Primitive and totally primitive Fricke families with applications

We introduce the primitivity of Fricke families, and give some examples. As its application, we first construct generators of the function field of the modular curve of level $N$ in terms of Fricke functions and Siegel functions, respectively. Furthermore, we use the special values of a certain function in a totally primitive Fricke family of level $N$ in order to generate ray class fields of imaginary quadratic fields

Ray class invariants over imaginary quadratic fields

Let $K$ be an imaginary quadratic field of discriminant less than or equal to -7 and $K_{(N)}$ be its ray class field modulo $N$ for an integer $N$ greater than 1. We prove that singular values of certain Siegel functions generate $K_{(N)}$ over $K$ by extending the idea of our previous work. These generators are not only the simplest ones conjectured by Schertz, but also quite useful in the matter of computation of class polynomials. We indeed give an algorithm to find all conjugates of such generators by virtue of Gee and Stevenhagen

Delayed presentation of cerebellar and spinal cord infarction as a complication of computed tomography-guided transthoracic lung biopsy: a case report

INTRODUCTION: Computed tomography-guided transthoracic needle biopsy is a common diagnostic procedure that is associated with various complications including pneumothorax, parenchymal hemorrhage, and hemoptysis. A systemic air embolism is a very rare (0.06 to 0.21%) but potentially fatal complication. CASE PRESENTATION: A 70-year-old Korean male was admitted to our hospital for evaluation of a solitary pulmonary nodule located adjacent to the right inferior pulmonary vein in the medial basal segment of the right lower lobe. A computed tomography-guided needle biopsy was performed by a radiologist using a coaxial needle. A computed tomography image obtained immediately after the biopsy showed intraluminal free air in the proximal ascending aorta. He complained of a mild electrical current sensation in both lower extremities. After three hours he complained of neurological deficit in both lower extremities as well as voiding difficulty. The brain and spine magnetic resonance images showed a right cerebellar and spinal cord infarction at the T8-10 levels. CONCLUSIONS: We report a case of air embolism to the cerebellum and spinal cord causing infarction presenting with an initial symptom of mild electrical current sensation in both lower extremities during the transthoracic needle biopsy. For this potentially fatal complication, early recognition, followed by prompt therapy is critical to reducing morbidity and mortality

Observation of photon-pair generation in the normal group-velocity-dispersion regime with slight detuning from the pump wavelength

A fiber-based photon-pair source in the telecom C-band is suitable for quantum information science including quantum communications. Spontaneous four-wave mixing effects are known to create photon pairs that are slightly detuned from the pump wavelength only in the anomalous group-velocity-dispersion (GVD) regime. Here, we achieve high-quality photon-pair generation slightly detuned from the pump wavelength in the normal GVD regime through a dispersion shifted fiber, for the first time. The photon pairs in C-band exhibit strong temporal correlation with each other and excellent heralded anti-bunching property. This photon-pair generation scheme can be exploited as telecom-band quantum light sources for quantum information applications.11Ysciescopu