On fixed point free involutions of
Gerhard X. Ritter (1976)
Colloquium Mathematicae
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Gerhard X. Ritter (1976)
Colloquium Mathematicae
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Stoyan Dimitrov (2021)
Czechoslovak Mathematical Journal
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We show that there exist infinitely many consecutive square-free numbers of the form , . We also establish an asymptotic formula for the number of such square-free pairs when does not exceed given sufficiently large positive number.
Ya-Fang Feng (2023)
Czechoslovak Mathematical Journal
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We show that for any given integer there exist infinitely many consecutive square-free numbers of the type , . We also establish an asymptotic formula for such that , are square-free. The method we used in this paper is due to Tolev.
Dömötör Pálvölgyi (2020)
Kybernetika
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Suppose that some polynomial with rational coefficients takes only natural values at natural numbers, i. e., . We show that the base- representation of is a context-free language if and only if is linear, answering a question of Shallit. The proof is based on a new criterion for context-freeness, which is a combination of the Interchange lemma and a generalization of the Pumping lemma.
Giulio Ciraolo, Rolando Magnanini, Shigeru Sakaguchi (2015)
Journal of the European Mathematical Society
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We consider the functional where is a bounded domain and is a convex function. Under general assumptions on , Crasta [Cr1] has shown that if admits a minimizer in depending only on the distance from the boundary of , then must be a ball. With some restrictions on , we prove that spherical symmetry can be obtained only by assuming that the minimizer has one level surface parallel to the boundary (i.e. it has only a level surface in common with the distance). We then discuss...
Rüdiger Göbel, Daniel Herden, Saharon Shelah (2014)
Journal of the European Mathematical Society
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It is a well-known fact that modules over a commutative ring in general cannot be classified, and it is also well-known that we have to impose severe restrictions on either the ring or on the class of modules to solve this problem. One of the restrictions on the modules comes from freeness assumptions which have been intensively studied in recent decades. Two interesting, distinct but typical examples are the papers by Blass [1] and Eklof [8], both jointly with Shelah. In the first case...
Carlo Greco (2017)
Commentationes Mathematicae Universitatis Carolinae
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In a cholesteric liquid crystal the director field tends to form a right-angle helicoid around a twist axis in order to minimize the internal energy; however, a fixed alignment of the director field at the boundary (strong anchoring) can give rise to distorted configurations of the director field, as oblique helicoid, in order to save energy. The transition to this distorted configurations depend on the boundary conditions and on the geometry of the liquid crystal, and it is known...
Martin Arkowitz, Mauricio Gutierrez (2002)
Fundamenta Mathematicae
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If f:G → H is a group homomorphism and p,q are the projections from the free product G*H onto its factors G and H respectively, let the group be the equalizer of fp and q:G*H → H. Then p restricts to an epimorphism . A right inverse (section) of is called a coaction on G. In this paper we study and the sections of . We consider the following topics: the structure of as a free product, the restrictions on G resulting from the existence of a coaction, maps of coactions and...
Yihong Du, Bendong Lou (2015)
Journal of the European Mathematical Society
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We study nonlinear diffusion problems of the form with free boundaries. Such problems may be used to describe the spreading of a biological or chemical species, with the free boundary representing the expanding front. For special of the Fisher-KPP type, the problem was investigated by Du and Lin [DL]. Here we consider much more general nonlinear terms. For any which is and satisfies , we show that the omega limit set of every bounded positive solution is determined by a stationary...
Wei Zhang (2023)
Czechoslovak Mathematical Journal
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We consider -free numbers over Beatty sequences. New results are given. In particular, for a fixed irrational number of finite type and any constant , we can show that where is the set of positive -free integers and the implied constant depends only on and This improves previous results. The main new ingredient of our idea is employing double exponential sums of the type
Svobodová, Ivona
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We consider functionals of a potential energy corresponding to . We are dealing with with . Various types of the subsoil of the plate are described by various types of the nonlinear term . The aim of the paper is to find a suitable computational algorithm.
Graziano Crasta (2006)
Journal of the European Mathematical Society
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We consider the integral functional , , where , , is a nonempty bounded connected open subset of with smooth boundary, and is a convex, differentiable function. We prove that if admits a minimizer in depending only on the distance from the boundary of , then must be a ball.
Per Åhag, Rafał Czyż, Pham Hoàng Hiêp (2007)
Annales Polonici Mathematici
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The energy class is studied for 0 < p < 1. A characterization of certain bounded plurisubharmonic functions in terms of and its pluricomplex p-energy is proved.
Zujin Zhang, Yali Zhang (2021)
Applications of Mathematics
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As observed by Yamazaki, the third component of the magnetic field can be estimated by the corresponding component of the velocity field in norm. This leads him to establish regularity criterion involving or . Noticing that can be greater than 6 in this paper, we can improve previous results.
Nakayashiki, Ryota
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In this paper, we consider a class of initial-boundary value problems for quasilinear PDEs, subject to the dynamic boundary conditions. Each initial-boundary problem is denoted by (S) with a nonnegative constant , and for any , (S) can be regarded as a vectorial transmission system between the quasilinear equation in the spatial domain , and the parabolic equation on the boundary , having a sufficient smoothness. The objective of this study is to establish a mathematical method,...
Gongrui Chen, Wenxiao Wang (2023)
Czechoslovak Mathematical Journal
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Let be a fixed integer. We study the asymptotic formula of , which is the number of positive integer solutions such that the polynomial is -free. We obtained the asymptotic formula of for all . Our result is new even in the case . We proved that , where is a constant depending on . This improves upon the error term obtained by G.-L. Zhou, Y. Ding (2022).