]‐6‐hydroxypyrimidines ( 4a , 4b , 4c , 4d , 4e , 4f ) was synthesized by multicomponent reaction of 3‐formylindole ( 1 ), cyanoethylacetate ( 2 ), and guanidine hydrochloride ( 3 ) with NaOH by using green chemical techniques, viz. microwave irradiation and grindstone technology. The same reactants when refluxed in ethanol also gave titled compounds ( 4a , 4b , 4c , 4d , 4e , 4f ). Compared with conventional procedure, the reaction can be carried out under milder conditions, requiring a shorter reaction time and giving higher yields following the green chemistry methodology. All the synthesized compounds have been characterized on the basis of elemental analyses and spectral data (IR, ¹H NMR, ¹³C NMR, and mass). All synthesized compounds were also evaluated for their antimicrobial activity against nine pathogenic bacteria, antifungal activity against Rhizopus stolonifer, Aspergillus flavus, and Fusarium oxysporum and antibacterial activity against Escherichia coli and Pseudomonas aeruginosa at different concentrations. Most of the compounds showed mild to moderate activity.     

Helmholtz-pair transmit coil with integrated receive array for high-resolution MRI of trabecular bone in the distal tibia at 7T

A Helmholtz-pair local transmit RF coil with an integrated four-element receive array RF coil and foot immobilization platform was designed and constructed for imaging the distal tibia in a whole-body 7T MRI scanner. Simulations and measurements of the B(1) field distribution of the transmit coil are described, along with SAR considerations for operation at 7T. Results of imaging the trabecular bone of three volunteers at 1.5T, 3T and 7T are presented, using identical 1.5T and 3T versions of the 7T four-element receive array. The spatially registered images reveal improved visibility for individual trabeculae and show average gains in SNR of 2.8× and 4.9× for imaging at 7T compared to 3T and 1.5T, respectively. The results thus display an approximately linear dependence of SNR with field strength and enable the practical utility of 7T scanners for micro-MRI of trabecular bone.     

Magnetic resonance in amorphous FexNi80-xP14B6: II. Spin glass alloys

We report EPR measurements on amorphous Fe_xNi_80-xP₁₄B₆ alloys for concentrations less than that required for ferromagnetism. Measurements were made at microwave frequencies between 10 and 35 GHz and at temperatures between 2 and 150 K. We find i) at high temperatures the alloys are simple paramagnets with ? ≈ 2.14 and a relaxation rate (linewidth) increasing linearly with temperature, ii) the linewidth increases at low T and follows an empirical form proposed earlier, iii) as the temperature is decreased, the susceptibility (measured by reference to the line intensities) increases, iv) in order to account for the frequency dependence of the resonance field we must introduce an anisotropy energy with uniaxial symmetry; the “hard axis” being normal to the sample plane. The associated anisotropy constant K' appears at several times the spin glass transition temperature T_SG, v) at still lower temperatures ( < 2T_SG) another type of anisotropy field appears. The corresponding anisotropy energy is similar to that introduced to explain data on the reentrant alloys of this system and the archetypal spin glasses CuMn and AgMn and the anisotropy constant K has the same type of temperature dependence. However, the frequency dependence of K is different.     

Magnetization of amorphous alloys — Deviations from spin wave theory at low temperatures

Spin resonance measurements have been used to obtain the temperature dependence of the magnetization in (Fe_xNi_1?x)₇₅P₁₆B₆A?₃ alloys for 4 ? T ? 300K. With x = 0.5, spin wave theory is adequate to account for the observations. For x = 0.4 and 0.3 marked deviations from $\text{T}{}^{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ behavior are noted below ～ 70K and we propose a simple model to account for these deviations.     

Magnetic phases of amorphous transition metal-metalloid alloys

Hysteresis loop and ac susceptibility measurements were performed on three series of amorphous alloys: (A_wB_1-w)₇₅P₁₆B₆Al₃, where (A, B) are (Fe, Ni), (Co, Ni) and (Fe, Mn). Upon cooling, low w alloys undergo paramagne t to spin glass transitions. Alloys with higher w first experience a Curie transition to a ferromagnetic state, and then a spin freezing transition to a spin glass state. the T dependence of the width of the ac hysteresis loop is used to determine the spin freezing transition temperature. A magnetic phase diagram is presented for each alloy series and the value of w required for ferromagnetism, w_C, is determined. When measured in the presence of small constant fields, the ac susceptibility of alloys with w just above w_C has maxima near both transition temperatures. The field and temperature dependences of the peaks are explained by scaling arguments, used to determine the critical exponent δ for the Curie transition, and suggest that a similar scaling law holds for the ferromagnet to spin glass transition.     

Evidence for correlation effects: −√T behaviour in the low temperature electrical resistance of disordered metals

It is found that the electrical resistance for several metal-metalloid amorphous alloys decreases with increasing temperature as ?√T from about 20 mK to several K. The form and magnitude of this temperature dependence is in agreement with recent predictions from interaction theories.