Our aim is the development and analysis of numerical schemes for approximately solving backward diffusion-wave problem, which involves a fractional derivative in time with order $\alpha\in(1,2)$. From terminal observations at two levels, i.e., $u(T_1)$ $u(T_2)$, we simultaneously recover initial data $u(0)$ $u_t(0)$ hence solution $u(t)$ all $t > 0$. First, existence, uniqueness, Lipschitz stab...

Strong anomalous diffusion is characterized by asymptotic power-law growth of the moments displacement, with exponents that do not depend linearly on order moment. The concerning small-order are dominated random motion, while higher-order grow faster trajectories, such as ballistic excursions or "light fronts". Often a situation two linear dependencies their order. Here, we introduce simple exa...

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...

We study the Kardar-Parisi-Zhang equation on half-line $x \geqslant 0$ with Neumann type boundary condition. Stationary measures of KPZ dynamics were characterized in recent work: they depend two parameters, parameter $u$ dynamics, and drift $-v$ initial condition at infinity. consider fluctuations height field when is given by one these stationary processes. At large time $t$, it natural to re...

We show that, in relativistic field theories, the thermal correlation function of N bosonic operators at sufficiently spacelike-separated points shows exponentially weak dependence on time variables t_1,...,t_N, when space separations are held fixed. For classical theory, vanishes all spacelike separated

In this paper we consider two recovery problems based on information given with an error. First is the problem of optimal class $W^T_q = \{(t_1h_1,t_2h_2,\ldots)\in \ell_q\,:\,\|h\|_q\leqslant 1\}$, where $1\le q < \infty$ and $t_1\geqslant t_2\geqslant \ldots \geqslant 0$, in space $\ell_q$ when capacity inexact know either first $n\in\mathbb{N}$ elements a sequence error measured finite seque...

We study the bi-commutators $[T_1, [b, T_2]]$ of pointwise multiplication and Calder\'on-Zygmund operators, characterize their $L^{p_1}L^{p_2} \to L^{q_1}L^{q_2}$ boundedness for several off-diagonal regimes mixed-norm integrability exponents $(p_1,p_2)\neq(q_1,q_2)$. The strategy is based on a bi-parameter version recent approximate weak factorization method.

Double blind $T$-private information retrieval (DB-TPIR) enables two users, each of whom specifies an index ($\theta_1, \theta_2$, resp.), to efficiently retrieve a message $W(\theta_1,\theta_2)$ labeled by the indices, from set $N$ servers that store all messages $W(k_1,k_2), k_1\in\{1,2,\cdots,K_1\}, k_2\in\{1,2,\cdots,K_2\}$, such users' indices are kept private any up $T_1,T_2$ colluding se...