Differential transform method for solving singularly perturbed Volterra integral equations

AbstractIn this work, the applications of differential transform method were extended to singularly perturbed Volterra integral equations. To show the efficiency of the method, some singularly perturbed Volterra integral equations are solved as numerical examples. Numerical results show that the differential transform method is very effective and convenient for solving a large number of singularly perturbed problems with high accuracy

Can NLR, PLR and LMR be used as prognostic indicators in patients with pulmonary embolism? Author’s reply on commentary

We appreciate the comments made by Dr Bedel and colleagues. NLR, PLR and LMR are affected by various diseases such as oncological, collagen tissue, inflammatory, or severe renal/liver diseases [1]. Because of this, we have listed some of the above-mentioned disorders in the tables. Hematological diseases, collagen tissue disease, inflammatory diseases, congenital heart disease, or severe renal/liver disease were therefore excluded from the study. However, the presence of malignancy did not affect our results in regression analysis. Platelets swell until 120 minutes in ethylene diamine tetra acetic (EDTA) and until 60 minutes in citrate [2]. Authors suggest that optimal measuring time should not exceed 120 minutes. The blood samples of the patients were taken within 1 hour after their emergency admission. All blood samples in our study were tested within 1 hour of collection [3]. We used EDTA for whole blood anticoagulation. The mean duration of symptoms prior to admission was 5.04 ± 6.9 days. The drugs such as corticosteroids affect inflammatory parameters. Therefore, we excluded inflammatory diseases without emphasizing corticosteroids or other anti-inflammatory drugs

The Black Hole in the Compact, High-dispersion Galaxy NGC 1271

Located in the Perseus cluster, NGC 1271 is an early-type galaxy with a small effective radius of 2.2 kpc and a large stellar velocity dispersion of 276 km/s for its K-band luminosity of 8.9x10^{10} L_sun. We present a mass measurement for the black hole in this compact, high-dispersion galaxy using observations from the integral field spectrograph NIFS on the Gemini North telescope assisted by laser guide star adaptive optics, large-scale integral field unit observations with PPAK at the Calar Alto Observatory, and Hubble Space Telescope WFC3 imaging observations. We are able to map out the stellar kinematics on small spatial scales, within the black hole sphere of influence, and on large scales that extend out to four times the galaxy's effective radius. We find that the galaxy is rapidly rotating and exhibits a sharp rise in the velocity dispersion. Through the use of orbit-based stellar dynamical models, we determine that the black hole has a mass of (3.0^{+1.0}_{-1.1}) x 10^9 M_sun and the H-band stellar mass-to-light ratio is 1.40^{+0.13}_{-0.11} M_sun/L_sun (1-sigma uncertainties). NGC 1271 occupies the sparsely-populated upper end of the black hole mass distribution, but is very different from the Brightest Cluster Galaxies (BCGs) and giant elliptical galaxies that are expected to host the most massive black holes. Interestingly, the black hole mass is an order of magnitude larger than expectations based on the galaxy's bulge luminosity, but is consistent with the mass predicted using the galaxy's bulge stellar velocity dispersion. More compact, high-dispersion galaxies need to be studied using high spatial resolution observations to securely determine black hole masses, as there could be systematic differences in the black hole scaling relations between these types of galaxies and the BCGs/giant ellipticals, thereby implying different pathways for black hole and galaxy growth.Comment: accepted for publication in Ap

MRK 1216 & NGC 1277 - An orbit-based dynamical analysis of compact, high velocity dispersion galaxies

We present a dynamical analysis to infer the structural parameters and properties of the two nearby, compact, high velocity dispersion galaxies MRK1216 & NGC1277. Combining deep HST imaging, wide-field IFU stellar kinematics, and complementary long-slit spectroscopic data out to 3 R_e, we construct orbit-based models to constrain their black hole masses, dark matter content and stellar mass-to-light ratios. We obtain a black hole mass of log(Mbh/Msun) = 10.1(+0.1/-0.2) for NGC1277 and an upper limit of log(Mbh/Msun) = 10.0 for MRK1216, within 99.7 per cent confidence. The stellar mass-to-light ratios span a range of Upsilon_V = 6.5(+1.5/-1.5) in NGC1277 and Upsilon_H = 1.8(+0.5/-0.8) in MRK1216 and are in good agreement with SSP models of a single power-law Salpeter IMF. Even though our models do not place strong constraints on the dark halo parameters, they suggest that dark matter is a necessary ingredient in MRK1216, with a dark matter contribution of 22(+30/-20) per cent to the total mass budget within 1 R_e. NGC1277, on the other hand, can be reproduced without the need for a dark halo, and a maximal dark matter fraction of 13 per cent within the same radial extent. In addition, we investigate the orbital structures of both galaxies, which are rotationally supported and consistent with photometric multi-S\'ersic decompositions, indicating that these compact objects do not host classical, non-rotating bulges formed during recent (z <= 2) dissipative events or through violent relaxation. Finally, both MRK 1216 and NGC 1277 are anisotropic, with a global anisotropy parameter delta of 0.33 and 0.58, respectively. While MRK 1216 follows the trend of fast-rotating, oblate galaxies with a flattened velocity dispersion tensor in the meridional plane of the order of beta_z = delta, NGC 1277 is highly tangentially anisotropic and seems to belong kinematically to a distinct class of objects.Comment: 27 pages, 15 figures and 4 tables. Accepted for publication in MNRA

