BALANCED INTERPOLATORY MULTIWAVELETS WITH MULTIPLICITY r

2012 ◽  
Vol 10 (04) ◽  
pp. 1250039 ◽  
Author(s):  
BAOBIN LI ◽  
TIEJIAN LUO ◽  
LIZHONG PENG
Keyword(s):  
Order Approximation ◽  
Approximation Order ◽  
Sampling Theorem ◽  
Complete Characterization ◽  
Refinable Functions ◽  
Practical Application ◽  
Sampling Property ◽  
Vector Valued ◽  
The Scaling Function

Vector-valued refinable interpolatory functions with multiplicity r are discussed in this paper. This kind of refinable functions have a sampling property like Shannon's sampling theorem, and corresponding matrix-valued refinable masks possess special structure. In the context of multiwavelets, some properties of multifilter banks related will be present. Based on these properties, it will be shown that there are no symmetric (or antisymmetric) vector-valued refinable functions with interpolatory property. In the practical application, multiwavelets are always required to possess a certain degree of smoothness, which is related to three different concepts: balancing order, approximation order and analysis-ready order. In the general case, three notions are different. But if the scaling function is interpolatory, three concepts will be verified to equal to each other. Finally, a complete characterization of multifilter banks {H, G} will also be given and it will be used to construct some new balanced multiwavelets with interpolatory property for case r = 2, corresponding to which, multifilter banks have rational coefficients.

scholarly journals A Characterization of a Local Vector Valued Bollobás Theorem

2021 ◽  
Vol 76 (4) ◽  
Author(s):  
Sheldon Dantas ◽  
Abraham Rueda Zoca
Keyword(s):  
Type Theorem ◽  
Complete Characterization ◽  
Strict Convexity ◽  
Bilinear Forms ◽  
Linear Functionals ◽  
Projective Tensor Product ◽  
Projective Tensor ◽  
Local Vector ◽  
Vector Valued

AbstractIn this paper, we are interested in giving two characterizations for the so-called property L$$_{o,o}$$ o , o , a local vector valued Bollobás type theorem. We say that (X, Y) has this property whenever given $$\varepsilon > 0$$ ε > 0 and an operador $$T: X \rightarrow Y$$ T : X → Y , there is $$\eta = \eta (\varepsilon , T)$$ η = η ( ε , T ) such that if x satisfies $$\Vert T(x)\Vert > 1 - \eta $$ ‖ T ( x ) ‖ > 1 - η , then there exists $$x_0 \in S_X$$ x 0 ∈ S X such that $$x_0 \approx x$$ x 0 ≈ x and T itself attains its norm at $$x_0$$ x 0 . This can be seen as a strong (although local) Bollobás theorem for operators. We prove that the pair (X, Y) has the L$$_{o,o}$$ o , o for compact operators if and only if so does $$(X, \mathbb {K})$$ ( X , K ) for linear functionals. This generalizes at once some results due to D. Sain and J. Talponen. Moreover, we present a complete characterization for when $$(X \widehat{\otimes }_\pi Y, \mathbb {K})$$ ( X ⊗ ^ π Y , K ) satisfies the L$$_{o,o}$$ o , o for linear functionals under strict convexity or Kadec–Klee property assumptions in one of the spaces. As a consequence, we generalize some results in the literature related to the strongly subdifferentiability of the projective tensor product and show that $$(L_p(\mu ) \times L_q(\nu ); \mathbb {K})$$ ( L p ( μ ) × L q ( ν ) ; K ) cannot satisfy the L$$_{o,o}$$ o , o for bilinear forms.

scholarly journals A Characterization of Refinable Rational Functions

2006 ◽  
Vol 5 (3) ◽  
Author(s):  
Paul Gustafson ◽  
Nathan Savir ◽  
Ely Spears
Keyword(s):  
Number Theory ◽  
Open Problem ◽  
National Science Foundation ◽  
Rational Functions ◽  
Complete Characterization ◽  
Refinable Functions ◽  
Research Experience ◽  
Interesting Connection ◽  
National Science

In recent decades, refinable functions have become increasingly popular due to their desirable properties in many applications. Rational functions, however, are not as well-behaved as some other classes of functions and have seemingly escaped notice in terms of refinability. The authors spent the summer of 2006 investigating the refinability of rational functions while attending a National Science Foundation funded Research Experience for Undergraduates program at Texas A & M University. Preliminary simplifications to the general case are presented in a chronological collection of lemmas. A complete characterization of refinable rational functions follows with an interesting connection to an open problem in number theory.

