Direct Resolution of Six Beta Blockers into their Enantiomers on Silica Plates Impregnated with l-Asp and l-Glu

JPC – Journal of Planar Chromatography – Modern TLC - Resolution of racemic metoprolol, propranolol, carvedilol, bisoprolol, salbutamol, and labetalol, commonly used ß-blockers,...     

Floquet theory and stability of nonlinear integro-differential equations

Summary One of the classical topics in the qualitative theory of differential equations is the Floquet theory. It provides a means to represent solutions and helps in particular for stability analysis. In this paper first we shall study Floquet theory for integro-differential equations (IDE), and then employ it to address stability problems for linear and nonlinear equations.     

Lines Avoiding Unit Balls in Three Dimensions

Let B be a set of n unit balls in ℝ³. We show that the combinatorial complexity of the space of lines in ℝ³ that avoid all the balls of B is O(n^3+ε), for any ε > 0. This result has connections to problems in visibility, ray shooting, motion planning, and geometric optimization.     

Electrical and thermal properties of bulk superconductors Eu0.95Pr0.05Ba2(Cu1−xMx)3O7−δ (M = Fe,Ni, Zn and Mn)

Measurements of transition temperature, magneto-resistance, thermal conductivity, thermo-electric power and specific heat have been carried out on co-doped samples of Eu_0.95Pr_0.05Ba₂(Cu_1?xM_x)₃O_7?δ (M = Fe, Ni, Zn and Mn) compounds. It is found that all samples exhibit metallic behavior, except the co-doped sample of Fe that shows semiconducting behavior. It is seen that the upper-critical field H_c2 decreases with Pr-doping. However, an increase in H_c2 for dopants like Fe and Mn is observed. Thermal conductivity for the pristine sample of EuBa₂Cu₃O_7?δ (Eu-123) exhibits a pronounced hump below the superconducting transition temperature T_C. However, the peak height of the hump decreases with Pr-doping and such a feature is further suppressed in the co-doped samples. The negative sign of the measured thermo-electric power of Eu-123 indicates that the dominant carrier in this sample is electron-like, whereas it turns to hole-like for all of the doped samples. A jump in specific heat C_P is detected in the pure sample of Eu-123 at T_C, while only a change in slope in C_P is seen around the transition temperature in the Pr-doped sample.     

Nonlinear Boundary Value Problems on Semi-Infinite Intervals using Weighted Spaces: An Upper and Lower Solution Approach

This paper presents a lower and upper solution approach for singular second order boundary value problems on the half line and establishes the existence of positive, unbounded and monotone solutions. The project is supported by the fund of National Natural Science(10571111) and the fund of Natural Science of Shandong Province(Y2005A07).     

Existence of Solutions to a Singular Initial Value Problem

Under the sign assumptions we investigate the global existence of solutions of the initial value problem x＇ =f（t, x, x＇）, x（0） = A, where the scalar function f（t, x,p） may be singular at x = A.     

Observation of dielectric relaxation modes in chiral smectic C liquid crystal mixture

The dielectric parameters in the frequency range 50 Hz to 1 MHz have been measured in a SmC* liquid crystal mixture in planar alignment. The relaxation frequency (f_r), distribution parameter (α) and dielectric strength (δε) have been evaluated and their corresponding values were found to be 206.62 Hz, 0.06 and 114.6 respectively. The Goldstone mode, domain mode, soft mode and a new relaxation mode have been observed.     

Covalent Hypercoordination: Can Carbon Bind Five Methyl Ligands?

C(CH₃)₅⁺ is the first reported example of a five‐coordinate carbon atom bound only to separate (that is, monodentate) carbon ligands. This species illustrate the limits of carbon bonding, exhibiting Lewis‐violating “electron‐deficient bonds” between the hypercoordinate carbon and its methyl groups. Though not kinetically persistent under standard laboratory conditions, its dissociation activation barriers may permit C(CH3)₅⁺ fleeting existence near 0 K.     

Direct Waste-Free Synthesis of Amides from Nonactivated Carboxylic Acids and Amines: Application to the Synthesis of Tetrahydroisoquinolines

An efficient, waste-free protocol has been developed for the synthesis of amides directly from nonactivated carboxylic acids and amines without any tedious purification. Fatty acids were also converted into corresponding amides by reaction with nonactivated amines. The synthesized amides were cyclized to tetrahydroisoquinolines in good yields.