A class of diophantine equations of norm form with polynomial right-hand side

1986 ◽  
Vol 39 (3) ◽  
pp. 165-168
Author(s):  
S. V. Kotov
Keyword(s):  
Diophantine Equations ◽  
Norm Form ◽  
Right Hand

Continued Fractions, Jacobi Symbols, and Quadratic Diophantine Equations

2000 ◽  
Vol 43 (2) ◽  
pp. 218-225 ◽  
Author(s):  
R. A. Mollin ◽  
A. J. van der Poorten
Keyword(s):  
Continued Fractions ◽  
Diophantine Equations ◽  
Norm Form

AbstractThe results herein continue observations on norm form equations and continued fractions begun and continued in the works [1]−[3], and [5]−[6].

scholarly journals MINOR ARC MOMENTS OF WEYL SUMS

2012 ◽  
Vol 55 (1) ◽  
pp. 97-113 ◽  
Author(s):  
M. P. HARVEY
Keyword(s):  
Diophantine Equations ◽  
Diagonal Form ◽  
Norm Form ◽  
Goldbach Problem ◽  
Weyl Sum ◽  
Diophantine Problems

AbstractWe obtain an improved bound for the 2k-th moment of a degree k Weyl sum, restricted to a set of minor arcs, when k is small. We then present some applications of this bound to some Diophantine problems, including a case of the Waring–Goldbach problem, and a particular family of Diophantine equations defined as the sum of a norm form and a diagonal form.

scholarly journals On the finiteness of solutions for polynomial-factorial Diophantine equations

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Wataru Takeda
Keyword(s):  
Diophantine Equations ◽  
Field Extension ◽  
Infinite Subset ◽  
Norm Form ◽  
Factorial Function ◽  
Integer Solutions

AbstractWe study the Diophantine equations obtained by equating a polynomial and the factorial function, and prove the finiteness of integer solutions under certain conditions. For example, we show that there exist only finitely many l such that {l!} is represented by {N_{A}(x)}, where {N_{A}} is a norm form constructed from the field norm of a field extension {K/\mathbf{Q}}. We also deal with the equation {N_{A}(x)=l!_{S}}, where {l!_{S}} is the Bhargava factorial. In this paper, we also show that the Oesterlé–Masser conjecture implies that for any infinite subset S of {\mathbf{Z}} and for any polynomial {P(x)\in\mathbf{Z}[x]} of degree 2 or more the equation {P(x)=l!_{S}} has only finitely many solutions {(x,l)}. For some special infinite subsets S of {\mathbf{Z}}, we can show the finiteness of solutions for the equation {P(x)=l!_{S}} unconditionally.

Editorial Note

1946 ◽  
Vol 11 (1) ◽  
pp. 2-2
Keyword(s):  
Editorial Note ◽  
Speech Sounds ◽  
Left Hand ◽  
Hand Column ◽  
Right Hand ◽  
Infant Speech ◽  
The Right

In the article “Infant Speech Sounds and Intelligence” by Orvis C. Irwin and Han Piao Chen, in the December 1945 issue of the Journal, the paragraph which begins at the bottom of the left hand column on page 295 should have been placed immediately below the first paragraph at the top of the right hand column on page 296. To the authors we express our sincere apologies.

Eosinophilic vasculitis: an inhabitual and resistant manifestation of a vasculitis

VASA ◽  
2010 ◽  
Vol 39 (4) ◽  
pp. 344-348 ◽  
Author(s):  
Jandus ◽  
Bianda ◽  
Alerci ◽  
Gallino ◽  
Marone
Keyword(s):  
Skin Biopsy ◽  
Intravenous Iron ◽  
Small Vessel Vasculitis ◽  
High Dose ◽  
Raynaud Phenomenon ◽  
The Third ◽  
Left Elbow ◽  
Right Hand ◽  
The Right ◽  
Trunk Skin

A 55-year-old woman was referred because of diffuse pruritic erythematous lesions and an ischemic process of the third finger of her right hand. She was known to have anaemia secondary to hypermenorrhea. She presented six months before admission with a cutaneous infiltration on the left cubital cavity after a paravenous leakage of intravenous iron substitution. She then reported a progressive pruritic erythematous swelling of her left arm and lower extremities and trunk. Skin biopsy of a lesion on the right leg revealed a fibrillar, small-vessel vasculitis containing many eosinophils.Two months later she reported Raynaud symptoms in both hands, with a persistent violaceous coloration of the skin and cold sensation of her third digit of the right hand. A round 1.5 cm well-delimited swelling on the medial site of the left elbow was noted. The third digit of her right hand was cold and of violet colour. Eosinophilia (19 % of total leucocytes) was present. Doppler-duplex arterial examination of the upper extremities showed an occlusion of the cubital artery down to the palmar arcade on the right arm. Selective angiography of the right subclavian and brachial arteries showed diffuse alteration of the blood flow in the cubital artery and hand, with fine collateral circulation in the carpal region. Neither secondary causes of hypereosinophilia nor a myeloproliferative process was found. Considering the skin biopsy results and having excluded other causes of eosinophilia, we assumed the diagnosis of an eosinophilic vasculitis. Treatment with tacrolimus and high dose steroids was started, the latter tapered within 12 months and then stopped, but a dramatic flare-up of the vasculitis with Raynaud phenomenon occurred. A new immunosupressive approach with steroids and methotrexate was then introduced. This case of aggressive eosinophilic vasculitis is difficult to classify into the usual forms of vasculitis and constitutes a therapeutic challenge given the resistance to current immunosuppressive regimens.

Visual context differentially mediates left- and right-hand reaching movements

2009 ◽  
Author(s):  
Jos J. Adam ◽  
Susan Hoonhorst ◽  
Rick Muskens ◽  
Jay Pratt ◽  
Martin H. Fischer
Keyword(s):  
Reaching Movements ◽  
Visual Context ◽  
Right Hand ◽  
Left And Right

Detection of Sarcoidosis Based on Subcutaneous Nodules in the Dorsum of the Right Hand

2014 ◽  
Vol 76 (1) ◽  
pp. 14-17
Author(s):  
Yoshiyuki KUWAE ◽  
Kunitaka HARUNA ◽  
Yasushi SUGA
Keyword(s):  
Subcutaneous Nodules ◽  
Right Hand ◽  
The Right
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