Article
Mathematics, Applied
Xing Fu, Jie Xiao
Summary: By subtly combining the Plancherel theorem with various inequalities including Chebyshev's inequality, generalized Holder's and Hausdorff-Young's inequalities, a new nonlinear uncertainty principle is established on the Lorentz spaces.
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
(2023)
Article
Physics, Particles & Fields
Fabian Wagner
Summary: The minimal and maximal uncertainties of position measurements are considered to be important characteristics of low-energy quantum and classical gravity. This study shows that the Generalized Extended Uncertainty Principle can be described in terms of quantum dynamics on a general curved cotangent manifold, with the curvature tensors being related to the noncommutativity of coordinates and momenta. The covariance of the approach leads to interesting subclasses of noncommutative geometries and enables the derivation of anisotropically deformed uncertainty relations from general background geometries.
EUROPEAN PHYSICAL JOURNAL C
(2023)
Article
Computer Science, Information Systems
Xuncai Zhang, Jiali Di, Ying Niu
Summary: This paper presents a double-permutation image encryption scheme based on DNA coding technology, which effectively solves the problem of adjacent pixels being difficult to disarrange in an image. The scheme achieves fast and effective image encryption through steps such as bit-level and pixel-level permutation, DNA encoding, and diffusion of the encoded image. The resulting cipher images demonstrate strong resistance against various attacks.
MULTIMEDIA TOOLS AND APPLICATIONS
(2023)
Article
Computer Science, Artificial Intelligence
Jianbin Qin, Chuan Xiao, Yaoshu Wang, Wei Wang, Xuemin Lin, Yoshiharu Ishikawa, Guoren Wang
Summary: This paper proposes a new form of the pigeonhole principle to optimize query processing for Hamming distance search. By allowing variable partitioning and threshold allocation, the constraint of candidates is improved and cost-aware methods are designed. Our solution shows strong robustness in skewed data distributions and superior query processing performance compared to state-of-the-art methods.
IEEE TRANSACTIONS ON KNOWLEDGE AND DATA ENGINEERING
(2021)
Article
Mathematics, Applied
Martino Borello, Wolfgang Willems, Giovanni Zini
Summary: This paper investigates properties of ideals in group algebras of finite groups over fields. It highlights the connection between their dimension, minimal Hamming distance, and group order, which is a generalized version of an uncertainty principle shown by Meshulam in 1992. It also introduces the notion of the Schur product of ideals in group algebras and explores its module structure and dimension. The paper provides structural results and conditions for ideals that coincide with their Schur square, with particular implications for group algebras of p-groups over fields of characteristic p.
FORUM MATHEMATICUM
(2022)
Article
Astronomy & Astrophysics
Pasquale Bosso, Fabrizio Illuminati, Luciano Petruzziello, Fabian Wagner
Summary: In this paper, the consequences of maximal length and minimal momentum scales on nonlocal correlations in a bipartite quantum system are investigated. The authors rely on the extended uncertainty principle, which is associated with non-negligible spacetime curvature at cosmological scales, to study this. It is found that quantum correlations are degraded when the deformed quantum mechanical model mimics a positive cosmological constant, suggesting the possibility of recovering classicality at large distances.
Article
Mathematics
Tarun K. Garg, Waseem Z. Lone, Firdous A. Shah, Hatem Mejjaoli
Summary: This study introduces a novel shearlet transform by utilizing the free metaplectic convolution structures. In addition to studying the properties of the proposed transform, the Heisenberg and logarithmic-type uncertainty principles associated with the free metaplectic shearlet transform are also investigated.
JOURNAL OF MATHEMATICS
(2021)
Article
Quantum Science & Technology
Francesco Buscemi, Kodai Kobayashi, Shintaro Minagawa, Paolo Perinotti, Alessandro Tosini
Summary: While there is consensus on incompatible POVMs definition, there is ambiguity in defining compatibility at the level of instruments. To address this, q-compatibility is introduced, which unifies different notions of POVMs, channels, and instruments into a hierarchy of resource theories for communication between separated parties. The obtained resource theories are complete, containing families of free operations and monotones with necessary and sufficient conditions for transformation. The framework is operational, characterizing free transformations using local operations aided by causally-constrained directed classical communication, and all monotones have a game-theoretic interpretation making them experimentally measurable in principle. It precisely defines the information-theoretic resources for each notion of incompatibility.
Article
Mathematics, Applied
Kazuo Yamazaki
Summary: Recent significant developments in the study of singular partial differential equations have been influenced by techniques borrowed from quantum field theory in physics. This note discusses the necessity of Wick products, their applications through Feynman diagrams, and the utility of Gaussian hypercontractivity theorem, as well as an open problem that is mathematically challenging and physically meaningful. The author aims to make this note accessible to a wide audience by providing sufficient details and including all relevant results necessary for discussions.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2021)
Article
Mathematics
Mawardi Bahri, Samsul Ariffin Abdul Karim
Summary: This paper reviews the definition of the fractional Fourier transform and its relation to the conventional Fourier transform. The main properties of the fractional Fourier transform are easily obtained through this relation. The sharp Hausdorff-Young inequality for the fractional Fourier transform is investigated and the related Matolcsi-Szucs inequality is established. Other versions of inequalities concerning the fractional Fourier transform are also discussed in detail. The results obtained in this paper are very significant, especially in the field of fractional differential equations.
