scholarly journals Polar decomposition and characterization of binormal operators

Filomat ◽  
2020 ◽  
Vol 34 (3) ◽  
pp. 1013-1024
Author(s):  
Mehdi Mohammadzadeh Karizaki
Keyword(s):  
Polar Decomposition ◽  
Matrix Representation ◽  
General Setting ◽  
Inner Product ◽  
Closed Range ◽  
Aluthge Transformation ◽  
The Matrix ◽  
Closed Range Operator ◽  
Equivalent Conditions

We illustrate the matrix representation of the closed range operator that enables us to determine the polar decomposition with respect to the orthogonal complemented submodules. This result proves that the reverse order law for the Moore-Penrose inverse of operators holds. Also, it is given some new characterizations of the binormal operators via the generalized Aluthge transformation. New characterizations of the binormal operators enable us to obtain equivalent conditions when the inner product of the binormal operator with its generalized Aluthge transformation is positive in the general setting of adjointable operators on Hilbert C*-modules.

scholarly journals The outer generalized inverse of an even-order tensor

2020 ◽  
Vol 36 (36) ◽  
pp. 599-615
Author(s):  
Jun Ji ◽  
Yimin Wei
Keyword(s):  
Generalized Inverse ◽  
Sufficient Conditions ◽  
Full Rank ◽  
Outer Inverse ◽  
The Matrix ◽  
Even Order ◽  
Rank Factorization ◽  
Necessary And Sufficient ◽  
Equivalent Conditions

Necessary and sufficient conditions for the existence of the outer inverse of a tensor with the Einstein product are studied. This generalized inverse of a tensor unifies several generalized inverses of tensors introduced recently in the literature, including the weighted Moore-Penrose, the Moore-Penrose, and the Drazin inverses. The outer inverse of a tensor is expressed through the matrix unfolding of a tensor and the tensor folding. This expression is used to find a characterization of the outer inverse through group inverses, establish the behavior of outer inverse under a small perturbation, and show the existence of a full rank factorization of a tensor and obtain the expression of the outer inverse using full rank factorization. The tensor reverse rule of the weighted Moore-Penrose and Moore-Penrose inverses is examined and equivalent conditions are also developed.

TEM characterization of reaction zone in a SiC fiber-reinforced titanium alloy

1988 ◽  
Vol 46 ◽  
pp. 738-739
Author(s):  
G. Das ◽  
R. E. Omlor
Keyword(s):  
Titanium Alloys ◽  
Reaction Zone ◽  
Carbon Layer ◽  
Fiber Reinforced ◽  
Reaction Products ◽  
Sic Fibers ◽  
Sic Fiber ◽  
The Matrix ◽  
Immense Potential

Fiber reinforced titanium alloys hold immense potential for applications in the aerospace industry. However, chemical reaction between the fibers and the titanium alloys at fabrication temperatures leads to the formation of brittle reaction products which limits their development. In the present study, coated SiC fibers have been used to evaluate the effects of surface coating on the reaction zone in the SiC/IMI829 system.IMI829 (Ti-5.5A1-3.5Sn-3.0Zr-0.3Mo-1Nb-0.3Si), a near alpha alloy, in the form of PREP powder (-35 mesh), was used a茸 the matrix. CVD grown AVCO SCS-6 SiC fibers were used as discontinuous reinforcements. These fibers of 142μm diameter contained an overlayer with high Si/C ratio on top of an amorphous carbon layer, the thickness of the coating being ∽ 1μm. SCS-6 fibers, broken into ∽ 2mm lengths, were mixed with IMI829 powder (representing < 0.1vol%) and the mixture was consolidated by HIP'ing at 871°C/0. 28GPa/4h.

scholarly journals Characterization of the Structure, Mechanical Properties and Erosive Resistance of the Laser Cladded Inconel 625-Based Coatings Reinforced by TiC Particles

Materials ◽  
2021 ◽  
Vol 14 (9) ◽  
pp. 2225
Author(s):  
Aleksandra Kotarska ◽  
Tomasz Poloczek ◽  
Damian Janicki
Keyword(s):  
Laser Cladding ◽  
Inconel 625 ◽  
Matrix Composites ◽  
Erosion Rates ◽  
Laser Cladding Process ◽  
Composition Variation ◽  
The Matrix ◽  
Reinforcing Material ◽  
Inconel 625 Superalloy

