On the stability of a modified Nyström method for Mellin convolution equations in weighted spaces

This paper deals with the numerical solution of second kind integral equations with fixed singularities of Mellin convolution type. The main difficulty in solving such equations is the proof of the stability of the chosen numerical method, being the noncompactness of the Mellin integral operator the chief theoretical barrier. Here, we propose a Nyström method suitably modified in order to achieve the theoretical stability under proper assumptions on the Mellin kernel. We also provide an error estimate in weighted uniform norm and prove the well-conditioning of the involved linear systems. Some numerical tests which confirm the efficiency of the method are shown

Numerical method for hypersingular integrals of highly oscillatory functions on the positive semiaxis

This paper deals with a quadrature rule for the numerical evaluation of hypersingular integrals of highly oscillatory functions on the positive semiaxis. The rule is of product type and consists in approximating the density function f by a truncated interpolation process based on the zeros of generalized Laguerre polynomials and an additional point. We prove the stability and the convergence of the rule, giving error estimates for functions belonging to weighted Sobolev spaces equipped with uniform norm. We also show how the proposed rule can be used for the numerical solution of hypersingular integral equations. Numerical tests which confirm the theoretical estimates and comparisons with other existing quadrature rules are presented

A NUMERICAL METHOD FOR SOLVING SYSTEMS OF HYPERSINGULAR INTEGRO-DIFFERENTIAL EQUATIONS

This paper is concerned with a collocation-quadrature method for solving systems of Prandtl's integro-differential equations based on de la Vallee Poussin filtered interpolation at Chebyshev nodes. We prove stability and convergence in Holder-Zygmund spaces of locally continuous functions. Some numerical tests are presented to examine the method's efficacy

MatLab Toolbox for the numerical solution of linear Volterra integral equations arising in metastatic tumor growth models

This paper introduces VIE Toolbox composed by fourteen MatLab functions used for the numerical resolution of Volterra Integral Equations (VIEs) of the second kind on infinite intervals. An application to metastatic tumor growth models is also considered, assuming five different tumor growth laws, e.g. exponential, power-law, Gompertz, generalized logistic and von Bertalanffy-West laws, for lung and breast tumors data

Neurosurgical implications of the Jugular Vein Nutcracker

In the last ten years, a new variant of Eagle Syndrome is emerging and being described: Styloid Jugular Nutcracker (SJN). In SJN, an elongated or vertically directed styloid process causes jugular vein stenosis by compressing the vein against the arch of C1. The clinical consequences appear to be various and misunderstood, ascribable mainly to venous flow impairment and consequent intracranial hypertension. The aim of this paper is to create an overview of Jugular Vein Nutcracker and to focus on its neurosurgical implications. A PRISMA-based literature search was performed to select the most relevant papers on the topic and to realize a mini-review. Future searches in the neurosurgical field should focus on collecting data about further causes of jugular stenosis compression and the association of SJN with cerebrovascular diseases. It would also be interesting to investigate the potential role of primary and secondary prevention, which is unknown so far

asociacion entre angioma cavernoso y glioma cerebral reporte de dos casos y revision de la literatura acerca de los llamados angiogliomas

La asociacion entre las malformaciones vasculares y los gliomas cerebrales es inusual. Mientras que la asociacion entre angioma cavernoso con lesiones gliomatosas es aun mas rara, es por esto considerado por algunos autores como una entidad patologica particular llamada angioglioma. Los autores reportan dos casos de asociacion de un angioma cavernoso con una ganglioglioma y un oligodendroglioma, respectivamente. Ademas se realizo una revision de la literatura sobre los llamados angiogliomas. En opinion de los autores, la entidad de los angiogliomas se presenta dentro de un espectro general de neoplasias angiomatosas, que incluyen tumores cerebrales, en su mayoria gliomas de bajo grado, asociados a su vez, con un componente vascular importante

Insulin-like growth factor-1 as predictive factor of difficult laryngoscopy in patients with GH-producing pituitary adenoma: A pilot study

Background: Growth hormone (GH)-producing pituitary tumors account for 10 to 15% of pituitary tumors. The hypersecretion of GH may induce changes in the airway anatomy through the activation of Insulin-like Growth factor 1(IGF-1) pathway. We sought investigate the role IGF-1 as a potential predictive factor of difficult laryngoscopy in patients with GH-producing pituitary adenoma. Methods: This study was a single center retrospective study. We included 33 patients undergoing transsphenoidal resection of GH-producing pituitary. We recorded demographic data, el-Ganzouri risk index (EGRI) and modified Look-Evaluate-Mallampati-Obstruction-Neck mobility (mLEMON) score, and pituitary hormone plasma levels. We performed ordinal logistic regression to analyze the relationship between IGF-1 and EGRI, mLEMON, and Cormack-Lehane Grade score and a multiple logistic regression to test the capability of EGRI, mLEMON and IGF-1 levels to predict Cormack-Lehane score. Receiver operating curve (ROC), area under the curve (AUC), and cut-off value of IGF-1 were calculated. Results: Only 14 (42.8%) and 12 (36.36%) patients showed predictive factors of difficult intubation according to EGRI and mLEMON score, respectively. IGF-1 significantly correlated with Cormack-Lehane (p = 0.005879) but not with mLEMON and EGRI (p = 0.3080 and 0.4146, respectively). In multiple regression model IGF-1 correlated only with Cormack-Lehane grade (p = 0.0089). Area under ROC was 0.8571 and cut-off value of IGF-1 was 186.15 ng/ml. Conclusion: Higher IGF-1 levels correlate with the probability of having a higher Cormack-Lehane score; classical bedside scores, such as mLEMON and EGRI, were not able to predict difficult laryngoscopy in our population

Thin walled pottery from Alife (Northern Campania, Italy)

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