scholarly journals Vector valued nonuniform nonstationary wavelets and associated MRA on local fields

2021 ◽  
Vol 17 (2) ◽  
pp. 19-46
Author(s):  
O. Ahmad ◽  
A. H. Wani ◽  
N. A. Sheikh ◽  
M. Ahmad
Keyword(s):  
Multiresolution Analysis ◽  
Complete Characterization ◽  
Local Fields ◽  
Dimension Function ◽  
Vector Valued

Abstract In this paper we study nonstationary wavelets associated with vector valued nonuniform multiresolution analysis on local fields. By virtue of dimension function a complete characterization of vector valued nonuniform nonstationary wavelets is obtained.

Experimental Characterization of Mechanical Behavior of Cord-Rubber Composites

1982 ◽  
Vol 10 (1) ◽  
pp. 37-54 ◽  
Author(s):  
M. Kumar ◽  
C. W. Bert
Keyword(s):  
Response Characteristic ◽  
Cord Compression ◽  
Complete Characterization ◽  
Strain Response ◽  
Strain Gages ◽  
Experimental Characterization ◽  
Rubber Composites ◽  
Stress Strain ◽  
Strain Data

Abstract Unidirectional cord-rubber specimens in the form of tensile coupons and sandwich beams were used. Using specimens with the cords oriented at 0°, 45°, and 90° to the loading direction and appropriate data reduction, we were able to obtain complete characterization for the in-plane stress-strain response of single-ply, unidirectional cord-rubber composites. All strains were measured by means of liquid mercury strain gages, for which the nonlinear strain response characteristic was obtained by calibration. Stress-strain data were obtained for the cases of both cord tension and cord compression. Materials investigated were aramid-rubber, polyester-rubber, and steel-rubber.

Characterization of CMOS Structures (0.6 µm process) Submitted to HBM and COM ESD Stress Tests

1997 ◽  
Author(s):  
G. Meneghesso ◽  
E. Zanoni ◽  
P. Colombo ◽  
M. Brambilla ◽  
R. Annunziata ◽  
...  
Keyword(s):  
Electron Microscopy ◽  
Electrostatic Discharge ◽  
Stress Test ◽  
Complete Characterization ◽  
Stress Tests ◽  
Test Procedures ◽  
Emission Microscopy ◽  
Fast Rise ◽  
Scanning Electron

Abstract In this work, we present new results concerning electrostatic discharge (ESD) robustness of 0.6 μm CMOS structures. Devices have been tested according to both HBM and socketed CDM (sCDM) ESD test procedures. Test structures have been submitted to a complete characterization consisting in: 1) measurement of the tum-on time of the protection structures submitted to pulses with very fast rise times; 2) ESD stress test with the HBM and sCDM models; 3) failure analysis based on emission microscopy (EMMI) and Scanning Electron Microscopy (SEM).

scholarly journals Complete characterization of spin chains with two Ising symmetries

2019 ◽  
Vol 125 (1) ◽  
pp. 10008 ◽  
Author(s):  
Bat-el Friedman ◽  
Atanu Rajak ◽  
Emanuele G. Dalla Torre
Keyword(s):  
Complete Characterization ◽  
Spin Chains

scholarly journals On the star forest polytope for trees and cycles

2019 ◽  
Vol 53 (5) ◽  
pp. 1763-1773
Author(s):  
Meziane Aider ◽  
Lamia Aoudia ◽  
Mourad Baïou ◽  
A. Ridha Mahjoub ◽  
Viet Hung Nguyen
Keyword(s):  
Undirected Graph ◽  
Dominating Set ◽  
Discrete Math ◽  
Complete Characterization ◽  
Facial Structure ◽  
Maximum Weight ◽  
Single Node ◽  
End Node ◽  
Vertex Disjoint

