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 $\text{Σ}{}_{\mathrm{<mtext>x(</mtext><mtext>mod</mtext><mtext>\; p)</mtext>}}\text{(}\text{f(x)}\text{p}\text{)}$.     

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.     

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.

     

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.     

A variable temperature EPR study of the manganites (La1/3Sm2/3)2/3SrxBa0.33−xMnO3 (x=0.0, 0.1, 0.2, 0.33): Small polaron hopping conductivity and Griffiths phase

Four manganite samples of the series, (La_1/3Sm_2/3)_2/3Sr_xBa_0.33−xMnO₃, with x=0.0, 0.1, 0.2 and 0.33, were investigated by X-band (∼9.5 GHz) electron paramagnetic resonance (EPR) in the temperature range 4-300 K. The temperature dependences of EPR lines and linewidths of the samples with x=0.0, 0.1 and 0.2, containing Ba²⁺ ions, exhibit similar behavior, all characterized by the transition temperatures (T_C) to ferromagnetic states in the 110-150 K range. However, the sample with x=0.33 (containing no Ba²⁺ ions) is characterized by a much higher T_C=205 K. This is due to significant structural changes effected by the substitution of Ba²⁺ ions by Sr²⁺ ions. There is an evidence of exchange narrowing of EPR lines near T_min, where the linewidth exhibits the minimum. Further, a correlation between the temperature dependence of the EPR linewidth and conductivity is observed in all samples, ascribed to the influence of small-polaron hopping conductivity in the paramagnetic state. The peak-to-peak EPR linewidth was fitted to ΔB_pp(T)=ΔB_pp,min+A/Texp(−E_a/k_BT), with E_a=0.09 eV for x=0.0, 0.1 and 0.2 and E_a=0.25 eV for x=0.33. From the published resistivity data, fitted here to σ(T)∝1/T exp(−E_σ/k_BT), the value of E_σ, the activation energy, was found to be E_σ=0.18 eV for samples with x=0.0, 0.1 and 0.2 and E_σ=0.25 eV for the sample with x=0.33. The differences in the values of E_a and E_σ in the samples with x= 0.0, 0.1and 0.2 and x=0.33 has been ascribed to the differences in the flip-flop and spin-hopping rates. The presence of Griffiths phase for the samples with x=0.1 and 0.2 is indicated; it is characterized by coexistence of ferromagnetic nanostructures (ferrons) and paramagnetic phase, attributed to electronic phase separation.     

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.     

Geometrical Model for Phenylthallium Dihalides

The geometry of the phenylthallium dihalides, PhTlX₂(X=F, Cl or Br) which has heitherto been unknown, has been proposed on the basis of several qualitative aspects and quantitative arguments. These molecules have a planar structure with C_2v symmetry and the ring geometry has been assumed to be the same as that of benzene. The ring-substituent bond length has been taken to be 2.218 A° in all the three molecules, and the Tl-F, Tl-Cl and Tl-Br bond lengths in respective molecules have been estimated to be 1.878, 2.366 and 2.520 A°. The remaining parameter inter-bond angle, F-Tl-F has been taken to be 116° in PhTlF₂, whereas, angles Cl-Tl-Cl and Br-Tl-Br in respective molecules have been taken to be 120°, as expected in the case of a pure sp² hybridization.     

Estimation of relative order tensors, and reconstruction of vectors in space using unassigned RDC data and its application

Advances in NMR instrumentation and pulse sequence design have resulted in easier acquisition of Residual Dipolar Coupling (RDC) data. However, computational and theoretical analysis of this type of data has continued to challenge the international community of investigators because of their complexity and rich information content. Contemporary use of RDC data has required a-priori assignment, which significantly increases the overall cost of structural analysis. This article introduces a novel algorithm that utilizes unassigned RDC data acquired from multiple alignment media (nD-RDC, n  3) for simultaneous extraction of the relative order tensor matrices and reconstruction of the interacting vectors in space.Estimation of the relative order tensors and reconstruction of the interacting vectors can be invaluable in a number of endeavors. An example application has been presented where the reconstructed vectors have been used to quantify the fitness of a template protein structure to the unknown protein structure. This work has other important direct applications such as verification of the novelty of an unknown protein and validation of the accuracy of an available protein structure model in drug design. More importantly, the presented work has the potential to bridge the gap between experimental and computational methods of structure determination.     

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.