A characterization of Riesz-dual sequences which are near-Markushevich bases

2021 ◽  
Author(s):  
Ali Reza Neisi ◽  
Mohammad Sadegh Asgari
Keyword(s):  
Wavelet Analysis ◽  
Banach Spaces ◽  
Basic Problem ◽  
Frame Theory ◽  
Type I ◽  
Special Cases ◽  
Dual Sequences ◽  
Dual Sequence

The concept of Riesz-duals of a frame is a recently introduced concept with broad implications to frame theory in general, as well as to the special cases of Gabor and wavelet analysis. In this paper, we introduce various alternative Riesz-duals, with a focus on what we call Riesz-duals of type I and II. Next, we provide some characterizations of Riesz-dual sequences in Banach spaces. A basic problem of interest in connection with the study of Riesz-duals in Banach spaces is that of characterizing those Riesz-duals which can essentially be regarded as M-basis. We give some conditions under which an Riesz-dual sequence to be an M-basis for [Formula: see text].

Signal Representations Via SIP p-frames and SIP Bessel Multipliers in Separable Banach Spaces

2021 ◽  
pp. 2150005
Author(s):  
Xianwei Zheng ◽  
Cuiming Zou ◽  
Shouzhi Yang
Keyword(s):  
Banach Spaces ◽  
Frame Theory ◽  
Inner Product ◽  
Riesz Bases ◽  
Digital Signals ◽  
Bessel Sequence ◽  
Fixed Sequence ◽  
Signal Representations ◽  
Special Cases ◽  
Bessel Multipliers

Digital signals are often modeled as functions in Banach spaces, such as the ubiquitous [Formula: see text] spaces. The frame theory in Banach spaces induces flexible representations of signals due to the robustness and redundancy of frames. Nevertheless, the lack of inner product in general Banach spaces limits the direct representations of signals in Banach spaces under a given basis or frame. In this paper, we introduce the concept of semi-inner product (SIP) [Formula: see text]-Bessel multipliers to extend the flexibility of signal representations in separable Banach spaces, where [Formula: see text]. These multipliers are defined as composition of analysis operator of an SIP-I Bessel sequence, a multiplication with a fixed sequence and synthesis operator of an SIP-II Bessel sequence. The basic properties of the SIP [Formula: see text]-Bessel multipliers are investigated. Moreover, as special cases, characterizations of [Formula: see text]-Riesz bases related to signal representations are given, and the multipliers for [Formula: see text]-Riesz bases are discussed. We show that SIP [Formula: see text]-Bessel multipliers for [Formula: see text]-Riesz bases are invertible. Finally, the continuity of SIP [Formula: see text]-Bessel multipliers with respect to their parameters is investigated. The results theoretically show that the SIP [Formula: see text]-Bessel multipliers offer a larger range of freedom than frames on signal representations in Banach spaces.

One Size Fits All?

Methodology ◽  
2012 ◽  
Vol 8 (1) ◽  
pp. 23-38 ◽  
Author(s):  
Manuel C. Voelkle ◽  
Patrick E. McKnight
Keyword(s):  
Repeated Measures ◽  
Structural Equation ◽  
Type I Error ◽  
Equation Modeling ◽  
Type I ◽  
Finite Sample ◽  
Traditional Methods ◽  
Repeated Measures Anova ◽  
Special Cases ◽  
Latent Curve

The use of latent curve models (LCMs) has increased almost exponentially during the last decade. Oftentimes, researchers regard LCM as a “new” method to analyze change with little attention paid to the fact that the technique was originally introduced as an “alternative to standard repeated measures ANOVA and first-order auto-regressive methods” (Meredith & Tisak, 1990, p. 107). In the first part of the paper, this close relationship is reviewed, and it is demonstrated how “traditional” methods, such as the repeated measures ANOVA, and MANOVA, can be formulated as LCMs. Given that latent curve modeling is essentially a large-sample technique, compared to “traditional” finite-sample approaches, the second part of the paper addresses the question to what degree the more flexible LCMs can actually replace some of the older tests by means of a Monte-Carlo simulation. In addition, a structural equation modeling alternative to Mauchly’s (1940) test of sphericity is explored. Although “traditional” methods may be expressed as special cases of more general LCMs, we found the equivalence holds only asymptotically. For practical purposes, however, no approach always outperformed the other alternatives in terms of power and type I error, so the best method to be used depends on the situation. We provide detailed recommendations of when to use which method.

