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

Objective : Sciatic nerve block (popliteal approach) and femoral N block is a new technique other than general anesthesia in below knee surgery because it provides adequate muscle relaxation, with good intraoperative and post-operative analgesia. Nefopam is non opioid, non-respiratory depressant and non-sedative was mixed with local anesthetics drug to study the effects. This study was done to compare the onset and duration of sensory and onset time and duration of action of motor block following administration of either bupivacaine alone with administration of bupivacaine and Nefopam in patients undergoing below knee lower limb surgeries under ultrasound guided regional anesthesia.
Methods: 100 patients with American society of anest

Let G be a graph, each edge e of which is given a weight w(e). The shortest path problem is a path of minimum weight connecting two specified vertices a and b, and from it we have a pre-topology. Furthermore, we study the restriction and separators in pre-topology generated by the shortest path problems. Finally, we study the rate of liaison in pre-topology between two subgraphs. It is formally shown that the new distance measure is a metric

Among a variety of approaches introduced in the literature to establish duality theory, Fenchel duality was of great importance in convex analysis and optimization. In this paper we establish some conditions to obtain classical strong Fenchel duality for evenly convex optimization problems defined in infinite dimensional spaces. The objective function of the primal problem is a family of (possible) infinite even convex functions. The strong duality conditions we present are based on the consideration of the epigraphs of the c-conjugate of the dual objective functions and the ε-c-subdifferential of the primal objective functions.

In this paper, we deal with games of fuzzy payoffs problem while there is uncertainty in data. We use the trapezoidal membership function to transform the data into fuzzy numbers and utilize the three different ranking function algorithms. Then we compare between these three ranking algorithms by using trapezoidal fuzzy numbers for the decision maker to get the best gains

This paper presents the matrix completion problem for image denoising. Three problems based on matrix norm are performing: Spectral norm minimization problem (SNP), Nuclear norm minimization problem (NNP), and Weighted nuclear norm minimization problem (WNNP). In general, images representing by a matrix this matrix contains the information of the image, some information is irrelevant or unfavorable, so to overcome this unwanted information in the image matrix, information completion is used to comperes the matrix and remove this unwanted information. The unwanted information is handled by defining {0,1}-operator under some threshold. Applying this operator on a given ma

Objective: Detection the level of YKL-40 biochemical marker and vitamin D level in sera of Iraqi uterine cancer
females' patients.
Methodology: This study included 90 female volunteers, 30 of them were healthy volunteers who were
considered as a control group, while sixty serum samples were collected from women patients suffering from
uterine tumors (30 malignant and 30 fibroid benign tumors), benign cases were considered as a disease
control group for malignant tumors. The average age of those females was 30-75 years, which matched the
control group. All the samples were collected from Azady hospital in Kirkuk and the gynecologic department at
Medical City in Baghdad during October /2012 to May /2013. All the serum

Background: The use of Miswak, chewing sticks (salvadorapersica) can be traced back to Babylonians some 7000 years ago. It is commonly used throughout the world especially for the purpose of oral hygiene. Muslims are using as the religious view. Current study aimed to test the ability of aqueous siwak extract to increase the resistance of enamel surface against acid dissolution compared to sodium fluoride. Materials and Method: Twenty maxillary first premolars were treated with the selected solutions included two aqueous siwak extract concentration(5%,10%) and sodium fluoride(0.05%)as control positive for 2 minutes once daily for 20days interval, de ionized water was used as control negative. The concentration of the dissolved phosphorus i

A streptococci has recognized as Streptococcus spp., associate with acute pharyngitis. S. pyogenes infection Has detected in the Hospital and Health Center in Tikrit city. Throat swabs sample has obtained and cultured on a sheep blood agar plate. Identification of S. pyogenes was performed by using the VITEK 2 automatic system. It detected of 50 samples from children included 25 were positive for S. pyogenes infection. were aged 10-35 years old and included 30 male and 20 female. . While 25 sample Negative of S. pyogenes infection (The control group included 25 clinically healthy children without S. pyogenes infection matched for age and sex with cases pateints). No significa