Negligible Variation and the Change of Variables Theorem

In this note we prove a necessary and sufficient condition for the change of variables formula for the HK integral, with implications for the change of variables formula for the Lebesgue integral. As a corollary, we obtain a necessary and sufficient condition for the Fundamental Theorem of Calculus to hold for the HK integral

THE MAST CELLS AND MASTOCYTOSIS

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The impact of economic activities on the social and political structures of Kuwait (1896-1946)

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A new look at the John–Nirenberg and John–Strömberg theorems for BMO

AbstractWe develop some techniques for studying various versions of the function space BMO. Special cases of one of our results give alternative proofs of the celebrated John–Nirenberg inequality and of related inequalities due to John and to Wik. Our approach enables us to pose a simply formulated “geometric” question, for which an affirmative answer would lead to a version of the John–Nirenberg inequality with dimension free constants

Homogeneous solutions of the heat equation

AbstractWe complete a characterization of homogeneous solutions of the heat equation begun by D. V. Widder. We determine regions of convergence for expansions of temperature functions in terms of the homogeneous solutions

A Robust Case of Allergic Contact Dermatitis to Propolis

Allergic contact dermatitis (ACD) occurs when an individual comes into cutaneous contact with a substance to which he or she has been sensitized to, causing a delayed-type hypersensitivity reaction. While the diagnosis may in some cases be easily suspected due to a classic history and exam, not all cases are obvious. Patch testing is an extremely useful process that allows for the diagnosis of ACD to be made while also identifying the specific chemical trigger. Present in beeswax and composed of a mixture of resins, waxes, oils, pollen, and various organic compounds, propolis is a well-known cause of ACD. Here we present the case of ACD to propolis in an unusual product and with impressive clinical findings. A 58 year-old woman of Native American descent with a history of Sjogren\u27s syndrome presented to Dermatology for a one year history of a painful and pruritic rash on her lips and face. She had temporary improvement with a previous course of prednisone followed by relapse upon tapering, but otherwise the rash had been worsening despite the use of high-potency topical steroids. She was also using bear grease and lip butter as moisturizers. On physical exam she had a well-demarcated symmetric perioral erythematous lichenified scaly plaque, as well as confluent erythema and scaling of her mucosal lips. After tinea incognito was ruled out by fungal culture, she subsequently underwent patch testing for suspected ACD. The diagnosis was confirmed with positive reactions at both the 2 day and 7 day reads to propolis and her bear grease and lip butter, both of which contained beeswax. The patient had complete resolution shortly after discontinuation of these products, and she was advised to avoid other products that contain propolis. With a soft and pliable texture and pleasant aroma, propolis is present in many creams, ointments, waxes, lipsticks, and balms. Moreover, with it\u27s reported anti-inflammatory and antimicrobial properties, it can also be found in various cosmeceutical, naturopathic, and homeopathic products. Made from bear fat and beeswax, the bear grease product the patient was using was advertised as having natural healing benefits and was purchased at a Native American craft store. This case is unique, as it represents a common allergen found in an uncommon vehicle. Moreover, it illustrates the importance of taking a comprehensive history when assessing for ACD, as well as the utility of patch testing.https://scholarlycommons.henryford.com/merf2020caserpt/1111/thumbnail.jp