Gravitational waves from binary neutron stars

I review the current global status of research on gravitational waves emitted from mergers of binary neutron star systems, focusing on general-relativistic simulations and their use to interpret data from the gravitational-wave detectors, especially in relation to the equation of state of compact stars.

Uniform and weak stability of Bresse system with one infinite memory in the shear angle displacements

In this paper, we consider a one-dimensional linear Bresse system in a bounded open interval with one infinite memory acting only on the shear angle equation. First, we establish the well posedness using the semigroup theory. Then, we prove two general (uniform and weak) decay estimates depending on the speeds of wave propagations and the arbitrary growth at infinity of the relaxation function.

Collapse of quasi-two-dimensional symmetrized Dresselhaus spin-orbit coupled Bose–Einstein condensate

Here, we study the collapse process of quasi-two-dimensional Bose–Einstein condensate with symmetrized Dresselhaus spin–orbit coupling. We show that at a sufficiently strong spin–orbit coupling the arising spin-dependent velocity compensates the attraction between particles and can prevent the collapse of the condensate. As a result, spin–orbit coupling can lead to a stable condensate rather than the collapse process.

Almost everywhere convergence and divergence of Cesàro means with varying parameters of Walsh–Fourier series

In the present paper, we prove the almost everywhere convergence and divergence of subsequences of Cesàro means with zero tending parameters of Walsh–Fourier series.

Optimality conditions for robust weak sharp efficient solutions of nonsmooth uncertain multiobjective optimization problems

In this paper, we investigate an uncertain multiobjective optimization problem involving nonsmooth and nonconvex functions. The notion of a (local/global) robust weak sharp efficient solution is introduced. Then, we establish necessary and sufficient optimality conditions for local and/or the robust weak sharp efficient solutions of the considered problem. These optimality conditions are presented in terms of multipliers and Mordukhovich/limiting subdifferentials of the related functions.

On the representations of the braid group constructed by C. M. Egea and E. Galina

In this paper, we determine a sufficient condition for the irreducibility of the family of representations of the braid group constructed by C. M. Egea and E. Galina without requiring that the representations are self-adjoint. Then, we construct a new subfamily of multi-parameter representations $$(\psi _m,V_m), $$ ( ψ m , V m ) , $$1\le m< n$$ 1 ≤ m < n , of dimension $$ V_m =\left( {\begin{array}{c}n\\ m\end{array}}\right) $$ V m = n m . Finally, we study the irreducibility of $$(\psi _m,V_m) $$ ( ψ m , V m ) .

A new self-adaptive accelerated method for generalized split system of common fixed-point problem of averaged mappings

The purpose of this paper is to propose a new inertial self-adaptive algorithm for generalized split system of common fixed point problems of finite family of averaged mappings in the framework of Hilbert spaces. The weak convergence theorem of the proposed method is given and its theoretical application for solving several generalized problems is presented. The behavior and efficiency of the proposed algorithm is illustrated by some numerical tests.

Approximation of functions by Bernoulli wavelet and its applications in solution of Volterra integral equation of second kind

In this paper, two new estimators $$ E_{2^{k-1},0}^{(1)}(f) $$ E 2 k - 1 , 0 ( 1 ) ( f ) and $$ E_{2^{k-1},M}^{(1)}(f) $$ E 2 k - 1 , M ( 1 ) ( f ) of characteristic function and an estimator $$ E_{2^{k-1},M}^{(2)}(f) $$ E 2 k - 1 , M ( 2 ) ( f ) of function of H$$\ddot{\text {o}}$$ o ¨ lder’s class $$H^{\alpha } [0,1)$$ H α [ 0 , 1 ) of order $$0<\alpha \leqslant 1$$ 0 < α ⩽ 1 have been established using Bernoulli wavelets. A new technique has been applied for solving Volterra integral equation of second kind using Bernoulli wavelet operational matrix of integration as well as product operational matrix. These matrices have been utilized to reduce the Volterra integral equation into a system of algebraic equations, which are easily solvable. Some examples are illustrated to show the validity and efficiency of proposed technique of this research paper.

Wormhole solutions with NUT charge in higher curvature theories

We present wormholes with a Newman–Unti–Tamburino (NUT) charge that arise in certain higher curvature theories, where a scalar field is coupled to a higher curvature invariant. For the invariants we employ (i) a Gauss–Bonnet term and (ii) a Chern–Simons term, which then act as source terms for the scalar field. We map out the domain of existence of wormhole solutions by varying the coupling parameter and the scalar charge for a set of fixed values of the NUT charge. The domain of existence for a given NUT charge is then delimited by the set of scalarized nutty black holes, a set of wormhole solutions with a degenerate throat and a set of singular solutions.

Scalarized black holes

Black holes represent outstanding astrophysical laboratories to test the strong gravity regime, since alternative theories of gravity may predict black hole solutions whose properties may differ distinctly from those of general relativity. When higher curvature terms are included in the gravitational action as, for instance, in the form of the Gauss–Bonnet term coupled to a scalar field, scalarized black holes result. Here we discuss several types of scalarized black holes and some of their properties.