Sums of two biquadrates and elliptic curves of rank ≥4\geq 4

If an integer $n$ is written as a sum of two biquadrates in two different ways, then the elliptic curve $y^2=x^3-nx$ has rank $\geq 3$. If moreover $n$ is odd and the parity conjecture is true, then it has even rank $\geq 4$. Finally, some examples of ranks equal to 4, 5, 6, 7, 8 and 10, are also obtained.Comment: 11 pages, 2 table

SUMS OF TWO BIQUADRATES AND ELLIPTIC CURVES OF RANK ≥ 4

If an integer n is written as a sum of two biquadrates in two different ways, then the elliptic curve y2 = x3 − nx has positive rank. We utilize Euler’s parametrization to introduce some homoge- neous equations to prove that En has rank ≥ 3. If moreover n is odd and the parity conjecture is true, then the curve has even rank ≥ 4. Finally, some examples of ranks equal to 4, 5, 6, 7, 8 and 10, are also obtained

Occult laryngeal foreign body mimicking normal thyroid cartilage

Introduction: Foreign body aspiration is common especially in children. The absence of history of choking does not rule out the diagnosis. Diagnosis required high index of suspicion. Case Presentation: Undiagnosed foreign body aspiration mostly occurs in bronchial airway rather than larynx and can cause severe complications. In this article, we report a silent laryngeal foreign body aspiration to show that careful history taking and accurate evaluation of radiography are important factors for diagnosis. Conclusions: The single most significant factor leading to detect of tracheobronchial foreign body aspiration is a high index of suspicion; this case highlights the possibility of a foreign body in the airway in patients who presents with a recent onset of chronic respiratory complaints. © 2015, Trauma Monthly

Malignant mixed mullerian tumor of the uterus associated with tamoxifen therapy in a patient with a history of breast cancer

Tamoxifen is the drug of choice in the treatment of breast cancer. Recent reports show an increased incidence of endometrial carcinoma in patients taking tamoxifen. In this article, we report a case of malignant mixed mullerian tumor after tamoxifen use. Copyright © 2006 by Razi Institute for Drug Research (RIDR)

Speed of light in the extended gravity theories

We shall investigate the possibility of formulation of varying speed of light (VSL) in the framework of Palatini non-linear Ricci scalar and Ricci squared theories. Different speeds of light including the causal structure constant, electromagnetic, and gravitational wave speeds are discussed. We shall see that two local frames are distinguishable and discuss about the velocity of light in these two frames. We shall investigate which one of these local frames is inertial.Comment: 19 pages. to appear in Classical Quantum Gravit

Allopregnanolone Improves Locomotor Activity and Arousal in the Aged CGG Knock-in Mouse Model of Fragile X-Associated Tremor/Ataxia Syndrome.

Carriers of the fragile X premutation (PM) can develop a variety of early neurological symptoms, including depression, anxiety and cognitive impairment as well as being at risk for developing the late-onset fragile X-associated tremor/ataxia syndrome (FXTAS). The absence of effective treatments for FXTAS underscores the importance of developing efficacious therapies to reduce the neurological symptoms in elderly PM carriers and FXTAS patients. A recent preliminary study reported that weekly infusions of Allopregnanolone (Allop) may improve deficits in executive function, learning and memory in FXTAS patients. Based on this study we examined whether Allop would improve neurological function in the aged CGG knock-in (CGG KI) dutch mouse, B6.129P2(Cg)-Fmr