24 papers · ranked by Valyu relevance
Alí Guzmán Adán
The aim of this paper is to obtain a generalized CK-extension theorem in superspace for the bi-axial Dirac operator ∂x + ∂y. In the classical commuting case, this result can be written as a power series of Bessel type of certain differential operators acting on a single initial function. In the superspace setting…
Graeme W. Milton
A natural connection between rational functions of several real or complex variables, and subspace collections is explored. A new class of function, superfunctions, are introduced which are the counterpart to functions at the level of subspace collections. Operations on subspace collections are found to correspond to…
Alexander Alldridge, Zain Shaikh
The superbosonisation identity of Littelmann–Sommers–Zirnbauer is a new tool for use in studying universality of random matrix ensembles via supersymmetry, which is applicable to non-Gaussian invariant distributions. We give a new conceptual interpretation of this formula, linking it to harmonic superanalysis of Lie…
Alí Guzmán Adán, Irene Sabadini, Frank Sommen
In this manuscript, we obtain a plane wave decomposition for the delta distribution in superspace, provided that the superdimension is not odd and negative. This decomposition allows for explicit inversion formulas for the super Radon transform in these cases. Moreover, we prove a more general Radon inversion formula…
Alí Guzmán Adán, F. Sommen
In this paper, we extend the distributional approach to integration over more general domains and surfaces in superspace. The notions of domain and surface in superspace are defined by smooth bosonic phase functions g. This allows to define domain integrals and oriented (as well as non-oriented) surface integrals in…
Alexander Alldridge, Zain Shaikh
Supersymmetry (SUSY) has its origins in Quantum Field Theory. It is usually associated with High Energy Physics, especially with SUGRA, where the fermionic fields correspond to physical quantities, the mathematical incarnation of a (as yet, hypothetical) fundamental phenomenon. However, beyond this fascinating and deep…
Fabrizio Colombo, Irene Sabadini, Daniele Carlo Struppa, Alain Yger
The phenomenon of superoscillations is of great interest in microscopy, antenna design, and material sciences. This phenomenon has been generalized and has given rise to the concept of supershift, which is a far reaching extension that applies to functions that may present discontinuous derivatives. From this…
Yakir Aharonov, Jussi Behrndt, Fabrizio Colombo, Peter Schlosser
Superoscillating functions and supershifts appear naturally in weak measurements in physics. Their evolution as initial conditions in the time-dependent Schrödinger equation is an important and challenging problem in quantum mechanics and mathematical analysis. The concept that encodes the persistence of…
Saad Ihsan Butt, Dawood Khan, Youngsoo Seol, Kavikumar Jacob
This study introduces for the first time a class of generalized superquadratic functions specifically on fractal sets and explores their unique features. The research develops several generalized inequalities, including Jensen’s, converse Jensen’s, Mercer Jensen’s and Hermite-Hadamard’s inequalities based on the…
Authors not listed
Curried functions provide a systematic way of transforming multi-argument functions into nested singleargument functions. This transformation allows partial application and supports many central principles of functional programming. Their extension, called curried 𝑘-ary functions, naturally generalizes the familiar…
David Thompson, Johan Gielis
Our understanding of quantum phenomena often begins with simple particle-in-a-box style problems, the solutions of which introduce the student to foundational quantum concepts such as degeneracy and quantization. Simple model geometries of confinement afford analytic solutions, which are readily derivable, easily…
Authors not listed
Hyperstructures and their hierarchical extensions [1]—SuperHyperStructures—provide a versatile formalism for modeling multi-layered and complex phenomena [2, 3]. A MicroStructure is a measurable mapping that assigns to each material point a single local state, representing attributes such as phase, crystal orientation…
Authors not listed
This paper investigates several chemical systems through the lens of hyperstructures and superhyperstructures. We first review Chemical HyperStructures and Chemical SuperHyperStructures defined by redox-driven hyperoperations on species sets with maximal electromotive force selection. Building on the general (m,n)-…
KI-AHM LEE, SE-CHAN LEE
We study the boundary continuity of solutions to fully nonlinear elliptic equations. We first define a capacity for operators in non-divergence form and derive several capacitary estimates. Secondly, we formulate the Wiener criterion, which characterizes a regular boundary point via potential theory. Our approach…
Arthur M. Lesk, Ramanan Subramanian, Lloyd Allison, David Abramson + 3 more
What is the architectural ‘basis set’ of the observed universe of protein structures? Using information-theoretic inference, we answer this question with a comprehensive dictionary of 1,493 substructural concepts. Each concept represents a topologically-conserved assembly of helices and strands that make contact. Any…
Roxana-Elena Avrămescu, Mihaela Violeta Ghica, Cristina Dinu-Pîrvu, Răzvan Prisada + 1 more
Since ancient times humans observed animal and plants features and tried to adapt them according to their own needs. Biomimetics represents the foundation of many inventions from various fields: From transportation devices (helicopter, airplane, submarine) and flying techniques, to sports’ wear industry (swimming…
Maria Littmann, Nicola Bordin, Michael Heinzinger, Christine Orengo + 1 more
Classifying proteins into functional families can improve our understanding of a protein’s function and can allow transferring annotations within the same family. Toward this end, functional families need to be “pure”, i.e., contain only proteins with identical function. Functional Families (FunFams) cluster proteins…
Authors not listed
The notion of a Classical Structure provides a broad mathematical framework, while a Hyperstructure emerges through the powerset construction, and an 𝑛-Superhyperstructure is obtained by iterating this process 𝑛 times [1]. Intuitively, the 𝑛-th powerset corresponds to 𝑛 successive applications of the powerset…
Pedro M. Pereira, Nils Gustafsson, Mark Marsh, Musa M. Mhlanga + 1 more
Localization based super-resolution microscopy relies on the detection of individual molecules cycling between fluorescent and non-fluorescent states. These transitions are commonly regulated by high-intensity illumination, imposing constrains to imaging hardware and producing sample photodamage. Here, we propose…
Authors not listed
The design of functional liquids like Deep Eutectic Solvents (DES) is hampered by an incomplete understanding of the link between molecular components and the physical properties of the resulting mixture. Traditional metrics like binding energy (ΔE)fail to explain why some strongly bound pairs form low-viscosity…
Authors not listed
The concept of aClassical Structure provides a broad mathematical framework, whereas a Hyperstructure arises via the powerset construction, and an 𝑛-Superhyperstructure is obtained by iterating this construction n times [1]. Intuitively, the n-th powerset corresponds to 𝑛 successive applications of the powerset…
Timothy H. Wong, Ismail M. Khater, Christian Hallgrimson, Y. Lydia Li + 2 more
Specificity of small molecules for their target molecule in the cell is critical to determine their effective use as biologics and therapeutics. Small molecule inhibitors of clathrin endocytosis, Pitstop 2, and the dynamin inhibitor Dynasore, have off-target effects and their specificity has been challenged. Here, we…
Hanieh Mazloom-Farsibaf, Farzin Farzam, Mohamadreza Fazel, Michael J. Wester + 2 more
Visualizing actin filaments in fixed cells is of great interest for a variety of topics in cell biology such as cell division, cell movement, and cell signaling. We investigated the possibility of replacing phalloidin, the standard reagent for super-resolution imaging of F-actin in fixed cells, with the actin binding…
Yongdeng Zhang, Lena K. Schroeder, Mark D. Lessard, Phylicia Kidd + 9 more
Combining the molecular specificity of fluorescent probes with three-dimensional (3D) imaging at nanoscale resolution is critical for investigating the spatial organization and interactions of cellular organelles and protein complexes. We present a super-resolution light microscope that enables simultaneous multicolor…