The Real Solutions of Equation of in Control Theory

2010 ◽  
Vol 121-122 ◽  
pp. 911-915
Author(s):  
Xue Ting Liu

. The research of matrix equations is an active research field, matrix equations have applied in many physical applications in recent years. As one of them, the equation is applied more and more extensively, such as control theory, chemistry and chemical engineering and so on. In this paper, motivated by [1], we give two discriminations about the real solutions of equation . The matrix is proved that it is a nonsingular solution of equation whenever are nonsingular solutions of equations at last.

2013 ◽  
Vol 85 (11) ◽  
pp. 2097-2116 ◽  
Author(s):  
Pengsheng Song ◽  
Bai Sun ◽  
Dewen Zeng

Solubility equilibria are relevant to many aspects of chemistry and chemical engineering. Studies on solubility phenomena are of importance in understanding chemistry and in the development of chemical technology. Solubility equilibria are especially useful for geochemists investigating the formation and evolution of natural salt deposits. China possesses an enormous variety of such resources, including salt lakes, underground brines, oilfield brines, and natural soda and borate deposits, etc. With the ongoing economic development of China, the exploitation and comprehensive utilization of these kinds of mineral resources are making great progress. Although much research on aqueous salt systems has been published, solubility equilibria studies have long been an active research field in China. This paper presents a review of solubility research on salt/water systems, encompassing more than 200 papers from Chinese researchers.


2009 ◽  
Vol 37 (6) ◽  
pp. 2060-2079 ◽  
Author(s):  
Qing-Wen Wang ◽  
Shao-Wen Yu ◽  
Qin Zhang

1964 ◽  
Vol 16 ◽  
pp. 473-478 ◽  
Author(s):  
Marvin Marcus ◽  
Adil Yaqub

In a recent interesting paper (3) H. Schwerdtfeger answered a question of W. R. Utz (4) on the structure of the real solutions A of A* = B, where A is skew-symmetric. (Utz and Schwerdtfeger call A* the "adjugate" of A ; A* is the n-square matrix whose (i, j) entry is (—1)i+j times the determinant of the (n — 1)-square matrix obtained by deleting row i and column j of A. The word "adjugate," however, is more usually applied to the matrix (AT)*, where AT denotes the transposed matrix of A ; cf. (1, 2).)The object of the present paper is to find all real n-square skew-symmetric solutions A to the equation


10.5772/50909 ◽  
2012 ◽  
Vol 9 (1) ◽  
pp. 7 ◽  
Author(s):  
Youxin Luo ◽  
Wei Yi ◽  
Qiyuan Liu

The hyper-chaotic least square method for finding all real solutions of nonlinear equations was proposed and the inverse displacement analysis of a general 6R manipulator was completed. Applying the D-H method, a 4 × 4 matrix transform was obtained and the first type twelve constrained equations were established. Analysing the characteristics of the matrix, the second type twelve constrained equations were established by adding variables and restriction. Combining the least square method with hyper-chaotic sequences, the hyper-chaotic least square method based on utilizing a hyper-chaotic discrete system to obtain and locate initial points to find all the real solutions of the nonlinear questions was proposed. The numerical example was given for two type constrained equations. The results show that all the real solutions have been obtained, and it proves the correctness and validity of the proposed method.


Molecules ◽  
2021 ◽  
Vol 26 (11) ◽  
pp. 3192
Author(s):  
Nicolas Giacoletto ◽  
Frédéric Dumur

Over the past several decades, photopolymerization has become an active research field, and the ongoing efforts to develop new photoinitiating systems are supported by the different applications in which this polymerization technique is involved—including dentistry, 3D and 4D printing, adhesives, and laser writing. In the search for new structures, bis-chalcones that combine two chalcones’ moieties within a unique structure were determined as being promising photosensitizers to initiate both the free-radical polymerization of acrylates and the cationic polymerization of epoxides. In this review, an overview of the different bis-chalcones reported to date is provided. Parallel to the mechanistic investigations aiming at elucidating the polymerization mechanisms, bis-chalcones-based photoinitiating systems were used for different applications, which are detailed in this review.


2012 ◽  
Vol 2012 ◽  
pp. 1-6
Author(s):  
Xuefeng Duan ◽  
Chunmei Li

Based on the alternating projection algorithm, which was proposed by Von Neumann to treat the problem of finding the projection of a given point onto the intersection of two closed subspaces, we propose a new iterative algorithm to solve the matrix nearness problem associated with the matrix equations AXB=E, CXD=F, which arises frequently in experimental design. If we choose the initial iterative matrix X0=0, the least Frobenius norm solution of these matrix equations is obtained. Numerical examples show that the new algorithm is feasible and effective.


Author(s):  
L. Merah ◽  
◽  
P. Lorenz ◽  
A. Ali-Pacha ◽  
N. Hadj-Said ◽  
...  

