The convolution of convex harmonic univalent functions in the unit disk, unlike analytic functions, may not be or even univalent. main purpose this work is to develop previous in...

We consider the anti-plane shear waves in a domain consisting of an infinite layer with thin coating lying on elastic half-space. The properties coating, layer, and half-space are assumed to be different. On free upper surface we assume compatibility condition within Gurtin–Murdoch elasticity, whereas at plane interface perfect contact. For this problem there exist two possible regimes related ...

Diffuse normolipemic plane xanthoma is characterized by thepresence of yellowish-orange plaques on the eyelids, neck, uppertrunk, buttocks and flexural surfaces of the extremities in patientswith a normal lipid profile. It mainly affects adults of both sexes.Diffuse normolipemic plane xanthomas are usually associatedwith reticuloendothelial system disorders, such a...

For a Schr\"odinger operator on the plane $\mathbb{R}^2$ with electric potential $V$ and Aharonov--Bohm magnetic field we obtain an upper bound number of its negative eigenvalues in terms $L^1(\mathbb{R}^2)$-norm $V$. Similar to Calogero's one dimension, result is true under monotonicity assumptions Our proof method relies generalisation operator-valued potentials. We also establish similar for...

The problem of constructing a conformal mapping from the upper half-plane to circular polygon is considered. preimages vertices and accessory parameters are determined by generalized method P. Kufarev for determining in Christoffel–Schwarz integral. based on Loewner equation with boundary normalization. onto exterior consisting straight-line segments solved separately. Examples mappings whose f...

Generalizing the classical theorems of Max Noether and Petri, we describe generators relations for canonical ring a stacky curve, including an explicit Gröbner basis. We work in general algebro-geometric context treat log spin rings as well. As application, give presentation graded modular forms arising from finite-area quotients upper half-plane by Fuchsian groups.