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in the category of mordell curves (e_d:y^2=x^3+d) with nontrivial torsion groups we find curves of the generic rank two as quadratic twists of (e_1), and of the generic rank at least two and at least three as cubic twists of (e_1). previous work, in the category of mordell curves with trivial torsion groups, has found infinitely many elliptic curves with rank at least seven as sextic tw...
1-type and biharmonic curves by using laplace operator in lorentzian 3-space arestudied and some theorems and characterizations are given for these curves.
the synthesis and characterization a new derivatives of 2'-iodo-meta terphenyl from the reaction ofexcess aryl-grignard and 2, 6- dichloroiodobenzene with quenching of m-terphenyl-2'-magnesiumbromide by iodine is reported. via the reactions three carbon-carbon bonds are constructed and mterphenylsare obtained in good yields.
In this study, a novel method to synthesis of 1,3,5,7-tetraacetyl octahydro-1,3,5,7-tetraazocine or 1,3,5,7-tetraacetyl-1,3,5,7-tetraazacyclooctane (TAT) was used through acetolysis of 3,7-diacetyl-1,3,5,7-tetraazabicyclo-[3.3.1]nonane (DAPT) with acetic anhydride in the presence of sodium acetate as catalyst. Optimized reaction conditions were obtained by changing temperature, time and startin...
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