The discussion in this paper gives several theorems and lemmas on the Sums of Squares of  consecutive Carol Numbers. These theorems are proved by using the definition of carol numbers and mathematical induction method. Here the matrix form and the recursive form of sum of squares of  consecutive Carol numbers is also given. The properties of the Carol numbers are also derived.

Machine learning models have recently provided great promise in diagnosis of several ophthalmic disorders, including keratoconus (KCN). Keratoconus, a noninflammatory ectatic corneal disorder characterized by progressive cornea thinning, is challenging to detect as signs may be subtle. Several machine learning models have been proposed to detect KCN, however most of the models are supervised and thus require large well-annotated data. This paper proposes a new unsupervised model to detect KCN, based on adapted flower pollination algorithm (FPA) and the k-means algorithm. We will evaluate the proposed models using corneal data collected from 5430 eyes at different stages of KCN severity (1520 healthy, 331 KCN1, 1319 KCN2, 1699 KCN3 a

   This research presents a comparison of performance between recycled single stage and double stage hydrocyclones in separating water from water/kerosene emulsion. The comparison included several factors such as: inlet flow rate (3,5,7,9, and 11 L/min), water feed concentration (5% and 15% by volume), and split ratio (0.1 and 0.9). The comparison extended to include the recycle operation; once and twice recycles. The results showed that increasing flow rate as well as the split ratio enhancing the separation efficiency for the two modes of operation. On the contrary, reducing the feed concentration gave high efficiencies for the modes. The operation with two cycles was more efficient than one cycle. The maximum obtained effici

Community structures are fundamental in understanding the structure and functionality of complex networks. Different optimization algorithms, including both single-objective and multi-objective approaches, have been employed to address the challenge of community detection. Recently, multi-objective evolutionary algorithms (MOEAs) have attracted many researchers to identify communities in static networks. Many algorithms have been proposed to find a solution that achieves a trade-off between exploring new areas of the solution space and improving the quality of existing solutions. In this trade-off is crucial; whereas exploitation improves existing solutions, it may fail to find better solutions from insufficiently explored regions o

The influence of an aortic aneurysm on blood flow waveforms is well established, but how to exploit this link for diagnostic purposes still remains challenging. This work uses a combination of experimental and computational modelling to study how aneurysms of various size affect the waveforms. Experimental studies are carried out on fusiform-type aneurysm models, and a comparison of results with those from a one-dimensional fluid–structure interaction model shows close agreement. Further mathematical analysis of these results allows the definition of several indicators that characterize the impact of an aneurysm on waveforms. These indicators are then further studied in a computational model of a systemic blood flow network. This demonstr

Human cytomegalovirus (HCMV) has a worldwide distribution and common infections. The presence of HCMV genome and antigens has been detected in many kinds of human cancers. The proto-oncogene Her2/neu is overexpressed in 25% to 30% of human breast cancers and frequently associated with tumor aggressiveness and worse prognosis. Examination was applied to detect different HCMV antigens and to demonstrate their correlation with Her2/neu overexpression in breast cancer. The present study includes samples from 70 women of 60 breast cancer patients and 10 normal breast tissues. Formalin-fixed paraffin embedded tissue blocks were obtained from each woman according to ethical approval. Human cytomegalovirus early antigen expression was detected in 5

Background: Breast cancer is the most common
malignancy affecting females worldwide. The association
of Epstein-Barr virus (EBV) with this cancer is a longstanding
interest to this field.
Aim: to investigate the presence of EBV in breast tumor
tissue in relation to age.
Patients and Methods: Paraffin-embedded tissue blocks
from 45 female patients with breast tumors (ranged in age
from 28 to 85 years) were retrieved. The cases were
grouped into two categories: group (A): included 30 cases
with breast carcinoma and group (B): included 15 cases
with benign breast diseases as a control group .The
expression of EBV protein was examined
immunohistochemically.
Results: Twelve (40%) of the 30 breast canc

Many previous investigations have found quercetin to be a powerful antioxidant and antitumor flavonoid, but its poor bioavailability has limited its use. This current study investigated the effects of two newly synthesized Quercetin Schiff bases containing 2-amino thiadiazole-5-thiol (Q1), and its benzyl derivatives (Q2) on MCF-7 human breast cancer cells. Cell viability and apoptosis were assessed to determine the toxic effects of Q1 and Q2. Cytotoxicity valuation showed that both compounds inhibited MCF-7 cell growth, and lactate dehydrogenase (LDH) activity increased in a dose-dependent aspect compared to the control group. Comet assay results observed that Q1 and Q2 induce more serious DNA damage than the control (untreated cell

Background: Breast cancer is the most common
malignancy affecting females worldwide. The association
of Epstein-Barr virus (EBV) with this cancer is a longstanding
interest to this field.
Aim: to investigate the presence of EBV in breast tumor
tissue in relation to age.
Patients and Methods: Paraffin-embedded tissue blocks
from 45 female patients with breast tumors (ranged in age
from 28 to 85 years) were retrieved. The cases were
grouped into two categories: group (A): included 30 cases
with breast carcinoma and group (B): included 15 cases
with benign breast diseases as a control group .The
expression of EBV protein was examined
immunohistochemically.
Results: Twelve (40%) of the 30 breast canc

Background: Breast cancer remains a substantial cause of morbidity and mortality, there is a need for continued efforts to understand the etiology of the disease, maintain screening effort, implement prevention strategies, and develop better treatments.Objective: To analyze the risk factors, improve early detection and prevention of breast cancer in Al-Russafa district- Baghdad, aiming to increase survival rate and improve the quality of life.Methods: A cross sectional audit of 258 breast cancer cases seen at Al-Elwiya maternity teaching hospital from January2009 to December 2011,data collected from patients files were: age, gender , residency, marital status, parity, age at menarche and menopause age at first live birth, hormonal therap