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A Geometric Proof of Fermat’s Little Theorem

Advances in Pure Mathematics 2018年第1期8卷 41-44页

作者： Thomas Beatty marc barry Andrew Orsini Florida Gulf Coast University Fort Myers USA

We present an intuitively satisfying geometric proof of Fermat's result for positive integers that for prime moduli p, provided p does not divide a. This is known as Fermat’s Little Theorem. The proof is novel in using the idea of colorings applied to regular polygons to establish a number-theoretic result. A lemma traditionally, if ambiguously, attributed to Burnside provides a critical enumeration step.

关键词： Fermat Carmichael Number Group Permutation Burnside’s Lemma Action Invariant Set Orbit Stabilizer Coloring Pattern Prime Regular Polygon Cyclic Group

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BK nephropathy in the native kidneys of patients with organ transplants: Clinical spectrum of BK infection

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World Journal of Transplantation 2016年第3期6卷 472-504页

作者： Darlene Vigil Nikifor K Konstantinov marc barry Antonia M Harford Karen S Servilla Young Ho Kim Yijuan Sun Kavitha Ganta Antonios H Tzamaloukas Nephrology Section Medicine Service Raymond G. Murphy VA Medical Center and Department of Medicine University of New Mexico School of Medicine Department of Medicine University of Minnesota School of Medicine Department of Pathology University of New Mexico School of Medicine Division of Nephrology Department of Medicine University of New Mexico School of Medicine Division of Nephrology University of North Carolina School of Medicine

Nephropathy secondary to BK virus, a member of the Papoviridae family of viruses, has been recognized for some time as an important cause of allograft dysfunction in renal transplant recipients. In recent times, BK nephropathy(BKN) of the native kidneys has being increasingly recognized as a cause of chronic kidney disease in patients with solid organ transplants, bone marrow transplants and in patients with other clinical entities associated with immunosuppression. In such patients renal dysfunction is often attributed to other factors including nephrotoxicity of medications used to prevent rejection of the transplanted organs. Renal biopsy is required for the diagnosis of BKN. Quantitation of the BK viral load in blood and urine are surrogate diagnostic methods. The treatment of BKN is based on reduction of the immunosuppressive medications. Several compounds have shown antiviral activity, but have not consistently shown to have beneficial effects in BKN. In addition to BKN, BK viral infection can cause severe urinary bladder cystitis, ureteritis and urinary tract obstruction as well as manifestations in other organ systems including the central nervous system, the respiratory system, the gastrointestinal system and the hematopoietic system. BK viral infection has also been implicated in tumorigenesis. The spectrum of clinical manifestations from BK infection and infection from other members of the Papoviridae family is widening. Prevention and treatment of BK infection and infections from other Papovaviruses are subjects of intense research.

关键词： BK viral infection BK nephropathy Cardiac transplant Bone marrow transplant Liver transplant Pancreatic transplant Lung transplant

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Nephropathy in dietary hyperoxaluria:A potentially preventable acute or chronic kidney disease

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World Journal of Nephrology 2014年第4期3卷 122-142页

作者： Robert H Glew Yijuan Sun Bruce L Horowitz Konstantin N Konstantinov marc barry Joanna R Fair Larry Massie Antonios H Tzamaloukas Department of Surgery University of New Mexico School of Medicine Renal Section Raymond G Murphy Veterans Affairs (VA) Medical Center and Department of MedicineUniversity of New Mexico School of Medicine Division of Nephrology Department of MedicineUniversity of New Mexico School of Medicine Rheumatology Section Raymond G Murphy VA Medical Center and Department of MedicineUniversity of New Mexico School of Medicine Department of Pathology University of New Mexico School of Medicine Radiology Service Raymond G Murphy VA Medical Center and Department of RadiologyUniversity of New Mexico School of Medicine Pathology Section Raymond G Murphy VA Medical Center and Department of PathologyUniversity of New Mexico School of Medicine

