Exact eigenvalue assignment of linear scalar systems with single delay using Lambert W function

Eigenvalue assignment problem of a linear scalar system with a single discrete delay is analytically and exactly solved. The existence condition of the desired eigenvalue is established when the current and delay states are present in the feedback loop. Design of the feedback controller is then followed. Furthermore, eigenvalue assignment for the input-delay system is also obtained as well. Numerical examples illustrate the procedure of assigning the desired eigenvalue

Dark Energy and Normalization of the Cosmological Wave Function

Dark energy is investigated from the perspective of quantum cosmology. It is found that, together with an appropriate normal ordering factor $q$, only when there is dark energy then can the cosmological wave function be normalized. This interesting observation may require further attention.Comment: Title changed, match the published versio

Cosmology-Independent Distance Moduli of 42 Gamma-Ray Bursts between Redshift of 1.44 and 6.60

This report is an update and extension of our paper accepted for publication in ApJ (arXiv:0802.4262). Since objects at the same redshift should have the same luminosity distance and the distance moduli of type Ia supernovae (SNe Ia) obtained directly from observations are completely cosmology independent, we obtain the distance modulus of a gamma-ray burst (GRB) at a given redshift by interpolating or iterating from the Hubble diagram of SNe Ia. Then we calibrate five GRB relations without assuming a particular cosmological model, from different regression methods, and construct the GRB Hubble diagram to constrain cosmological parameters. Based upon these relations we list the cosmology-independent distance moduli of 42 GRBs between redshift of 1.44 and 6.60, with the 1-$\sigma$ uncertainties of 1-3%.Comment: 6 pages, 2 figures, 3 tables. To appear in the proceedings of "2008 Nanjing GRB conference", Nanjing, 23-27 June 200

Development Of Contrast Enhancement Algorithm For Images Captured Under Insufficient Illumination

Many methods have been proposed to improve the contrast, quality and to optimize the insufficient illumination images. In the image enhancement, the main goal is to improve the contrast in the images. Images with high quality contain a great variety of information. The images quality is very easily affected by lighting, climate or equipment’s that have been used to capture the image. Some of these conditions such as insufficient illumination lead to darker images where the image may suffer information loss. Therefore, this thesis puts forward an optimized enhancement method in order to retain the information in the image. This proposed method performs on the insufficient light images. The proposed algorithm is decomposed by Haar wavelet to obtain the decomposition coefficient in all directions of the image, adjusts the threshold values of wavelet coefficient, then reconstruct the image. Finally, do the suitable postprocessing for the reconstructed image. The experimental results demonstrate that the proposed method successfully improves the image quality and contrast and these proven by a series of experiments. The proposed method shows good results for image enhancement. Whether it is in the image contrast enhancement, or extent of noise pollution. The proposed method was enhanced the contrast value more than fifty thousand at the same time, the variance was controlled less than ten thousand

Channel characterization for 1D molecular communication with two absorbing receivers

This letter develops a one-dimensional (1D) diffusion-based molecular communication system to analyze channel responses between a single transmitter (TX) and two fully-absorbing receivers (RXs). Incorporating molecular degradation in the environment, rigorous analytical formulas for i) the fraction of molecules absorbed, ii) the corresponding hitting rate, and iii) the asymptotic fraction of absorbed molecules as time approaches infinity at each RX are derived when an impulse of molecules are released at the TX. By using particle-based simulations, the derived analytical expressions are validated. Simulations also present the distance ranges of two RXs that do not impact molecular absorption of each other, and demonstrate that the mutual influence of two active RXs reduces with the increase in the degradation rate

Parameter Estimation in a Noisy 1D Environment via Two Absorbing Receivers

This paper investigates the estimation of different parameters, e.g., propagation distance and flow velocity, by utilizing two fully-absorbing receivers (RXs) in a one-dimensional (1D) environment. The time-varying number of absorbed molecules at each RX and the number of absorbed molecules in a time interval as time approaches infinity are derived. Noisy molecules in this environment, that are released by sources in addition to the transmitter, are also considered. A novel estimation method, namely difference estimation (DE), is proposed to eliminate the effect of noise by using the difference of received signals at the two RXs. For DE, the Cramer-Rao lower bound (CRLB) on the variance of estimation is derived. Independent maximum likelihood estimation is also considered at each RX as a benchmark to show the performance advantage of DE. Aided by particle-based simulation, the derived analytical results are verified. Furthermore, numerical results show that DE attains the CRLB and is less sensitive to the change of noise than independent estimation at each RX.Comment: 7 pages, 5 figures, accepted by Globecom 202