The purpose of this paper is to consider the physical curvature-deformation of a physical matter-free astro-region, generated by an external field energy attack. The deformed but stable state of the situation suggests an appropriate dynamical view on the physical structure of this region which is based on the existing real physical external disturbances, and on the real surviving answer-disturbances. This physical understanding of the situation, i.e., stress-answer-stress, leads to a corresponding attack-deformation formal theoretical view. Such physically deformed real physical region will demonstrate itself in two ways - physicallyand geometrically, i.e., new energy distribution, and new geometrical structure. Our purpose is these real coherence and surviving aspects of the new physical stress-strain condition to acquire formal tensor presentation. The spherically symmetric case is considered from this physical-geometrical view.

We study the existence and the location of coupled fixed points for a composition of two pseudo-contractive-type set-valued mappings in the setting of partial metric spaces by using Bianchini-Grandolfi gauge functions.

We study the spectral properties of the family of self-adjoint bounded discrete Schr{\"o}dinger-type operators in the Hilbert space of square-summable complex-valued functions defined on the d-dimensional lattice. We completely describe the discrete spectrum of Schr{\"o}dinger-type operators lying outside the essential spectrum and study the location and the uniqueness, analyticity, monotonicity and convexity properties of eigenvalues depending on all of the parameters. Moreover, in the case of existence we obtain the asymptotics of eigenvalues of Schr{\"o}dinger-type operator.

One parameter deformation of gamma function is given by means of convergent star product, where the deformation parameter is a complex number with negative real part. Several basic identities of gamma function are deformed to give ones for the deformed gamma function.