Reducibility number

Let P be a poset in a class of posets P. A smallest positive integer r is called reducibility number of P with respect to P if there exists a non-empty subset S of P with |S|=r and P-S∈P. The reducibility numbers for the power set 2ⁿ of an n-set (n?2) with respect to the classes of distributive lattices, modular lattices and Boolean lattices are calculated. Also, it is shown that the reducibility number r of the lattice of all subgroups of a finite group G with respect to the class of all distributive lattices is 1 if and only if the order of G has at most two distinct prime divisors; further if r is a prime number then order of G is divisible by exactly three distinct primes. The class of pseudo-complemented u-posets is shown to be reducible. Deletable elements in semidistributive posets are characterized.     

Synthesis and antimycobacterial screening of new 4-(4-(1-benzyl-1H-1,2,3-triazol-4-yl)-1-phenyl-1H-pyrazol-3-yl)quinoline derivatives

A new series of 4-(4-(1-benzyl-1H-1,2,3-triazol-4-yl)-1-phenyl-1H-pyrazol-3-yl)quinoline ( 6a-t ) have been synthesized by a click reaction of 4-(4-ethynyl-1-phenyl-1H-pyrazol-3-yl)quinoline ( 4a-d ) with a substituted benzyl azide ( 5a-e ). The starting alkyne derivatives 4a-d are obtained from Bestmann-Ohira reaction of 1-phenyl-3-(quinolin-4-yl)-1H-pyrazole-4-carbaldehyde and dimethyl(1-diazo-2-oxopropyl)phosphonate. The newly synthesized compounds are screened against M. tuberculosis H37Ra dormant and active, Escherichia coli, Pseudomonas fluorescence, Staphylococcus aureus and Bacillus subtilis strains at 30 μg/mL concentration. Most of the screened compounds showed good to moderate antibacterial activity against S. aureus, B. subtilis, and Mycobacterium tuberculosis H37Ra strains. The synthesized derivatives of quinolinyl-pyrazole-4-carbaldehyde and quinolinyl-pyrazole-4-ethyne reportd good to moderate activity against both strains of M. tuberculosis H37Ra. Ten derivatives of quinolinyl-pyrazole presented good activity against B. subtilis. These results suggested that further optimization and development of quinolinyl-pyrazolyl-1,2,3-triazole moeity could serve as lead compounds for antimycobacterial activity.     

Are all charge-repulsed carbocations really unstable? Dramatic difference in reactivities of benzyl- and p -methoxybenzyl halides in benzene

Two distinct reaction mechanisms are proposed for the reactions of1,5 and6 with nucleophiles as against those of11,12 and16. The former set undergoes the reactions through carbocation type intermediates2 and3 as efficiently as the stable carbocation4 does, even under similar and very mild conditions. The compounds from the latter group do not form the carbocations under the same conditions and undergo only direct substitution by strong nucleophiles.     

Keggin type heteropolyacids-catalyzed synthesis of quinoxaline derivatives in water

Keggin type heteropolyacids was found to be an efficient and reusable catalyst for the synthesis of biologically active quinoxaline derivatives from the condensation of 1,2-diamine with 1,2-dicarbonyl compounds in excellent yields in water.This method provides a new and efficient protocol in terms of small quantity of catalyst,a wide scope of substrates,and simple work-up procedure.     

A convenient synthesis of methyl 2-hydroxy-4-oxo-4-(substituted phenyl) butanoates from malic acid

A synthesis of methyl 2-hydroxy-4-oxo-4-(substituted phenyl)butanoates has been accomplished using Friedel-Crafts acylation of substituted benzenes with 2-acetoxybutanoyl chloride.The key feature of this strategy is that various 4-arylbutanoates can be obtained conveniently,which are important intermediates for the synthesis of biologically active compounds including ACE inhibitors.     

PEG-SO_3H as catalyst for the Beckmann rearrangement and dehydration of oximes

Under mild conditions, conversion of a variety of ketoximes and aldoximes to their corresponding amides and nitriles proceeded in the presence of PEG-SO3H with high yields.     

