scholarly journals A new inequality about matrix products and a Berger-Wang formula

2020 ◽  
Vol 7 ◽  
pp. 185-200
Author(s):  
Eduardo Oregón-Reyes
Keyword(s):  
Matrix Products

scholarly journals A low-area high-efficiency video coding inverse transform core using resource and time sharing architecture

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Yuan-Ho Chen ◽  
Chieh-Yang Liu
Keyword(s):  
Video Coding ◽  
Large Scale ◽  
High Efficiency ◽  
Vlsi Design ◽  
Cmos Technology ◽  
Oxide Semiconductor ◽  
Time Sharing ◽  
High Efficiency Video Coding ◽  
Low Area ◽  
Matrix Products

AbstractIn this paper, a very-large-scale integration (VLSI) design that can support high-efficiency video coding inverse discrete cosine transform (IDCT) for multiple transform sizes is proposed. The proposed two-dimensional (2-D) IDCT is implemented at a low area by using a single one-dimensional (1-D) IDCT core with a transpose memory. The proposed 1-D IDCT core decomposes a 32-point transform into 16-, 8-, and 4-point matrix products according to the symmetric property of the transform coefficient. Moreover, we use the shift-and-add unit to share hardware resources between multiple transform dimension matrix products. The 1-D IDCT core can simultaneously calculate the first- and second-dimensional data. The results indicate that the proposed 2-D IDCT core has a throughput rate of 250 MP/s, with only 110 K gate counts when implemented into the Taiwan semiconductor manufacturing (TSMC) 90-nm complementary metal-oxide-semiconductor (CMOS) technology. The results show the proposed circuit has the smallest area supporting the multiple transform sizes.

scholarly journals Infinite Matrix Products and the Representation of the Matrix Gamma Function

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
J.-C. Cortés ◽  
L. Jódar ◽  
Francisco J. Solís ◽  
Roberto Ku-Carrillo
Keyword(s):  
Gamma Function ◽  
Infinite Product ◽  
Infinite Matrix ◽  
Convergence Results ◽  
Matrix Products ◽  
The Matrix ◽  
Definition Of

We introduce infinite matrix products including some of their main properties and convergence results. We apply them in order to extend to the matrix scenario the definition of the scalar gamma function given by an infinite product due to Weierstrass. A limit representation of the matrix gamma function is also provided.

scholarly journals Factorizations for q-Pascal matrices of two variables

2015 ◽  
Vol 3 (1) ◽  
Author(s):  
Thomas Ernst
Keyword(s):  
Matrix Products ◽  
Natural Way

AbstractIn this second article on q-Pascal matrices, we show how the previous factorizations by the summation matrices and the so-called q-unit matrices extend in a natural way to produce q-analogues of Pascal matrices of two variables by Z. Zhang and M. Liu as followsWe also find two different matrix products for

Trace Forms on Lie Algebras

1962 ◽  
Vol 14 ◽  
pp. 553-564 ◽  
Author(s):  
Richard Block
Keyword(s):  
Lie Algebra ◽  
Lie Algebras ◽  
Bilinear Form ◽  
Symmetric Bilinear Form ◽  
Trace Form ◽  
Finite Degree ◽  
Trace Forms ◽  
Matrix Products ◽  
The Matrix ◽  
Image Position

If L is a Lie algebra with a representation Δ a→aΔ (a in L) (of finite degree), then by the trace form f = fΔ of Δ is meant the symmetric bilinear form on L obtained by taking the trace of the matrix products:Then f is invariant, that is, f is symmetric and f(ab, c) — f(a, bc) for all a, b, c in L. By the Δ-radical L⊥ = L⊥ of L is meant the set of a in L such that f(a, b) = 0 for all b in L. Then L⊥ is an ideal and f induces a bilinear form , called a quotient trace form, on L/L⊥. Thus an algebra has a quotient trace form if and only if there exists a Lie algebra L with a representation Δ such that

A literature review of commercially available demineralized bone matrix products and their clinical evidence in acute fractures, nonunions, and fusion procedures

2021 ◽  
Vol Publish Ahead of Print ◽  
Author(s):  
Michael Downing ◽  
Timothy Niedzielak ◽  
Charles De La Rosa ◽  
Alexander Ting ◽  
Joshua Berko ◽  
...  
Keyword(s):  
Literature Review ◽  
Clinical Evidence ◽  
Demineralized Bone Matrix ◽  
Bone Matrix ◽  
Matrix Products ◽  
Demineralized Bone

Participation of two different mesenchymes in the developing mouse mammary gland: synthesis of basement membrane components by fat pad precursor cells

Development ◽  
1985 ◽  
Vol 89 (1) ◽  
pp. 243-257
Author(s):  
Koji Kimata ◽  
Teruyo Sakakura ◽  
Yutaka Inaguma ◽  
Masato Kato ◽  
Yasuaki Nishizuka
Keyword(s):  
Extracellular Matrix ◽  
Mammary Gland ◽  
Flank Region ◽  
Mouse Mammary Gland ◽  
Precursor Cells ◽  
Basement Membranes ◽  
Immunofluorescent Staining ◽  
Fat Pad ◽  
Matrix Products ◽  
Membrane Components

Two different types of mesenchyme, fat pad precursor cells (FP) and fibroblastic cells (MM) are involved in the morphogenesis of mammary gland epithelium of mouse embryo. Especially, an interaction between FP and the epithelium is necessary for its characteristic shaping of ductal branching structure. To assess the relative participations of the mesenchymes, we have analysed the extracellular matrix products by immunofluorescent staining method using antibodies to laminin, proteoheparan sulphate, and fibronectin. The staining patterns suggested that, after the 16th day of gestation when fatty substances first appeared in FP and the epithelial rudiments started to elongate and branch rapidly, FP initiated synthesis of laminin and proteoheparan sulphate, while MM synthesized fibronectin at all times. Attention was also paid to differences in the epithelial basement membranes (BM) concomitant with ones in the mesenchyme. BM were always stained with antibodies to laminin and proteoheparan sulphate. However, topographical differences in thickness were observed: the one facing FP, often seen at the tip region of the end bud, was thin, while the other surrounded by MM, often at the flank region of the duct, was thick. Specific elaboration of BM-like extracellular matrix products by FP may attribute to observed differences in BM thickness which are related to the characteristic shaping of the mammary gland.

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