Walsh Spectral Characteristics and the Auto-Correlation Function Characteristics of Forming Orthomorphic Permutations of Multi-Output Functions

Orthomorphic permutations have good characteristics in cryptosystems. In this paper, by using of knowledge about relation between orthomorphic permutations and multi-output functions, and conceptions of the generalized Walsh spectrum of multi-output functions and the auto-correlation function of multi-output functions to investigate the Walsh spectral characteristics and the auto-correlation function characteristics of orthormophic permutations, several results are obtained.

Chrestenson Spectrum and Auto-Correlation Function of Inverse Permutations of Quick Trickle Permutations

In this paper, a sufficient and necessary condition of quick trickle permutations is given from the point of inverse permutations. The bridge is built between quick trickle permutations and m-value logic functions. By the methods of the Chrestenson spectrum of m-value logic functions and the auto-correlation function of m-value logic functions to investigate the Chrestenson spectral characteristics and the auto-correlation function charac- teristics of inverse permutations of quick trickle permutations, a determinant arithmetic of quick trickle permutations is given. Using the results, it becomes easy to judge that a permutation is a quick trickle permutation or not by using computer. This gives a new pathway to study constructions and enumerations of quick trickle permutations.

Wave Energy Estimation by Using A Statistical Analysis and Wave Buoy Data near the Southern Caspian Sea

Statistical analysis was done on simultaneous wave and wind using data recorded by discus-shape wave buoy. The area is located in the southern Caspian Sea near the Anzali Port. Recorded wave data were obtained through directional spectrum wave analysis. Recorded wind direction and wind speed were obtained through the related time series as well. For 12-month measurements（May 25 2007-2008）, statistical calculations were done to specify the value of nonlinear auto-correlation of wave and wind using the probability distribution function of wave characteristics and statistical analysis in various time periods. The paper also presents and analyzes the amount of wave energy for the area mentioned on the basis of available database. Analyses showed a suitable comparison between the amounts of wave energy in different seasons. As a result, the best period for the largest amount of wave energy was known. Results showed that in the research period, the mean wave and wind auto correlation were about three hours. Among the probability distribution functions, i.e Weibull, Normal, Lognormal and Rayleigh, ＂Weibull＂ had the best consistency with experimental distribution function shown in different diagrams for each season. Results also showed that the mean wave energy in the research period was about 49.88 k W/m and the maximum density of wave energy was found in February and March, 2010.

Design for Vibrator Field Experiment Based-on Vibrator-earth System

Source-generated energy in seismic vibrator records high frequency harmonic behavior. Conventional vibrator-earth coupling model was set up on the linear system. Some assumptions in the application of linear theory to the vibrator problem play an insignificant role in the overall coupling structure. Obviously, non-linear behaviors can be modeled using a “hard-spring” form of the Duffing equation. Model dedicates that a qualitatively similar harmonic component is present for a broad range of possible mathematical descriptions. After some qualitative analysis about the non-linear system, some conclusion can be drawn. Firstly, The design of the vibrator weight should be abided by two points as followed: In order to avoid decoupling for the vibrator to the earth, the weight should be greater than the peak of the driving force amplitude as to keep the resultant force pointing to the earth’s core. On the other hand, for the limited energy output, the vibrator overweight may damage the system high-frequency ability.Secondly, as the driving force frequency approaching to the ground hard-spring inherent frequency, the energy transmission was found to climb its peak from the system energy absorbed curve. At last, due to the non-linear coupling model system, its load curve would come into unstable frequency range, which might limit the application of the Vibroseis conventional sweeping pattern-linear sweep. A new sweeping pattern was listed: the driving signal was the pseudo-random sequence modulated by a fixed frequency cosine signal satisfying with the exploration precision and absorbing efficiency. The synthesized signal was ready to be realized by the electromagnetic driven system. Even the side-lobes noise of its auto-correlation function was restrained well. The theory coming from the Vibrator-earth coupling model was applied to the design of the Portable High-frequency Vibrator System (PHVS), and the good result was obtained. By the analysis of the vibrator base plate signal, the model was proved to be true. The exploration research on PHVS made a first step on its following optimal design.

ROLLLING BEARING FAULT DETECTION USING CORRELATION TECHNIQUE

It's known that auto-correlation technique is effective in extracting periodical signals from random noises. In the case of fault monitoring of rolling element bearing, we can't acquire the fault information directly from the original signal because of the difference of signal phases. And the signal is shown as the wide band random signal in auto-correlation function. In this paper, the signal is pre-processed and the results are proved effective. Moreover, by taking the auto-correlation function we can obtain the determined and comparable samples. This is very important for establishing the data base of running condition and for detecting the faults.

Modelling HIV/AIDS Cases in Zambia: A Comparative Study of the Impact of Mandatory HIV Testing

In this study, a time series modeling approach is used to determine an ARIMA model and advance counterfactual forecasting at a point of policy intervention. We consider monthly data of HIV/AIDS cases from the Ministry of Health (Copperbelt province) of Zambia, for the period 2010 to 2019 and have a total of 120 observations. Results indicate that ARIMA (1, 0, 0) is an adequate model which best fits the HIV/AIDS time series data and is, therefore, suitable for forecasting cases. The model predicts a reduction from an average of 3500 to 3177 representing 14.29% in HIV/AIDS cases from 2017 (year of policy activation) to 2019, but the actual recorded cases dropped from 3500 to 1514 accounting for 57.4% in the same time frame.

The autocorrelation distribution of balanced Boolean function

The global avalanche characteristics （the sum- of-squares indicator and the absolute indicator） measure the overall avalanche characteristics of a cryptographic Boolean function. Sung et al. （1999） gave the lower bound on the sum- of-squares indicator for a balanced Boolean function satisfy- ing the propagation criterion with respect to some vectors. In this paper, if balanced Boolean functions satisfy the propaga- tion criterion with respect to some vectors, we give three nec- essary and sufficient conditions on the auto-correlation distri- bution of these functions reaching the minimum the bound on the sum-of-squares indicator. And we also find all Boolean functions with 3-variable, 4-variable, and 5-variable reaching the minimum the bound on the sum-of-squares indicator.

Numerical Investigation on the Boundary Conditions for the Multiscale Base Functions

We study the multiscale finite element method for solving multiscale elliptic problems with highly oscillating coefficients,which is designed to accurately capture the large scale behaviors of the solution without resolving the small scale characters.The key idea is to construct the multiscale base functions in the local partial differential equation with proper boundary conditions.The boundary conditions are chosen to extract more accurate boundary information in the local problem.We consider periodic and non-periodic coefficients with linear and oscillatory boundary conditions for the base functions.Numerical examples will be provided to demonstrate the effectiveness of the proposed multiscale finite element method.

CORRELATION PROPERTIES OF DE BRUIJN SEQUENCES

Several new bounds for the correlation functions of de Bruijn sequences are derived.It is shown that the set of all primitive de Bruijn sequences have the following two properties:1)for each sequence a in the set with large span n,the magnitude of its auto-correlation funct-ion|ra（k）|is relatively small compared with the peak 2n for all k≠0 mod 2n;2)for each pair of sequences a,b in the set with large span n,the magnitude of their cross-correlation function |rab（k）| is relatively small compared with the peak 2n for all k.Some generalizations of the result are also presented.

ANALYSIS OF SG SEQUENCE

Let be binary sequences. Put λ_i=#{0≤j<i|c_j=0}, μ_i=#{0≤j<i|c_j=1},