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 ...

The purpose of this paper is to study the distribution zeros solutions a first-order neutral differential equation form \begin{equation*} \left[x(t) + p(t) x(t-\tau)\right]' q(t) x(t-\sigma) = 0, \quad t \geq t_0, \end{equation*} where $p\in C([t_0,\infty),[0,\infty))$, $q \in C([t_0,\infty),(0,\infty))$, $\tau,\sigma>0$, and $\sigma>\tau$. We obtain new upper bound estimates for distance betwe...

We report anisotropic resistivity measurements of the heavy-fermion superconductor CeRh$_2$As$_2$ in magnetic fields up to 16 T and temperatures down 0.35 K. The measured shows a signature corresponding suggested quadrupole density wave order state at $T_0 \sim$ 0.5 K for both directions. For field applied along tetragonal $a$ axis, $T_0$ is enhanced with reaching $\sim$1.75 T. Further, field-i...

In this paper, we characterize explicitly the separation properties $T_0$ and $T_1$ at a point p in topological category of quantale-valued preordered spaces investigate how these characterizations are related. Moreover, prove that local hereditary productive.

We prove that Simulated Annealing with an appropriate cooling schedule computes arbitrarily tight constant-factor approximations to the minimum spanning tree problem in polynomial time. This result was conjectured by Wegener (2005). More precisely, denoting $n, m, w_{\max}$, and $w_{\min}$ number of vertices edges as well maximum edge weight MST instance, we simulated annealing initial temperat...

In this short note, we prove that if u solves $$(\partial _t - \Delta )^s = Vu$$ in $${\mathbb {R}}^n_x \times {\mathbb {R}}_t$$ , and vanishes to infinite order at a point $$(x_0, t_0)$$ then $$u \equiv 0$$ . This sharpens (and completes) our earlier result proves $$u(\cdot t) for $$t \le t_0$$ it

In this paper, we prove the mean-convex neighborhood conjecture for neck singularities of mean curvature flow in $${\mathbb {R}}^{n+1}$$ all $$n\ge 3$$ : show that if a $$\{M_t\}$$ has an $$S^{n-1}\times {\mathbb {R}}$$ singularity at $$(x_0,t_0)$$ , then there exists $$\varepsilon =\varepsilon (x_0,t_0)>0$$ such $$M_t\cap B(x_0,\varepsilon )$$ is $$t\in (t_0-\varepsilon ^2,t_0+\varepsilon ^2)$...

It is well-known that observability (and, by duality, controllability) of the elliptic wave equation, i.e., with a Riemannian Laplacian, in time $T_0$ almost equivalent to Geometric Control Condition (GCC), which stipulates any geodesic ray meets control set within $T_0$. We show subelliptic setting, GCC never verified, and equations are observable finite time. More precisely, given Laplacian $...