We revisit the formalism for analytic derivative couplings between excited states in time-dependent density functional theory (TDDFT). We derive and implement these couplings using quadratic response theory, then numerically compare this response-theory formulation to couplings implemented previously based on a pseudo-wavefunction formalism and direct differentiation of the Kohn-Sham determinan...

My research lies in the intersection of three fields of mathematics: stochastic processes, representation theory and the theory of Lie groups; in particular, Lévy processes in nilpotent Lie groups. In Euclidean space, these processes are generated by a particularly nice class of operator, referred to as a pseudo-differential operator. These operators have traditionally been of interest in the s...

because of using principles such as principality, unity, gradation of existence and concomitance between existence and unity, along with an exhaustive understanding of ibn sina's philosophical principle about our knowledge of unity and multiplicity, mulla sadra believed new philosophical-aesthetical principles such as principality, unity and gradation of beauty, though he didn't use t...

theory atoms LTL(Th) formula φ φabs pseudo-Boolean input variables Xabs Input variables X Output variables Y pseudo-Boolean LTL LTL controller check whether the input formula is realizable synthesis

nationalism and modernism, and the relationship between them from the perspective of different scholars and schools of thought have always been a subject of debate. many scholars have concerned themselves with the concepts of ethnicity, nation, and nationalism and their relationship with modernism and modern age. the main controversy among scholars and schools of thought has been centered on th...

The author develops the theory of pseudo differential equations and boundary value problems in nonsmooth domains. A model pseudo differential equation in a special cone is reduced to a certain integral equation. AMS Subject Classifications: 35S15, 45F05.

edited by José Ferreirós and Jeremy Gray Oxford University Press, 2006, 442 pp. $ 69.50 US, ISBN 0198567936 REVIEWED BY ANDREW ARANA This collection of essays explores what makes modern mathematics ‘modern’, where ‘modern mathematics’ is understood as the mathematics done in the West from roughly 1800 to 1970. This is not the trivial matter of exploring what makes recent mathematics recent. The...