Consider the (p,q) simple connected graph . The sum absolute values of the spectrum of quotient matrix of a graph  make up the graph's quotient energy. The objective of this study is to examine the quotient energy of identity graphs and zero-divisor graphs  of commutative rings using group theory, graph theory, and applications. In this study, the identity graphs  derived from the group  and a few classes of zero-divisor graphs  of the commutative ring R are examined.

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This paper is concerned with pre-test single and double stage shrunken estimators for the mean (?) of normal distribution when a prior estimate (?0) of the actule value (?) is available, using specifying shrinkage weight factors ?(?) as well as pre-test region (R). Expressions for the Bias [B(?)], mean squared error [MSE(?)], Efficiency [EFF(?)] and Expected sample size [E(n/?)] of proposed estimators are derived. Numerical results and conclusions are drawn about selection different constants included in these expressions. Comparisons between suggested estimators, with respect to classical estimators in the sense of Bias and Relative Efficiency, are given. Furthermore, comparisons with the earlier existing works are drawn.

The ionospheric characteristics exhibit significant variations with the solar cycle, geomagnetic conditions, seasons, latitudes and even local time. Representation of this research focused on global distribution of electron (Te) and ion temperatures (Ti) during great and severe geomagnetic storms (GMS), their daily and seasonally variation for years (2001-2013), variations of electron and ion temperature during GMS with plasma velocity and geographic latitudes. Finally comparison between observed and predicted Te and Ti get from IRI model during the two kinds of storm selected. Data from satellite Defense Meteorological Satellite Program (DMSP) 850 km altitude are taken for Te, Ti and plasma velocity for different latitudes during great

The present work aimed to study the effect of Grave's disease on the different tissues and organs of the body by using Wayne Thyrotoxicosis Diagnostic Index (WTDI) and Basel Metabolic Index (BMI). To reach such aim, (35) patients were involved (25 females and 10 males). A control group of (15) healthy individuals (10 females and 5 males) was selected for comparison , as well as , the following: 1- Wayne Thyrotoxicosis Diagnostic Index (WTDI) applied on patient group and control group under the supervision of specialist medical team , this index include (19) sign and symptom , the appearance of one of them may be lead to the others. The sings and symptoms of the index appear only on the patients. There is no Significant di

Background: Periodontal diseases are bacterial infections of the gingiva, bone and attachment fibers that support the teeth and hold them in the jaw. Lactoferrin is a multifunctional glycoprotein and it is the main component of neutrophil polymorphonuclear leukocytes that activated during inflammatory processes such as Periodontal diseases Aims of the study: Determine the salivary levels of Lactoferrin and pH and their correlations with clinical periodontal parameters(Plaque Index , Gingival Index , Bleeding on Probing , Probing Pocket Depth , and Clinical Attachment Level ) and the correlation between Lactoferrin with potential of hydrogen ion (PH) ,flow rate and α-amylase of study groups that consisted of patients had gingivitis and pa

Presents here in the results of comparison between the theoretical equation stated by Huang and Menq and laboratory model tests used to study the bearing capacity of square footing on geogrid-reinforced loose sand by performing model tests. The effects of several parameters were studied in order to study the general behavior of improving the soil by using the geogrid. These parameters include depth of first layer of reinforcement, vertical spacing of reinforcement layers, number of reinforcement layers and types of reinforcement layers The results show that the theoretical equation can be used to estimate the bearing capacity of loose sand.