Article
Astronomy & Astrophysics
Michael Bishop, Peter Martin, Douglas Singleton
Summary: This paper discusses new methods to bridge the gap between the observed and calculated values for the cosmological constant using the generalized uncertainty principle (GUP) in quantum field theory and cosmology. The study suggests that if quantum gravity GUP models are the solution to this puzzle, a parity transformation of the gravitationally modified position operator at high energies may be necessary.
Article
Physics, Multidisciplinary
Andrii Hopanchuk
Summary: This paper explores the consequences of space discretization in quantum mechanics. The author shows that under normal conditions, where the wave function is uniform, Heisenberg's uncertainty principle is satisfied. The author derives an equation similar to the uncertainty principle, which imposes constraints on the precision of space. Furthermore, it is shown that in discretized space, simultaneous minimum position and momentum uncertainties are unphysical.
INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS
(2023)
Article
Mathematics, Applied
Navneet Kaur, Bivek Gupta, Amit K. Verma
Summary: In this paper, a new definition of continuous fractional wavelet transform (MFrWT) in RN is given and some of the basic properties are studied, including the inner product relation and the reconstruction formula. It is also shown that the range of the proposed transform is a reproducing kernel Hilbert space and the associated kernel is obtained. The uncertainty principles of the multidimensional fractional Fourier transform (MFrFT) are obtained, similar to Heisenberg's uncertainty principle, logarithmic uncertainty principle, and local uncertainty principle. Based on these uncertainty principles of MFrFT, the corresponding uncertainty principles, namely Heisenberg's, logarithmic, and local uncertainty principles, are obtained for the proposed MFrWT.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2023)
Article
Computer Science, Artificial Intelligence
Namratha Urs, Sahar Behpour, Angie Georgaras, Mark V. Albert
Summary: This study examines neural coding strategies in sensory processing, demonstrating the efficiency of ICA in modeling early visual and auditory neural processing. The results indicate that neural codes are better suited to natural inputs and outperform models based on common compression strategies.
ARTIFICIAL INTELLIGENCE REVIEW
(2022)
Article
Astronomy & Astrophysics
Markus B. Froeb, Albert Much, Kyriakos Papadopoulos
Summary: This paper discusses the connection between a fundamentally noncommutative spacetime and the conservative perturbative approach to quantum gravity. It raises two natural questions: can perturbative quantum gravity predict noncommutative geometrical effects? Is noncommutativity introduced manually or does it arise from quantum gravitational effects? The study shows that the first question has a positive answer, while the second question has a negative answer: perturbative quantum gravity predicts noncommutativity at the Planck scale, as long as the structure of observables in the quantum theory is clarified.
Article
Mathematics
Xi Chen
Summary: This article investigates the relationship between the half wave Schrodinger equation and the non-chiral cubic Szeg6 equation, and proves the existence of modified wave operators between them. Meanwhile, by combining with other research results, it deduces the characteristic of the global solutions for the half wave Schrodinger equation.
JOURNAL OF FUNCTIONAL ANALYSIS
(2024)
Article
Mathematics
Yi Han
Summary: This article constructs unique martingale solutions to the damped stochastic wave equation and shows their applicability to a wider class of SPDEs. It also demonstrates the validity of the Smoluchowski-Kramers approximation.
JOURNAL OF FUNCTIONAL ANALYSIS
(2024)
Article
Mathematics
Michael Didas, Jorg Eschmeier, Michael Hartz, Marcel Scherer
Summary: We investigate the Taylor spectra of quotient tuples of the d-shift on Drury-Arveson spaces with finite-dimensional coefficient spaces. We demonstrate that the Taylor spectrum can be characterized by the approximate zero set of the annihilator ideal and the pointwise behavior of the inner multiplier associated with the quotient tuple.
JOURNAL OF FUNCTIONAL ANALYSIS
(2024)
Article
Mathematics
Anupam Gumber, Nimit Rana, Joachim Toft, Ruya Uster
Summary: This article deduces continuity properties for pseudo-differential operators with symbols in Orlicz modulation spaces when acting on other Orlicz modulation spaces, extending well-known results in the literature. The article also shows the continuity properties of the entropy functional on a suitable Orlicz modulation space, even though it is discontinuous on M2 = L2.
JOURNAL OF FUNCTIONAL ANALYSIS
(2024)
Article
Mathematics
Xiaofang Lin, Alexandra Neamtu, Caibin Zeng
Summary: This article contributes to the understanding of stable manifolds for parabolic SPDEs driven by nonlinear multiplicative fractional noise. It proves the existence and smoothness of local stable manifolds through interpolation theory and the construction of a suitable function space.
