Synthesis of some new triamide derivatives via Ugi five-component reaction in aqueous solution

Triamide derivatives have been synthesized in good yields in a novel, one-pot, five-component, and efficient process by the reaction of Z-oxazolone, water, primary amines, aldehydes, isocyanides, in the presence of catalytic amount of KAl(SO₄)₂·12H₂O (alum) as a non-toxic, reusable, inexpensive, and easily available reagent via Ugi reaction in aqueous solution.     

A new two-point scheme for multiple roots of nonlinear equations

In most of the earlier research for multiple zeros, in order to obtain a new iteration function from the existing scheme, the usual practice is to make no change at the first substep. In this paper, we explore the idea that what are the advantages if the flexibility of choice is also given at the first substep. Therefore, we present a new two-point sixth-order scheme for multiple roots (m>1). The main advantages of our scheme over the existing schemes are flexibility at both substeps, simple body structure, smaller residual error, smaller error difference between two consecutive iterations, and smaller asymptotic error constant. The development of the scheme is based on midpoint formula and weight functions of two variables. We compare our methods with the existing methods of the same order with real-life applications as well as standard test problems. From the numerical results, we find that our methods can be considered as better alternates for the existing methods of the same order. Finally, dynamical study of the proposed schemes is presented that confirms the theoretical results.     

Scattering problem with nonlocal separable potential of rank-two: Application to statistical mechanics

In this paper, we present a formulation of statistical mechanics of a thermodynamic system consisting of free particles and independent correlated pairs interacting via nonlocal potential in terms of the scattering properties. Some quantum statistical properties such as energy, heat capacity, second virial coefficient, virial pressure and quantum correction of kinetic energy are described analytically. The difference between the resolvents of the interacting and free Hamiltonians, represented as , that is associated with particle correlations is used for the evaluation of the properties. The statistical properties are related to correlated states, when making a pole expansion of the analytically continued momentum matrix element of . The present work illustrates these relations for a three-dimensional nonlocal separable potential of rank-two.     

A sagittally focusing double‐multilayer monochromator for ultrafast X‐ray imaging applications

The development of a sagittally focusing double‐multilayer monochromator is reported, which produces a spatially extended wide‐bandpass X‐ray beam from an intense synchrotron bending‐magnet source at the Advanced Photon Source, for ultrafast X‐ray radiography and tomography applications. This monochromator consists of two W/B₄C multilayers with a 25 Å period coated on Si single‐crystal substrates. The second multilayer is mounted on a sagittally focusing bender, which can dynamically change the bending radius of the multilayer in order to condense and focus the beam to various points along the beamline. With this new apparatus, it becomes possible to adjust the X‐ray beam size to best match the area detector size and the object size to facilitate more efficient data collection using ultrafast X‐ray radiography and tomography.     

Singular solutions for the constant Q-curvature problem

This paper is devoted to the construction of weak solutions to the singular constant Q-curvature problem. We build on several tools developed in the last years. This is the first construction of singular metrics on closed manifolds of sufficiently large dimension with constant (positive) Q-curvature.     

Effect of sintering temperature and the particle size on the structural and magnetic properties of nanocrystalline Li0.5Fe2.5O4

Sintering temperature and particle size dependent structural and magnetic properties of lithium ferrite (Li_0.5Fe_2.5O₄) were synthesized and sintered at four different temperatures ranging from 875 to 1475 K in the step of 200 K. The sample sintered at 875 K was also treated for four different sintering times ranging from 4 to 16 h. Samples sintered at 1475 K have the cubic spinel structure with a small amount of α-Fe₂O₃ (hematite) and γ-Fe₂O₃ (maghemite). The samples sintered at≤1275 K do not show hematite and maghemite phases and the crystals form the single phase spinel structure with the cation ordering on octahedral sites. Particle size of lithium ferrite is in the range of 13-45 nm, and is depend on the sintering temperature and sintering time. The saturation magnetization increased from 45 to 76 emu/g and coercivity decreases from 151 to 139 Oe with an increase in particle size. Magnetization temperature curve recorded in ZFC and FC modes in an external magnetic field of 100 Oe. Typical blocking effects are observed below about 244 K. The dielectric constant increases with an increase in sintering temperature and particle size.     

Homo- and heteronuclear 2D NMR approaches to analyse a mixture of deuterated unlike/like stereoisomers using weakly ordering chiral liquid crystals

We describe several homo- and heteronuclear 2D NMR strategies dedicated to the analysis of anisotropic (2)H spectra of a mixture of dideuterated unlike/like stereoisomers with two remote stereogenic centers, using weakly orienting chiral liquid crystals. To this end, we propose various 2D correlation experiments, denoted "D(H)(n)D" or "D(H)(n)C" (with n=1, 2), that involve two heteronuclear polarization transfers of INEPT-type with one or two proton relays. The analytical expressions of correlation signals for four pulse sequences reported here were calculated using the product-operators formalism for spin I=1 and S=1/2. The features and advantages of each scheme are presented and discussed. The efficiency of these 2D sequences is illustrated using various deuterated model molecules, dissolved in organic solutions of polypeptides made of poly-gamma-benzyl-L-glutamate (PBLG) or poly-epsilon-carbobenzyloxy-L-lysine (PCBLL) and NMR numerical simulations.     

Efficient visible-light-induced photocatalytic degradation of MO on the Cr-nanocrystalline titania-S

In order to improve visible light photocatalytic activities of the nanometer TiO₂, a novel and efficient Cr,S-codoped TiO₂ (Cr-TiO₂-S) photocatalyst was prepared by precipitation-doping method. The crystalline structure, morphology, particle size, and chemical structure of Cr-TiO₂-S were characterized by X-ray diffraction (XRD), transmission electron microscopy (TEM), scanning electron microscopy (SEM), and Fourier transform infrared (FT-IR) techniques, respectively. Results indicate that the doping of Cr and S, cause absorption edge shifts to the visible light region (λ > 420 nm) compare to the pure TiO₂, reduces average size of the TiO₂ crystallites, enhances desired lattice distortion of Ti, promotes separation of photo-induced electron and hole pair, and thus improves pollutant decomposition under visible light irradiation. The photocatalytic activities of Cr-TiO₂-S nanoparticles were evaluated using the photodegradation of methyl orange (MO) as probe reaction under the irradiation of UV and visible light and it was observed that the Cr-TiO₂-S photocatalyst shows higher visible photocatalytic activity than the pure TiO₂. The optimal Cr-TiO₂-S concentration to obtain the highest photocatalytic activity was 5 mol% for both of Cr and S.     

Detection of corrosion beneath a paint layer by use of spectral polarization optical imaging

The spectral and polarization properties of scattered light were used to image corrosion beneath the surface of a painted aluminum plate. The quality of imaging of the corrosion on the metal surface was significantly enhanced by the spectral polarization optical imaging technique. Depolarization scattered light was used to detect and image corrosion beneath the paint layer.     

On some problems of Petrich concerning Bruck and Reilly semigroups

For an inverse semigroupS with its idempotents dually well-ordered, we prove thatS is isomorphic to the semigroup of all one-to-one partial right translations ofS. Also, we prove for a Bruck semigroupS=B(T, α) thatS isE-unitary if and only ifT isE-unitary and α is an idempotent pure homomorphism. Moreover, we characterize allE-unitary covers ofB(T, α), whereT is a finite chain of groups.