STARLIKENESS ASSOCIATED WITH THE SINE HYPERBOLIC FUNCTION

Let q_(λ)(z)=1+λsinh(ζ),0<λ<1/sinh(1)be a non-vanishing analytic function in the open unit disk.We introduce a subclass S^(*)(q_(λ))of starlike functions which contains the functions f such that zf'/f is subordinated by q_(λ).We establish inclusion and radii results for the class S^(*)(q_(λ))for several known classes of starlike functions.Furthermore,we obtain sharp coefficient bounds and sharp Hankel determinants of order two for the class S^(*)(q_(λ)).We also find a sharp bound for the third Hankel determinant for the caseλ=1/2.

Whole Perfect Vectors and Fermat’s Last Theorem

A naïve discussion of Fermat’s last theorem conundrum is described. The present theorem’s proof is grounded on the well-known properties of sums of powers of the sine and cosine functions, the Minkowski norm definition, and some vector-specific structures.

A Fast Underwater Optical Image Segmentation Algorithm Based on a Histogram Weighted Fuzzy C-means Improved by PSO

The S/N of an underwater image is low and has a fuzzy edge.If using traditional methods to process it directly,the result is not satisfying.Though the traditional fuzzy C-means algorithm can sometimes divide the image into object and background,its time-consuming computation is often an obstacle.The mission of the vision system of an autonomous underwater vehicle (AUV) is to rapidly and exactly deal with the information about the object in a complex environment for the AUV to use the obtained result to execute the next task.So,by using the statistical characteristics of the gray image histogram,a fast and effective fuzzy C-means underwater image segmentation algorithm was presented.With the weighted histogram modifying the fuzzy membership,the above algorithm can not only cut down on a large amount of data processing and storage during the computation process compared with the traditional algorithm,so as to speed up the efficiency of the segmentation,but also improve the quality of underwater image segmentation.Finally,particle swarm optimization (PSO) described by the sine function was introduced to the algorithm mentioned above.It made up for the shortcomings that the FCM algorithm can not get the global optimal solution.Thus,on the one hand,it considers the global impact and achieves the local optimal solution,and on the other hand,further greatly increases the computing speed.Experimental results indicate that the novel algorithm can reach a better segmentation quality and the processing time of each image is reduced.They enhance efficiency and satisfy the requirements of a highly effective,real-time AUV.

3D inversion modeling of joint gravity and magnetic data based on a sinusoidal correlation constraint

Joint inversion based on a correlation constraint utilizes a linear correlation function as a structural constraint.The linear correlation function contains a denominator,which may result in a singularity as the objective function is optimized,leading to an unstable inversion calculation.To improve the robustness of this calculation,this paper proposes a new method in which a sinusoidal correlation function is employed as the structural constraint for joint inversion instead of the conventional linear correlation function.This structural constraint does not contain a denominator,thereby preventing a singularity.Compared with the joint inversion method based on a cross-gradient constraint,the joint inversion method based on a sinusoidal correlation constraint exhibits good performance.An application to actual data demonstrates that this method can process real data.

Active disturbance rejection control FCS-MPC strategy based on ESO of PMSM system

In order to improve the control performance of three-phase permanent magnet synchronous motor(PMSM)system,an active disturbance rejection finite control set-mode predictive control(FCS-MPC)strategy based on improved extended state observer(ESO)is proposed in this paper.ESO is designed based on the arc-hyperbolic sine function to obtain estimations of rotating speed and back electromotive force(EMF)term of motor speed.Active disturbance rejection control(ADRC)is applied as speed controller.The proposed FCS-MPC strategy aims to reduce the electromagnetic torque ripple and the complexity and calculation of the algorithm.Compared with the FCS-MPC strategy based on PI controller,the constructed control strategy can guarantee the reliable and stable operation of PMSM system,and has good speed tracking,anti-interference ability and robustness.

