Research
Research
Research
Research
713+ open-access research outputs.
We study the set $S(q)$ of residue classes $r$ modulo the Pisano period $\pi(q)$ for which $q \mid \varphi(F_m)$ for every $m \equiv r \pmod{\pi(q)}$. We prove that if $q$ is a Sophie Germain prime an…
By using parallel corona decomposition, the Kerman-Sawyer trace inequality is extended from Lebesgue spaces to product Morrey spaces.…
We study the dynamics of a parametric family of rational functions of odd degree, where each function is a generalized Blaschke product that maps the unit circle onto itself. The action of the Blaschk…
Large-scale disaster response operations frequently involve spontaneous volunteers who arrive independently at disaster sites and must be coordinated under severe time pressure. Assigning such volunte…
Special prime families (twin, Sophie Germain, safe, cousin, sexy, Chen, and isolated primes) are central objects of analytic number theory, yet no efficiently computable probabilistic filter exists fo…
We study properties of Diophantine exponents of lattices and so-called related "weak" uniform approximations introduced in recent papers by Oleg German, in the simplest two-dimensional case. In contra…
Let $G$ be a reductive group quasi-split at $p$. Using arguments of Hansen--Thorne, we show that under the non-abelian Leopoldt conjecture (NALC), Hansen's $p$-adic overconvergent cohomology eigenvari…
We confirm a conjecture of Darmon-Vonk on the antisymmetry of real quadratic singular moduli. The proof relies on a careful analysis of rigid meromorphic cocycles \`a la Darmon-Gehrmann-Lipnowski for …
In recent work, Stokes and Vermant considered graph-of-groups realisations of hypergraphs as a new description of rigidity-theoretic problems. In this paper, we show that the infinitesimal aspects of …
Arrow patterns were introduced by Berman and Tenner as a generalization of vincular patterns. They observed that arrow patterns have the potential to bridge the divide between a permutation's cycle no…
The $\pi$-series is attributed to Madhava, Gregory and Leibniz based on the chronology of its discovery. While this acknowledges the fact that Madhava of Sangamagrama an Indian mathematician who lived…
We investigate Newton's method applied to any odd or any even elliptic function with an arbitrary period lattice. For any function of this type whose set of poles coincides with its period lattice, we…
We give a counterexample to a conjecture made by Cigler, Jerman and Wojciechowski stating that all posets are conclusive. We also provide combinatorial characterizations for conclusiveness of finite p…
Carbon capture and storage or utilization (CCUS) will play an important role to achieve climate neutrality in many economies. Pipelines are widely regarded as the most efficient means of CO2 transport…
We consider a $d$-dimensional continuous martingale $X(t)$ with quadratic variation matrix $\langle X\rangle_t=\int_0^t \Sigma(s)\,ds$ and develop tests for the rank of its spot covariance matrix $\Si…
For a graph $G$ on $n$ vertices, denote by $a(G)$ the number of vertices in the largest induced forest in $G$. The Albertson-Berman conjecture, which has been open since 1979, states that $a(G) \geq \…
We study the expansions of permutation statistics in the basis of functions counting occurrences of a fixed pattern in a permutation. We show the finiteness of these pattern expansions for a class of …
Geometric Quantization is a term used to describe a wide collection of techniques dating back to the 1960s in the work of Kirillov, Kostant, and Souriau, which take symplectic manifolds and produce co…
The existence of the Herman ring of a function adds interest and complexity to the dynamics of the function. We present a detailed and understandable summary of the core discoveries and recent develop…
Let $L$ be a big and semipositive line bundle on a complex projective manifold $X$, and let $\theta\in c_1(L)$ be a smooth semipositive representative. In the adjoint setting $H^0(X,L^k\otimes K_X)$, …
Free open-access publishing with Google Scholar indexing.
Submission Guide →