JOURNAL OF FUNCTIONAL ANALYSIS
(2024)
Article
Mathematics
Ramlal Debnath, Deepak K. Pradhan, Jaydeb Sarkar
Summary: This paper investigates the classification of inner projections and their relationships with other problems. Two independent applications are presented as well.
JOURNAL OF FUNCTIONAL ANALYSIS
(2024)
Article
Mathematics
Valentina Ciccone, Felipe Goncalves
Summary: We establish a sharp adjoint Fourier restriction inequality for the end-point Tomas-Stein restriction theorem on the circle under a certain arithmetic constraint on the support set of the Fourier coefficients of the given function, which is a generalization of a B3-set.
JOURNAL OF FUNCTIONAL ANALYSIS
(2024)
Article
Mathematics
Qiaochu Ma
Summary: This paper studies the asymptotic expansion of analytic torsion forms associated with a certain series of flat bundles, proving the existence of the full expansion and providing a formula for the sub-leading term. In comparison to previous studies, we delve into the first order expansion and express the leading term as the integral of a locally computable differential form.
JOURNAL OF FUNCTIONAL ANALYSIS
(2024)
Article
Mathematics
Zoltan M. Balogh, Alexandru Kristaly, Francesca Tripaldi
Summary: The article investigates the sharp L-p-log-Sobolev inequality on noncompact metric measure spaces satisfying the CD(0, N) condition, and proves it using isoperimetric inequality, symmetrization, and scaling argument. It also establishes hypercontractivity estimate for the Hopf-Lax semigroup and obtains Gaussian-type L-2-log-Sobolev inequality and hypercontractivity estimate in RCD(0, N) spaces.
JOURNAL OF FUNCTIONAL ANALYSIS
(2024)
Article
Mathematics
Nora Doll
Summary: The orientation flow of paths of real skew-adjoint Fredholm operators with invertible endpoints was studied, as well as the properties of paths with odd-dimensional kernel. The flow is independent of the reference projection when applied to closed paths, and provides an isomorphism to Z2 for the fundamental group of the space of real skewadjoint Fredholm operators with odd-dimensional kernel.
JOURNAL OF FUNCTIONAL ANALYSIS
(2024)
Article
Mathematics
Matthieu Fradelizi, Mokshay Madiman, Mathieu Meyer, Artem Zvavitch
Summary: This paper explores some inequalities in convex geometry restricted to the class of zonoids. It shows the equivalence between a local Alexandrov-Fenchel inequality, a local Loomis-Whitney inequality, the log-submodularity of volume, and the Dembo-Cover-Thomas conjecture on the monotonicity of the ratio of volume to the surface area in the class of zonoids. Additionally, it confirms these conjectures in R3 and establishes an improved inequality in R2. The paper also provides a negative answer to a question of Adam Marcus regarding the roots of the Steiner polynomial of zonoids, and investigates analogous questions in the Lp-Brunn-Minkowski theory, confirming all of the above conjectures in the case p = 2, in any dimension.
JOURNAL OF FUNCTIONAL ANALYSIS
(2024)
Article
Mathematics
Sayan Bagchi, Rahul Garg
Summary: In this article, analogues of pseudo-differential operators associated to the joint functional calculus of the Grushin operator are defined using their spectral resolution, and Calderon-Vaillancourt-type theorems for these operators are studied.
JOURNAL OF FUNCTIONAL ANALYSIS
(2024)
Article
Mathematics
Elena Danesi
Summary: In this paper, we continue the analysis of the dispersive properties of the 2D and 3D massless Dirac-Coulomb equations that has been started in [7] and [8]. We prove a priori estimates of the mentioned systems' solutions, particularly Strichartz estimates with an additional angular regularity, using the tools developed in previous works. As an application, we demonstrate local well-posedness results for a Dirac-Coulomb equation perturbed with Hartree-type nonlinearities.
JOURNAL OF FUNCTIONAL ANALYSIS
(2024)
Article
Mathematics
Aswin Govindan Sheri, Jonathan Hickman, James Wright
Summary: This paper examines the Lp bounds of maximal functions associated with lacunary dilates of a fixed measure in the setting of homogeneous groups. It is found that classical arguments of Ricci-Stein can be used to prove these properties, recovering recent results on Koranyi spheres averages and horizontal spherical averages of a certain type introduced by Nevo-Thangavelu. In addition, the main theorem has a much broader application, which is explored through various explicit examples.
JOURNAL OF FUNCTIONAL ANALYSIS
(2024)
Article
Mathematics
Thomas Lamby, Samuel Nicolay
Summary: By replacing the given exponent with Boyd functions, we generalize the notion of interpolation space and present some results in this general setting.
JOURNAL OF FUNCTIONAL ANALYSIS
(2024)