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In this paper, the effects of electron beam on the X pinch produced spectra of L-shell Mo plasma have been investigated by principal component analysis (PCA), and this analysis is compared with that of line ratio diagnostics. Spectral database for PCA extraction was arranged using the non-LTE collisional radiative L-shell Mo model. PC vector spectra of L shell Mo including F, Ne, Na and Mg- like transitions were studied to investigate the polarization types of these transitions. PC1 vector spectra of F, Ne, Na and Mg- like transitions resulted in linear polarization of Stokes Q profiles. Besides, PC2 vector spectra showed linear polarization of Stokes U profiles of 2p53s of Ne like transitions which were recognized as responsive to the magnetic field (Trabert et al., 2017). 3D representation of PCA coefficients demonstrated that addition of electron beam to the non-LTE model generates the quantized collective clusters which are translations of each other and follow V-shaped cascade trajectories except for the case f = 0.0. The extracted principal coefficients were used as a database for the Artifical Neural Network (ANN) to estimate the plasma electron temperature, density and beam fractions of time integrated spatially resolved L-shell Mo X-pinch plasma spectrum. PCA based ANN provides advantage in reducing the network topology with a more efficient Backpropagation supervised learning algorithm. The modeled plasma electron temperature is about Te~660 eV and density ne=1x1020 cm-3 in the presence of the fraction of the beams with f~0.1 and centered energy of 5 keV.

Here, we have employed Principal Component Analysis (PCA) and Linear Discriminant Analysis (LDA) to analyze Mie calculated UV-Vis spectra of gold nanospheres (GNS). Eigen spectra of PCA perform the Fano type resonances.3D vector field spectra reveal the Homoclinic orbit Lorenz attractor. Quantum confinement effects are observed by 3D representation of LDA. Standing wave patterns resulting from oscillations of ion acoustic phonon and electron waves are illustrated through the eigen spectra of LDA. Such capabilities of GNPs have brought high attention for the high energy density physics applications. Furthermore, accurate prediction of gold nanoparticle (GNP) sizes using machine learning could provide rapid analysis without the need for expensive analysis. Two hybrid algorithms consist of unsupervised PCA and two different supervised ANN have been used to estimate the diameters of GNPs. PCA based artificial neural network (ANN) were found to estimate the diameters with a high accuracy.

In this paper, we establish some weighted fractional inequalities for differentiable mappings whose derivatives in absolute value are convex. These results are connected with the celebrated Hermite-Hadamard-Fejer type integral inequality. The results presented here would provide extensions of those given in earlier works.

In this paper, we obtain some new integral inequalities like Hermite-Hadamard type for third derivatives absolute value are log-convex. We give some applications to quadrature formula for midpoint error estimate.

In this paper, we derive new estimates for the remainder term of the midpoint, trapezoid, and Simpson formulae for functions whose derivatives in absolute value at certain power are P-functions. Some applications to special means of real numbers are also given.

In this paper, we establish several new inequalities for n- time differentiable mappings that are connected with the celebrated Hermite-Hadamard integral inequality.

In this paper, the authors establish some new estimates for the remainder term of the midpoint, trapezoid, and Simpson formula using functions whose derivatives in absolute value at certain power are s-convex. Some applications to special means of real numbers are provided as well.

In this paper we establish Hermite-Hadamard type inequalities for mappings whose derivatives are s-convex in the second sense and concave.

In this paper, we obtain some inequalities for functions whose first derivatives in absolute value are preinvex and prequasiinvex., Comment: arXiv admin note: text overlap with arXiv:1301.3447; and with arXiv:1203.4759 by other authors

In this paper, we obtain some Hermite-Hadamard type inequalities for functions whose third derivatives in absolute value are preinvex and prequasiinvex., Comment: 7 pages. arXiv admin note: text overlap with arXiv:1203.4759 by other authors

In this paper, we obtain some new inequalities of Hermite-Hadamard type and Simpson type for functions whose third derivatives belong to Godunova-Levin class.

