In this paper, the pseudo-inversion of degenerate metric is considered. We extend Szabó operators associated to algebraic covariant derivative curvature maps (tensors) to lightlike hypersurfaces. Some examples are given with explicit determination of their Szabó operators. Finally, we introduce the notion of lightlike Szabó hypersurfaces and give some characterization results of locally symmetric lightlike hypersurfaces and semi-symmetric lightlike hypersurfaces from Szabó condition.

The purpose of this paper is to study left multipliers satisfying certain identities on Jordan ideals of rings with involution. Some well known results characterizing commutativity of prime rings by left multipliers have also been extended to Jordan ideals.

In this paper, we investigate some new existence results for nonlinear fractional differential equations of order $q \in (1,2]$ with four-point nonlocal integral boundary conditions by applying standard fixed point theorems and Leray-Schauder degree theory. Our results are new in the sense that the nonlocal parameters in four-point integral boundary conditions for the problem appear in the integral part of the conditions in contrast to the available literature on four-point fractional boundary value problems which deals with the four-point boundary conditions restrictions on the solution or gradient of the solution of the problem. Some illustrative examples are presented.

In this paper, we attempt to construct a class of Armendariz-Like properties. We investigate the transfer of the Armendariz-Like properties to trivial ring extensions to localization and direct product of rings, and then generate new families of rings with zero-divisors subject to some given Armendariz-like properties. The article includes a brief discussion of the scope and precision of our results.

Global existence of solutions to the coupled Einstein-Maxwell system which rules the dynamics of the considered relativistic charged fluid is proved and asymptotic behavior is investigated, in the case of positive cosmological constant and positive initial velocity of the cosmological expansion factor..

We consider the existence of a periodic solution to the first-order nonlinear problem

\begin{eqnarray*} &&x'(t) = -a(t)x(t)+ q ( t, x(t) ),\; \mbox{ a.e. on } (0, T),\\ &&x(0) = x(T), \end{eqnarray*}

where the nonlinear term $q$ is Carathéodory with respect to $L^1[0, T]$. The coefficient function $a$ is such that the differential equation is non-invertible. The technique used to establish our existence result is Mahwin's coincidence degree theory.

For a given vector field $\nu(x)$ around a nonsingular point $x_0$, we provide explicit coordinates $z=\varphi(x)$ in which the vector field is straightened out, i. e., $\varphi_{*}(\nu)(z)=\frac{\partial}{\partial z_1}.$ The procedure is generalized to Frob\"{e}nius Theorem, namely, for an involutive distribution $\Delta={\rm span} \, \left \{\nu_1, \dots, \nu_m \right \}$ around a nonsingular point $x_0$, we give explicit coordinates $z=\varphi(x)$ in which

$$ {\varphi_{*}\Delta= {\rm span} \left \{\frac{\partial}{\partial z_1}, \dots, \frac{\partial}{\partial z_m} \right \}.} $$

The method is illustrated by several examples and is applied to the linearization of control systems.

This paper deals with affine Osserman connections on 2-dimensional manifolds. We give in an explicit form, a sufficient condition for an affine connection to be Osserman. As applications, examples of affine Osserman connections are given.

This paper addresses exponential stability problem for a class of nonlinear systems with mixed time-varying delays. The time delays are non-differentiable functions belonging to a given interval, in which the lower bound of delay is not restricted to zero. By constructing a suitable augmented Lyapunov’s functional, new criteria for the exponential stability of the system are established in terms of linear matrix inequalities. The result has been applied to robust stability problem of uncertain systems with interval time-varying delays. Numerical examples are given to show the effectiveness of the conditions.

In this paper we study the exact controllability of the following semilinear stochastic evolution equation in a Hilbert space $X$

$$ dx(t)=\{Ax(t)+Bu(t)+f(t,\omega,x(t),u(t)) \}dt + \{\Sigma(t) +\sigma(t,\omega,x(t),u(t)) \}dw(t), $$

where the control $u$ is a stochastic process in the Hilbert space $U$, $A:D(A)\subset X\rightarrow X,$ is the infinitesimal generator of a strongly continuous semigroup $\left\{S(t)\right\}_{t\geq 0}$ on $X$ and $B\in L(U,X)$. To this end, we give necessary and sufficient conditions for the exact controllability of the linear part of this system

$$ dx(t)=Ax(t)dt+Bu(t)dt+\Sigma(t)dw(t). $$

Then, under a Lipschitzian condition on the non linear terms $f$ and $\sigma$ we prove that the exact controllability of this linear system is preserved by the semilinear stochastic system. Moreover, we obtain explicit formulas for a control steering the system from the initial state $\xi_0$ to a final state $\xi_1$ on time $T >0$, for both system, the linear and the nonlinear one. Finally, we apply this result to a semilinear damped stochastic wave equation.