scholarly journals Multi-step inertial proximal contraction algorithms for monotone variational inclusion problems

2020 ◽  
Vol 36 (1) ◽  
pp. 159-177
Author(s):  
JIAJIA CHEN ◽  
QIAO-LI DONG ◽  
CUIJIE ZHANG
Keyword(s):  
Hilbert Space ◽  
Numerical Experiments ◽  
Monotone Operators ◽  
Iterative Sequence ◽  
Unconditional Convergence ◽  
Inclusion Problems ◽  
Proximal Contraction ◽  
Lipschitz Continuous ◽  
One Step ◽  
The One

"In this article, we introduce the multi-step inertial proximal contraction algorithms (MiPCA) to approximate a zero of the sum of two monotone operators, with one of the two operators being monotone and Lipschitz continuous. The weak convergence of the MiPCA is shown under the summability condition formulated in terms of the iterative sequence in a Hilbert space setting. We also investigate the unconditional convergence of the one-step inertial proximal contraction algorithm. Finally, numerical experiments are given to illustrate the advantage of the multi-step inertial proximal contraction algorithms."

scholarly journals Simulation of a Walking Robot-Exoskeleton Movement on a Movable Base

2021 ◽  
Author(s):  
Sergey Jatsun ◽  
Andrei Malchikov ◽  
Andrey Yatsun ◽  
Al Manji Khalil ◽  
Andres Santiago Martinez Leon
Keyword(s):  
Numerical Experiments ◽  
Position Control ◽  
Software Implementation ◽  
Dynamic Parameters ◽  
Mathematical Apparatus ◽  
Walking Robot ◽  
Walking Machine ◽  
One Step ◽  
The One ◽  
Position Control System

The paper studies the problem of movement of a two-legged walking machine on a movable base. This task is relevant for design rehabilitation and mechanotherapy complexes for people with impaired functions of the musculoskeletal system. Presents a mathematical model that allows obtaining the kinematic and dynamic parameters of the movement of the executive units of the device under study. The paper presents a method for planning the trajectory of exoskeleton links, its algorithmic and software implementation. The paper proposes the structure of the automatic link position control system, which ensures the movement of the executive links along a given trajectory. A mathematical apparatus is proposed for studying the dynamics of the controlled movement of the links of the human-machine system of the exoskeleton. The article presents the results of numerical experiments on the movement of the low-limb exoskeleton leg in the one step mode and analyzes them.

A Study on the Rearrangement of Dialkyl 1-Aryl-1-hydroxymethylphosphonates to Benzyl Phosphates

2020 ◽  
Vol 24 (4) ◽  
pp. 465-471 ◽  
Author(s):  
Zita Rádai ◽  
Réka Szabó ◽  
Áron Szigetvári ◽  
Nóra Zsuzsa Kiss ◽  
Zoltán Mucsi ◽  
...  
Keyword(s):  
Quantum Chemical ◽  
Room Temperature ◽  
Phase Transfer ◽  
One Pot ◽  
Substrate Dependence ◽  
Triethylbenzylammonium Chloride ◽  
One Step ◽  
The Pudovik Reaction ◽  
The One ◽  
Solid Liquid

The phospha-Brook rearrangement of dialkyl 1-aryl-1-hydroxymethylphosphonates (HPs) to the corresponding benzyl phosphates (BPs) has been elaborated under solid-liquid phase transfer catalytic conditions. The best procedure involved the use of triethylbenzylammonium chloride as the catalyst and Cs2CO3 as the base in acetonitrile as the solvent at room temperature. The substrate dependence of the rearrangement has been studied, and the mechanism of the transformation under discussion was explored by quantum chemical calculations. The key intermediate is an oxaphosphirane. The one-pot version starting with the Pudovik reaction has also been developed. The conditions of this tandem transformation were the same, as those for the one-step HP→BP conversion.

scholarly journals Inducing strong convergence of trajectories in dynamical systems associated to monotone inclusions with composite structure

2020 ◽  
Vol 10 (1) ◽  
pp. 450-476
Author(s):  
Radu Ioan Boţ ◽  
Sorin-Mihai Grad ◽  
Dennis Meier ◽  
Mathias Staudigl
Keyword(s):  
Dynamical Systems ◽  
Strong Convergence ◽  
Equilibrium Problems ◽  
Monotone Operators ◽  
Inclusion Problem ◽  
Minimum Norm ◽  
Monotone Inclusion ◽  
Inclusion Problems ◽  
Monotone Inclusion Problem ◽  
Maximally Monotone Operators

