On the Maximum Arc Length of Monotonic Functions

International audienceWe revisit a problem solved in 1963 by Zaanen & Luxemburg in this monthly: what is the largest possible length of the graph of a monotonic function on an interval? And is there such a function that attains this length? This is an interesting and intriguing problem with a somewhat surprising answer, that should be of interest to a broad spectrum of mathematicians starting with upper level undergraduates. The proof given by Zaanen & Luxemburg is very short and elegant but not accessible to an undergraduate. We give here a longer, but elementary, proof

Geocaching History Challenge: Using High-Tech Toys to Learn History

Do you love local history? Do you love a good treasure hunt? Do you love high-tech gadgets? Put them together to get your library patrons out and about in your local area. Learn how the Ramsey County Library teamed up with the White Bear Lake Area Historical Society to teach about local historic sites using geocaches in this Legacy-funded program. Learn to play the high-tech game yourself using handheld GPS receivers or smartphones! Participants will go outside for the last half of the session so be prepared for the weather

Mucosal Melanomas of the Head and Neck: The Role of Postoperative Radiation Therapy

Objectives. Mucosal melanomas are rarer than their cutaneous counterparts and are associated with a poorer prognosis. We report the clinical outcomes of patients with mucosal melanomas of the head and neck region generally treated with definitive surgery followed by postoperative radiation therapy (RT). Methods. We reviewed the records of 17 patients treated at the University of Miami in 1990–2007. Patients generally received conventionally fractionated RT regimens to the postoperative bed. Elective nodal RT was not routinely delivered. Eight patients received adjuvant chemotherapy or immunotherapy. Results. Median followup was 35.2 months (range 5–225). As the first site of failure: 3 patients recurred locally, 2 regionally and 2 distantly. All 3 patients who recurred locally had not received RT. Of the 5 locoregional recurrences, 4 were salvaged successfully with multimodality therapy with no evidence of disease at last followup. Overall survival was 64.7% at 2 years and 51.5% at 5 years. Conclusions. Patients with mucosal melanoma of the head and neck are best treated with surgery to achieve negative margins, followed by postoperative RT to optimize local control. Elective nodal irradiation may not be indicated in all cases, as regional failures were not predominant. Distant metastases were fewer when compared to historical data, potentially due to advancements in adjuvant therapies as well as aggressive multi-modality salvage at time of failure

Long-Term Followup Comparing Two Treatment Dosing Strategies of 125

Objective. To investigate the efficacy of two different dosing strategies of radioactive iodine-125 (125I) in the management of small- and medium-sized posterior uveal melanoma. Patients and Methods. The medical records of consecutive patients with choroidal melanomas between 1.5 and 5.0 mm in apical height treated initially with 125I plaque radiotherapy were reviewed. Patients were treated with one of the following two treatment dosing strategies: (1) 85 Gy to the apical height of the tumor (group 1) or (2) 85 Gy to a prescription point of 5.0 mm (group 2). Results. Of 95 patients, 55 patients were treated to the apical height of the tumor, and 40 were treated to a prescription point of 5.0 mm. Comparative analysis of the incidence rates of specific complications between the two groups demonstrates that group 2 had a significantly higher incidence of radiation retinopathy, radiation optic neuropathy, and/or visually significant cataract formation than group 1 (). Conclusion. Treatment of choroidal melanomas less than 5 mm in apical height with 125I brachytherapy to the true apical height is equally effective when compared to treatment with 85 Gy to 5.0 mm. Treatment to the apical height of the tumor may result in lower incidence of radiation-related complications

Trkalian fields: ray transforms and mini-twistors

We study X-ray and Divergent beam transforms of Trkalian fields and their relation with Radon transform. We make use of four basic mathematical methods of tomography due to Grangeat, Smith, Tuy and Gelfand-Goncharov for an integral geometric view on them. We also make use of direct approaches which provide a faster but restricted view of the geometry of these transforms. These reduce to well known geometric integral transforms on a sphere of the Radon or the spherical Curl transform in Moses eigenbasis, which are members of an analytic family of integral operators. We also discuss their inversion. The X-ray (also Divergent beam) transform of a Trkalian field is Trkalian. Also the Trkalian subclass of X-ray transforms yields Trkalian fields in the physical space. The Riesz potential of a Trkalian field is proportional to the field. Hence, the spherical mean of the X-ray (also Divergent beam) transform of a Trkalian field over all lines passing through a point yields the field at this point. The pivotal point is the simplification of an intricate quantity: Hilbert transform of the derivative of Radon transform for a Trkalian field in the Moses basis. We also define the X-ray transform of the Riesz potential (of order 2) and Biot-Savart integrals. Then, we discuss a mini-twistor respresentation, presenting a mini-twistor solution for the Trkalian fields equation. This is based on a time-harmonic reduction of wave equation to Helmholtz equation. A Trkalian field is given in terms of a null vector in C3 with an arbitrary function and an exponential factor resulting from this reduction.Comment: 37 pages, http://dx.doi.org/10.1063/1.482610

Clinical Study Long-Term Followup Comparing Two Treatment Dosing Strategies of 125 I Plaque Radiotherapy in the Management of Small/Medium Posterior Uveal Melanoma

Objective. To investigate the efficacy of two different dosing strategies of radioactive iodine-125 ( 125 I) in the management of smalland medium-sized posterior uveal melanoma. Patients and Methods. The medical records of consecutive patients with choroidal melanomas between 1.5 and 5.0 mm in apical height treated initially with 125 I plaque radiotherapy were reviewed. Patients were treated with one of the following two treatment dosing strategies: (1) 85 Gy to the apical height of the tumor (group 1) or (2) 85 Gy to a prescription point of 5.0 mm (group 2). Results. Of 95 patients, 55 patients were treated to the apical height of the tumor, and 40 were treated to a prescription point of 5.0 mm. Comparative analysis of the incidence rates of specific complications between the two groups demonstrates that group 2 had a significantly higher incidence of radiation retinopathy, radiation optic neuropathy, and/or visually significant cataract formation than group 1 ( = 0.028). Conclusion. Treatment of choroidal melanomas less than 5 mm in apical height with 125 I brachytherapy to the true apical height is equally effective when compared to treatment with 85 Gy to 5.0 mm. Treatment to the apical height of the tumor may result in lower incidence of radiation-related complications

The Lantern Vol. 75, No. 2, Spring 2008

• In a French Courtyard at the Philadelphia Museum of Art • Picky Mangoes • And for My Un-Birthday I Drank Poets\u27 Tea and Got to See • Tree-Baby • Wrestling With Plants • I Smile • Walking Home • The Wall Between • Phalangese, or the Art of Speaking to Fingers • Early Spring • Karma Kids • A Bazaar Triptych • The Joys of Ritual Circumcision • [Of] Archetype[s] or I Don\u27t Like Your Poetry • Truth and Beauty Bombed • Chevalier Anachronistic • Kinds of Birds • Sparknotes Entry for The Changing Tide by Eric Relvas • Thirst • The Devil\u27s Dictionary • Portrait of an Artist Who Loves Icarus • Dinner at the Old House • The Meaning of a Dust-Busterhttps://digitalcommons.ursinus.edu/lantern/1172/thumbnail.jp