The rank one Gross conjecture for Deligne-Ribet $p$-adic $L$-functions was solved in works of Darmon-Dasgupta-Pollack and Ventullo by the Eisenstein congruence among Hilbert modular forms. purpose this paper is to prove an analogue Katz attached imaginary quadratic fields via congruences between CM forms non-CM new ingredient apply Rankin-Selberg method construct a Hida family which congruent a...

Capture-recapture methods are used to estimate the size of a population of interest which is only partially observed. In such studies, each member of the population carries a count of the number of times it has been identified during the observational period. In real-life applications, only positive counts are recorded, and we get a truncated at zero-observed distribution. We need to use the tr...

in this paper we study isotropic lagrangian submanifolds , in complex space forms . it is shown that they are either totally geodesic or minimal in the complex projective space , if . when , they are either totally geodesic or minimal in . we also give a classification of semi-parallel lagrangian h-umbilical submanifolds.

Borcea-Voisin threefolds are Calabi-Yau manifolds. They are constructed by Borcea ([B]) and Voisin ([V]) in the construction of mirror manifolds. In [SYZ], Strominger, Yau and Zaslow propose a geometric construction of mirror manifolds using special Lagrangian tori (called SYZ-construction below). Using degenerate Calabi-Yau metrics Gross and Wilson show that SYZ-construction works for any Borc...

The aim of this paper is to investigate geometrically nonlinear static analysis of axially functionally graded cantilever beam subjected to transversal non follower load. The considered problem is solved by finite element method with total Lagrangian kinematic approach. The material properties of the beam vary along the longitudinal direction according to the power law function. The finite elem...

Related living kidney donors (LKDs) are at higher risk of end-stage renal disease (ESRD) compared with unrelated LKDs. A genetic panel was developed to screen 115 genes associated with renal diseases. We used this panel to screen six negative controls, four transplant candidates with presumed genetic renal disease and six related LKDs. After removing common variants, pathogenicity was predicted...

Hamiltonian stationary Lagrangian spheres in Kähler-Einstein surfaces are minimal. We prove that in the family of non-Einstein Kähler surfaces given by the product Σ1×Σ2 of two complete orientable Riemannian surfaces of different constant Gauss curvatures, there is only a (non minimal) Hamiltonian stationary Lagrangian sphere. This example is defined when the surfaces Σ1 and Σ2 are spheres.

Intricately and inextricably bound within the process of higher degree study in Australia today is the phenomenon of supervision, the guiding process towards the attainment of the degree. The nature of tertiary supervision is believed to be a critical factor not only in influencing student satisfaction or dissatisfaction during the course of the studies. It is also argued that supervision helps...

In this note an improvement of the Katz’s bound on the number of elements in a finite field with given trace and norm is given. The improvement is obtained by reducing the problem to estimating the number of rational points on certain toric Calabi-Yau hypersurface, and then to use detailed cohomological calculations by Rojas-Leon and the second author for such toric hypersurfaces.