Abstract We consider fragments of uniform reflection for formulas in the analytic hierarchy over theories second order arithmetic. The main result is that any arithmetic theory $T_0$ extending $\mathsf {RCA}_0$ and axiomatizable by a $\Pi ^1_{k+2}$ sentence, $n\geq k+1$ , $$\begin{align*}T_0+ \mathrm{RFN}_{\varPi^1_{n+2}}(T) \ = T_0 + \mathrm{TI}_{\varPi^1_n}(\varepsilon_0), \end{align*}$$ \mat...

Assume that $${\mathbb {F}}$$ is an algebraically closed field and let q denote a nonzero scalar in not root of unity. The universal Askey–Wilson algebra $$\triangle _q$$ unital associative -algebra defined by generators relations. are A, B, C the relations state each $$\begin{aligned} A+\frac{q BC-q^{-1} CB}{q^2-q^{-2}}, \qquad B+\frac{q CA-q^{-1} AC}{q^2-q^{-2}}, C+\frac{q AB-q^{-1} BA}{q^2-q...

Recently, a first-order differentiator based on time-varying gains was introduced in the literature, its non recursive form, for class of differentiable signals $y(t)$, satisfying $|\ddot{y}(t)|\leq L(t-t_0)$, known function $L(t-t_0)$, such that $\frac{1}{L(t-t_0)}\left|\frac{d {L}(t-t_0)}{dt}\right|\leq M$ with constant $M$. It has been shown is globally finite-time convergent. In this paper,...

Let $E/\mathbb Q(t)$ be an elliptic curve and let $t_0 \in \mathbb Q$ a rational number for which the specialization $E_{t_0}$ is curve. In 2015, Gusić Tadić gave easy-to-check criterion, based only on Weierstrass equation $E/\

Volterra subdiffusion problems with weakly singular kernel describe the dynamics of processes well. The graded L1 scheme is often chosen to discretize such since it can handle singularity solution near $$t = 0$$ . In this paper, we propose a modification. We first split time interval [0, T] into $$[0, T_0]$$ and $$[T_0, T]$$ , where $$T_0$$ ( $$0< T_0 < T$$ ) reasonably small. Then, applied in ...

We study here $T_{0}$-$Q$-bitopological spaces and sober $Q$-bitopological spaces and their relationship with two particular Sierpinski objects in the category of $Q$-bitopological spaces. The epireflective hulls of both these Sierpinski objects in the category of $Q$-bitopological spaces turn out to be the category of $T_0$-$Q$-bitopological spaces. We show that only one of these Sierpinski ob...

In this paper we study a gradient flow generated by the Landau--de Gennes free energy that describes nematic liquid crystal configurations in space of $Q$-tensors. This density functional is composed three quadratic terms as elastic part, and singular potential bulk part considered natural enforcement physical constraint on eigenvalues $Q$. The system nondiagonal parabolic with which trends to ...