Covariant first order differential calculus over quantum complex Grassmann manifolds is considered. It is shown by a Pusz–Woronowicz type argument that under restriction to calculi close to classical Kähler differentials there exist exactly two such calculi for the homogeneous coordinate ring. Complexification and localization procedures are used to induce covariant first order differential cal...

We introduce and study a system of coupled nonlocal nonlinear Schrödinger equations that interpolates between the mixed, focusing–defocusing Manakov on one hand limiting case intermediate equation other. show this new system, which we call mixed (IMM) admits multi-soliton solutions governed by complexification hyperbolic Calogero–Moser (CM) system. Furthermore, spatially periodic version IMM fo...

Suppose that an algebraic torus G acts algebraically on a projective manifold X with generically trivial stabilizers. Then the Zariski closure of the set of pairs {(x, y) ∈ X × X | y = gx for some g ∈ G} defines a nonzero equivariant cohomology class [∆G] ∈ H G×G(X×X). We give an analogue of this construction in the case where X is a compact symplectic manifold endowed with a hamiltonian action...

Open-ended machine learning problems require various level of flexibility from learning agents. Stanley (2004) presented in his paper that incremental complexification in neural network structure usually results in more effective learning process, while subsequent researches by James and Tucker showed simplifying the structures often results in similarly good solution. In this paper, we test va...

The article focuses on the hypothesis that the structural complexity of languages is variable and historically changeable. By means of a quantitative statistical analysis of naturalistic corpus data, the question is raised as to what role language contact and adult second language acquisition play in the simplification and complexification of language varieties. The results confirm that there i...

The soft photon theorem, in its standard form, requires corrections when the asymptotic particle states carry magnetic charges. These corrections are deduced using electromagnetic duality and the resulting soft formula conjectured to be exact for all Abelian gauge theories. Recent work has shown that the standard soft theorem implies an infinity of conserved electric charges. The associated sym...

A Dirac picture perturbation theory is developed for the time evolution operator in classical dynamics in the spirit of the Schwinger-Feynman-Dyson perturbation expansion and detailed rules are derived for computations. Complexification formalisms are given for the time evolution operator suitable for phase space analyses, and then extended to a two-dimensional setting for a study of the geomet...

Let D = G/K be an irreducible Hermitian symmetric domain. Then G is contained in a complexification GC, and there exists a closed complex subsemigroup G ⊂ Γ ⊂ GC characterised by fact that all holomorphic discrete series representations of G extend holomorphically to Γ◦, the socalled minimal Ol’shanskĭı semigroup. Parallel to the classical theory of boundary strata for the symmetric domain D, d...

This work aims at modelising the use of the suprasegmental system and its relation with the enunciative structure in young children in a dialogue situation with a competent speaker. The role of the intonative and temporal parameters during the grammaticalisation period, which takes place between 2 and 3.5 years of age is investigated in this paper. Results show that children who use intonation ...