On the Oscillatory Behavior of Some Qeneralized Differential Equation

In this article, using the Riccati-type transformation, we study the oscillatory nature of the solutions of the generalized differential equation and give some criteria of the Kamenev type that generalizes several well-known results on the topic.

Fixed Point Theorems for Generalized Set-Valued Weak θ-Contractions in Complete Metric Spaces

In this paper, the notion of generalized set-valued weak θ-contractions is introduced and a new fixed point theorem for such contractions is established in the setting metric spaces. The main result is a generalization of fixed point theorems in the literature. An example and an application to generalized differential equation are given to support the validity of the main theorem.

Identification of highly deformed even–even nuclei in the neutron- and proton-rich regions of the nuclear chart from the B(E2)↑ and E2 predictions in the generalized differential equation model

We identify here the possible occurrence of large deformations in the neutron- and proton-rich ([Formula: see text]-rich and [Formula: see text]-rich) regions of the nuclear chart from extensive predictions of the values of the reduced quadrupole transition probability [Formula: see text] for the transition from the ground state to the first [Formula: see text] state and the corresponding excitation energy [Formula: see text] of even–even nuclei in the recently developed generalized differential equation (GDE) model exclusively meant for these physical quantities. This is made possible from our analysis of the predicted values of these two physical quantities and the corresponding deformation parameters derived from them such as the quadrupole deformation [Formula: see text], the ratio of [Formula: see text] to the Weisskopf single-particle [Formula: see text] and the intrinsic electric quadrupole moment [Formula: see text], calculated for a large number of both known as well as hitherto unknown even–even isotopes of oxygen to fermium (0 to FM; [Formula: see text]–100). Our critical analysis of the resulting data convincingly support possible existence of large collectivity for the nuclides [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text], whose values of [Formula: see text] are found to exceed 0.3 and even 0.4 in some cases. Our findings of large deformations in the exotic [Formula: see text]-rich regions support the existence of another “island of inversion” in the heavy-mass region possibly caused by breaking of the [Formula: see text] subshell closure.

Study onH-Index of Stochastic Linear Continuous-Time Systems

This paper studies theH-index problem. We obtain a necessary and sufficient condition ofH-index larger thanγ>0. A generalized differential equation is introduced and it is proved that its solvability and the feasibility of theH-index are equivalent. We extend the deterministic cases to the stochastic models. Our results can be used to fault detection filter analysis. Finally, the effectiveness of the proposed results is illustrated by an example.

On Solutions for a Generalized Differential Equation Arising in Boundary Layer Problem

We treat the existence and uniqueness of a solution for the generalized Blasius problem which arises in boundary layer theory. The shooting method is used in the proof of our main result. An example is included to illustrate the results.