scholarly journals Feedback exponential stabilization of the semilinear heat equation with nonlocal initial conditions

2021 ◽  
Vol 26 (6) ◽  
pp. 1106-1122
Author(s):  
Ionuţ Munteanu
Keyword(s):  
Heat Equation ◽  
Closed Loop ◽  
Initial Conditions ◽  
Dimensional Structure ◽  
One Dimensional ◽  
Loop Equation ◽  
Nonlocal Initial Conditions ◽  
Semilinear Heat Equation ◽  
Finite Dimensional ◽  
The One

The present paper is devoted to the problem of stabilization of the one-dimensional semilinear heat equation with nonlocal initial conditions. The control is with boundary actuation. It is linear, of finite-dimensional structure, given in an explicit form. It allows to write the corresponding solution of the closed-loop equation in a mild formulation via a kernel, then to apply a fixed point argument in a convenient space.

One-Dimensional Fluorescent Nanosized-Diamond Nanowires with Fluorescent Detection of Vitamin B12

NANO ◽  
2019 ◽  
Vol 14 (07) ◽  
pp. 1950084 ◽  
Author(s):  
Jilong Wang ◽  
Siheng Su ◽  
Jingjing Qiu ◽  
Shiren Wang
Keyword(s):  
Electron Microscopy ◽  
Photoelectron Spectroscopy ◽  
High Sensitivity ◽  
Anodic Aluminum Oxide Template ◽  
Fluorescent Detection ◽  
Dimensional Structure ◽  
Fluorescent Properties ◽  
One Dimensional ◽  
Sensitivity And Selectivity ◽  
The One

In this paper, a novel and facile method to achieve fluorescent nanosized-diamond based nanowire (NW) is reported. One-dimensional (1D) organic NW has received tremendous attention due to its superior chemical functionality and size-, shape-, and material-dependent properties. In addition, nanosized-diamond is comprehensively studied and investigated due to superior tunable fluorescent properties, cost-effectiveness, facile manufacturing and high biocompatibility. Through thermal treatment, sulfur-modified nanosized-diamond was fabricated by mixing oxidized nanosized-diamond and dibenzyl disulfide at 900∘C. Fourier transform infrared spectroscopy (FTIR), X-ray photoelectron spectroscopy (XPS) and zeta potential were employed to characterize sulfur-modified nanosized-diamond. After that, porous anodic aluminum oxide template-assisted cathodic electrophoretic deposition method was used to achieve sulfur-modified nanosized-diamond NW. Scanning electron microscopy and transmission electron microscopy were applied to present the one-dimensional structure of the NWs. The optical properties of sulfur nanosized-diamond NW were characterized via ultraviolet-visible spectroscopy and photoluminescence spectroscopy. Finally, the as-synthesized sulfur-modified nanosized-diamond NW-based optical sensor was fabricated to detect vitamin B[Formula: see text] with high sensitivity and selectivity.

scholarly journals Optimising Matrix Product State Simulations of Shor's Algorithm

Quantum ◽  
2019 ◽  
Vol 3 ◽  
pp. 116 ◽  
Author(s):  
Aidan Dang ◽  
Charles D. Hill ◽  
Lloyd C. L. Hollenberg
Keyword(s):  
Dimensional Structure ◽  
Matrix Product ◽  
Product State ◽  
One Dimensional ◽  
Matrix Product State ◽  
Shor's Algorithm ◽  
The One ◽  
High Level ◽  
Space Requirements ◽  
Factoring Algorithm

We detail techniques to optimise high-level classical simulations of Shor's quantum factoring algorithm. Chief among these is to examine the entangling properties of the circuit and to effectively map it across the one-dimensional structure of a matrix product state. Compared to previous approaches whose space requirements depend on r, the solution to the underlying order-finding problem of Shor's algorithm, our approach depends on its factors. We performed a matrix product state simulation of a 60-qubit instance of Shor's algorithm that would otherwise be infeasible to complete without an optimised entanglement mapping.

scholarly journals Identifying the heat sink

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
J. D. Audu ◽  
A. Boumenir ◽  
K. M. Furati ◽  
I. O. Sarumi
Keyword(s):  
Inverse Problem ◽  
Heat Equation ◽  
Temperature Profile ◽  
Spectral Methods ◽  
Heat Sink ◽  
Evolution Equations ◽  
Identification Problem ◽  
One Dimensional ◽  
Finite Dimensional ◽  
Pseudo Spectral

<p style='text-indent:20px;'>In this paper we examine the identification problem of the heat sink for a one dimensional heat equation through observations of the solution at the boundary or through a desired temperature profile to be attained at a certain given time. We make use of pseudo-spectral methods to recast the direct as well as the inverse problem in terms of linear systems in matrix form. The resulting evolution equations in finite dimensional spaces leads to fast real time algorithms which are crucial to applied control theory.</p>

scholarly journals On the Reachable Set for the One-Dimensional Heat Equation

2018 ◽  
Vol 56 (3) ◽  
pp. 1692-1715 ◽  
Author(s):  
Jérémi Dardé ◽  
Sylvain Ervedoza
Keyword(s):  
Heat Equation ◽  
Reachable Set ◽  
One Dimensional ◽  
The One
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