The enormous progress in communication technology has led to a tremendous need to provide an ideal environment for the transmission, storing, and processing of digital multimedia content, where the audio signal takes the lion's share of it. Audio processing covers many diverse fields, its main aim is presenting sound to human listeners. Recently, digital audio processing became an active research area, it covers everything from theory to practice in relation to transmission, compression, filtering, and adding special effects to an audio signal. The aim of this work is to present the real-time implementation steps of some audio effects namely, the echo and Flanger effects on Field Programmable Gate Array (FPGA). Today, FPGAs are the best choice in data processing because they provide more flexibility, performance, and huge processing capabilities with great power efficiency. Designs are achieved using the XSG tool (Xilinx System Generator), which makes complex designs easier without prior knowledge of hardware description languages. The paper is presented as a guide with deep technical details about designing and real-time implementation steps. We decided to transfer some experience to designers who want to rapidly prototype their ideas using tools such as XSG. All the designs have been simulated and verified under Simulink/Matlab environment, then exported to Xilinx ISE (Integrated Synthesis Environment) tool for the rest of the implementation steps. The paper also gives an idea of interfacing the FPGA with the LM4550 AC’97 codec using VHDL coding. The ATLYS development board based on Xilinx Spartan-6 LX45 FPGA is used for the real-time implementation.


2018 ◽  
Vol 34 (10) ◽  
pp. 885-890 ◽  
Author(s):  
Bertrand Jordan

Senescent cells are involved in many age-related diseases, and the effects of their elimination by “senolytic” drugs is an active research field. A recent paper describes a convenient murine model of induced senescence and uses it to convincingly demonstrate the positive effects of senolytics on performance and lifespan. Clinical studies have already been initiated; this approach hold promise to eventually improve human “healthspan”.


2021 ◽  
Author(s):  
Qiwei Chen ◽  
Yu Zhang ◽  
Kun Li ◽  
Zhikai Zhang ◽  
Ya Wang ◽  
...  

Abstract Background: Organoid is an artificially grown mass of cells or tissues, which is similar to an organ. It can replicate the complexity of an organ and can be used for gaining a better understanding of diseases. In this study, the hot spots of “organoids” were classified into 6 categories and 10 aspects, and organoids used for studying genetic mechanisms, drug effect, and metabolism of tumors showed the greatest potential for future development.Methods: A total of 1550 articles relevant to organoid in tumor research field were recruited as research samples. High-frequency words and text/co-word matrix were constructed by BICOMB software. gCLUTO software was applied to analyze the matrix by double-clustering and visual analysis subsequently to identify the hotspot in this area.Results: We constructed a text and co-word matrix composed of 21 high-frequency words and 1550 articles and generated a hotspot “peak map” based on double-clustering analysis. The strategic coordinates approach was used to assess the research prospects of each hotspot and the connections between these hotspots.Conclusions: In this study, we classified the hot-spots of “organoid” into 6 categories and 10 aspects. Calculation and analysis revealed that the field of tumor organoid shows a slight trend of polarization, and organoid for studying the genetic mechanisms, drug effects and metabolism of tumor shows the greatest potential for future development.


F1000Research ◽  
2021 ◽  
Vol 10 ◽  
pp. 1129
Author(s):  
Marvin Martens ◽  
Rob Stierum ◽  
Emma L. Schymanski ◽  
Chris T. Evelo ◽  
Reza Aalizadeh ◽  
...  

Toxicology has been an active research field for many decades, with academic, industrial and government involvement. Modern omics and computational approaches are changing the field, from merely disease-specific observational models into target-specific predictive models. Traditionally, toxicology has strong links with other fields such as biology, chemistry, pharmacology and medicine. With the rise of synthetic and new engineered materials, alongside ongoing prioritisation needs in chemical risk assessment for existing chemicals, early predictive evaluations are becoming of utmost importance to both scientific and regulatory purposes. ELIXIR is an intergovernmental organisation that brings together life science resources from across Europe. To coordinate the linkage of various life science efforts around modern predictive toxicology, the establishment of a new ELIXIR Community is seen as instrumental. In the past few years, joint efforts, building on incidental overlap, have been piloted in the context of ELIXIR. For example, the EU-ToxRisk, diXa, HeCaToS, transQST, and the nanotoxicology community have worked with the ELIXIR TeSS, Bioschemas, and Compute Platforms and activities. In 2018, a core group of interested parties wrote a proposal, outlining a sketch of what this new ELIXIR Toxicology Community would look like. A recent workshop (held September 30th to October 1st, 2020) extended this into an ELIXIR Toxicology roadmap and a shortlist of limited investment-high gain collaborations to give body to this new community. This Whitepaper outlines the results of these efforts and defines our vision of the ELIXIR Toxicology Community and how it complements other ELIXIR activities.


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