In this paper, we introduce a new extension of the power Lindley distribution, called
the exponentiated generalized power Lindley distribution. Several mathematical properties of
the new model such as the shapes of the density and hazard rate functions, the quantile function,
moments, mean deviations, Bonferroni and Lorenz curves and order statistics are derived.
Moreover, we discuss the parameter estimation of the new distribution using the maximum
likelihood and diagonally weighted least squares methods. A simulation study is performed to
evaluate the estimators. We use two real data sets to illustrate the applicability of the new
model. Empirical findings show that the proposed model provides better fits than some other
well-known extensions of Lindley distributions.

In this paper, we discuss the closed finite-to-one mapping theorems on generalized
metric spaces and their applications. It is proved that point-G properties, @0-snf-countability
and csf-countability are invariants and inverse invariants under closed finite-to-one mappings.
By the relationships between the weak first-countabilities, we obtain the closed finite-to-one
mapping theorems of weak quasi-first-countability, quasi-first-countability, snf-countability, gf-
countability and sof-countability. Furthermore, these results are applied to the study of symmetric
products of topological spaces.

In this paper, in terms of Wiener index, hyper-Wiener index and Harary index, we
first give some sufficient conditions for a nearly balance bipartite graph with given minimum
degree to be traceable. Secondly, we establish some conditions for a k-connected graph to be
Hamilton-connected and traceable for every vertex, respectively.

The parity operator P and time reversal operator T are two important operators in
the quantum theory, in particular, in the PT -symmetric quantum theory. By using the concrete
forms of P and T , we discuss their geometrical properties in two dimensional spaces. It is showed
that if T is given, then all P links with the quadric surfaces; if P is given, then all T links with
the quadric curves. Moreover, we give out the generalized unbroken PT -symmetric condition of
an operator. The unbroken PT -symmetry of a Hermitian operator is also showed in this way.

Under linear expectation (or classical probability), the stability for stochastic differential
delay equations (SDDEs), where their coefficients are either linear or nonlinear but
bounded by linear functions, has been investigated intensively. Recently, the stability of highly
nonlinear hybrid stochastic differential equations is studied by some researchers. In this paper,
by using Peng’s G-expectation theory, we first prove the existence and uniqueness of solutions
to SDDEs driven by G-Brownian motion (G-SDDEs) under local Lipschitz and linear growth
conditions. Then the second kind of stability and the dependence of the solutions to G-SDDEs
are studied. Finally, we explore the stability and boundedness of highly nonlinear G-SDDEs.

Since the financial crisis in 2008, the risk measures which are the core of risk management,
have received increasing attention among economists and practitioners. In this review,
the concentration is on recent developments in the estimation of the most popular risk measures,
namely, value at risk (VaR), expected shortfall (ES), and expectile. After introducing the concept
of risk measures, the focus is on discussion and comparison of their econometric modeling.
Then, parametric and nonparametric estimations of tail dependence are investigated. Finally,
we conclude with insights into future research directions.

Similarity measure is an essential tool to compare and determine the degree of
similarity between intuitionistic fuzzy sets (IFSs). In this paper, a new similarity measure
between intuitionistic fuzzy sets based on the mid points of transformed triangular fuzzy numbers
is proposed. The proposed similarity measure provides reasonable results not only for the sets
available in the literature but also gives very reasonable results, especially for fuzzy sets as well
as for most intuitionistic fuzzy sets. To provide supportive evidence, the proposed similarity
measure is tested on certain sets available in literature and is also applied to pattern recognition
and medical diagnosis problems. It is observed that the proposed similarity measure provides a
very intuitive quantification.