In this work, the generalization of Friedel formula and Krein's theorem in complex potential scattering theory is presented. The consequences various symmetry constraints on dynamical systems are discussed. addition, Muskhelishvili-Omn\`es representation also given

Water-miscible organic co-solvents can be used in DNA-based catalytic asymmetric reactions at appreciable concentration without a negative effect on enantioselectivity. While the rate of the copper(II) Diels-Alder reaction is affected negatively by the presence of organic co-solvents, the copper(II) catalyzed Michael addition and Friedel-Crafts alkylation reaction are significantly faster. Addi...

The pioneering experiment [Nature 385, 417 (1997)] reported the measurement of the transmission phase of the electron traversing a quantum dot and found the intriguing feature of the sudden phase drop in conductance valleys. Based on the Friedel sum rule for a spinless effective one-dimensional system, it has been previously argued [Phys. Rev. Lett. 82, 2358 (1999)] that the sudden phase drop s...

The most widely known electrophilic agents are protic acids and compounds with an electronsextet partial structure. Recent research has aimed at the development of new electrophilic reagents, with greater reactivity on the one hand and higher selectivity on the other, which would largely obviate the addition of Lewis acids (Friedel-Crafts catalysts), and also alIow control of the isomer ratio i...