The article presents research in the field of laser cladding of metal-matrix composite (MMC) coatings. Nickel-based superalloys show attractive properties including high tensile strength, fatigue resistance, high-temperature corrosion resistance and toughness, which makes them widely used in the industry. Due to the insufficient wear resistance of nickel-based superalloys, many scientists are investigating the possibility of producing nickel-based superalloys matrix composites. For this study, the powder mixtures of Inconel 625 superalloy with 10, 20 and 40 vol.% of TiC particles were used to produce MMC coatings by laser cladding. The titanium carbides were chosen as reinforcing material due to high thermal stability and hardness. The multi-run coatings were tested using penetrant testing, macroscopic and microscopic observations, microhardness measurements and solid particle erosive test according to ASTM G76-04 standard. The TiC particles partially dissolved in the structure during the laser cladding process, which resulted in titanium and carbon enrichment of the matrix and the occurrence of precipitates formation in the structure. The process parameters and coatings chemical composition variation had an influence on coatings average hardness and erosion rates.

Mechanical characterization of LM25 alloy matrix composite reinforced with boron carbide

2021 ◽  
pp. 002199832110055
Author(s):  
Zeeshan Ahmad ◽  
Sabah Khan
Keyword(s):  
Tensile Strength ◽  
Boron Carbide ◽  
Mechanical Characterization ◽  
Stir Casting ◽  
Surface Mapping ◽  
Alloy Matrix ◽  
Casting Technique ◽  
The Matrix ◽  
Carbide Particles

Alumnium alloy LM 25 based composites reinforced with boron carbide at different weight fractions of 4%, 8%, and 12% were fabricated by stir casting technique. The microstructures and morphology of the fabricated composites were studied by scanning electron microscopy and energy dispersive spectroscopy. Elemental mapping of all fabricated composites were done to demonstrate the elements present in the matrix and fabricated composites. The results of microstructural analyses reveal homogenous dispersion of reinforcement particles in the matrix with some little amount of clustering found in composites reinforced with 12% wt. of boron carbide. The mechanical characterization is done for both alloy LM 25 and all fabricated composites based on hardness and tensile strength. The hardness increased from 13.6% to 21.31% and tensile strength 6.4% to 22.8% as reinforcement percentage of boron carbide particles increased from 0% to 12% wt. A fractured surface mapping was also done for all composites.

scholarly journals On a New Geometric Constant Related to the Euler-Lagrange Type Identity in Banach Spaces

Mathematics ◽  
2021 ◽  
Vol 9 (2) ◽  
pp. 116
Author(s):  
Qi Liu ◽  
Yongjin Li
Keyword(s):  
Banach Spaces ◽  
Product Space ◽  
Sufficient Conditions ◽  
Normal Structure ◽  
The Other ◽  
Inner Product ◽  
Equivalent Characterization ◽  
Geometric Constant ◽  
Geometric Constants

In this paper, we will introduce a new geometric constant LYJ(λ,μ,X) based on an equivalent characterization of inner product space, which was proposed by Moslehian and Rassias. We first discuss some equivalent forms of the proposed constant. Next, a characterization of uniformly non-square is given. Moreover, some sufficient conditions which imply weak normal structure are presented. Finally, we obtain some relationship between the other well-known geometric constants and LYJ(λ,μ,X). Also, this new coefficient is computed for X being concrete space.

scholarly journals Reliability Assessment of a Multi-State HVDC System by Combining Markov and Matrix-Based Methods

Energies ◽  
2021 ◽  
Vol 14 (11) ◽  
pp. 3097
Author(s):  
Roberto Benato ◽  
Antonio Chiarelli ◽  
Sebastian Dambone Sessa
Keyword(s):  
Current System ◽  
Estimation Method ◽  
Reliability Estimation ◽  
Voltage Source ◽  
Voltage Source Converter ◽  
Hvdc System ◽  
Critical Elements ◽  
The Matrix ◽  
The Impact

The purpose of this paper is to highlight that, in order to assess the availability of different HVDC cable transmission systems, a more detailed characterization of the cable management significantly affects the availability estimation since the cable represents one of the most critical elements of such systems. The analyzed case study consists of a multi-terminal direct current system based on both line commutated converter and voltage source converter technologies in different configurations, whose availability is computed for different transmitted power capacities. For these analyses, the matrix-based reliability estimation method is exploited together with the Monte Carlo approach and the Markov state space one. This paper shows how reliability analysis requires a deep knowledge of the real installation conditions. The impact of these conditions on the reliability evaluation and the involved benefits are also presented.