Towards Improving the Intrusion Detection through ELM (Extreme Learning Machine)

An IDS(intrusion detection system)provides a foremost front line mechanism to guard networks,systems,data,and information.That’s why intrusion detection has grown as an active study area and provides significant contribution to cyber-security techniques.Multiple techniques have been in use but major concern in their implementation is variation in their detection performance.The performance of IDS lies in the accurate detection of attacks,and this accuracy can be raised by improving the recognition rate and significant reduction in the false alarms rate.To overcome this problem many researchers have used different machine learning techniques.These techniques have limitations and do not efficiently perform on huge and complex data about systems and networks.This work focused on ELM(Extreme Learning Machine)technique due to its good capabilities in classification problems and dealing with huge data.The ELM has different activation functions,but the problem is to find out which function is more suitable and performs well in IDS.This work investigates this problem.Here,Well-known activation functions like:sine,sigmoid and radial basis are explored,investigated and applied to measure their performance on the GA(Genetic Algorithm)features subset and with full features set.The NSL-KDD dataset is used as a benchmark.The empirical results are analyzed,addressed and compared among different activation functions of the ELM.The results show that the radial basis and sine functions perform better on GA feature set than the full feature set while the performance of the sigmoid function is almost equal on both features sets.So,the proposal of GA based feature selection reduced 21 features out of 41 that brought up to 98%accuracy and enhanced overall efficiency of extreme learning machine in intrusion detection.

Novel two-directional grid multi-scroll chaotic attractors based on the Jerk system

A new method is presented to generate two-directional (2D) grid multi-scroll chaotic attractors via a specific form of the sine function and sign function series, which are applied to increase saddle points of index 2. The scroll number in the x-direction is modified easily through changing the thresholds of the specific form of the sine function, while the scroll number in the y-direction is controlled by the sign function series. Some basic dynamical properties, such as equilibrium points, bifurcation diagram, phase portraits, and Lyapunov exponents spectrum are studied. Furthermore, the electronic circuit of the system is designed and its simulation results are given by Multisim 10.

On the Stability of the Generalized Sine Functional Equations

The aim of this paper is to study the stability problem of the generalized sine functional equations as follows：g（x）f（y）=f（x＋y/2）^2-f（x-y/2）^2 f（x）g（y）=f（x＋y/2）^2-f（x-y/2）^2,g（x）g（y）=f（x＋y/2）^-f（x-y/2）^2Namely, we have generalized the Hyers Ulam stability of the （pexiderized） sine functional equation.

Study on a New Spline Adaptive Filter Using Convex Combination of Exponential Hyperbolic Sine

In this paper, a new spline adaptive filter using a convex combination of exponential hyperbolic sinusoidal is presented. the algorithm convexly combines an exponential hyperbolic sinusoidal Hammerstein spline adaptive filter and a Wiener-type spline adaptive filter to maintain the robustness in non-Gaussian noise environments when dealing with both the Hammerstein nonlinear system and the Wiener nonlinear system. The convergence analyses and simulation experiments are carried out on the proposed algorithm. The experimental results show the superiority of the proposed algorithm to other algorithms.

MULTIVARIATE FOURIER TRANSFORM METHODS OVER SIMPLEX AND SUPER-SIMPLEX DOMAINS

In this paper we propose the well-known Fourier method on some non-tensor product domains in Rd, including simplex and so-called super-simplex which consists of （d ＋ 1）! simplices. As two examples, in 2-D and 3-D case a super-simplex is shown as a parallel hexagon and a parallel quadrilateral dodecahedron, respectively. We have extended most of concepts and results of the traditional Fourier methods on multivariate cases, such as Fourier basis system, Fourier series, discrete Fourier transform （DFT） and its fast algorithm （FFT） on the super-simplex, as well as generalized sine and cosine transforms （DST, DCT） and related fast algorithms over a simplex. The relationship between the basic orthogonal system and eigen-functions of a LaDlacian-like operator over these domains is explored.

The General Solution of Ming Antu's Problem

In two centuries ago, Ming Autu discovered the famous Catalan numbers while he tried to expand the function sin(2px) as power series of sin(x) for the case p = 1, 2, 3. Very recently, P. J. Larcombe shows that for any p, sin(2px) can always be expressed as an infinite power series of sin(x) involving precise combinations of Catalan numbers as part of all but the initial p terms and gave all expansions for the case p = 4, 5. The present paper presents the desired expansion for arbitrary integer p.

An Extended Weibull Model with Variable Periodicity

A new distribution for the fluctuation of materials＇ lifetime cumulative hazard rate is firstly proposed. The new distribution is extended from the Weibull distribution by adding a sine function. After that, the properties of its hazard rate function, cumulative hazard rate function, probability density function and cumulative distribution function are studied. The analysis result shows this distribution can well model the lifetime with variable and periodic hazard rate. Finally, the new distribution is verified with two real data sets as examples to demonstrate its capability.