Grey system theory is a multidisciplinary scientific approach, which deals with systems that have partially unknown information (small sample and uncertain information). Grey modeling as an important component of such theory gives successful results with limited amount of data. Grey Models are divided into two types; univariate and multivariate grey models. The univariate grey model with one order derivative equation GM (1,1) is the base stone of the theory, it is considered the time series prediction model but it doesn’t take the relative factors in account. The traditional multivariate grey models GM(1,M) takes those factor in account but it has a complex structure and some defects in " modeling mechanism", "parameter estimation "and "m

This paper develops a fuzzy multi-objective model for solving aggregate production planning problems that contain multiple products and multiple periods in uncertain environments. We seek to minimize total production cost and total labor cost. We adopted a new method that utilizes a Zimmermans approach to determine the tolerance and aspiration levels. The actual performance of an industrial company was used to prove the feasibility of the proposed model. The proposed model shows that the method is useful, generalizable, and can be applied to APP problems with other parameters.

In the beta decay process, a neutron converts into a proton, or vice versa, so the atom in this process changes to a more stable isobar. Bethe-Weizsäcker used a quasi-experimental formula in the present study to find the most stable isobar for isobaric groups of mass nuclides (A=165-175). In a group of isobars, there are two methods of calculating the most stable isobar. The most stable isobar represents the lowest parabola value by calculating the binding energy value (B.E) for each nuclide in this family, and then drawing these binding energy values as a function of the atomic number (Z) in order to obtain the mass parabolas, the second method is by calculating the atomic number value of the most stable isobar (ZA). The results show

Active Magnetic Bearings (AMBs) are progressively being implemented in a wide variety of applications. Their exclusive appealing features make them suitable for solving traditional rotor-bearing problems using novel design approaches for rotating machinery.  In this paper, a linearized uncertain model of AMBs is utilized to develop a nonlinear sliding mode controller based on Lyapunov function for the electromechanical system. The controller requires measurements of the rotor displacements and their derivatives. Since the control law is discontinuous, the proposed controller can achieve a finite time regulation but with the drawback of the chattering problem. To reduce the effect of this problem, the gain of the uni

This research includes the study of dual data models with mixed random parameters, which contain two types of parameters, the first is random and the other is fixed. For the random parameter, it is obtained as a result of differences in the marginal tendencies of the cross sections, and for the fixed parameter, it is obtained as a result of differences in fixed limits, and random errors for each section. Accidental bearing the characteristic of heterogeneity of variance in addition to the presence of serial correlation of the first degree, and the main objective in this research is the use of efficient methods commensurate with the paired data in the case of small samples, and to achieve this goal, the feasible general least squa

Background: Beta thalassemia major is an inherited disorder that may affect general and oral health.The purpose of this study was toassess the severity of dental caries in relation to oral cleanliness, mutans streptococciamong a group of boys with beta thalassemia majorin comparison with a control group. Materials and Methods: The study involved 30 boys with BTM aged 10-12 years compared to 30 healthy boys with the same age group. d1-4mfs and D1-4 MFS indices were applied (Muhlemann, 1976), the viable counts of mutans streptococci in stimulated saliva were also determined. Results: The entire thalassemic group was caries-active. For both dentitions, a higher dmfs/DMFS values were recorded for study compared to control group, difference was

The present study aimed to determine the serum sex hormone levels among Benign Prostatic Hyperplasia (BPH) patients before and after 3 months of oral administration of 5-α reductase inhibitor(finasteride). Forty BPH patients and 40 healthy men from Amara city were involved in this study, their ages were between 40-59 year. They were all subjected  to direct estimation of hormones by MinVidas method including Testosterone (T), Estradiol (E2), Follicle Stimulating Hormone (FSH), Luteinizing Hormone (LH), Prolactin (PRL), and Dihydrotestosterone (DHT) before and after 3 months of treatment with 5α-reductase inhibitor (finasteride) (the healthy individuals didn’t take finasteride).The results showed that T level was significantly lo

Objectives: To compare early pregnancy outcomes, including miscarriage, ectopic pregnancy, multiple pregnancy, and congenital anomalies, among women who conceived following ovulation induction with letrozole or clomiphene citrate. Methods: A prospective comparative observational study was conducted at Al-Elwiya Maternity Teaching Hospital and a private clinic in Baghdad, Iraq, from March 2023 to December 2024. One hundred infertile women aged 21–35 years who conceived after ovulation induction with either letrozole (5 mg/day) or clomiphene citrate (100 mg/day) for five days (cycle days 3–7) were enrolled. Participants were followed through early pregnancy with serial sonography at 6, 8–11, and 18–20 weeks of gestation. Data