Abstract In this work we investigate dynamical systems designed to approach the solution sets of inclusion problems involving the sum of two maximally monotone operators. Our aim is to design methods which guarantee strong convergence of trajectories towards the minimum norm solution of the underlying monotone inclusion problem. To that end, we investigate in detail the asymptotic behavior of dynamical systems perturbed by a Tikhonov regularization where either the maximally monotone operators themselves, or the vector field of the dynamical system is regularized. In both cases we prove strong convergence of the trajectories towards minimum norm solutions to an underlying monotone inclusion problem, and we illustrate numerically qualitative differences between these two complementary regularization strategies. The so-constructed dynamical systems are either of Krasnoselskiĭ-Mann, of forward-backward type or of forward-backward-forward type, and with the help of injected regularization we demonstrate seminal results on the strong convergence of Hilbert space valued evolutions designed to solve monotone inclusion and equilibrium problems.

scholarly journals Integrating Semilinear Wave Problems with Time-Dependent Boundary Values Using Arbitrarily High-Order Splitting Methods

Mathematics ◽  
2021 ◽  
Vol 9 (10) ◽  
pp. 1113
Author(s):  
Isaías Alonso-Mallo ◽  
Ana M. Portillo
Keyword(s):  
Numerical Experiments ◽  
Splitting Method ◽  
Method Of Lines ◽  
Time Integration ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
High Order ◽  
Time Dependent ◽  
Boundary Values ◽  
Lipschitz Continuous

The initial boundary-value problem associated to a semilinear wave equation with time-dependent boundary values was approximated by using the method of lines. Time integration is achieved by means of an explicit time method obtained from an arbitrarily high-order splitting scheme. We propose a technique to incorporate the boundary values that is more accurate than the one obtained in the standard way, which is clearly seen in the numerical experiments. We prove the consistency and convergence, with the same order of the splitting method, of the full discretization carried out with this technique. Although we performed mathematical analysis under the hypothesis that the source term was Lipschitz-continuous, numerical experiments show that this technique works in more general cases.

scholarly journals One-Year Clinical Evaluation of the Bonding Effectiveness of a One-Step, Self-Etch Adhesive in Noncarious Cervical Lesion Therapy

2015 ◽  
Vol 2015 ◽  
pp. 1-5 ◽  
Author(s):  
Babacar Faye ◽  
Mouhamed Sarr ◽  
Khaly Bane ◽  
Adjaratou Wakha Aidara ◽  
Seydina Ousmane Niang ◽  
...  
Keyword(s):  
Clinical Performance ◽  
Retention Rate ◽  
Recall Rate ◽  
Acid Etching ◽  
Significant Difference ◽  
Usphs Criteria ◽  
One Step ◽  
One Year ◽  
The One ◽  
Self Etch

This study evaluated the one-year clinical performance of a one-step, self-etch adhesive (Optibond All-in-One, Kerr, CA, USA) combined with a composite (Herculite XRV Ultra, Kerr Hawe, CA, USA) to restore NCCLs with or without prior acid etching. Restorations performed by the same practitioner were evaluated at baseline and after 3, 6, and 12 months using modified USPHS criteria. At 6 months, the recall rate was 100%. The retention rate was 84.2% for restorations with prior acid etching, but statistically significant differences were observed between baseline and 6 months. Without acid etching, the retention rate was 77%, and no statistically significant difference was noted between 3 and 6 months. Marginal integrity (93.7% with and 87.7% without acid etching) and discoloration (95.3% with and 92.9% without acid etching) were scored as Alpha or Bravo, with better results after acid etching. After one year, the recall rate was 58.06%. Loss of pulp vitality, postoperative sensitivity, or secondary caries were not observed. After one year retention rate was of 90.6% and 76.9% with and without acid conditioning. Optibond All-in-One performs at a satisfactory clinical performance level for restoration of NCCLs after 12 months especially after acid etching.

scholarly journals Building up cyclodextrins from scratch – templated enzymatic synthesis of cyclodextrins directly from maltose

2021 ◽  
Author(s):  
Dennis Larsen ◽  
Sophie R. Beeren
Keyword(s):  
Enzymatic Synthesis ◽  
Combinatorial Libraries ◽  
One Step ◽  
The One ◽  
Kinetic Trapping

