The Structure and Properties of a Class of Affine Subspaces and Applications in Mechatronics Science

2013 ◽  
Vol 321-324 ◽  
pp. 2385-2388
Author(s):  
Su Luo Song
Keyword(s):  
Information Science ◽  
Fundamental Question ◽  
Orthogonal Complement ◽  
Affine Subspace ◽  
Wavelet Frame ◽  
Structure And Properties ◽  
Direct Sum ◽  
Affine Subspaces ◽  
Reducing Subspaces

Information science focuses on understanding problems from the perspective of the stakeholders involved and then applying information and other technologies as needed. We show that every affine subspace is the orthogonal direct sum of at most three purely non-reducing subspaces. This result is obtained through considering the basicquestion as to when the orthogonal complement of an afffine subspace in another one is still affine subspace. Motivated by the fundamental question as to whethor every affine subspace is singly-generated wavelet frame, we prove that every affine sub -space can be decomposed into the direct sum of a singly-generated afffine subspace.

Semi-Orthogonal Parseval Wavelets Frames on Local Fields and Applications in Manufacturing Science

2013 ◽  
Vol 712-715 ◽  
pp. 2464-2468
Author(s):  
Shi Heng Wang
Keyword(s):  
Local Fields ◽  
Affine Subspace ◽  
Parseval Frame ◽  
Direct Sum ◽  
Reducing Subspaces ◽  
Dilation Factor ◽  
Definition Of ◽  
Frame Wavelets ◽  
Manufacturing Science ◽  
Orthogonal Frame

Manufacturing science focuses on understanding problems from the perspective of the stakeholders involved and then applying manufacturing science as needed. We investigate semi-orthogonal frame wavelets and Parseval frame wavelets in with a dilation factor. We show that every affine subspace is the orthogonal direct sum of at most three purely non-reducing subspaces. This result is obtained through considering the basicquestion as to when the orthogonal complement of an afffine subspace in another one is still affine subspace.The definition of multiple pseudofames for subspaces with integer translation is proposed. The notion of a generalized multiresolution structure of is also introduced. The construction of a generalized multireso-lution structure of Paley-Wiener subspaces of is investigated.

scholarly journals Reducing Subspaces of Some Multiplication Operators on the Bergman Space over Polydisk

2015 ◽  
Vol 2015 ◽  
pp. 1-12
Author(s):  
Yanyue Shi ◽  
Na Zhou
Keyword(s):  
Bergman Space ◽  
Multiplication Operators ◽  
Direct Sum ◽  
Reducing Subspace ◽  
Reducing Subspaces

We consider the reducing subspaces ofMzNonAα2(Dk), wherek≥3,zN=z1N1⋯zkNk, andNi≠Njfori≠j. We prove that each reducing subspace ofMzNis a direct sum of some minimal reducing subspaces. We also characterize the minimal reducing subspaces in the cases thatα=0andα∈(-1,+∞)∖Q, respectively. Finally, we give a complete description of minimal reducing subspaces ofMzNonAα2(D3)withα>-1.

scholarly journals Some Properties of Fuzzy Inner Product Space

2021 ◽  
pp. 2384-2392
Author(s):  
Jehad R. Kider
Keyword(s):  
Normed Space ◽  
Product Space ◽  
Closed Subspace ◽  
Cross Product ◽  
Inner Product Space ◽  
Inner Product ◽  
Orthogonal Complement ◽  
Fuzzy Normed Space ◽  
Direct Sum ◽  
New Type

     Our goal in the present paper is to introduce a new type of fuzzy inner product space. After that, to illustrate this notion, some examples are introduced. Then we prove that that every fuzzy inner product space is a fuzzy normed space. We also prove that the cross product of two fuzzy inner spaces is again a fuzzy inner product space. Next, we prove that the fuzzy inner product is a non decreasing function. Finally, if U is a fuzzy complete fuzzy inner product space and D is a fuzzy closed subspace of U, then we prove that U can be written as a direct sum of D and the fuzzy orthogonal complement    of D.

scholarly journals Simultaneous Approximation on Affine Subspaces

2019 ◽  
Author(s):  
Jing-Jing Huang ◽  
Jason J Liu
Keyword(s):  
Upper Bound ◽  
Simultaneous Approximation ◽  
Rational Points ◽  
Affine Subspace ◽  
Approximation Function ◽  
Affine Subspaces ◽  
Asymptotic Formulae ◽  
The Matrix

AbstractWe solve the convergence case of the generalized Baker–Schmidt problem for simultaneous approximation on affine subspaces, under natural diophantine type conditions. In one of our theorems, we do not require monotonicity on the approximation function. In order to prove these results, we establish asymptotic formulae for the number of rational points close to an affine subspace. One key ingredient is a sharp upper bound on a certain sum of reciprocals of fractional parts associated with the matrix defining the affine subspace.