Let G = (V, E) be an undirected graph where the edges in E have non-negative weights. A star in G is either a single node of G or a subgraph of G where all the edges share one common end-node. A star forest is a collection of vertex-disjoint stars in G. The weight of a star forest is the sum of the weights of its edges. This paper deals with the problem of finding a Maximum Weight Spanning Star Forest (MWSFP) in G. This problem is NP-hard but can be solved in polynomial time when G is a cactus [Nguyen, Discrete Math. Algorithms App. 7 (2015) 1550018]. In this paper, we present a polyhedral investigation of the MWSFP. More precisely, we study the facial structure of the star forest polytope, denoted by SFP(G), which is the convex hull of the incidence vectors of the star forests of G. First, we prove several basic properties of SFP(G) and propose an integer programming formulation for MWSFP. Then, we give a class of facet-defining inequalities, called M-tree inequalities, for SFP(G). We show that for the case when G is a tree, the M-tree and the nonnegativity inequalities give a complete characterization of SFP(G). Finally, based on the description of the dominating set polytope on cycles given by Bouchakour et al. [Eur. J. Combin. 29 (2008) 652–661], we give a complete linear description of SFP(G) when G is a cycle.

scholarly journals Protein complex formation in methionine chain-elongation and leucine biosynthesis

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Li-Qun Chen ◽  
Shweta Chhajed ◽  
Tong Zhang ◽  
Joseph M. Collins ◽  
Qiuying Pang ◽  
...  
Keyword(s):  
Protein Complexes ◽  
Complete Characterization ◽  
Bimolecular Fluorescence Complementation ◽  
Chain Elongation ◽  
Substrate Channeling ◽  
Leucine Biosynthesis ◽  
Protein Complex Formation ◽  
Genes Encoding ◽  
Isopropylmalate Dehydrogenase

AbstractDuring the past two decades, glucosinolate (GLS) metabolic pathways have been under extensive studies because of the importance of the specialized metabolites in plant defense against herbivores and pathogens. The studies have led to a nearly complete characterization of biosynthetic genes in the reference plant Arabidopsis thaliana. Before methionine incorporation into the core structure of aliphatic GLS, it undergoes chain-elongation through an iterative three-step process recruited from leucine biosynthesis. Although enzymes catalyzing each step of the reaction have been characterized, the regulatory mode is largely unknown. In this study, using three independent approaches, yeast two-hybrid (Y2H), coimmunoprecipitation (Co-IP) and bimolecular fluorescence complementation (BiFC), we uncovered the presence of protein complexes consisting of isopropylmalate isomerase (IPMI) and isopropylmalate dehydrogenase (IPMDH). In addition, simultaneous decreases in both IPMI and IPMDH activities in a leuc:ipmdh1 double mutants resulted in aggregated changes of GLS profiles compared to either leuc or ipmdh1 single mutants. Although the biological importance of the formation of IPMI and IPMDH protein complexes has not been documented in any organisms, these complexes may represent a new regulatory mechanism of substrate channeling in GLS and/or leucine biosynthesis. Since genes encoding the two enzymes are widely distributed in eukaryotic and prokaryotic genomes, such complexes may have universal significance in the regulation of leucine biosynthesis.

scholarly journals Topological Approach to Mathematical Programs with Switching Constraints

2021 ◽  
Author(s):  
Vladimir Shikhman
Keyword(s):  
Stationary Point ◽  
Mountain Pass Theorem ◽  
Strong Stability ◽  
Complete Characterization ◽  
Stationary Points ◽  
Mathematical Programs ◽  
Linear Independence Constraint Qualification ◽  
Point Set ◽  
Stationary Level

AbstractWe study mathematical programs with switching constraints (for short, MPSC) from the topological perspective. Two basic theorems from Morse theory are proved. Outside the W-stationary point set, continuous deformation of lower level sets can be performed. However, when passing a W-stationary level, the topology of the lower level set changes via the attachment of a w-dimensional cell. The dimension w equals the W-index of the nondegenerate W-stationary point. The W-index depends on both the number of negative eigenvalues of the restricted Lagrangian’s Hessian and the number of bi-active switching constraints. As a consequence, we show the mountain pass theorem for MPSC. Additionally, we address the question if the assumption on the nondegeneracy of W-stationary points is too restrictive in the context of MPSC. It turns out that all W-stationary points are generically nondegenerate. Besides, we examine the gap between nondegeneracy and strong stability of W-stationary points. A complete characterization of strong stability for W-stationary points by means of first and second order information of the MPSC defining functions under linear independence constraint qualification is provided. In particular, no bi-active Lagrange multipliers of a strongly stable W-stationary point can vanish.

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