In this note, we obtain some singular values inequalities for Positive semidefinite matrices by using block matrix technique. Our results are similar to some inequalities shown by Bhatia and Kittaneh in [Linear Algebra Appl. 308 (2000) 203-211] and [Linear Algebra Appl. 428 (2008) 2177-2191].

Background: Cervical cancer is the most common gynecologic cancer in developingcountries. Although this malignancy is preventable, problems exist with screening this cancer. Numerous studies have researched immunohistochemistry methods, such as the KI-67 biomarkeras a proliferation marker, to improve screening for cervical intraepithelial neoplasia as theprecancerous phase of cervical cancer. These studies mostly screened cytological samples. Inthe current study, we sought to analyze the correlation between the KI-67 proliferative biomarkerand HPV infection in order to predict short-time prognosis in cervical intraepithelial neoplasiaas an alternative or ancillary method to current screening methods. Our assessment was basedon histologic samples from a different geographic population. Methods: This descriptive cohort prospective study included 40 patients diagnosed withlow grade cervical intraepithelial neoplasia based on cervical punch biopsy samples aftercolposcopy examination. We enrolled patients who referred to the Department of Gynecology-Oncology of an academic hospital of Mashhad University of Medical Sciences from 2016 to2017. All low grade cervical intraepithelial neoplasia samples were investigated for HR-HPVDNA with the Cobas test and immunostaining for the KI-67 biomarker. After a one-yearfollow-up, we evaluated the prognosis for all patients based on liquid based cytology and HRHPVtest. Data were analyzed by SPSS version 23. 0 and the Mann-Whitney U and Fisher's exacttests. A P-value < 0. 05 was considered significant. Results: We observed a significant difference between HR-HPV Positive and negative testsin KI-67 expression (P<0. 001), but there were no significant differences in reactivity level ofcervical epithelium (P=0. 5) and in KI-67 expressions in metaplastic and non-metaplasticepithelium (P=0. 88). After one year, most low grade cervical intraepithelial neoplasia cases ingroup A that had a low staining KI-67 biomarker had evidence of regression. On the contrary, all cases with high grade KI-67 expression didn’ t persist or progressed necessarily. Conclusion: The KI-67 biomarker is recommended as a complementary screening test, butnot an alternative for triage of high-risk patients with low grade cervical intraepithelial neoplasia. Patients with low grade cervical intraepithelial neoplasia/HR-HPV Positive cervical samplesand low staining KI-67 antigen could be offered a less aggressive follow-up protocol.

Screening of cervical cancer is the most common gynecologic cancer in developing countries. Despite being preventable, but we have still some problems with the screening of this cancer. Recently, many studies have been done on immunohistochemistry to improve screening of cervical intraepithelial neoplasia (CIN) as a precancerous lesion. But, the majority of the studies are based on cytological samples. The objective of this study was to analyze the correlation KI-67 biomarker and HPV infection in predict short time prognosis in CIN as an alternative or auxiliary method to the current screening method in a different geographic population. This descriptive cohort prospective study included 40 patients with a diagnosis of CIN based on cervical punch biopsy samples after colposcopy examination. They were referred to the department of gynecology and oncology of an academic hospital, Mashhad University of 2016 to 2017. All samples were investigated for HR-HPV DNA with Cobas test and immunostaining for KI-67 biomarker. Finally, after one year follows up, the prognosis for all patients was evaluated. Data were analyzed by SPSS software program version 23. 0 and Mann-Whitney U test and Fisher's exact test. P<0. 05 was considered significant. Significant difference was found between HR-HPV Positive and negative tests in KI-67 expression (P<0. 001), but no significant difference was observed in reactivity level (P=0. 5), also no significant difference was found in KI-67 expression in the metaplastic and non-metaplastic epithelium (P=0. 88). KI-67 biomarker is recommended as complementary screening tests not alternative for differentiating in high risks patients with CIN1. The patients with low KI-67 / HR-HPV Positive test could be offered for a less aggressive follow-up protocol.