Results 31 to 40 of about 7,755,587 (178)
Математичні СтудіїThis paper has involved the use of a variety of variations of the Fermat-type equation $f^n(z)+g^n(z)=1$, where $n(\geq 2)\in\mathbb{N}$. Many researchers have demonstrated a keen interest to investigate the Fermat-type equations for entire and ...
R. Mandal, R. Biswas
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Observations on Fermat Motives ofK3-Type [PDF]
, 1998 In [8, 9], Zarhin introduced the notion of varieties ofK3-typein even dimension over finite fields. Zarhin showed that ordinary abelian surfaces, ordinaryK3 surfaces, and ordinary cubic fourfolds are examples of such varieties.
Yui, Noriko, Gouvêa, Fernando Q
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Note on a Fermat-type diophantine equation
Journal of Number Theory, 2003 The author extends his previous results [J.\ Number Theory 80, 174-186 (2000; Zbl 0972.11015)] concerning the Diophantine equation \(x^p+y^p=cpz^p\), where \(p\) is an odd prime and the prime factors of \(c\) are of the form \(kp-1\) with \((k,p)=1\). Let \(x,y,z\) be a solution. Then, as shown by the author [op. cit.], \(p\) is irregular.
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On solutions of several Fermat-type partial differential-difference equations in C2
Demonstratio MathematicaIn this paper, we study entire solutions of several Fermat-type partial differential-difference equations in C2 ${\mathbb{C}}^{2}$ by applying Nevanlinna theory of meromorphic functions in several complex variables.
Tang Caoqiang, Huang Zhigang
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On the existence of solutions of a Fermat-type difference equation
Annales Academiae Scientiarum Fennicae Mathematica, 2015 Let \(F_C(n)\) be the smallest positive integer \(k\) such that \[ f_1^n+f_2^n+\cdots+f_k^n=1 \] has a solution consisting of \(k\) non-constant functions \(f_1,f_2,\dots,f_k\) in the field (or ring) \(C\). In their comprehensive review article, \textit{G. G. Gundersen} and \textit{W. K. Hayman} [Bull. Lond. Math. Soc.
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Micro/Nanoscale Acoustic Manipulation: From Particle Control to Autonomous Microswimmers
Advanced Science, EarlyView.This conceptual framework illustrates acoustic technology as a multifunctional platform enabling passive particle manipulation across scales and autonomous propulsion of microswimmers. ABSTRACT Acoustic manipulation and propulsion technologies have emerged as powerful platforms for micro/nanoscale control, enabled by their non‐contact operation, label ...
Jiahui Chu +4 more
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Magnetic Resonance in Medicine, EarlyView.ABSTRACT Purpose To enable MRI‐based nongated 3D depiction of forced expiration with both high spatio‐temporal resolution and fidelity of lung dynamics. Methods An undersampled 3D Fermat looped, orthogonally encoded trajectory (FLORET) was optimized for nonsegmented dynamic acquisitions during forced expiration and a corresponding model‐based ...
Sebastian Scheidel +6 more
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Solving Fermat-type equations $x^5+y^5=dz^p$ [PDF]
Mathematics of Computation, 2010 In this paper we are interested in solving the Fermat-type equations x^5+y^5=dz^p where d is a positive integer and p a prime number $\ge 7$. We describe a new method based on modularity theorems which allows us to improve all the results in a previous paper of the first author. We finally discuss the present limitations of the method by looking at the
Nicolas Billerey, Luis V. Dieulefait
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The Epistemology and Semantics of Ignorance
Philosophy and Phenomenological Research, EarlyView.ABSTRACT This paper is concerned with ignorance. It develops a novel, full account of the nature and epistemic normativity of objectual and factual ignorance, degrees of ignorance, comparative ignorance, and the semantics of permissible outright attributions of ignorance of facts and phenomena.
Mona Simion, Christoph Kelp, Lilith Mace
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Further Results about a Special Fermat-Type Difference Equation
Journal of Function Spaces, 2020 In this paper, we prove the difference equation Fz3+ΔcFz+c3=1 does not have meromorphic solution of finite order over the complex plane C. We also discuss an application to the unique range set problem.
Hongwei Ma, Jianming Qi, Zhenjie Zhang
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