The concept of the order sum graph associated with a finite group based on the order of the group and order of group elements is introduced. Some of the properties and characteristics such as size, chromatic number, domination number, diameter, circumference, independence number, clique number, vertex connectivity, spectra, and Laplacian spectra of the order sum graph are determined. Characterizations of the order sum graph to be complete, perfect, etc. are also obtained.

This is a survey study that presents recent researches concerning factional controllers. It presents several types of fractional order controllers, which are extensions to their integer order counterparts. The fractional order PID controller has a dominant importance, so thirty-one paper are presented for this controller. The remaining types of controllers are presented according to the number of papers that handle them; they are fractional order sliding mode controller (nine papers), fuzzy fractional order sliding mode controller (five papers), fractional order lag-lead compensator (three papers), fractional order state feedback controller (three papers), fractional order fuzzy logic controller (three papers). Finally, several conclusions

This is a survey study that presents recent researches concerning factional controllers. It presents several types of fractional order controllers, which are extensions to their integer order counterparts. The fractional order PID controller has a dominant importance, so thirty-one paper are presented for this controller. The remaining types of controllers are presented according to the number of papers that handle them; they are fractional order sliding mode controller (nine papers), fuzzy fractional order sliding mode controller (five papers), fractional order lag-lead compensator (three papers), fractional order state feedback controller (three papers), fractional order fuzzy logic controller (three papers). Finally,

Statistical control charts are widely used in industry for process and measurement control . in this paper we study the use of markov chain approach in calculating the average run length (ARL) of cumulative sum (Cusum) control chart for defect the shifts in the mean of process , and exponentially weighted moving average (EWMA) control charts for defect the shifts for process mean and , the standard deviation . Also ,we used the EWMA charts based on the logarithm of the sample variance for monitoring a process standard deviation when the observations (products are selected from al_mamun factory ) are identically and independently distributed (iid) from normal distribution in continuous manufacturing .

in this paper sufficient conditions of oscillation of all of nonlinear second order neutral differential eqiation and sifficient conditions for nonoscillatory soloitions to onverage to zero are obtained

In this work ,the modified williamos-Hall method was used to analysis the x-ray diffraction lines for powder of magnesium oxide nanoparticles (Mgo) .and for diffraction lines (111),(200),(220),(311) and (222).where by used special programs such as origin pro Lab and Get Data Graph ,to calculate the Full width at half maximum (FWHM) and integral breadth (B) to calculate the area under the curve for each of the lines of diffraction .After that , by using modified Williamson –Hall equations to determin the values of crystallite size (D),lattice strain (ε),stress( σ ) and energy (U) , where was the results are , D=17.639 nm ,ε =0.002205 , σ=0.517 and U=0.000678 respectively. And then using the scherrer method can by calculated the crystal

The aim of this research is to use robust technique by trimming, as the analysis of maximum likelihood (ML) often fails in the case of outliers in the studied phenomenon. Where the (MLE) will lose its advantages because of the bad influence caused by the Outliers. In order to address this problem, new statistical methods have been developed so as not to be affected by the outliers. These methods have robustness or resistance. Therefore, maximum trimmed likelihood: (MTL) is a good alternative to achieve more results. Acceptability and analogies, but weights can be used to increase the efficiency of the resulting capacities and to increase the strength of the estimate using the maximum weighted trimmed likelihood (MWTL). In order to perform t

My research tagged [the lights of the statement in the first part of the Koran] came to show that the dear book was developed according to a precise linguistic system is not increased by a word or letter or movement - Aldmh and Kira and the hole - and does not lack anything of it except with the wisdom required by the meanings of the Koranic text or Sura generally . The Koran does not come falsehood from his hands or from behind it is infallible and preserved; because it was revealed by the sage Hamid Hamid ﭽﮗ ﮘ ﮙ ﮚ ﮛ ﮜ ﮝ ﮞ ﭼ [stone]. The Qur'an is safe from any verbal or moral dominance and dominates all the heavenly books and exists at any time and place that speaks the truth ﭽ ﯛ ﯜ ﯝ ﯞ ﯟ ﯹ ﯺﭼ [The

Background: Obesity is an evolving major health problem in both developed and developing countries. Traditional obesity indices as body mass index, waist circumference, waist-hip-ratio are well known measures to identify obese subjects, however, neck circumference as an index of upper-body obesity was found to be a simple and time-saving screening measure that can be used to identify obesity and the likelihood of developing metabolic syndrome in type 2 diabetic patients.
Aim: to investigate the relationship of neck circumference (NC) to obesity and metabolic syndrome in Iraqi subjects with type 2 diabetes.
Methods: The study group included 90 type 2 diabetic subjects (48 men and 42 women) aged 30-68 years. The subjects were those w

Free-electron lasers (FELs) are disruptive light sources that offer ultrashort pulses, wide spectral tunability, and superior coherence, making them promising candidates for next-generation photonic technologies. However, conventional FEL facilities are large-scale and complex, limiting their integration into communication systems. This study investigates the potential of compact FELs as scalable and versatile light sources for beyond-6G and quantum communication infrastructures. A theoretical framework was established to model resonance conditions, gain dynamics, coherence properties, pulse-duration-limited bit rates, and signal-to-noise ratio (SNR). These models were implemented in MATLAB simulations using parameters representativ