In real-life problems, we use square roots in natural distributions such as (the probability density function), distances and lengths in the Pythagorean theorem, and quadratic formulas in (the height of falling objects), radius of circles, harmonic movements (pendulum and springs), and standard deviation in statistics. We have observed that using fuzzy sets in real-life problems is more convenient than ordinary sets. Therefore, they are important in algebraic structures. As a result, more effort has been made to study square root structures in fuzzy sets. This paper introduces the notion of square roots fuzzy of QS-ideals on QS-algebras and some important characteristics. Some illustrative examples have been provided which prove tha

We present a reliable algorithm for solving, homogeneous or inhomogeneous, nonlinear ordinary delay differential equations with initial conditions. The form of the solution is calculated as a series with easily computable components. Four examples are considered for the numerical illustrations of this method. The results reveal that the semi analytic iterative method (SAIM) is very effective, simple and very close to the exact solution demonstrate reliability and efficiency of this method for such problems.

Background: Conventional  MR imaging is essential for diagnosis and evaluation of the posterior fossa tumors  Objectives: To assess the value of diffusion weighted imaging and apparent diffusion coefficient in making distinction between different histological types of posterior fossa tumors.

Type of the study: Cross-sectional study.

Methods: Brain MRI and DWI assessed 19 patients (12 female and 7 male) with MRI diagnosis of posterior fossa tumors. absolute ADC values of contrast -enhancing solid tumor region and ADC ratio of solid tumor to ADC of normal -appearing deep White matter were compared with histological diagnosis postoperatively .The m

In the present study, free convection heat and mass transfer of fluid in a square packed bed enclosure is numerically investigated. For the considered geometrical shape, the left vertical wall of enclosure was assumed to be kept at high temperature and concentration while the opposite wall was kept at low temperature and concentration with insulating both the top and bottom walls of enclosure. The Brinkman– Forchheimer extended Darcy model was used to solve the momentum equations, while the energy equations for fluid and solid phases were solved by using the local thermal non-equilibrium (LTNE) model.Computations are performed for a range of the Darcy number from 10-5 to 10-1, the porosity from 0.5 to 0.9, and buoyancy ratio from -15 t

Photoacoustic is a unique imaging method that combines the absorption contrast of light or radio frequency waves with ultrasound resolution. When the deposition of this energy is sufficiently short, a thermo-elastic expansion takes place whereby acoustic waves are generated. These waves can be recorded and stored to construct an image. This work presents experimental procedure of laser photoacoustic two dimensional imaging to detect tumor embedded within normal tissue. The experimental work is accomplished using phantoms that are sandwiched from fish heart or blood sac (simulating a tumor) 1-14mm mean diameter embedded within chicken breast to simulate a real tissue. Nd: YAG laser of 1.064μm and 532nm wavelengths, 10ns pulse duration, 4

Objectives: Recently, there have been important advances in the clinical application of targeted hybrid near-infrared (NIR) fluorescent-radioactive tracers. ICG-99mTc-nanocolloid, for example, is already being used by some centres for sentinel lymph node biopsy in head and neck cancer. The radioactive component allows imaging at depths which would not be possible with NIR alone and, once exposed, the NIR fluorescence reporter can be imaged at very high resolution. Gamma detection is currently carried out with a separate hand-held gamma camera or with a non-imaging probe. Visualisation of NIR fluorescence during surgery requires a dedicated NIR camera, several of which are available commercially. We describe a novel hand-held hybrid NIR-gamm

Circular data (circular sightings) are periodic data and are measured on the unit's circle by radian or grades. They are fundamentally different from those linear data compatible with the mathematical representation of the usual linear regression model due to their cyclical nature. Circular data originate in a wide variety of fields of scientific, medical, economic and social life. One of the most important statistical methods that represents this data, and there are several methods of estimating angular regression, including teachers and non-educationalists, so the letter included the use of three models of angular regression, two of which are teaching models and one of which is a model of educators. ) (DM) (MLE) and circular shrinkage mod

The issue of the Circular Economy is not a new issue to several countries, especially the developed ones. Here in Iraq it is considered newly introduced, despite the few attempts to establish projects that concern recycling most of them were doomed to fail, due to two main reasons: the first one is the financial and administrative corruption widespread in all departments of the country, the second one is the priorities of public spending. It is well known that Iraq was subjected to two major attacks, the ISIS entry attack in 2014 to Iraq. ISIS occupied about a third of Iraqi lands which resulted in a collapse in oil prices, as Iraq depends almost entirely on oil revenues in its budget which is the second attack. This made the Iraqi governme

Long-term organic amendments are a key strategy to build soil organic carbon (SOC) stocks in semiarid agroecosystems, where low biomass inputs and calcareous parent material constrain carbon accumulation. This 14-year field experiment in central Iraq (2000–2014) evaluated how a gradient of organic matter (OM) additions (0, 1, 2.5, 5, 10, and 20%) affects SOC dynamics, nutrient availability, and soil organic matter composition in clay-dominated, semiarid soils. Surface and subsurface samples (0–30, 30–60, and 60–90 cm) were analysed for SOC, nutrients, and mid-infrared Fourier transform infrared (FTIR) spectra, which were then integrated with Partial Least Squares (PLS) regression and RothC simulations. Moderate OM inputs (5