https://www.mscand.dk/ Mathematica Scandinavica en-US MATHEMATICA SCANDINAVICA 0025-5521 https://www.mscand.dk/article/view/156272 <p>&nbsp;&nbsp;&nbsp;</p> Math Scand Copyright (c) 2025 MATHEMATICA SCANDINAVICA 2025-03-25 2025-03-25 131 1 https://www.mscand.dk/article/view/156273 <p>Announcement of the board of associate editors for Mathematica Scandinavica</p> Arne Jensen Copyright (c) 2025 MATHEMATICA SCANDINAVICA 2025-03-25 2025-03-25 131 1 10.7146/math.scand.a-156273 https://www.mscand.dk/article/view/151573 <p>Let $\mathfrak {a}$ be an ideal of a Noetherian ring $R$ such that the category of $\mathfrak {a}$-cofinite modules is an Abelian subcategory of the category of $R$-modules. Let $M$ be a finitely generated $R$-module such that the $R$-modules $H^i_{\mathfrak {a}}(M)$ are $\mathfrak {a}$-cofinite for all integers $i\in \mathbb{N}_0$. In this paper it is shown that $\dim H^i_{\mathfrak {a}}(M)\leq 1$ for all integers $i\geq 2$.</p> Kamal Bahmanpour Copyright (c) 2025 MATHEMATICA SCANDINAVICA 2025-03-25 2025-03-25 131 1 10.7146/math.scand.a-151573 https://www.mscand.dk/article/view/151576 <p>We study the distribution of sequences of the form $(q_ny)_{n=1}^\infty $, where $(q_n)_{n=1}^\infty $ is some increasing sequence of integers. In particular, we study the Lebesgue measure and find bounds on the Hausdorff dimension of the set of points $\gamma \in [0,1)$ which are well approximated by points in the sequence $(q_ny)_{n=1}^\infty $. The bounds on Hausdorff dimension are valid for almost every $y$ in the support of a measure of positive Fourier dimension. When the required rate of approximation is very good or if our sequence is sufficiently rapidly growing, our dimension bounds are sharp. If the measure of positive Fourier dimension is itself Lebesgue measure, our measure bounds are also sharp for a very large class of sequences.</p> Simon Kristensen Tomas Persson Copyright (c) 2025 MATHEMATICA SCANDINAVICA 2025-03-25 2025-03-25 131 1 10.7146/math.scand.a-151576 https://www.mscand.dk/article/view/153210 <p>Let $C$ be a smooth curve of genus $g$ and let $d$,$r$ be integers with $1 \leq r \leq g-2$ and $2r\leq d \leq g-2+r$. H. Martens' Theorem states that $\dim (W^r_d(C))=d-2r$ implies $C$ is hyperelliptic. It is known that for a metric graph Γ of genus $g$ such statement using $\dim (W^r_d(\Gamma ))$ does not hold. However replacing $\dim (W^r_d(\Gamma ))$ by the so-called Brill-Noether rank $w^r_d(\Gamma )$ it was stated as a conjecture. Using a similar definition in the case of curves one has $\dim (W^r_d(C))=w^r_d(C)$.</p> <p>Let $\Gamma$ be a chain of cycles of genus $g$ and let $r,d$ be integers with $1 \leq r \leq g-2$ and $2r\leq d \leq g-3+r$. If $w^r_d(\Gamma )=d-2r$ then we prove Γ is hyperelliptic. In case $g \geq 2r+3$ then we prove there exist non-hyperelliptic chains of cycles satisfying $w^r_{g-2+r}(\Gamma )=g-2-r$, contradicting the conjecture. We give a complete description of all counterexamples within the set of chains of cycles to the statement of H. Martens' Theorem. Those counterexamples also give rise to chains of cycles such that $w^r_{g-2+r}(\Gamma ) \neq w^1_{g-r}(\Gamma )$. This shows that the Riemann-Roch duality does not hold for the Brill-Noether ranks of metric graphs.</p> Marc Coppens Copyright (c) 2025 MATHEMATICA SCANDINAVICA 2025-03-25 2025-03-25 131 1 10.7146/math.scand.a-153210 https://www.mscand.dk/article/view/150634 <p>Utilizing the concept of Reeb Jacobi operator of Codazzi type, we investigate Hopf real hypersurfaces in the complex hyperbolic two-plane Grassmannian $G^{*}_2(\mathbb {C}^{m+2})$ which admit a constant Reeb function α along the Reeb direction of ξ. If the Reeb function α is constant along the Reeb direction, then the Reeb vector field $\xi =-JN$ either belongs to the distribution ${\mathfrak D}$ or the distribution ${\mathfrak D}^{\bot }$. By virtue of this fact, we have proved a new result about Reeb Jacobi operator of Codazzi type according to the Reeb vector field $\xi \in \mathfrak {D}^{\bot }$ or $\xi \in \mathfrak {D}$, respectively.</p> Young Jin Suh Copyright (c) 2025 MATHEMATICA SCANDINAVICA 2025-03-25 2025-03-25 131 1 10.7146/math.scand.a-150634 https://www.mscand.dk/article/view/152461 <p>This work discusses the existence and uniqueness of the weak solution to a spatial fractional diffusion equation, which can be applied in image processing. The proposed model combines the advantages of both second- and fourth-order diffusion equations along with Gaussian filtering by employing spatial fractional derivatives and a Gaussian filter. This approach enhance edges preservation and robustness to noise. The existence and uniqueness of the weak solution for the model are proved by applying Schauder's fixed-point theorem.</p> Imane Boudrissa Noureddine Benhamidouche Copyright (c) 2025 MATHEMATICA SCANDINAVICA 2025-03-25 2025-03-25 131 1 10.7146/math.scand.a-152461 https://www.mscand.dk/article/view/148979 <p>In this note we show that a weakly geometrically flat map $\pi \colon M\rightarrow N$ between pure dimensional complex spaces has the local lifting property for cycles. From this result we also deduce that, under these hypotheses, several properties of $M$ are transferred to $N$.</p> Daniel Barlet Jón Magnússon Copyright (c) 2025 MATHEMATICA SCANDINAVICA 2025-03-25 2025-03-25 131 1 10.7146/math.scand.a-148979 https://www.mscand.dk/article/view/151062 <p>Let $u\colon \Omega \subset \mathbb {C}^n \to \mathbb {C}^m$, for $n \geq 2$ and $m \geq 1$. Let $1 \leq p \leq 2$, and $2(2n)^2 -1 \leq q &lt; \infty $ such that $\frac {1}{p} + \frac {1}{p'} = 1$ and $\frac {1}{p} - \frac {1}{p'} = \frac {1}{q}$. Suppose $\lvert \overline \partial u\rvert \leq V \lvert u\rvert $, where $V \in L^q_{\textrm {loc}}(\Omega )$. Then $u$ has a unique continuation property in the following sense: if $u \in W^{1,p}_{\textrm {loc}}(\Omega )$ and for some $z_0 \in \Omega $, $\lVert u \rVert _{L^{p'}(B(z_0,r))} $ decays faster than any powers of $r$ as $r \to 0$, then $u \equiv 0$. The same result holds for $q=\infty $ if $u$ is scalar-valued ($m=1$)</p> Ziming Shi Copyright (c) 2025 MATHEMATICA SCANDINAVICA 2025-03-25 2025-03-25 131 1 10.7146/math.scand.a-151062