SOME REMARKS ON THE SMARANDACHE FUNCTION

Remarks on a Function in the Number Theory

Secondary giant cell glioblastoma in a multiple drug abuser - simple association or ethiopathogenic correlation? Case presentation and literature review

Experimental investigations have shown that drug abuse initiates a cascade of pathophysiological events including toxic and hypoxic-ischemic injury on neurons, microglia and astrocytes, which finally lead to widespread disturbances in the brain. There are many reports about the psychiatric and neurologic effects of multiple drug abuse, but only a few clinical studies reporting possible correlation between recreational illicit drugs and gliomas. In this paper we present the case of a 40 years-old male patient, with a long history (almost ten years) of multiple drug abuse, including cocaine, heroin, marijuana, ethnobotanical drugs and nicotine, who was diagnosed and surgically treated for a supratentorial secondary giant cell glioblastoma (sgcGB) developed in a diffuse astrocytoma NOS. Depending on the type of the illicit drug used by the patient and the moment of life he used them, the morphological features identified in the histological samples of our patient confirmed the gliomagenesis effect of chronic multiple drug abuse, but also its inhibitory effects on tumour cells growth. This was due to the fact that although the tumour was large in size and caused brain sub-falcine herniation, the patient reported the onset of seizures only late in the evolution. In conclusion, the diagnosis of a brain tumour should take into consideration not only patient's clinical and imaging data, but also his lifestyle, especially his addiction to recreational drugs

A monotonicity property of Riemann's xi function and a reformulation of the Riemann Hypothesis

We prove that Riemann's xi function is strictly increasing (respectively, strictly decreasing) in modulus along every horizontal half-line in any zero-free, open right (respectively, left) half-plane. A corollary is a reformulation of the Riemann Hypothesis.Comment: 4 pages, published versio

Management of unknown origin cerebral metastases

Aim: The present study attempts todetermine the steps for obtaining theetiological diagnosis of brain metastaseswith unknown origin.Material and methods: A total of 190patients with brain metastases diagnosed inthe Department of Neurosurgery inEmergency Hospital ”N. Oblu” Iasibetween 2007-2010 were included in thisstudy. The clinical characteristics andpathological features were analyzed.Results: There were 102 males and 88females with a M:F ratio of 1.15:1. Themedian age of patients was 47.07 years(range 31-77 years). Females patients wereolder (mean age 57.21 years) than malespatients (49.15 years). 154 patients (81.05%)had single brain metastasis, and 36 patients(18.95%) had more than two. The lesionswere supratentorial in 142 patients(74.73%), infratentorial in 18 (9.47%), andboth infratentorial and supratentorial in 30patients (15.78%). Surgical treatmentinvolved complete resection in 47.9% ofcases, subtotal resection in 26.8%, andbiopsy alone in the remainder (25.3%).Brain metastases originating in lung cancerrepresented the most common type(47.39%), followed by those from breastcancer (19.79%), then those from skin(melanoma) (8.33%), genitourinarycarcinoma (6.30%), and gastrointestinalcarcinoma (2.62%). In 16.31% of cases, theprimary tumor remained unknown, despiteextensive investigation.Conclusion: The primary cancer leadingto brain metastases can be detected eitherby obtaining a sample of tumoral tissuethrough a neurosurgical operation on theintracerebral tumor (total ablation orstereotactic biopsy) with histopathologicalexamination, or by additional tests of thewhole body. Taken into consideration theresults of our own study, the managementof the patients with brain metastases shouldinclude a thoracic CT scan oranteroposterior and lateral chest X-ray,clinical breast examination andmammography, abdominal ultrasoundexploration, and skin, kidney and prostateexamination. With the most sophisticatedmethods of diagnosis in approximately 16%of cases the origin of metastasis remainsunknown. The identification of the primarysite by the neuropathologist afterstereotactic biopsy would clearly beadvantageous