The nuclear quadrupole interaction at 111Cd and 181Ta sites in anatase and rutile TiO2: A TDPAC study

The nuclear quadrupole interaction of the I=5/2 state of the nuclear probes ¹¹¹Cd and ¹⁸¹Ta in the anatase and rutile polymorphs of bulk TiO₂ was studied using the time differential perturbed angular correlation (TDPAC) method. The fast–slow coincidence setup is based on CAMAC electronics. For anatase, the asymmetry parameter of the electric field gradient was η=0.22(1) and a quadrupole interaction frequency of ω_Q=44.01(3) Mrad/s was obtained for ¹⁸¹Ta. For rutile, the respective values are η=0.56(1) and ω_Q=130.07(9) Mrad/s. The values for rutile match closely with the literature values. In case of the ¹¹¹Cd probe produced from the beta decay of ¹¹¹Ag, the quadrupole interaction frequency for anatase was negligibly small as indicated by an unperturbed angular correlation in anatase. On the other hand for rutile the quadrupole frequency is ω_Q=61.74(2) Mrad/s and the asymmetry parameter η=0.23(1) for the ¹¹¹Cd probe. The results are interpreted in terms of the surrounding atom positions in the lattice and the charge state of the probe nucleus.     

Synthesis of (s)-1-{3-[4-(4-benzo[d]isothiazol-3-yl-piperazin-1-yl)-3-fluoro-phenyl]-2-oxo-oxazolidin-5-ylmetyl}-3-substituted-urea derivatives as antibacterial agents

A new series of (s)-1-{3-[4-(4-benzo[d]isothiazol-3-yl-piperazin-1-yl)-3-fluoro-phenyl]-2-oxo-oxazolidin-5-ylmetyl}-3-substituted-urea derivatives have been synthesized and characterized with spectral data, such as IR, NMR and Mass spectroscopies. All compounds are in vitro evaluated for their efficacy as antimicrobial agent against the gram-positive pathogenic strains such as Bacillus subtilis ATCC 6633, Staphylococcus aureus ATCC 25923, Staphylococcus epidermidis ATCC 12228 and Streptococcus pyogens ATCC 8668. Five compounds ( 19k , 19l , 19m , 19n and 19o ) out of 15 compounds showed moderate activity.     

Axially Symmetric Universe in Creation-Field Cosmology

Axially symmetric space-time is considered in the Hoyle-Narlikar C-field cosmology. Using methods of Narlikar and Padmanabhan (Phys. Rev. D 32:1928, 1985), the solutions have been studied when the creation field C is a function of time t only. The geometrical and physical aspects for models are also studied.     

An alternative route for the preparation of the medical isotope 99Mo from the 238U(γ, f) and 100Mo(γ, n) reactions

The radionuclide ⁹⁹Mo, which has a half-life of 65.94 h was produced from ²³⁸U(γ, f) and ¹⁰⁰Mo(γ, n) reactions using a 10 MeV electron linac at EBC, Kharghar Navi-Mumbai, India. This has been investigated since the daughter product ^99mTc is very important from a medical point of view and can be produced in a generator from the parent ⁹⁹Mo. The activity of ⁹⁹Mo was analyzed by a γ-ray spectrometric technique using a HPGe detector. From the detected γ-rays activity of 140.5 and 739.8 keV, the amount of ⁹⁹Mo produced was determined. For comparison, the amount of ⁹⁹Mo from ²³⁸U(γ, f) and ¹⁰⁰Mo(γ, n) reactions was also estimated using the experimental photon flux from ¹⁹⁷Au(γ, n)¹⁹⁶Au reaction. The amount of ⁹⁹Mo from the detected γ-lines is in agreement with the estimated value for ²³⁸U(γ, f) and ¹⁰⁰Mo(γ, n) reactions. The production of ⁹⁹Mo activity from ²³⁸U(γ, f) and ¹⁰⁰Mo(γ, n) reactions is a relevant and novel approach, which provides alternative routes to ^235,238U(n, f) and ⁹⁸Mo(n, γ) reactions, circumventing the need for a reactor. The viability and practicality of the ⁹⁹Mo production from the ²³⁸U(γ, f) and ¹⁰⁰Mo(γ, n) reactions alternative to ^235,238U(n, f) and ⁹⁸Mo(n, γ) reactions has been emphasize. An estimate has been also arrived based on the experimental data of present work to fulfill the requirement of DOE.