This article is based on lectures given by the authors in 2005 and 2006. Our first goal is to present an introduction to the orbit method with an emphasis on the character theory of finite nilpotent groups. The second goal (motivated by a recent work of G. Lusztig) is to explain several nontrivial aspects of character theory for finite groups of the form G(Fqn), where G is a unipotent algebraic...

Personality is defined as an individual integration of mental and somatic properties, which is manifested in social interactions and its structure consists of temperament, character and intelligence. It is also responsible for the human’s adaptation capability, behavior, emotional processing, feeling and experiencing well-being and illness. This is also the reason why personality type is an imp...

The character of the intermolecular interactions in Cl2-HX (X =F, Cl and Br) complexes has been investigated by means of the second-order Möller–Plesset perturbation theory (MP2) and the density functional theory (DFT) calculations. The results show that there are two types of lowest interaction potential equilibrium structures in the interactions between Cl2 and HX: X∙∙∙Cl type geometry and hy...

The human character can be understood as an extension of the life mission or purpose of life, and explained as the primary tool of a person to impact others and express the purpose of life. Repression of the human character makes it impossible for a person to realize his personal mission in life and, therefore, is one of the primary causes of self-repression resulting in poor quality of life, h...

We propose a trajectory planning and control theory for continuous movements such as connected cursive handwriting and continuous natural speech. Its hardware is based on our previously proposed forward-inverse-relaxation neural network (Wada & Kawato, 1993). Computationally, its optimization principle is the minimum torquechange criterion. Regarding the representation level, hard constraints s...

We present detailed theoretical studies of the H-bonded complexes formed from interaction between 5-fluorouracil and various six-membered cyclic nitrosamine compounds. In this study, an investigation on intermolecular interactions in X-NU (X = CH2, SiH2,BH, AlH, NH, PH, O and S) complexes is carried out using density functional theory. The calculations are conducted on B3L...

A difficult problem in the character theory of solvable groups is to show that the number c.d. (G) of irreducible character degrees of a solvable group G is equal to or greater than d.l. (G), the derived length of G. Isaacs [4] has shown that d.l. (G) ^ 3 c.d. (G)-2 for every solvable group. Berger [1] subsequently proved that d.l. (G) < c.d. (G) when | G | is odd. This problem belongs to the c...

A family of small graphene patches, i.e., rectangular polyaromatic hydrocarbons (PAHs), that have both zigzag and armchair edges is investigated to establish their ground state electronic structure. Broken symmetry density functional theory (DFT) and plane wave DFT were used to characterize the onset of diradical character via relative energies of open-shell and closed-shell singlet states. The...

For an orbifold X and α ∈ H(X,Z), we introduce the twisted cohomologyH c (X, α) and prove that the Connes-Chern character establishes an isomorphism between the twisted K-groups K α (X)⊗C and twisted cohomologyH c (X, α). This theorem, on the one hand, generalizes a classical result of Baum-Connes, Brylinski-Nistor, and others, that if X is an orbifold then the Chern character establishes an is...