Adil Huseynov

An eigenvalue problem for quadratic pencils of q-difference equations and its applications

Abstract This work is devoted to the study of the properties of eigenvalues and eigenvectors of a quadratic pencil of q -difference equations. The results obtained are then used to solve the corresponding system of differential equations with boundary and initial conditions.

Evaluation of neutrophil-to-lymphocyte ratio prior to prostate biopsy to predict biopsy histology: Results of 1836 patients.

INTRODUCTION We evaluate the role of NLR prior to prostate biopsy to predict biopsy histology and Gleason score in patients with prostate cancer. METHODS In this retrospective study, we evaluated data of patients underwent prostate biopsy between May 2005 and March 2015. We collected the following data: age, prostate-specific antigen (PSA), biopsy histology, Gleason score (GS) in prostate cancer patients, neutrophil counts, and lymphocyte counts. Patients were grouped as benign prostatic hyperplasia (BPH), prostate cancer, and prostatitis. The Chi square test was used to compare categorical variables and analysis of variance (ANOVA) was applied for continuous variables. RESULTS Data of 1836 patients were investigated. The mean age, total PSA and neutrophil-lymphocyte ratio (NLR) of the population were 66.8 ± 8.17 years, 9.38 ± 4.7 ng/dL, and 3.11 ± 1.71, respectively. Patients were divided as follows: 625 in the group with BPH history, 600 in the prostatitis group, and 611 in the prostate cancer histology group. The mean NLR of the prostatitis group was higher compared to the prostate cancer and BPH groups (p = 0.0001). The mean NLR of the prostate cancer group was significantly higher compared to the BPH group (p = 0.002). The GS 8-10 group had a significantly higher mean NLR compared to GS 5-6 (3.64 vs. 2.54, p = 0.0001) and GS 7 (3.64 vs. 2.58, p = 0.0001) patients. CONCLUSIONS NLR was found to differ with regard to histology of prostate biopsy and higher GS was associated with higher NLR in patients with prostate cancer. However prostatitis prevents the use of NLR in predicting prostate cancer before a prostate biopsy. Also, the retrospective nature and lack of multivariate analysis in this study somewhat limits the relevance of these results.

The Riesz representation theorem on time scales

Abstract In this study, the Riesz representation formula for continuous linear functionals on the space of continuous functions on a compact metric space is specified when the metric space is a compact interval of a time scale. The result obtained unifies the continuous and discrete versions of the Riesz representation formula and extends them to numerous different time scales.

Eigenfunction expansion associated with the one-dimensional Schrödinger equation on semi-infinite time scale intervals

We prove the existence of a spectral function (spectral measure or orthogonality measure) for the one-dimensional Schrodinger equation on semi-infinite time scale intervals. A Parseval equality and an expansion formula in eigenfunctions are established in terms of the spectral function. The result obtained unifies and extends the well-known results on the existence of a spectral measure for the one-dimensional Schrodinger operator on the semi-axis and for semi-infinite Jacobi matrices.

Evaluation of postoperative hydronephrosis following semirigid ureteroscopy: Incidence and predictors

OBJECTIVE Hydronephrosis developing following ureteroscopy (URS) is an important issue associated with the long-term postoperative renal functions. Studies investigating the role of postoperative imaging revealed conflicting results. In this study, we aimed to determine the incidence and predictors of hydronephrosis following semirigid URS. MATERIAL AND METHODS We evaluated the results of 455 patients who underwent U RS a nd postoperative imaging with non-contrast computed tomography (CT). Primary endpoints of the study were to determine the frequency of development of hydronephrosis and factors associated with the development of hydronephrosis. Logistic regression analysis was used to define factors effecting on the development of hydronephrosis. RESULTS Postoperative non-contrast CT revealed hydronephrosis in 81 (17.8%) patients. Stone-free status was achieved in 415 (91.2%) patients. Univariate analysis revealed history of ipsilateral URS (p=0.001), duration of operation (p=0.022), presence of multiple stones (p=0.001), and occurrence of a renal colic episode postoperatively (p=0.013) as the parameters associated with increased risk of postoperative hydronephrosis. In the multivariate analysis, history of ipsilateral URS (OR: 2.724, p=0.017) and presence of multiple stones (OR: 2.116, p=0.032) were found to be the independent prognostic markers of developing postoperative hydronephrosis. CONCLUSION Ipsilateral hydronephrosis following URS develops in a significant number of patients. In patients with history of ipsilateral hydronephrosis and multiple stones, risk of development of postoperative hydronephrosis is higher, therefore physicians should be keep these parameters in mind in the decision making process of selective imaging postoperatively.

Weyl’s Limit Point and Limit Circle for a Dynamic Systems

We show that analogues of classical concepts of the Weyl limit point and limit circle cases can be introduced and investigated for second order linear dynamic equations on time scales. Since dynamical equations on time scales unifies and extends continuous and discrete dynamical equations (i.e., differential and difference equations), in this way, we establish more general theory of the limit point and limit circle cases.