Sine-type Function Research Articles

Aerodynamic Performance of the Three-Dimensional Lumped Flexibility Wing Under Wind Fluctuating Condition

Understanding the effect of fluctuating wind on the aerodynamic performance of the wing is important for designing practical using flapping-wing micro air vehicles (FMAV). This paper aims at providing a systematic synthesis on the fluctuating wind influence on the performance of the three dimensional lumped flexibility wing based on the numerical analysis approach. The fluctuating wind is simplified as a sine type function, and the flexibility of the wing is modeled as the passive pitching motion by connecting a rigid wing to a torsional spring at the root of the wing. The interaction between the fluctuating wind and the lumped flexibility wing is performed on a high-resolution computational grid. The evaluation is based on validation with published experiment data. The results indicate that the fluctuating wind cannot enhance the flexible wings’ propulsive and lifting performance simultaneously, however, it influences the aerodynamic characteristics of the wing greatly. Comparing to the rigid wing, the suppress leading edge vortex and trailing edge vortex are observed of the flexible wing under appropriate fluctuating wind, which leads the flexible wing to not only have better propulsive and lifting performance, but also flight stability performance.

A sampling theorem by perturbing the zeros of a sine-type function

ABSTRACT In this paper, we present a generalisation of the classical Shannon sampling theorem that allows for sampling sets that are perturbations of the set of zeros of a sine-type function. Such sampling sets may be non-equidistant and non-periodic.

The zeros of a sine-type function and the peak value problem

The problem of finding an upper bound for the infinity norm of signals from their sample values is called the peak value problem. The peak value problem is a significant problem related to orthogonal frequency division multiplexing (OFDM) which has applications in wireless networks, audio broadcasting, and mobile communications. In this article, we will first answer the question of whether the zeros of a π-sine-type function form a stable sampling set for Bβπ∞,0<β<1. Then, we will address a related question of bounding the infinity norm of a given signal. The sampling set we use only requires a bound on the maximum distance between two consecutive sampling points. Our result for estimating the bound works for a nonuniform sampling set.

Riesz basis of exponential family for a hyperbolic system

Abstract This paper studies a linear hyperbolic system with boundary conditions that was first studied under some weaker conditions in [8, 11]. Problems on the expansion of a semigroup and a criterion for being a Riesz basis are discussed in the present paper. It is shown that the associated linear system is the infinitesimal generator of a C 0 {C_{0}} -semigroup; its spectrum consists of zeros of a sine-type function, and its exponential system { e λ n ⁢ t } n ≥ 1 {\{e^{\lambda_{n}t}\}_{n\geq 1}} constitutes a Riesz basis in L 2 ⁢ [ 0 , T ] {L^{2}[0,T]} . Furthermore, by the spectral analysis method, it is also shown that the linear system has a sequence of eigenvectors, which form a Riesz basis in Hilbert space, and hence the spectrum-determined growth condition is deduced.

High temperature deformation behavior and constitutive modeling for 20CrMnTiH steel

The hot compressive deformation behavior of 20CrMnTiH steel, which is one of the most widely used gear steels in China, was investigated at the temperatures from 950°C to 1150°C and strain rates from 0.01 to 5s−1 on Gleeble-3500 thermo-simulation machine. Stress–strain data collected from the tests were employed to establish the constitutive equation. The results show that the flow stress decreases with increasing deformation temperature and decreasing strain rate and the stress–strain curves exhibit single-peak dynamic recrystallization (DRX). The average grain sizes decreased with the increasing strain rate and the decreasing deformation temperature and the higher the deformation temperature, the larger the dynamic recrystallization degree. The exponential law and the hyperbolic sine-type function constitutive equation were established to describe the relationship among σ, T and ε̇ for 20CrMnTiH steel at the strain rate range of 0.01–0.1s−1 and 1–5s−1, respectively. The peak stress values predicted by the proposed constitutive model agree well with the corresponding experimental results, which confirmed the accuracy and reliability of the developed constitutive equation of 20CrMnTiH steel.