The Characterization of Multiple Harmanic Riesz Bases of Affine Subspaces and Applications

2013 ◽  
Vol 321-324 ◽  
pp. 2371-2374
Author(s):  
Shu De Du ◽  
Bao Xian Lv
Keyword(s):  
Decision Making ◽  
Information Technology ◽  
Information System ◽  
Operations Management ◽  
Information Science ◽  
Riesz Bases ◽  
Decomposition Scheme ◽  
Affine Subspaces ◽  
Definition Of

An information system is any combination of information technology and people's act- ivities that support operations, management and decision making. Information science focuses on understanding problems from the perspective of the stakeholders involved and then applying information and other technologies as needed. The definition of multiple harmonic frames for subs -paces with integer translation is proposed. The notion of a generalized multiresolution structure of is also introduced. The construction of a generalized multiresolution structure of Paley -Wiener subspaces of is investigated. The pyramid decomposition scheme is derived based on a generalized multiresolution structure.

REVERSED WAVELET FUNCTIONS AND SUBSPACES

2007 ◽  
Vol 05 (05) ◽  
pp. 699-707 ◽  
Author(s):  
NHAN LEVAN ◽  
CARLOS S. KUBRUSLY
Keyword(s):  
Orthonormal Basis ◽  
Orthogonal Decomposition ◽  
Wavelet Theory ◽  
Direct Sum ◽  
Multiplicity One ◽  
Reducing Subspaces ◽  
Infinite Multiplicity ◽  
Countably Infinite ◽  
Bilateral Shift

Let the operators D and T be the dilation-by-2 and translation-by-1 on [Formula: see text], which are both bilateral shifts of infinite multiplicity. If ψ(·) in [Formula: see text] is a wavelet, then {DmTnψ(·)}(m,n)∈ℤ2 is an orthonormal basis for the Hilbert space [Formula: see text] but the reversed set {TnDmψ(·)}(n,m)∈ℤ2 is not. In this paper we investigate the role of the reversed functions TnDmψ(·) in wavelet theory. As a consequence, we exhibit an orthogonal decomposition of [Formula: see text] into T-reducing subspaces upon which part of the bilateral shift T consists of a countably infinite direct sum of bilateral shifts of multiplicity one, which mirrors a well-known decomposition of the bilateral shift D.

Structure of second phases in TiAl alloys containing Cr and B

1991 ◽  
Vol 49 ◽  
pp. 576-577
Author(s):  
Ernest L. Hall ◽  
Shyh-Chin Huang
Keyword(s):  
Grain Size ◽  
Second Phase ◽  
Structure And Properties ◽  
Tial Alloys ◽  
Second Phases ◽  
Interstitial Elements

Addition of interstitial elements to γ-TiAl alloys is currently being explored as a method for improving the properties of these alloys. Previous work in which a number of interstitial elements were studied showed that boron was particularly effective in refining the grain size in castings, and led to enhanced strength while maintaining reasonable ductility. Other investigators have shown that B in γ-TiAl alloys tends to promote the formation of TiB2 as a second phase. In this study, the microstructure of Bcontaining TiAl alloys was examined in detail in order to describe the mechanism by which B alters the structure and properties of these alloys.

Relationships between hierarchical structure and properties in macromolecular systems

1987 ◽  
Vol 45 ◽  
pp. 440-443
Author(s):  
E. Baer
Keyword(s):  
Uniaxial Tension ◽  
Hierarchical Structure ◽  
Inorganic Material ◽  
Hierarchical Structures ◽  
Bone Collagen ◽  
Structure And Properties ◽  
Connective Tissues ◽  
Scale Level ◽  
Fibrous Protein ◽  
Macromolecular Systems

The most advanced macromolecular materials are found in plants and animals, and certainly the connective tissues in mammals are amongst the most advanced macromolecular composites known to mankind. The efficient use of collagen, a fibrous protein, in the design of both soft and hard connective tissues is worthy of comment. Very crudely, in bone collagen serves as a highly efficient binder for the inorganic hydroxyappatite which stiffens the structure. The interactions between the organic fiber of collagen and the inorganic material seem to occur at the nano (scale) level of organization. Epitatic crystallization of the inorganic phase on the fibers has been reported to give a highly anisotropic, stress responsive, structure. Soft connective tissues also have sophisticated oriented hierarchical structures. The collagen fibers are “glued” together by a highly hydrated gel-like proteoglycan matrix. One of the simplest structures of this type is tendon which functions primarily in uniaxial tension as a reinforced elastomeric cable between muscle and bone.

The Structure and Properties of MoSi2 Thin Film in Mos Process

1980 ◽  
Vol 38 ◽  
pp. 326-327
Author(s):  
C.K. Wu ◽  
P. Chang ◽  
N. Godinho
Keyword(s):  
Thin Film ◽  
Integrated Circuits ◽  
High Performance ◽  
Large Scale ◽  
Process Development ◽  
Structure And Properties ◽  
Metal Silicides ◽  
High Oxidation ◽  
Important Approach ◽  
High Oxidation Resistance

Recently, the use of refractory metal silicides as low resistivity, high temperature and high oxidation resistance gate materials in large scale integrated circuits (LSI) has become an important approach in advanced MOS process development (1). This research is a systematic study on the structure and properties of molybdenum silicide thin film and its applicability to high performance LSI fabrication.

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