Evolutionary forms, as well as exterior forms, are skew-symmetric differential forms. But in contrast to the exterior forms, the basis of evolutionary forms is deforming manifolds (manifolds with unclosed metric forms). Such forms possess a peculiarity, namely, the closed inexact exterior forms are obtained from that. The closure conditions of inexact exterior form (vanishing the differentials ...

in this paper, we introduce a new class of implicit functions and also common property (e.a) in modified intuitionistic fuzzy metric spaces and utilize the same to prove some common fixed point theorems in modified intuitionistic fuzzy metric spaces besides discussing related results and illustrative examples. we are not aware of any paper dealing with such implicit functions in modified intuit...

In this paper, we give a fixed point theorem for $(psi,varphi)$-weakly contractive mappings in complete $b$-metric spaces. We also give a common fixed point theorem for such mappings in complete $b$-metric spaces via altering functions. The given results generalize two known results in the setting of metric spaces. Two examples are given to verify the given results.

In this paper, the poset $BX$ of formal balls is studied in fuzzy partial metric space $(X,p,*)$. We introduce the notion of layered complete fuzzy partial metric space and get that the poset $BX$ of formal balls is a dcpo if and only if $(X,p,*)$ is layered complete fuzzy partial metric space.

For a family of compact Riemann surfaces Xt of genus g > 1, parameterized by the Schottky space Sg, we define a natural basis of H(Xt, ω n Xt ) which varies holomorphically with t and generalizes the basis of normalized abelian differentials of the first kind for n = 1. We introduce a holomorphic function F (n) on Sg which generalizes the classical product ∏ ∞ m=1 (1 − q) for n = 1 and g = 1. W...

The proper Euclidean geometry is considered to be metric space and described in terms of only metric and finite metric subspaces (σ-immanent description). Constructing the geometry, one does not use topology and topological properties. For instance, the straight, passing through points A and B, is defined as a set of such points R that the area S(A,B,R) of triangle ABR vanishes. The triangle ar...

The analysis of holomorphic sections of high powers L of holomorphic ample line bundles L → M over compact Kähler manifolds has been widely applied in complex geometry and mathematical physics. Any polarized Kähler metric g with respect to the ample line bundle L corresponds to the Ricci curvature of a hermitian metric h on L. Any orthonormal basis {SN 0 , ..., S dN} of H(M,L ) induces a holomo...

In 2014, Zead Mustafa introduced $b_2$-metric spaces, as a generalization of both $2$-metric and $b$-metric spaces. Then new fixed point results for the classes of  rational Geraghty contractive mappings of type I,II and III in the setup of $b_2$-metric spaces are investigated. Then, we prove some fixed point theorems under various contractive conditions in partially ordered $b_2$-metric spaces...

The use of coal is responsible for (1)/(5) of global greenhouse gas (GHG) emissions. Substitution of coal with biomass fuels is one of a limited set of near-term options to significantly reduce these emissions. We investigate, on a life cycle basis, 100% wood pellet firing and cofiring with coal in two coal generating stations (GS) in Ontario, Canada. GHG and criteria air pollutant emissions ar...