Characterization of flow regimes in two phase flow using wavelet analysis

2018 ◽  
Author(s):  
Munzarin Morshed ◽  
Syed Imtiaz ◽  
Mohammad Aziz Rahman
Keyword(s):  
Wavelet Analysis ◽  
Two Phase Flow ◽  
Flow Regimes ◽  
Phase Flow ◽  
Two Phase

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.

Characterization of type I-F CRISPR-Cas system in Laribacter hongkongensis isolates from animals, the environment and diarrhea patients

2021 ◽  
Vol 346 ◽  
pp. 109153
Author(s):  
Ling Wang ◽  
Li Wang ◽  
Youzhao Liu ◽  
Zhiyun Wang ◽  
Qing Chen ◽  
...  
Keyword(s):  
Type I ◽  
Laribacter Hongkongensis

scholarly journals Molecular and Pharmacological Characterization of the Interaction between Human Geranylgeranyltransferase Type I and Ras-Related Protein Rap1B

2021 ◽  
Vol 22 (5) ◽  
pp. 2501
Author(s):  
Sonja Hinz ◽  
Dominik Jung ◽  
Dorota Hauert ◽  
Hagen S. Bachmann
Keyword(s):  
Protein Function ◽  
Tumor Development ◽  
Cysteine Residue ◽  
Type I ◽  
Pharmacological Characterization ◽  
Anti Cancer ◽  
And Function ◽  
Caax Motif ◽  
Important Drug

Geranylgeranyltransferase type-I (GGTase-I) represents an important drug target since it contributes to the function of many proteins that are involved in tumor development and metastasis. This led to the development of GGTase-I inhibitors as anti-cancer drugs blocking the protein function and membrane association of e.g., Rap subfamilies that are involved in cell differentiation and cell growth. In the present study, we developed a new NanoBiT assay to monitor the interaction of human GGTase-I and its substrate Rap1B. Different Rap1B prenylation-deficient mutants (C181G, C181S, and ΔCQLL) were designed and investigated for their interaction with GGTase-I. While the Rap1B mutants C181G and C181S still exhibited interaction with human GGTase-I, mutant ΔCQLL, lacking the entire CAAX motif (defined by a cysteine residue, two aliphatic residues, and the C-terminal residue), showed reduced interaction. Moreover, a specific, peptidomimetic and competitive CAAX inhibitor was able to block the interaction of Rap1B with GGTase-I. Furthermore, activation of both Gαs-coupled human adenosine receptors, A2A (A2AAR) and A2B (A2BAR), increased the interaction between GGTase-I and Rap1B, probably representing a way to modulate prenylation and function of Rap1B. Thus, A2AAR and A2BAR antagonists might be promising candidates for therapeutic intervention for different types of cancer that overexpress Rap1B. Finally, the NanoBiT assay provides a tool to investigate the pharmacology of GGTase-I inhibitors.

scholarly journals A Functional Characterization of Almost Greedy and Partially Greedy Bases in Banach Spaces

Mathematics ◽  
2021 ◽  
Vol 9 (15) ◽  
pp. 1827
Author(s):  
Pablo Manuel Berná ◽  
Diego Mondéjar
Keyword(s):  
Banach Spaces ◽  
Functional Characterization

In 2003, S. J. Dilworth, N. J. Kalton, D. Kutzarova and V. N. Temlyakov introduced the notion of almost greedy (respectively partially greedy) bases. These bases were characterized in terms of quasi-greediness and democracy (respectively conservativeness). In this paper, we show a new functional characterization of these type of bases in general Banach spaces following the spirit of the characterization of greediness proved in 2017 by P. M. Berná and Ó. Blasco.

Sign in / Sign up

Export Citation Format

Share Document