A solution of the DGLAP equation for gluon at low x

We obtain a solution of the DGLAP equation for the gluon at low x first by expanding the gluon in a Taylor series and then using the method of characteristics. We test its validity by comparing it with that of Glück, Reya and Vogt. The convergence criteria of the approximation used are also discussed. We also calculate εF ₂(x,Q)²/ε In Q ² using its approximate relations with the gluon distribution at low x. The predictions are then compared with the HERA data.     

Overtone spectroscopy of some benzaldehyde derivatives

Overtone spectrum of o, m and p-nitrobenzaldehydes and p-chlorobenzaldehyde has been studied in 2000–12000 cm⁻¹ region. Vibrational frequencies and anharmonicity constants for aryl as well as alkyl CH stretch vibrations have been determined. We have also determined the internuclear distances for the aryl CH bond in the different molecules. The small variation observed in these distances is an indication of the substitution effect. It is observed that in the case of p-disubstituted benzens, the shift in aryl CH bond is proportional to sum of the Hammet σ of the substituents. However in the case of o-disubstituted benzenes it is only 80% of the para-substituted shift.     

Microfluidic rheology of soft colloids above and below jamming

The rheology near jamming of a suspension of soft colloidal spheres is studied using a custom microfluidic rheometer that provides the stress versus strain rate over many decades. We find non-Newtonian behavior below the jamming concentration and yield-stress behavior above it. The data may be collapsed onto two branches with critical scaling exponents that agree with expectations based on Hertzian contacts and viscous drag. These results support the conclusion that jamming is similar to a critical phase transition, but with interaction-dependent exponents.     

Multiple ionization of argon in coincidence with projectile ions in 60–120 MeV Si q+-Ar collisions

A projectile ion-recoil ion coincidence technique has been employed to study the multiple ionization and the charge transfer processes in collisions of 60–120 MeV Si ^q+ (q = 4−14) ions with neutral argon atoms. The relative contribution of different ionization channels, namely; direct ionization, electron capture and electron loss leading to the production of slow moving multiply charged argon recoil ions have been investigated. The data reported on the present collision system result from a direct measurement in the considered impact energy for the first time. The total ionization cross-sections for the recoil ions are shown to scale as q ^1.7/E _p ^0.5 , where E _p is the energy in MeV of the projectile and q its charge state. The recoil fractions for the cases of total- and direct ionizations are found to decrease with increasing recoil charge state j. The total ionization fractions of the recoils are seen to depend on q and to show the presence of a ‘shell-effect’ of the target. Further, the fractions are found to vary as 1/j ² upto j = 8+. The average recoil charge state 〈j〉 increases slowly with q and with the number of lost or captured electrons from or into the projectile respectively. The projectile charge changing cross-sections σ _qq′ are found to decrease with increasing q for loss ionization and to increase with q for direct-and capture ionization processes respectively. The physics behind various scaling rules that are found to follow our data for different ionization processes is reviewed and discussed.     

Salen-type compounds of calcium and strontium

Salen complexes of the heavy alkaline-earth metals, calcium and strontium, were prepared by the reaction of various salen(t-Bu)H(2) ligands with the metals in ethanol. Six new calcium and strontium compounds, [Ca(salen(t-Bu))(HOEt)(2)(thf)] (1), [Ca(salen(t-Bu))(HOEt)(2)] (2), [Ca(salpen(t-Bu))(HOEt)(3)] (3), [Ca(salophen(t-Bu))(HOEt)(thf)] (4), [Sr(salen(t-Bu))(HOEt)(3)] (5), and [Sr(salophen(t-Bu))(HOEt)(thf)(2)] (6), were formed in this way with the quatridentate Schiff-base ligands N,N'-bis(3,5-di-tert-butylsalicylidene)ethylenediamine (salen(t-Bu)H(2)), N,N'-bis(3,5-di-tert-butylsalicylidene)-1,3-propanediamine (salpen(t-Bu)H(2)), and N,N'-o-phenylenebis(3,5-di-tert-butylsalicylideneimine (salophen(t-Bu)H(2)). Initially, ammonia solutions of the metals were combined with the salen(t-Bu)H(2) ligands, and in the reaction of strontium with salen(t-Bu)H(2), the unusual tetrametallic cluster [(OC(6)H(2)(t-Bu)(2)CHN(CH(2))(2)NH(2))Sr(mu(3)-salean(t-Bu)H(2))Sr(mu(3)-OH)](2) (7) was produced (salean(t-Bu)H(4) = N,N'-bis(3,5-di-tert-butyl-2-hydroxybenzyl)ethylenediamine). In this compound, the imine bonds of the salen(t-Bu)H(2) ligand were reduced to form the known ligands salean(t-Bu)H(4) and (HO)C(6)H(2)(t-Bu)(2)CHN(CH(2))(2)NH(2). Compounds 1, 5, 6, and 7 were structurally characterized by single-crystal X-ray diffraction. Crystal data for 1 (C(44)H(74)CaN(2)O(6)): triclinic space group P(-)1, a = 8.3730(10) A, b = 14.8010(10) A, c = 18.756(2) A, alpha = 72.551(10) degrees, beta = 81.795(10) degrees, gamma = 78.031(10) degrees, Z = 2. Crystal data for 5 (C(38)H(64)SrN(2)O(5)): monoclinic space group P2(1)/c, a = 23.634(3) A, b = 8.4660(10) A, c = 24.451(3) A, beta = 101.138(10) degrees, Z = 4. Crystal data for 6 (C(46)H(67)N(2)O(5)Sr): orthorhombic space group P2(1)2(1)2(1), a = 10.5590(2) A, b = 16.2070(3) A, c = 26.7620(6) A, Z = 4. Crystal data for 7 (C(98)H(156)N(8)O(8)Sr(4)): triclinic space group P(-)1, a = 14.667(1) A, b = 15.670(1) A, c = 18.594(2) A, alpha = 92.26(1) degrees, beta = 111.84(1) degrees, gamma = 117.12(1) degrees, Z = 4.     

Microwave absorption studies of MgB2 superconductor

Microwave absorption studies have been carried out on MgB₂ superconductor using a standard X-band EPR spectrometer. The modulated low-field microwave absorption signals recorded for polycrystalline (grain size ∼ 10 μm) samples suggested the absence of weak-link character. The field dependent direct microwave absorption has been found to obey a ✓H dependence with two different slopes, which indicated a transition from strongly pinned lattice to flux flow regime.     

Effect of substrate temperature on electrical and magnetic properties of epitaxial La1−x Pb x MnO3 films

Epitaxial La_1−x Pb _x MnO₃ (LPMO) thin films, grown on (100) SrTiO₃ substrates by laser ablation technique at different temperatures between 600 and 850°C, have been characterized for electrical and magnetic properties. The temperature dependence of resistivity showed that the metal-insulator transition temperature (T _MI) decreases with increasing substrate temperature, which has been attributed to decrease in Pb content in the filsm. The YBa₂Cu₃O _x /La_1−x MnO₃ heterostructures, exhibiting both superconductivity and ferromagnetism, have been fabricated.     

Generalized Quivers for Locally Unipotent Rings

In this article, we generalize the definition of a Gabriel quiver in order to provide an analogous combinatorial object for the study of certain locally Artinian rings. We are then able to extend Gabriel's Theorem to locally unipotent rings whose generalized left and right quivers are trees.