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The main purpose of this article is to study the Caffarelli-Kohn-Nirenberg type inequalities (1.2) with p = 1. We show that symmetry breaking of the best constants occurs provided that a parameter ∣∣γ is large enough. In the argument we effectively employ equivalence between the Caffarelli-Kohn-Nirenberg type inequalities with p = 1 and the isoperimetric inequalities with weights [ABSTRACT FROM AUTHOR]

Reports on the Urea breath test (UBT) used in the detection of Helicobacter pylori infection. Popularity of the UBT as a noninvasive test for diagnosing H. pylori and for confirming eradication after treatment; Biggest problem which lies in its unavailability; Elimination of the need for a gastroscopic or barium examination when the UBT is used properly.