Hyperoxaluria can cause not only nephrolithiasis and nephrocalcinosis,but also renal parenchymal disease histologically characterized by deposition of calcium oxalate crystals throughout the renal parenchyma,profound tubular damage and interstitial inflammation and *** nephropathy presents clinically as acute or chronic renal failure that may progress to endstage renal disease(ESRD).This sequence of events,well recognized in the past in primary and enteric hyperoxalurias,has also been documented in a few cases of dietary *** of oxalate intake in patients with chronic dietary hyperoxaluria who developed chronic kidney disease or ESRD were comparable to the reported average oxalate content of the diets of certain populations worldwide,thus raising the question whether dietary hyperoxaluria is a primary cause of ESRD in these *** addressing this question have the potential of improving population health and should be undertaken,alongside ongoing studies which are yielding fresh insights into the mechanisms of intestinal absorption and renal excretion of oxalate,and into the mechanisms of development of oxalate-induced renal parenchymal *** preventive and therapeutic strategies for treating all types of hyperoxaluria are expected to develop from these studies.

关键词：高草酸血症肾结石治疗方法临床分析

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Association between Hyperhomocysteinemia and Microangiopathic Complications (Neuropathy and Nephropathy) in Subjects with Type 1 and Type 2 Diabetes

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Journal of Diabetes Mellitus 2023年第4期13卷 325-339页

作者： Nene Oumou Kesso barry Soukeyna Gueye Moustapha Djité Pape Matar Kandji Michel Assane Ndour El Hadj Malick Ndour Demba Diedhiou Fatou Gueye-Tall Ndeye Mareme Thioune Najah Fatou Coly Dominique Doupa Maïmouna Ndour Mbaye Philomène Lopez Sall Papa Madieye Gueye Laboratory of Pharmaceutical Biochemistry University Cheikh Anta DIOP Dakar Senegal Laboratory of Biochemistry University Hospital Fann Dakar Senegal Department of Internal Medicine Abass Ndao Hospital Center Dakar Senegal Medical Biology Laboratory Diamniadio Children Hospital Dakar Senegal Department of Medical Biochemistry Saint-Louis University Saint-Louis Senegal

This prospective case-control study aimed to assess the prevalence of hyperhomocysteinemia and explore its potential correlation with microangiopathic complications, specifically nephropathy and neuropathy, in a cohort of both type 1 and type 2 diabetic patients. Conducted at the marc Sankalé Center of Abass Ndao Hospital in Dakar from June to September 2018, the study enrolled a total of 106 diabetic patients, comprising 93 type 2 diabetics and 13 type 1 diabetics, who were matched with control subjects free from clinically detectable pathologies, based on sex and age ± 2 years. The mean age of type 1 and type 2 diabetic patients was 24.46 ± 8.41 years and 57.28 ± 11.28 years, respectively. Our findings revealed a statistically significant elevation in mean homocysteine levels among patients when compared to controls (12.63 vs. 9.88;p < 0.0001). Hyperhomocysteinemia was observed in 24.5% of the patients, exclusively among those with type 2 diabetes. Within the hyperhomocysteinemia subgroup, 58% were male, and 42% were female. The analysis of neuropathy and nephropathy frequencies among type 2 diabetic patients, stratified by homocysteine concentrations, demonstrated a notably higher prevalence of diabetic nephropathy in patients with hyperhomocysteinemia compared to those with normohomocysteinemia (23.07% vs. 8.75%;p = 0.052). Similarly, diabetic neuropathy exhibited a significantly greater frequency in patients with hyperhomocysteinemia as opposed to normohomocysteinemia (80.76% vs. 50%;p = 0.005). Furthermore, our results established a significant positive correlation between homocysteine concentrations and both age (r = 0.402;p < 0.0001) and creatinine levels (r = 0.461;p < 0.0001). Bivariate logistic regression analysis indicated that patients with hyperhomocysteinemia faced 3 times and 6 times higher risks of developing neuropathy (OR = 3.5;p = 0.061) and diabetic nephropathy (OR = 6.092;p = 0.014), respectively.

关键词： Homocysteine Hyperhomocysteinemia Diabetes Mellitus Type 1 Diabetes Type 2 Diabetes Nephropathy Neuropathy

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