Towards a general theory of reconstruction of bandlimited signals from sine wave crossings

Arbitrary bounded bandlimited signals that are real on the real axis cannot be reconstructed from their zero crossings in general, because they can have complex zeros. However, a simple invertible transformation, which consists of taking the difference of such a signal with a properly chosen sine function, creates a function that has only simple and real zeros. It can be shown that the original signal can be reconstructed from these zeros, or, equivalently, from the sine wave crossings of the signal. In this paper we study the reconstruction of bandlimited signals from their sine wave crossings by sampling series, which is one possible method of reconstruction. The reconstruction functions and the sampling points that are used in the reconstruction process are determined by the signal which shall be reconstructed and therefore are, in a certain sense, adapted to the signal. We address the convergence behavior of the reconstruction process without oversampling. Although we have local uniform convergence, we conjectured in a previous paper that the adaptivity is not sufficient for global uniform convergence. By developing a rigorous convergence theory for different signal spaces, and by showing that the Paley–Wiener space PW π 1 of signals that are the inverse Fourier transform of some absolutely integrable function is the border case, we prove that this conjecture is true. The solution of this problem has far reaching consequences for the approximation of stable linear time-invariant systems by sampling series, because it shows that the adaptivity of the system approximation process is not sufficient for its pointwise convergence. The theory of sine-type functions is an important tool for our analysis, and we give several sufficient conditions for the sine-wave crossings of a signal to be the zero sequence of a sine-type function.

Bases of exponentials in weighted spaces generated by zeros of functions of sine type

If ω is an Ap-weight with some additional condition and (λ) is a separated sequence of all zeros of a sine-type function possessing a certain multiplier (in the sense of Fourier transforms) property, then the corresponding system of exponentials \((e^{i\lambda _n t} )\) constitutes a basis in the weighted space Lp((−π, π), ω(t)dt), 1 < π < ∞.

Bounded mean oscillation and bandlimited interpolation in the presence of noise

We study some problems related to the effect of bounded, additive sample noise in the bandlimited interpolation given by the Whittaker–Shannon–Kotelnikov (WSK) sampling formula. We establish a generalized form of the WSK series that allows us to consider the bandlimited interpolation of any bounded sequence at the zeros of a sine-type function. The main result of the paper is that if the samples in this series consist of independent, uniformly distributed random variables, then the resulting bandlimited interpolation almost surely has a bounded global average. In this context, we also explore the related notion of a bandlimited function with bounded mean oscillation. We prove some properties of such functions, and in particular, we show that they are either bounded or have unbounded samples at any positive sampling rate. We also discuss a few concrete examples of functions that demonstrate these properties.

Expansion of solution in terms of generalized eigenfunctions for a hyperbolic system with static boundary condition

This paper studies a linear hyperbolic system with static boundary condition that was first studied in Neves et al. [J. Funct. Anal. 67(1986) 320–344]. It is shown that the spectrum of the system consists of zeros of a sine-type function and the generalized eigenfunctions of the system constitute a Riesz basis with parentheses for the root subspace. The state space thereby decomposes into topological direct sum of root subspace and another invariant subspace in which the associated semigroup is superstable: that is to say, the semigroup is identical to zero after a finite time period.

Q—Type Sampling Theorems

This paper introduces q—versions of the classical sampling theorem of Whittaker, Kotel’nikov and Shannon as well as Kramer’s analytic theorem. q—type band-limited signals are defined in terms of Jackson’s q—integral and their sampling representations are given. The sampling points are the zeros of a q—sine type function, derived by Bustoz and Cardoso (2001).

Fast learning in a backpropagation algorithm with a sine-type thresholding function

A new approach to learning in a multilayer neural network based on a backpropagation algorithm is presented. With a sine-type thresholding function the model is more efficient and able to learn nonnegative interconnections that are suitable for optical implementations.

On some riesz bases

In this paper we consider three problems concerning systems of vector exponentials. In the first part we prove a conjecture of V. Komornik raised in [14] on the independence of the movement of a rectangular membrane in different points. It was independently proved by M. Horvath [9] and S. A. Avdonin (personal communication). The analogous problem for the circular membrane was partly solved in [3] — the complete solution is given in [10]. In the second part we fill in a gap in the theory of Blaschke-Potapov products developed in the paper [19] of Potapov. Namely we prove that the Blaschke-Potapov product is determined by its kernel sets up to a multiplicative constant matrix. In the third part of the present paper we give a multidimensional generalization of the notion of sine type function developed by Levin [16], [17] and by our generalization we prove the multidimensional variant of the Levin-Golovin basis theorem [16], [6].