Misiurewicz parameters in the exponential family

Abstract A complex exponential map is said to be Misiurewicz if the forward trajectory of the asymptotic value 0 lies in the Julia set and is bounded. We prove that the set of Misiurewicz parameters in the exponential family λ exp(z), λ ∈ C \ {0}, has Lebesgue measure zero

No entire function with real multipliers in class S

We prove that there is no entire transcendental function in class S with real multipliers of all repelling periodic orbits.Comment: 7 page

Atypical Hemolytic Uremic Syndrome (aHUS) and Adenosine Deaminase (ADA)-Deficient Severe Combined Immunodeficiency (SCID)—Two Diseases That Exacerbate Each Other: Case Report

Hemolytic uremic syndrome (HUS) is defined by the triad of microangiopathic hemolytic anemia, thrombocytopenia, and acute kidney injury (AKI). Atypical HUS (aHUS), distinguished by its etiology, is caused by uncontrolled overactivation of the alternative complement pathway. The correct diagnosis of aHUS is complex and involves various gene mutations. Severe combined immunodeficiency (SCID), characterized by severe T-cell lymphocytopenia and a lack of antigen-specific T-cell and B-cell immune responses, is of seldom occurrence. In 10–15% of pediatric patients, SCID is caused by adenosine deaminase (ADA) deficiency. The authors describe the case of a boy who suffered from both aHUS and ADA-deficient SCID. At the age of 9 months, the patient presented acute kidney injury with anuria and coagulopathy. The diagnosis of aHUS was established on the basis of alternative complement pathway deregulation and disease-associated gene mutations. Further examination revealed immune system failure and, at the age of 13 months, the ADA deficiency was confirmed by genetic tests and the boy was diagnosed with ADA-SCID. ADA SCID has recently been described as a possible triggering factor of aHUS development and progression. However, more research is required in this field. Nevertheless, it is crucial in clinical practice to be aware of these two co-existing life-threatening diseases