We introduce the weighted orthogonal Ricci curvature – a two-parameter version of Ni–Zheng's curvature. This serves as very natural object in study relationship between curvature(s) and holomorphic sectional In particular, determining optimal constraints for compact Kähler manifold to be projective. this direction, we prove number vanishing theorems using both Hermitian category.

In the paper [2], Hitchin studied pairs (E,φ), where E is a vector bundle of rank two with a fixed determinant on a curve C and φ : E −→ E ⊗ KC is a trace free homomorphism, and constructed a moduli space for them. This moduli space carries the structure of a non-complete, quasi-projective algebraic variety. Later, Nitsure [5] gave an algebraic construction of moduli spaces of pairs (E,φ) over ...

Around 1940, Lind [Lin] and (independently, but shortly later) Reichardt [Re] discovered that some genus 1 curves over Q, such as 2y = 1− 17x, violate the Hasse principle; i.e., there exist x, y ∈ R satisfying the equation, and for each prime p there exist x, y ∈ Qp satisfying the equation, but there do not exist x, y ∈ Q satisfying the equation. In fact, even the projective nonsingular model h...

This paper discusses a class issue of finite-time lag projective synchronization (FTLPS) delayed fractional-order quaternion-valued neural networks (FOQVNNs) with parameter uncertainties, which is solved by non-decomposition method. Firstly, new FOQVNNs model uncertain parameters designed. Secondly, two types feedback controller and adaptive without sign functions are designed in the quaternion...

Using the theory of rational elliptic fibrations, we construct and discuss a one parameter family configurations $12$ conics $9$ points in projective plane that realizes an abstract configuration $(12_6,9_8)$. This is analogous to famous Hesse lines forming $(12_3,9_4)$. We also show any Halphen fibration index $2$ with four triangular singular fibers arises from such conics.

This paper describes how to determine the parameter values of the chaotic Lorenz system from one of its variables waveform. The geometrical properties of the system are used firstly to reduce the parameter search space. Then, a synchronization-based approach, with the help of the same geometrical properties as coincidence criteria, is implemented to determine the parameter values with the wante...

let r be an associative ring with identity, c(r) be the category of com-plexes of r-modules and flat(c(r)) be the class of all at complexes of r-modules. we show that the at cotorsion theory (flat(c(r)); flat(c(r))−)have enough injectives in c(r). as an application, we prove that for each atcomplex f and each complex y of r-modules, exti (f,x)= 0, whenever ris n-perfect and i > n.

let $r$ be a commutative ring with identity and $m$ be a finitely generated unital $r$-module. in this paper, first we give necessary and sufficient conditions that a finitely generated module to be a multiplication module. moreover, we investigate some conditions which imply that the module $m$ is the direct sum of some cyclic modules and free modules. then some properties of fitting ideals of...