In this work, we present a two-dimensional mixed-hybrid finite element model of variably saturated flow on unstructured triangular meshes. Velocities are approximated using lowest order Raviart-Thomas (RT0) elements with piecewise constant pressure. The resulting nonlinear systems of algebraic equations are solved using Picard or Newton iterations in combination with ad hoc preconditioning tech...

Recently J.C. Rohde constructed families of Calabi-Yau threefolds parametrised by Shimura varieties. The points corresponding to threefolds with CM are dense in the Shimura variety and, moreover, the families do not have boundary points with maximal unipotent monodromy. Both aspects are of interest for Mirror Symmetry. In this paper we discuss one of Rohde’s examples in detail and we explicitly...

The Delta and Omicron variants’ system was used in this research study to replicate the complex process of SARS-CoV-2 outbreak. generalised fractional designed rigorously analysed order gain a comprehensive understanding transmission dynamics both variants. proposed dynamical has heredity memory effects, which greatly improved our ability perceive disease propagation dynamics. non-singular Atan...

Cellular automata have been useful artificial models for exploring how relatively simple rules combined with spatial memory can give rise to complex emergent patterns. Moreover, studying the dynamics of how rules emerge under artificial selection for function has recently become a powerful tool for understanding how evolution can innovate within its genetic rule space. However, conventional cel...

We formulate a detailed conjectural Eichler–Shimura type formula for the cohomology of local systems on Picard modular surface associated to group unitary similitudes $\operatorname{GU}(2,1, \mathbb{Q}(\sqrt{-3}))$. The is based counting points over finite fields curves genus three which are cyclic triple covers projective line. Assuming conjecture we able calculate traces Hecke operators space...

Being inspired by a work of Curtis T. McMullen about a very impressive automorphism of K3 surface of Picard number zero, we shall clarify the structure of the automorphism group of a Picard generic hyperkähler manifold (Definition 1.4), in an optimal form up to finite group factor. Our argument uses Yau’s solution of Calabi’s conjecture, Dirichlet’s unit theorem and theory of Salem polynomials....

Infinite triangular matrices and, in particular, the redecoration operation on them, were studied by Matthes and Picard. In their work, redecoration is characterized as the cobind operation of what the authors call a “weak constructive comonad”. In this work, we identify weak constructive comonads as an instance of the more general notion of relative comonad. Afterwards, building upon the work ...

We compute the cohomology of the Picard bundle on the desingularization J̃ d (Y ) of the compactified Jacobian of an irreducible nodal curve Y . We use it to compute the cohomology classes of the Brill–Noether loci in J̃ d (Y ). We show that the moduli space M of morphisms of a fixed degree from Y to a projective space has a smooth compactification. As another application of the cohomology of the...

We continue our studies in higher order uniform convergence with rates and in Lp convergence with rates. Namely, in this article we establish some Lipschitz type results for the smooth Picard type singular integral operators and for the smooth GaussWeierstrass type singular integral operators. RESUMEN Continuamos nuestros estudios sobre convergencia uniforme de orden superior con radios y sobre...