The structural and dynamical properties of compact elliptical galaxies

Dedicated photometric and spectroscopic surveys have provided unambiguous evidence for a strong stellar mass-size evolution of galaxies within the last 10 Gyr. The likely progenitors of today's most massive galaxies are remarkably small, disky, passive and have already assembled much of their stellar mass at redshift z=2. An in-depth analysis of these objects, however, is currently not feasible due to the lack of high-quality, spatially-resolved photometric and spectroscopic data. In this paper, we present a sample of nearby compact elliptical galaxies (CEGs), which bear resemblance to the massive and quiescent galaxy population at earlier times. Hubble Space Telescope (HST) and wide-field integral field unit (IFU) data have been obtained, and are used to constrain orbit-based dynamical models and stellar population synthesis (SPS) fits, to unravel their structural and dynamical properties. We first show that our galaxies are outliers in the present-day stellar mass-size relation. They are, however, consistent with the mass-size relation of compact, massive and quiescent galaxies at redshift z=2. The compact sizes of our nearby galaxies imply high central stellar mass surface densities, which are also in agreement with the massive galaxy population at higher redshift, hinting at strong dissipational processes during their formation. Corroborating evidence for a largely passive evolution within the last 10 Gyr is provided by their orbital distribution as well as their stellar populations, which are difficult to reconcile with a very active (major) merging history. This all supports that we can use nearby CEGs as local analogues of the high-redshift, massive and quiescent galaxy population, thus providing additional constraints for models of galaxy formation and evolution.Comment: 33 pages, 27 figures and 20 tables (with most of the tables provided as online-only supporting information). Accepted for publication in MNRA

Usefulness of the uric acid and CHA2DS2-VASc score in prediction of left atrial thrombosis in patients with mitral stenosis and sinus rhythm

Background: The risk of thrombus formation in the left atrium is known to be very high in patients with both mitral stenosis (MS) and atrial fibrillation (AF). However, that risk should not be ignored in patients with MS in sinus rhythm (SR). The aim of this study was to determine the clinical, echocardiographic, and biochemical factors that could have a determining role in the formation of a left atrial (LA) thrombus in patients with MS in SR. Method: A total of 207 consecutive patients with MS who underwent both transthoracic echocardiography (TTE) and transesophageal echocardiography (TEE) for diagnosis or to investigate the presence of a thrombus in the LA and appendage were enrolled in this study. Results: LA thrombus was detected in 21 of 207 patients. CHA2DS2-VASc score was not found to be a predictor of LA thrombosis in patients with MS in SR, despite the higher CHA2DS2-VASc scores observed in those patients. The mitral valve area and mitral valve gradient were not predictive of LA thrombus development; however, LA anteroposterior diameter (LAAPD) was found to be a predictor of LA thrombosis. Levels of high sensitivity-C-reactive protein and uric acid were higher in the patients with LA thrombosis, but only uric acid was found to be a predictor of LA thrombosis in multivariate analysis. Conclusions: A larger LAAPD and an elevated serum uric acid level were found to be independent predictors of LA thrombosis in patients with MS in SR.

Tip 1 Diyabetes Mellituslu Çocuklarda Tanı Anındaki Klinik ve Laboratuvar Bulgularının Değerlendirilmesi

Objective: The aim of our study is to evaluation of clinical and laboratory findings at the time of diagnosis in children with Type 1 Diabetes Mellitus (T1DM). Methods: In this study, 142 children diagnosed with T1DM who were referred to Pediatric Endocrinology Policlinic and Emergency Policlinic of Dicle University Medical Faculty between 2013 and 2016 were evaluated. Retrospectively, the sociodemographic characteristics, symptoms and laboratory findings of the patients were recorded from the files. All the data obtained were evaluated statistically. Results: Sixty two (43.66%) of the patients were girls. The mean age was 10,10 ± 1,39 years. The blood glucose level at diagnosis was 425,85 ± 12,51 mg/dl and HbA1c was 13,57 ± 3,77. Anti-Glutamate Decarboxylase (anti-GAD) positivity was detected in 47.8% of the cases. 18.3% of the patients had a T1DM story in their family. Patients were diagnosed mostly in January (12.6%) and November (11.9%). 83.8% of cases had both polyuria and polydipsia, 41.5% had consciousness level change and 6.3% had coma. Ketoacidosis was present in 43% of the patients at the time of admission, ketosis in 48.5% and only hyperglycemia in 8.5%. Conclusion: Type 1 DM is mostly observed in adolescence. The most common symptoms of the disease are polyuria and polydipsia. For this reason the community needs to be educated that polyuria and polydipsia may have T1DM findings. Awareness of the community in this issue can reduce the frequency of diabetic ketoacidosis, the most important complication of diabetes