Local reconstruction method and voice system

AbstractIt is shown that a local reconstruction method from a nonuniform sampled data along with discrete wavelet transform and a simple statistical method is applicable in a voice system

A Note on the Completeness of All Translates of a Function in the Orlicz Spaces

We give a characterization of those functions whose all translates are complete in certain Orlicz space $L^{\Phi}(\mathbb{R})$. As a consequence, we identified those discrete sets $\Lambda \subseteq \mathbb{R}$ such that there exists a function in $L^{\Phi}(\mathbb{R})$ whose $\Lambda$-translates are complete. We then prove the completeness of all translates of any simple step function in other Orlicz spaces

Completeness of Discrete Translates in H1(R)H^1(\mathbb{R})

We provide a characterization of discrete sets $\Lambda \subset \mathbb{R}$ that admit a function whose $\Lambda$-translates are complete in the Hardy space $H^1(\mathbb{R})$. In particular, we show that such a set cannot be uniformly discrete. We then give a uniformly discrete $\Lambda \subset \mathbb{R}$ which admits a pair of functions such that their $\Lambda$-translates are complete in $H^1(\mathbb{R})$

Random sampling of signals concentrated on compact set in localized reproducing kernel subspace of Lp(Rn)L^p({\mathbb R}^n)

The paper is devoted to studying the stability of random sampling in a localized reproducing kernel space. We show that if the sampling set on $\Omega$ (compact) discretizes the integral norm of simple functions up to a given error, then the sampling set is stable for the set of functions concentrated on $\Omega$. Moreover, we prove with an overwhelming probability that ${\mathcal O}(\mu(\Omega)(\log \mu(\Omega))^3)$ many random points uniformly distributed over $\Omega$ yield a stable set of sampling for functions concentrated on $\Omega$.Comment: 17 page

Structure of CdTe/ZnTe superlattices

The structure of CdTe/ZnTe superlattices has been analyzed through θ/2θ x‐ray diffraction, photoluminescence, and in situ reflection high‐energy electron diffraction (RHEED) measurements. Samples are found to break away from Cd_(x)Zn_(1−x)Te buffer layers as a consequence of the 6% lattice mismatch in this system. However, defect densities in these superlattices are seen to drop dramatically away from the buffer layer interface, accounting for the intense photoluminescence and high‐average strain fields seen in each of our samples. Observed variations in residual strains suggest that growth conditions play a role in forming misfit defects. This could explain discrepancies with calculated values of critical thickness based on models which neglect growth conditions. Photoluminescence spectra reveal that layer‐to‐layer growth proceeded with single monolayer uniformity, suggesting highly reproducible growth. Our results give hope for relatively defect‐free Cd_(x)Zn_(1−x)Te/Cd_(y)Zn_(1−y)Te superlattices with the potential for applications to optoelectronics offered by intense visible light emitters

Random Sampling of Mellin Band-limited Signals

In this paper, we address the random sampling problem for the class of Mellin band-limited functions BT which is concentrated on a bounded cube. It is established that any function in BT can be approximated by an element in a finite-dimensional subspace of BT. Utilizing the notion of covering number and Bernstein's inequality to the sum of independent random variables, we prove that the random sampling inequality holds with an overwhelming probability provided the sampling size is large enough

Discrete Translates of an Operator in the Schatten pp-Classes

In this manuscript, we investigate the properties of systems formed by translations of an operator in the Schatten $p$-classes $\mathcal{T}^p$. We establish the existence of Schauder frames of integer translates in $\mathcal{T}^p$ for $p>2$. Later, we provide an instance of a uniformly discrete $\Lambda \subset \mathbb{R}^{2d}$ such that there exists an operator whose $\Lambda$-translates are complete in $\mathcal{T}^p$ for all $p>1$

Adaptive parameter choice for one-sided finite difference schemes and its application in diabetes technology

AbstractIn this paper we discuss the problem of approximation of the first derivative of a function at the endpoint of its definition interval. This problem is motivated by diabetes therapy management, where it is important to provide estimations of the future blood glucose trend from current and past measurements. A natural way to approach the problem is to use one-sided finite difference schemes for numerical differentiation, but, following this way, one should be aware that the values of the function to be differentiated are noisy and available only at given fixed points. Then (as we argue in the paper) the number of used point values is the only parameter to be employed for regularization of the above mentioned ill-posed problem of numerical differentiation. In this paper we present and theoretically justify an adaptive procedure for choosing such a parameter. We also demonstrate some illustrative tests, as well as the results of numerical experiments with simulated clinical data

Differentiated MSCs seeded in a highly dense collagenous matrix produce novel biphasic Osteochondral constructs

Structural damage to both the articular cartilage and subchondral bone results in pain and disability for millions of people worldwide, representing a major clinical challenge. Being a hybrid of both bone and cartilage, requirements for osteochondral tissue engineering are more complex than previously investigated single tissue types. Novel methods of integrating bone and cartilage tissue constructs need to be explored. In this study, two hyper-hydrated collagen gels, containing osteogenic and chondrogenic cells, were integrated to create a biphasic osteochondral construct