We introduce a large class of bicovariant differential calculi on any quantum group A, associated to Ad-invariant elements. For example, the deformed trace element on SLq(2) recovers Woronowicz’ 4D± calculus. More generally, we obtain a sequence of differential calculi on each quantum group A(R), based on the theory of the corresponding braided groups B(R). Here R is any regular solution of the...

New static regular axially symmetric solutions of SU (2) Euclidean Yang-Mills theory are constructed numerically. They represent calorons having trivial Polyakov loop at spacial infinity. The solutions are labeled by two integers m, n. It is shown that besides known, charge one self-dual periodic instanton solution, there are other non-self dual solutions of the Yang-Mills equations naturally c...

Deflection analysis of a simply supported microbeam subjected to a concentrated load at the middle is investigated on the basis of a shear deformable beam theory and non-classical theory. Effects of shear deformation and small size are taken into consideration by hyperbolic shear deformable beam theory and modified strain gradient theory, respectively. The governing differential equations and c...

In 1984 Milnor had shown how to deduce the Lie-Palais theorem on integration of infinitesimal actions of finite-dimensional Lie algebras on compact manifolds from general theory of regular Lie groups modelled on locally convex spaces. We show how, in the case of effective action, one can eliminate from Milnor’s argument the abstract Lie-Cartan theorem, making the deduction rather elementary. A ...

We study a Riemann problem for the two-dimensional isentropic gas dynamics equations which models transonic regular reflection. When written in self-similar coordinates, the system changes type from hyperbolic to mixed hyperbolic-elliptic. Using the theory of one-dimensional hyperbolic conservation laws, we formulate a free boundary problem in the subsonic region and we outline the main ideas f...

New static regular axially symmetric solutions of SU(2) Euclidean Yang-Mills theory are constructed numerically. They represent calorons having non-trivial Polyakov loop at spacial infinity. The solutions are labeled by two integers m,n. It is shown that besides known, charge one self-dual periodic instanton solution, there are other non-self dual solutions of the Yang-Mills equations naturally...

Some rigorous results connected with the conventional statistical theory of turbulence in both twoand three-dimensional cases are discussed. Such results are based on the concept of stationary statistical solution, related to the notion of ensemble average for turbulence in statistical equilibrium, and concern, in particular, the mean kinetic energy and enstrophy fluxes and their corresponding ...

*Correspondence: [email protected] 2College of Power and Energy Engineering, Harbin Engineering University, Harbin, 150001, China Full list of author information is available at the end of the article Abstract In this paper, we prove that there exists a weak solution for Schrödingerean technique for order performance by similarity (TOPSIS) equations on cylinders. Meanwhile, the boundary behaviors of...