In this papaer, we put forward some new definitions and integral inequalities by using fairly elementary analysis., Comment: 8 pages

In this paper, we obtain some new inequalities for ({\alpha},m)-convex functions. The analysis used in the proofs is fairly elementary and based on the use of Power-mean inequality., Comment: 7 pages

In this paper, we obtain some new estimations of Iyengar-type inequality in which quasi-convex(quasi-concave) functions are involved. These estimations are improvements of some recently obtained estimations. Some error estimations for the trapezoidal formula are given. Applications for special means are also provided., Comment: This study has been presented at "International Conference on Functional Equations, Geometric Functions and Applications(ICFGA2012)" in 10-12 May 2012

In this paper, we introduce the notion of (g,\Phi_{h})-convex dominated function and present some properties of them. Finally, we present a version of Hermite-Hadamard-type inequalities for (g,\Phi_{h})-convex dominated functions. Our results generalize the Hermite-Hadamard-type inequalities in [2], [4] and [6]., Comment: 7 pages

In this paper, we obtain some Simpson type inequalities for functions whose second derivatives absolute value or q-th power of them are Q-class functions. Also we give applications to numerical integration., Comment: 4 pages

In this paper, we obtain some inequalities by using a kernel and an inequality which is a result of Young inequality. Besides we give some applications to special means., Comment: 7 pages

In this paper, we obtain some new inequalities for functions which are introduced by Godunova and Levin., Comment: 6 pages

In this paper, we obtain some Simpson type inequalities for functions whose derivatives in absolute value are $\varphi$-convex., Comment: 11 pages. arXiv admin note: text overlap with arXiv:1203.2282, arXiv:1204.0923, arXiv:1203.2278 by other authors

In this paper, we establish Ostrowski's type inequalities for strongly-convex functions where c>0 by using some classical inequalities and elemantery analysis. We also give some results for product of two strongly-convex functions.

In this paper, we obtained some inequalities for \phi_{s}-convex function, \phi-Godunova-Levin function, \phi-P-function and log-\phi-convex function. Finally, we defined the class of \phi-quasi-convex functions and we examined some properties of this class.

In this paper, we prove some new inequalities of Hadamard-type for s-convex functions on the co-ordinates.

In this paper, we prove some new inequalities of Hadamard-type for convex functions on the co-ordinates., Comment: 18 pages

In this paper, we establish some new inequalities of the Hermite-Hadamard like for class of (h-s)_{1,2}-convex functions which are ordinary, super-multiplicative or similarly ordered and nonnegative.

In this paper, we establish two new convex dominated function and then we obtain new Hadamard type inequalities related to this denitions., Comment: 5 pages

In this paper, we establish several new convex dominated functions and then we obtain new Hadamard type inequalities., Comment: 10 pages

In this study, we obtain some new integral inequalities for different classes of convex functions by using some elementary inequalities and classical inequalities like general Cauchy inequality and Minkowski inequality.

New identity for fractional integrals have been defined. By using of this identity, some new Hermite-Hadamard type inequalities for Riemann-Liouville fractional integral have been developed. Our results have some relationships with the result of Avci et al., proved in AKO., Comment: 9 pages

In this paper, two new classes of convex functions as a generalization of convexity which is called (h-s)_{1,2}-convex functions are given. We also prove some Hadamard-type inequalities and applications to the special means are given., Comment: 11 pages

In this paper, we establish several inequalities for s-convex mappings that are connected with the Riemann-Liouville fractional integrals. Our results have some relationships with certain integral inequalities in the literature., Comment: manuscript

In this paper some new inequalities are proved related to left hand side of Hermite-Hadamard inequality for the classes of functions whose derivatives of absolute values are m-convex. New bounds and estimations are obtained. Applications for some Theorems are given as well.

In this paper, we established some new inequalities via s-convex and s-concave functions.