Related papers: Implementations of Derivations on the Quantum Annu…
We develop the theory of hyperelliptic Kleinian functions. As applications we consider construction of the explicit matrix realization of the hyperelliptic Kummer varieties, differential operators to have the hyperelliptic curve as spectral…
We show that the bicovariant first order differential calculi on a factorisable semisimple quantum group are in 1-1 correspondence with irreducible representations $V$ of the quantum group enveloping algebra. The corresponding calculus is…
A regular way to define an additive coproduct (or ``coaddition'') on the q-deformed differential complexes is proposed for quantum groups and quantum spaces related to the Hecke-type R-matrices. Several examples of braided coadditive…
A theory of principal bundles possessing quantum structure groups and classical base manifolds is presented. Structural analysis of such quantum principal bundles is performed. A differential calculus is constructed, combining differential…
We give the lower bound for the modulus of the radial derivatives and Jacobian of harmonic injective mappings from the unit ball onto convex domain in plane and space. As an application we show co-Lipschitz property of some classes of qch…
Representations of quantum computations are almost always based on a tensor product $\otimes$-structure. This coincides with what we are able to execute in our experiments, as well as what we observe in Nature, but it makes certain familiar…
In the talk we investigate the question of commutation of the whole-partial derivatives, which should be considered when the function, which is subjected to differentiation, has both explicit and implicit dependence. We apply the results to…
In this note, we will define the formulas of curvature and it's covariant derivatives for holomorphic curves on C*-algebras for the multivariable case. As applications, the unitarily and similarly classification theorems for holomorphic…
We present quantum Monte Carlo calculations of total energy derivatives, consistently performed in the fixed-node approximation. Contributions from nodal displacements, neglected or approximated in previous investigations, are properly…
The topic of this thesis is the development of a versatile and geometrically motivated differential calculus on non-commutative or quantum spaces, providing powerful but easy-to-use mathematical tools for applications in physics and related…
We generalize the concept of stabilizer subgroups to compact quantum groups.
We give a proper fractional extension of the classical calculus of variations by considering variational functionals with a Lagrangian depending on a combined Caputo fractional derivative and the classical derivative. Euler-Lagrange…
We introduce functional Wulff shapes based on the classical construction for compact convex sets. With this new tool, we establish a functional version of Aleksandrov's variational lemma in the family of convex functions with compact…
We propose a categorical and algebraic study of quantale modules. The results and constructions presented are also applied to abstract algebraic logic and to image processing tasks.
QR factorisation plays an important role in matrix computations. Within the context of optimisation and of automatic differentiation of such computations, we need to compute the derivative of this factorisation. For tall matrices, however,…
Convenient parameterizations of matrices in terms of vectors transform (certain classes of) matrix equations into covariant (hence rotation-invariant) vector equations. Certain recently introduced such parameterizations are tersely…
The algebraic formulation of the quantum group gauge models in the framework of the $R$-matrix approach to the theory of quantum groups is given. We consider gauge groups taking values in the quantum groups and noncommutative gauge fields…
Using differential and integral calculi on the quantum plane which are invariant with respect to quantum inhomogeneous Euclidean group E(2)q , we construct path integral representation for the quantum mechanical evolution operator kernel of…
Some notes and observations on analytic functions defined on an annulus
We have introduced q-analogues of bounded symmetric domains in our work q-alg/9703005. Given the simplest ones among those, the works q-alg/9603012 and math.QA/9803110 announce the relations describing the algebras of functions,…