Considering the Lennard-Jones (LJ) intermolecular potential function and solving simultaneously the ORNSTEIN-ZERNIKE(OZ) and the percus-yevick(PY) EQUATIONs, the radial distribution function (RDF) and the correlation functions are obtained and used in the kjellander EQUATION to calculate the reduced residual chemical potential at infinite-dilution for binary mixtures. The calculations are performed for various values of size ratio and energy ratio in order to determine the effect of solute size on the residual chemical potential. Also in this work for the first time, the phase equilibrium EQUATION based on the integral EQUATION is applied to calculate the solubility of naphthalene in supercritical carbon dioxide. To represent the intermolecular interactions, the Lennard-Jones (LJ) potential function is used.

In the present work, the integral EQUATIONs method is used to calculate transport properties of polar fluids. For this goal, we use the Stockmayer potential and examine theoretically the thermal conductivity of several refrigerant mixtures such as R125+R134a, R125+R32, R125+R152a, R134a+R32, R152a+R32, R134a+R143a, and R125+R143a. We solve numerically the ORNSTEIN-ZERNIKE (OZ) EQUATION using the Hypernetted Chain (HNC) approximation for binary fluid mixtures and obtain the pair correlation functions. Finally, the temperature dependence of thermal conductivity is studied using Vesovic-Wakeham method and compared with available results.

The goal of multi-frame Super Resolution (SR) is to fuse multiple Low Resolution (LR) images to produce one High Resolution (HR) image. The major challenge of classic SR approaches is accurate motion estimation between the frames. To handle this challenge, fuzzy motion estimation method has been proposed that replaces value of each pixel using the weighted averaging all its neighboring pixels in all LR images which carries the degree of similarity between image blocks centered on two pixels. Since in case of rotation between LR images, comparing the gray level of blocks around the pixels is not a suitable criterion for calculating weight, so, magnitude of ZERNIKE Moments (ZM) has been used as a rotation invariant feature. Due to the lower sensitivity of Pseudo ZERNIKE Moments (PZM) to noise and the higher discrimination capability of it for the same order compared to ZM, in this paper, we propose a new method based on magnitude of PZM of the blocks as a rotation invariant descriptor for representation of pixels in weight calculation. Experimental results on several image sequences show that the performance of the proposed algorithm is better than the existing and new techniques from the aspect of PSNR and visual image quality.

Most of the contour detection methods suffers from some drawbacks such as noise, occlusion of objects, shifting, scaling and rotation of objects in image which they suppress the recognition accuracy. To solve the problem, this paper utilizes ZERNIKE Moment (ZM) and Pseudo ZERNIKE Moment (PZM) to extract object contour features in all situations such as rotation, scaling and shifting of object inside the image. The proposed method consist of three steps: first step employs Line Detection with Contours (LDC) in order to find the object region based on the connected components objects inside the image. In the second step, PZM is applied on the detected object regions to extract feature vector. Regarding to investigate the effectiveness of classifier at the final stage, the SVM and KNN classifiers are employed to extract final object contours. Experimental results on Caltech-101 dataset shows that classification rate is improved to 96.46%. In comparison to the former contour detectors, that proves the ability of the proposed method to detect object boundary in the most of the contour’s changes such as rotation or scaling.

This paper presents a nonlinear autoregressive model with ORNSTEIN Uhlenbeck processes innovation driven with white noise. Notations and preliminaries are presented about the ORNSTEIN Uhlenbeck processes that have important applications in finance. The parameter estimation for these processes is constructed from the time continuous likelihood function that leads to an explicit maximum likelihood estimator. A semiparametric method is proposed to estimate the nonlinear autoregressive function using the conditional least square method for parametric estimation and the nonparametric kernel approach by using the nonparametric factor that is derived by a local L2-fitting criterion for the regression adjustment estimation . Then the Monte Carlo numerical simulation studies are carried out to show the efficiency and accuracy of the present work. The mean square error ( MSE) is a measure of the average squared deviation of the estimated function values from the actual ones. The values of MSE indicate that the innovation in noise structure is performed well in comparison with the existing noise in the nonlinear autoregressive models.

Identification systems based on biometrics have been conventional more than traditional identification systems in the last two decades. Many biometrics have been provided such as fingerprint, palm, iris, the vein of palm and veins of fingerprint and such. One of the challenges discussed in biometrics is physical damages. The biometric of fingers knuckles is one of the biometrics less exposed to the physical damages. Several methods have been suggested for identification with various weak points such as high mathematical complications and a very low rate of identification. The present study suggests a new method for identification which is based on ZERNIKE Moment. ZERNIKE moment extracts the features of the picture several times. What distinguishes this algorithm from its counterparts is that it has got high accuracy in demarcating similar pictures of different classifications. In addition to its logical calculating complications, this method was able to record a very appropriate rate of identification facing some challenges such as noise, rotation, and transition.

Context: Aberrometric analysis of thewavefront in patients with refractive disorders is performed using the ZERNIKE pyramidmode and based on that, a treatment plan is determined however, it is not clear what ZERNIKE modes are derived from mathematical analysis, exactly how much they correspond to the clinical facts this article discusses ways to study this issue. Evidence Acquisition: One of the methods for studying optical systems is the aberrometry of wavefront. the wavefront is a twodimensional surface perpendicular to a bunch of parallel light rays, that all these rays have the same phase on this surface (because light emits sinusoidally and therefore has multiple identical phases) whenever these rays pass through a refractive surface, it is also called the reference level this refractive index will be ideal if the homogeneity of these rays is maintained and the rays of this bunch of light will be able to focus at one point, but if the by passing light through the refractive surface thewavefront will be disturbedand the lights on this surface have different phases than the reference surface then it is said there is a discrepancy or deviation between the reference surface and thewavefront. Therefore, aberration is the creation of the distance of thewavefront in a certain phase from the refractive surface or reference surface. When we say refractive surface, we do not mean a specific place like the cornea because other than the cornea other factors such as crystalline lens, vitreous, retin even tear layer they are involved in creating aberrations, but usually the pupil range is considered as the reference surface. Results: Modes z-13 and z13 of the fourth order and modes z04 and z-24, z24 from the fifth order and modes z-15, z15 of six order and modes z06, z-26, z26 of seventh order they are not pure and mathematically they have some lower order whichmaycause in analysis aberrometry disruption as a result, the relevant orders have a little more or less value. Conclusions: There are no strong clinical reasons for ZERNIKE modes to be a fully accurate description of aberromerty, so clinicians should consider other clinical data and findings in their interpretation. Some modes of high-order ZERNIKE have sentences of loworder This can cause abnormal analysis.