Template-induced kinetic trapping of specific cyclodextrins in enzyme-mediated dynamic combinatorial libraries of linear and cyclic α-glucans enables the one-step synthesis of cyclodextrins from maltose in water.

scholarly journals Efficient Cryopreservation of Populus tremula by In Vitro-Grown Axillary Buds and Genetic Stability of Recovered Plants

Plants ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 77
Author(s):  
Elena O. Vidyagina ◽  
Nikolay N. Kharchenko ◽  
Konstantin A. Shestibratov
Keyword(s):  
Survival Rate ◽  
Axillary Buds ◽  
Long Term Storage ◽  
Average Survival ◽  
Transgenic Lines ◽  
Ssr Loci ◽  
One Step ◽  
The One

Axillary buds of in vitro microshoots were successfully frozen at –196 °C by the one-step freezing method using the protective vitrification solution 2 (PVS2). Microshoots were taken from 11 transgenic lines and three wild type lines. Influence of different explant pretreatments were analyzed from the point of their influence towards recovery after cryopreservation. It was found out that the use of axillary buds as explants after removal of the apical one increases recovery on average by 8%. The cultivation on growth medium of higher density insignificantly raises the regenerants survival rate. Pretreatment of the osmotic fluid (OF) shows the greatest influence on the survival rate. It leads to the increase in survival rate by 20%. The cryopreservation technology providing regenerants average survival rate of 83% was developed. It was based on the experimental results obtained with explant pretreatment. Incubation time in liquid nitrogen did not affect the explants survival rate after thawing. After six months cryostorage of samples their genetic variability was analyzed. Six variable simple sequence repeat (SSR) loci were used to analyze genotype variability after the freezing-thawing procedure. The microsatellite analysis showed the genetic status identity of plants after cryopreservation and of the original genotypes. The presence of the recombinant gene in the transgenic lines after cryostorage were confirmed so as the interclonal variation in the growth rate under greenhouse conditions. The developed technique is recommended for long-term storage of various breeding and genetically modified lines of aspen plants, as it provides a high percentage of explants survival with no changes in genotype.

scholarly journals Understanding mathematics of Grover’s algorithm

2021 ◽  
Vol 20 (5) ◽  
Author(s):  
Paweł J. Szabłowski
Keyword(s):  
Phase Change ◽  
Unitary Operator ◽  
Mathematical Structure ◽  
Complex Numbers ◽  
Unitary Operators ◽  
Grover’S Algorithm ◽  
Great Probability ◽  
Grover's Algorithm ◽  
One Step ◽  
The One

AbstractWe analyze the mathematical structure of the classical Grover’s algorithm and put it within the framework of linear algebra over the complex numbers. We also generalize it in the sense, that we are seeking not the one ‘chosen’ element (sometimes called a ‘solution’) of the dataset, but a set of m such ‘chosen’ elements (out of $$n>m)$$ n > m ) . Besides, we do not assume that the so-called initial superposition is uniform. We assume also that we have at our disposal an oracle that ‘marks,’ by a suitable phase change $$\varphi $$ φ , all these ‘chosen’ elements. In the first part of the paper, we construct a unique unitary operator that selects all ‘chosen’ elements in one step. The constructed operator is uniquely defined by the numbers $$\varphi $$ φ and $$\alpha $$ α which is a certain function of the coefficients of the initial superposition. Moreover, it is in the form of a composition of two so-called reflections. The result is purely theoretical since the phase change required to reach this heavily depends on $$\alpha $$ α . In the second part, we construct unitary operators having a form of composition of two or more reflections (generalizing the constructed operator) given the set of orthogonal versors. We find properties of these operations, in particular, their compositions. Further, by considering a fixed, ‘convenient’ phase change $$\varphi ,$$ φ , and by sequentially applying the so-constructed operator, we find the number of steps to find these ‘chosen’ elements with great probability. We apply this knowledge to study the generalizations of Grover’s algorithm ($$m=1,\phi =\pi $$ m = 1 , ϕ = π ), which are of the form, the found previously, unitary operators.

KSeCN as an Efficient Cyanide Source for the One-Step Synthesis of Imino-1-oxoisoindolines via Copper-Promoted C−H Activation

2021 ◽  
pp. 153062
Author(s):  
Yue Zhang ◽  
Xinpeng Liu ◽  
Yanan Wang ◽  
Yinan Zhang ◽  
Junwei Wang ◽  
...  
Keyword(s):  
One Step ◽  
The One
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