scholarly journals Characterization of Mmp37p, aSaccharomyces cerevisiaeMitochondrial Matrix Protein with a Role in Mitochondrial Protein Import

2006 ◽  
Vol 17 (9) ◽  
pp. 4051-4062 ◽  
Author(s):  
Michelle R. Gallas ◽  
Mary K. Dienhart ◽  
Rosemary A. Stuart ◽  
Roy M. Long
Keyword(s):  
Matrix Protein ◽  
Protein Import ◽  
Mitochondrial Protein ◽  
Temperature Sensitive ◽  
Inner Membrane ◽  
Mitochondrial Inner Membrane ◽  
Close Proximity ◽  
The Matrix ◽  
Targeting Signal

Many mitochondrial proteins are encoded by nuclear genes and after translation in the cytoplasm are imported via translocases in the outer and inner membranes, the TOM and TIM complexes, respectively. Here, we report the characterization of the mitochondrial protein, Mmp37p (YGR046w) and demonstrate its involvement in the process of protein import into mitochondria. Haploid cells deleted of MMP37 are viable but display a temperature-sensitive growth phenotype and are inviable in the absence of mitochondrial DNA. Mmp37p is located in the mitochondrial matrix where it is peripherally associated with the inner membrane. We show that Mmp37p has a role in the translocation of proteins across the mitochondrial inner membrane via the TIM23-PAM complex and further demonstrate that substrates containing a tightly folded domain in close proximity to their mitochondrial targeting sequences display a particular dependency on Mmp37p for mitochondrial import. Prior unfolding of the preprotein, or extension of the region between the targeting signal and the tightly folded domain, relieves their dependency for Mmp37p. Furthermore, evidence is presented to show that Mmp37 may affect the assembly state of the TIM23 complex. On the basis of these findings, we hypothesize that the presence of Mmp37p enhances the early stages of the TIM23 matrix import pathway to ensure engagement of incoming preproteins with the mtHsp70p/PAM complex, a step that is necessary to drive the unfolding and complete translocation of the preprotein into the matrix.

scholarly journals Stability of Nonlinear Autonomous Quadratic Discrete Systems in the Critical Case

2010 ◽  
Vol 2010 ◽  
pp. 1-23 ◽  
Author(s):  
Josef Diblík ◽  
Denys Ya. Khusainov ◽  
Irina V. Grytsay ◽  
Zdenĕk Šmarda
Keyword(s):  
Lyapunov Functions ◽  
Critical Case ◽  
Autonomous Systems ◽  
Discrete Systems ◽  
Simple Eigenvalue ◽  
Discrete Equations ◽  
The Matrix ◽  
The Stability ◽  
Important Characterization

Many processes are mathematically simulated by systems of discrete equations with quadratic right-hand sides. Their stability is thought of as a very important characterization of the process. In this paper, the method of Lyapunov functions is used to derive classes of stable quadratic discrete autonomous systems in a critical case in the presence of a simple eigenvalueλ=1of the matrix of linear terms. In addition to the stability investigation, we also estimate stability domains.

scholarly journals MATRIX THEORY, HILBERT SCHEME AND INTEGRABLE SYSTEM

1998 ◽  
Vol 13 (34) ◽  
pp. 2731-2742 ◽  
Author(s):  
YUTAKA MATSUO
Keyword(s):  
Hilbert Scheme ◽  
Matrix Theory ◽  
Fock Space ◽  
Homology Class ◽  
Orthogonal Basis ◽  
Inner Product ◽  
Virasoro Symmetry ◽  
Hilbert Scheme Of Points ◽  
The Matrix ◽  
Boson Fock Space

We give a reinterpretation of the matrix theory discussed by Moore, Nekrasov and Shatashivili (MNS) in terms of the second quantized operators which describes the homology class of the Hilbert scheme of points on surfaces. It naturally relates the contribution from each pole to the inner product of orthogonal basis of free boson Fock space. These bases can be related to the eigenfunctions of Calogero–Sutherland (CS) equation and the deformation parameter of MNS is identified with coupling of CS system. We discuss the structure of Virasoro symmetry in this model.

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