This paper presents seven modified Adomian Decomposition Method (ADM) techniques for efficiently solving initial value problems, especially those involving non-homogeneous and nonlinear differential equations. While the classical ADM is effective for linear homogeneous cases, it has difficulties solving more complex problems. The proposed modifications—from MADM1 to MLADM—include Maclaurin and Taylor expansions, Laplace transforms, and single-step iterations.• These modifications enhance convergence, reduce complexity, and improve accuracy.• Each method offers specific advantages, such as accelerating convergence (MADM2, RADM4), simplifying computation (TSADM5), and achieving higher accuracy (MLADM).• Numerical examples confirm th

Estimation of the unknown parameters in 2-D sinusoidal signal model can be considered as important and difficult problem. Due to the difficulty to find estimate of all the parameters of this type of models at the same time, we propose sequential non-liner least squares method and sequential robust  M method after their development through the use of sequential  approach in the estimate suggested by Prasad et al to estimate unknown frequencies and amplitudes for the 2-D sinusoidal compounds but depending on Downhill Simplex Algorithm in solving non-linear equations for the purpose of obtaining non-linear parameters estimation which represents frequencies and then use of least squares formula to estimate

This article deals with the approximate algorithm for two dimensional multi-space fractional bioheat equations (M-SFBHE). The application of the collection method will be expanding for presenting a numerical technique for solving M-SFBHE based on “shifted Jacobi-Gauss-Labatto polynomials” (SJ-GL-Ps) in the matrix form. The Caputo formula has been utilized to approximate the fractional derivative and to demonstrate its usefulness and accuracy, the proposed methodology was applied in two examples. The numerical results revealed that the used approach is very effective and gives high accuracy and good convergence.

The utilization of targeted therapy for programmed death ligand 1 (PD‑L1) has emerged as a prominent focus in contemporary clinical trials, particularly in the context of immune checkpoint inhibitors. The prognostic significance of the expression of PD‑L1 in invasive mammary cancer remains a subject of discussion in clinical oncology, requiring further exploration, despite its recognition as a biomarker for responsiveness to anti‑PDL1 immunotherapy. The present study was conducted to investigate the immunohistological expression of PD‑L1 in women with triple‑negative breast cancer (TNBC), with a particular focus for searching for the associated clinical and pathological characteristics. The present retrospective study examined the

Hypertension is identified as one of the most significant risk factors for cardiovascular diseases (CVDs). There is growing evidence showing that oxidative stress plays a major role in hypertension. Increased production of reactive oxygen species and decrease bioavailability of antioxidant have been demonstrated in experimental and human hypertension. The present study was directed to determine the beneficial effect of the antioxidant vitamin C in patients with essential hypertension treated with the calcium channel blocker (amlodipine) or with the angiotensin converting enzyme inhibitor (enalapril). Ninety six patients (50 females and 46 males) with essential hyp

The second most commonly diagnosed cancer is colorectal cancer (CRC) is in female. The levels of progranulin, obestatin and liver enzymes including ALT, AST and ALP were measured in forty five sera in female patients suffering from CRC before chemotherapy initiation treatment as G1, G2 after first chemotherapy cycle and G3 after second chemotherapy cycle compared with thirty female as a healthy control G4. Results showed a high significant increased in progranulin concentration and a high significant decrease in obestatin in G2 than other groups. The correlation between progranulin and ALP was a significant negative (-ve) relation while obestatin with AST gave a significant positive (+ve) correlation in G. The results also showed non signif

Diabetes mellitus type 2 [DMT2] is a disturbance of metabolism and complex diseases influenced by environmental, genetic agents, and linked with inflammation, happens when the pancreas either does not use the insulin as it should or the body does not make enough insulin, lead to insulin resistance [IR] alongside with gradual loss of ß-cell secretory ability. The aim of this study was to investigate the role of soluble L-selectin (sL-selectin) in diabetes mellitus type 2 patients in Iraqi Arabs patient. Study includes seventy six Iraqi Arabs patients (male and female) having newly diagnosed type 2 diabetes mellitus (T2DM), with Fifty three Iraqi Arabs healthy subjects matched in age, sex and ethnic group. Patients and healthy subjec