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Journal of Mathematics, Volume 2026, Issue 1, 2026.Topological indices are essential for encoding molecular information and have traditionally focused on the properties of individual atoms and their connections. In this work, we study and analyze the first and second entire Zagreb indices. We explore their predictive power through rigorous analysis of octane isomers and benzenoid hydrocarbons ...
Buthinah A. Bin Dehaish +3 more
wiley +1 more source
Role of Intersections in Fracture Connectivity
Journal of Geophysical Research: Solid Earth, Volume 130, Issue 12, December 2025.Abstract Networks of intersecting fractures often provide the flow paths through subsurface reservoirs. Assessing network connectivity is challenging because fracture intersections compose a vanishingly small fraction of the network void volume. In this paper, motivated by 3D X‐ray imaging of the simplest element of fracture network, that is, two ...
L. J. Pyrak‐Nolte, D. D. Nolte
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Connected generalised Sierpiński carpets [PDF]
, 2010 Generalised Sierpiński carpets are planar sets that generalise the well-known Sierpiński carpet and are defined by means of sequences of patterns. We present necessary and sufficient conditions, under which generalised Sierpiński carpets are connected ...
Cristea, Ligia Loreta +3 more
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First‐order Sobolev spaces, self‐similar energies and energy measures on the Sierpiński carpet
Communications on Pure and Applied Mathematics, Volume 78, Issue 9, Page 1523-1608, September 2025.Abstract For any p∈(1,∞)$p \in (1,\infty)$, we construct p$p$‐energies and the corresponding p$p$‐energy measures on the Sierpiński carpet. A salient feature of our Sobolev space is the self‐similarity of energy. An important motivation for the construction of self‐similar energy and energy measures is to determine whether or not the Ahlfors regular ...
Mathav Murugan, Ryosuke Shimizu
wiley +1 more source
A lower bound on volumes of end‐periodic mapping tori
Journal of Topology, Volume 18, Issue 3, September 2025.Abstract We provide a lower bound on the volume of the compactified mapping torus of a strongly irreducible end‐periodic homeomorphism f:S→S$f: S \rightarrow S$. This result, together with work of Field, Kim, Leininger, and Loving [J. Topol. 16 (2023), no.
Elizabeth Field +3 more
wiley +1 more source
Graphical models for topological groups: A case study on countable Stone spaces
Bulletin of the London Mathematical Society, Volume 57, Issue 8, Page 2311-2335, August 2025.Abstract By analogy with the Cayley graph of a group with respect to a finite generating set or the Cayley–Abels graph of a totally disconnected, locally compact group, we detail countable connected graphs associated to Polish groups that we term Cayley–Abels–Rosendal graphs.
Beth Branman +3 more
wiley +1 more source
Fractal Scaling of Explosively Driven Product Gases
Propellants, Explosives, Pyrotechnics, Volume 50, Issue 5, May 2025.The expanding interface between explosive product gases and ambient air is characterized as a function of time by the fractal dimension of the interface which is extracted from high‐speed image sequences. The interface is observed to increase in fractal dimension, and thus complexity, as time from detonation progresses.
Christian R. Peterson +1 more
wiley +1 more source
Some properties of generalized Sierpiński graphs [PDF]
, 2019 V magistrskem delu so obravnavane in s slikovnimi zgledi predstavljene nekatere lastnosti posplošenih grafov Sierpińskega, zgrajenih na poljubnem baznem grafu G.
Bezgovšek, Teja
core
Learning Image Fractals Using Chaotic Differentiable Point Splatting
Computer Graphics Forum, Volume 44, Issue 2, May 2025.Abstract Fractal geometry, defined by self‐similar patterns across scales, is crucial for understanding natural structures. This work addresses the fractal inverse problem, which involves extracting fractal codes from images to explain these patterns and synthesize them at arbitrary finer scales.
A. Djeacoumar +3 more
wiley +1 more source
Angewandte Chemie, Volume 137, Issue 17, April 17, 2025.Adel verpflichtet! Das Edelgas Argon kann für die Synthese von Kohlenstoff‐Schwefel‐Kohlenstoff Thioether‐basierten Nanostrukturen auf inerten Oberflächen wie beispielsweise Graphit eingesetzt werden. Im Gegensatz zur Oberflächensynthese auf Metallen könnte dieser Ansatz die Erforschung von Feldeffekt‐Bauelementen ermöglichen.
Lukas Grossmann +6 more
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