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Traces of certain integral operators related to the Riemann hypothesis.
Publication Type: Academic Journal
Source(s): AIMS Mathematics (2473-6988). 2023, Vol. 8 Issue 10, p24971-24983. 13p.
Abstract: ≤We prove the existence of a nontrivial singular trace τ defined on an ideal J closed with respect to the logarithmic submajorization such that τ(Aρ(α))=0, where Aρ(α) : L²(0, 1) → L²(0, 1) [Aρ(α)ƒ](θ) = ∫¹0 ρ(αθ/x)ƒ(x)dx, 0 < α 1. We also show that τ(...
Representations by Beurling Systems.
Publication Type: Academic Journal
Source(s): Mathematics (2227-7390). Sep2023, Vol. 11 Issue 17, p3663. 17p.
Abstract: We prove that a Beurling system with F ∈ H p (D) , 1 ≤ p < ∞ is an M —basis in H p (D) with an explicit dual system. Any function f ∈ H p (D) , 1 ≤ p < ∞ can be expanded as a series by the system { z m F (z) } m = 0 ∞. For different summation methods, ...
Sensing Travel Source–Sink Spatiotemporal Ranges Using Dockless Bicycle Trajectory via Density-Based Adaptive Clustering.
Publication Type: Academic Journal
Source(s): Remote Sensing. Aug2023, Vol. 15 Issue 15, p3874. 22p.
Abstract: The travel source–sink phenomenon is a typical urban traffic anomaly that reflects the imbalanced dissipation and aggregation of human mobility activities. It is useful for pertinently balancing urban facilities and optimizing urban structures to accur...
A Pair of Derivations on Prime Rings with Antiautomorphism.
Publication Type: Academic Journal
Source(s): Mathematics (2227-7390). Aug2023, Vol. 11 Issue 15, p3337. 15p.
Abstract: This article examines the commutativity of rings with antiautomorphisms, specifically when they are equipped with derivations that satisfy certain algebraic identities. Moreover, we present examples to demonstrate the necessity of the various restricti...
Impact of cooling on shaping ability of thermally treated files in canal models with double curvature.
Publication Type: Academic Journal
Source(s): PeerJ. Aug2023, p1-13. 13p.
Abstract: Background. This study compared the ability of thermally treated files in shaping simulated canals with double curvature. Fifty-six canals were enlarged to a final size of 25 with ProTaper Next (PTN) or ZenFlex (ZF). Materials. Half of the samples were...
The Preference of Inter-Organizational Trust on Corporate Benefit-Seeking Behaviors: A Mechanisms-Based and Policy-Capturing Analysis.
Publication Type: Academic Journal
Source(s): Sustainability (2071-1050). Aug2023, Vol. 15 Issue 15, p11630. 23p.
Abstract: In the realm of organizational cooperation, the choice of benefit behaviors has a profound impact on the sustainability of the collaboration. The influence of trust relationships on firms' decisions regarding private versus common benefit behaviors has...
Testing Hypotheses for Geological Controls on Hydraulic-Fracturing-Induced Seismicity in the Montney Formation, Canada.
Publication Type: Academic Journal
Source(s): Energies (19961073). Jul2023, Vol. 16 Issue 14, p5322. 19p.
Abstract: Hydraulic fracturing (HF) can trigger induced seismicity, but documented occurrences tend to be localized compared with the regional extent of industry operations. Factors that determine intrinsic geological susceptibility of a given region to induced ...
In Memoriam: Dr Joel Weinstock-A Pioneer of the Hygiene Hypothesis.
Publication Type: Editorial & Opinion
Source(s): Gastroenterology [Gastroenterology] 2022 Oct; Vol. 163 (4), pp. 785-786. Date of Electronic Publication: 2022 Jul 19.
Development of a New Zeta Formula and Its Role in Riemann Hypothesis and Quantum Physics.
Publication Type: Academic Journal
Source(s): Mathematics (2227-7390). Jul2023, Vol. 11 Issue 13, p3025. 20p.
Abstract: In this study, we investigated a new zeta formula in which the zeta function can be expressed as the sum of an infinite series of delta and cosine functions. Our findings demonstrate that this formula possesses duality characteristics and we establishe...
Assessing Multinomial Distributions with a Bayesian Approach.
Publication Type: Academic Journal
Source(s): Mathematics (2227-7390). Jul2023, Vol. 11 Issue 13, p3007. 16p.
Abstract: This paper introduces a unified Bayesian approach for testing various hypotheses related to multinomial distributions. The method calculates the Kullback–Leibler divergence between two specified multinomial distributions, followed by comparing the chan...