A versatile route for the synthesis of 3-(1′, 1′-dimethyllallyl)coumarins

Synthesis of 3-(′, 1′-dimethylallyl)herniarin and 3-(′, 1′-dimethylallyl)desmothosyherniarin has been carried out by a versatile route.     

Acid catalyzed condensation of isoprene with orcinol: Synthesis of 2,2-dimethylchromans and 5-methylxanthyletin derivatives

Condensation of orcinol with 2-methylbuta-1,3-diene (isoprene) has been achieved in the presence of orthophosphoric acid as catalyst leading to the exclusive formation of 2,2-dimethylchromans in one step. A novel route for the synthesis of 5-methylxanthyletin derivatives is described.     

Optical behaviour of swift heavy ions irradiated poly(vinyl alcohol) films

Polyvinyl alcohol films were irradiated to 90 MeV O ⁶⁺ and 150 MeV Si ¹⁴⁺ ions at fluence ranging from 10¹⁰ to 10¹² ions/cm². The observed changes in optical energy gap of this polymer have been investigated and results are tried to be explained in terms of energy transferred by the incident ions. It has been noticed that the value of optical energy gap decreases with increasing energy loss during the ion–polymer interaction process.     

Magneto-resistance above 300 K in nano-crystalline Co–Ag metastable solid solutions

A series of nano-crystalline Co_xAg_100−x solid solutions have been prepared by NaBH₄ reduction of the corresponding metal salts at room temperature in Ar gas flow. Alloys heat-treated at 600 °C in Ar/H₂ (5%) show the evolution of metastable fcc Co precipitates in Ag. Magnetic studies indicate that all the compositions are ferromagnetic with Curie temperatures >400 K. For a nominal composition of Co₆₀Ag₄₀, heat-treated at 600 °C, an effective negative magneto-resistance (MR) ratio of the order of ∼21% at 350 K, at 2 T is observed. This could arise from the influence of magnetic field on the electron–phonon scattering effects near to T_c and to the spin-mixing scattering by magnons.     

Duality for Coloured Quantum Groups

Duality between the coloured quantum group and the coloured quantum algebra corresponding to GL(2) is established. The coloured L ^± functionals are constructed and the dual algebra is derived explicitly. These functionals are then employed to give a coloured generalisation of the differential calculus on quantum GL(2) within the framework of the R-matrix approach.     

Density functional study of $$\hbox {AgScO}_2$$: Electronic and optical properties

Dielectric relaxation studies of binary (jk) polar mixtures of tetrahydrofuran with N-methyl acetamide, N,N-dimethyl acetamide, N-methyl formamide and N,N-dimethyl formamide dissolved in benzene(i) for different weight fractions (w _{j k} ’s) of the polar solutes and mole fractions (x _j ’s) of tetrahydrofuran at 25 ^°C are attempted by measuring the conductivity of the solution under 9.90 GHz electric field using Debye theory. The estimated relaxation time (τ _{j k} ’s) and dipole moment (μ _{j k} ’s) agree well with the reported values signifying the validity of the proposed methods. Structural and associational aspects are predicted from the plot of τ _{j k} and μ _{j k} against x _j of tetrahydrofuran to arrive at solute–solute (dimer) molecular association upto x _j =0.3 of tetrahydrofuran and thereafter solute–solvent (monomer) molecular association upto x _j =1.0 for all systems except tetrahydrofuran + N,N-dimethyl acetamide.     

Electrochemical behavior of different structural states of the alloy Ti60Ni40

Potentiodynamic polarization studies were carried out on nanocrystalline I, nanocrystalline II and nanocrystalline III states having crystallite size 35 ± 5 nm, 18 ± 2 nm and 10 ± 2 nm of the alloy Ti₆₀Ni₄₀ in 1 M H₂SO₄ aqueous medium. It was observed that the nanocrystalline III state exhibits superior corrosion resistance as compared to the nanocrystalline II and nanocrystalline I states of the alloy Ti₆₀Ni₄₀. XPS studies were also performed after corrosion test and it was observed that nanocrystalline III state contains only Ti²⁺ and Ti⁴⁺ species whereas nanocrystalline I and nanocrystalline II state contains Ti²⁺, Ti³⁺and Ti⁴⁺ along with some unoxidized metallic Ti⁰ in the case of nanocrystalline I state. Thus the small crystallite size and the presence of only Ti²⁺ and Ti⁴⁺ species in the form of TiO and TiO₂ leads to the formation of a protective oxide film which is adherent, stable and improves the corrosion resistance of the nanocrystalline III state of the alloy Ti₆₀Ni₄₀.     

A convenient synthesis of crotylbenzaldehydes and 2-methylformyl-chromans

Condensation of hydroxybenzaldehydes viz., 2,3,4-trihydroxy-, 2,4-dihydroxy-, 2,4-dihydroxy-6-methyl-, and 2,4-dihydroxy-3-iodo-6-methylbenzaldehydes with buta-1,3-diene in the presence of orthophosphoric acid yields crotylbenzaldehydes in one step. The latter compounds on cyclisation afford the corresponding 2-methylformylchromans.

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Eine einfache Synthese von Crotylbenzaldehyden und 2-Methylformyl-chromanen

Zusammenfassung Die Kondensation von Hydroxybenzaldehyden (2,3,4-Trihydroxy-, 2,4-Dihydroxy-, 2,4-Dihydroxy-6-methyl-, und 2,4-Dihydroxy-3-jod-6-methyl-benzaldehyd) mit Buta-1,3-dien in Gegenwart von Orthophosphorsäure ergibt in einer Stufe Crotylbenzaldehyde. Diese lassen sich durch Cyclisierung zu den entsprechenden 2-Methylformylchromanen umsetzen.

     

Evaluation of a cubic character sum using the √−19 division points of the curve Y2 = X3 − 23 · 19X + 2 · 192

The √?19 division points on the curve y² = f(x) of the title are calculated explicitly and the effect of the Frobenius map on these points is found in order to evaluate the cubic character sum $\text{Σ}{}_{\mathrm{<mtext>x(</mtext><mtext>mod</mtext><mtext>\; p)</mtext>}}\text{(}\text{f(x)}\text{p}\text{)}$.