In high-dimensional semiparametric regression, balancing accuracy and interpretability often requires combining dimension reduction with variable selection. This study intro- duces two novel methods for dimension reduction in additive partial linear models: (i) minimum average variance estimation (MAVE) combined with the adaptive least abso- lute shrinkage and selection operator (MAVE-ALASSO) and (ii) MAVE with smoothly clipped absolute deviation (MAVE-SCAD). These methods leverage the flexibility of MAVE for sufficient dimension reduction while incorporating adaptive penalties to en- sure sparse and interpretable models. The performance of both methods is evaluated through simulations using the mean squared error and variable selection cri

In this paper, the delay integral equations in population growth will be described,discussed , studied and transfered this model to integro-differential equation. At last,we will solve this problem by using variational approach.

In this paper, we proposed to zoom Volterra equations system Altfazlah linear complementarity of the first type in this approximation were first forming functions notch Baschtdam matrix and then we discussed the approach and stability, to notch functions

Original Research Paper Mathematics 1-Introduction : In the light of the progress and rapid development of the applications of research in applications fields, the need to rely on scientific tools and cleaner for data processing has become a prominent role in the resolution of decisions in industrial and service institutions according to the real need of these methods to make them scientific methods to solve the problem Making decisions for the purpose of making the departments succeed in performing their planning and executive tasks. Therefore, we found it necessary to know the transport model in general and to use statistical methods to reach the optimal solution with the lowest possible costs in particular. And you know The Transportatio

In this paper, three approximate methods namely the Bernoulli, the Bernstein, and the shifted Legendre polynomials operational matrices are presented to solve two important nonlinear ordinary differential equations that appeared in engineering and applied science. The Riccati and the Darcy-Brinkman-Forchheimer moment equations are solved and the approximate solutions are obtained. The methods are summarized by converting the nonlinear differential equations into a nonlinear system of algebraic equations that is solved using Mathematica®12. The efficiency of these methods was investigated by calculating the root mean square error (RMS) and the maximum error remainder (𝑀𝐸𝑅n) and it was found that the accuracy increases with increasi

In this paper, visible image watermarking algorithm based on biorthogonal wavelet
transform is proposed. The watermark (logo) of type binary image can be embedded in the
host gray image by using coefficients bands of the transformed host image by biorthogonal
transform domain. The logo image can be embedded in the top-left corner or spread over the
whole host image. A scaling value (α) in the frequency domain is introduced to control the
perception of the watermarked image. Experimental results show that this watermark
algorithm gives visible logo with and no losses in the recovery process of the original image,
the calculated PSNR values support that. Good robustness against attempt to remove the
watermark was s

A frequently used approach for denoising is the shrinkage of coefficients of the noisy signal representation in a transform domain. This paper proposes an algorithm based on hybrid transform (stationary wavelet transform proceeding by slantlet transform); The slantlet transform is applied to the approximation subband of the stationary wavelet transform. BlockShrink thresholding technique is applied to the hybrid transform coefficients. This technique can decide the optimal block size and thresholding for every wavelet subband by risk estimate (SURE). The proposed algorithm was executed by using MATLAB R2010aminimizing Stein’s unbiased with natural images contaminated by white Gaussian noise. Numerical results show that our algorithm co