On Bousfield’s conjectures for the unstable Adams spectral sequence for $SO$ and $U$ by Nguyễn, Thế Cường

“…Bousfield and Davis created algebraic spectral sequences and conjectured that they agreed with the unstable Adams spectral sequences for $SO $ and $U $. …”
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C-Reactive Protein (CRP) and Autoimmune Disease: Facts and Conjectures by Alexander J. Szalai

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Short-hair black holes and the strong cosmic censorship conjecture by Zhiqin Tu, Meirong Tang, Zhaoyi Xu

“…To address this issue, Penrose proposed the cosmic censorship conjecture, with the Strong Cosmic Censorship Conjecture (SCCC) being particularly crucial. …”
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The difference vectors for convex sets and a resolution of the geometry conjecture by Alwadani, Salihah, Bauschke, Heinz H., Revalski, Julian P., Wang, Xianfu

“…The geometry conjecture, which was posed nearly a quarter of a century ago, states that the fixed point set of the composition of projectors onto nonempty closed convex sets in Hilbert space is actually equal to the intersection of certain translations of the underlying sets.In this paper, we provide a complete resolution of the geometry conjecture. …”
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How many numbers satisfy the 3x+1 conjecture? by I. Krasikov

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A Mean Value Related to Primitive Roots and Golomb’s Conjectures by Weiqiong Wang, Wenpeng Zhang

“…The main purpose of this paper is using the properties of Gauss sums and the estimate for character sums to study a mean value problem related to the primitive roots mod p and the different forms of Golomb’s conjectures and propose an interesting asymptotic formula for it.…”
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The Baum-Connes conjecture, noncommutative Poincaré duality, and the boundary of the free group by Heath Emerson

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Proof of Some Conjectures of Melham Using Ramanujan’s  1ψ1 Formula by Bipul Kumar Sarmah

“…We employ Ramanujan's  1ψ1 formula to prove three conjectures of R. S. Melham on representation of an integer n as sums of polygonal numbers.…”
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Nanodeserts: A Conjecture in Nanotechnology to Enhance Quasi-Photosynthetic CO2 Absorption by Wenfeng Wang, Xi Chen, Yifan Zhang, Jianjun Yu, Tianyi Ma, Zhihan Lv, Jing Zhang, Fanyu Zeng, Hui Zou

“…This paper advances “nanodeserts” as a conjecture on the possibility of developing the hierarchical structured polymeric nanomaterials for enhancing abiotic CO2 fixation in the soil-groundwater system beneath deserts (termed as quasi-photosynthetic CO2 absorption). …”
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Bound Associated with Certain Hankel Determinants and Zalcman Conjecture for Multivalent Functions of Bounded Turning by Deekonda Vamshee Krishna, Nallamothu Vani, Biswajit Rath, Karri Sanjay Kumar

“…In this paper, we investigate for a sharp upper bound to certain generalized second Hankel determinant, the Zalcman conjecture and an upper bound for the third, fourth Hankel determinants for the class of multivalent analytic bounded turning functions. …”
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Counterexamples to F. Morel’s conjecture on $\protect \pi _0^{\protect \mathbb{A}^1}$ by Ayoub, Joseph

“…We exhibit counterexamples to F. Morel’s conjecture on the $\mathbb{A}^1$-invariance of the sheaves of connected components of $\mathbb{A}^1$-local spaces.…”
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Warm non-minimally coupled Peccei–Quinn inflation and de Sitter Swampland conjecture by Jureeporn Yuennan, Phongpichit Channuie, Davood Momeni

“…In this study, we explore the dynamics of warm inflation within a non-minimally coupled Peccei–Quinn (PQ) framework and evaluate its compatibility with the de Sitter Swampland Conjecture. Our model incorporates a PQ scalar field that is non-minimally coupled to gravity, facilitating inflation through a dissipative process that sustains a thermal bath, thereby distinguishing it from conventional cold inflation. …”
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Impact of Strontium and Krypton Release from Ghana’s MNSR following a Conjectural Accident Scenario by S. A. Birikorang, R. G. Abrefah, H. K. Obeng, K. Gyamfi

“…The objective was to estimate specifically the approximate total effective dose equivalent (TEDE) of Sr-90 and Kr-85 by considering a conjectural accident scenario using a well-recognized and user-friendly known atmospheric dispersion model before the preparatory period. …”
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Self-Inhibiting Modules Can Self-Organize as a Brain of a Robot: A Conjecture by J. Negrete-Martínez

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Graph Theory Algorithms of Hamiltonian Cycle from Quasi-Spanning Tree and Domination Based on Vizing Conjecture by T. Anuradha, T. Lakshmi Surekha, Praveena Nuthakki, Bullarao Domathoti, Ganesh Ghorai, Faria Ahmed Shami

“…Proceeding this work, the Vizing’s conjecture states that for each pair of graphs S,L.…”
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$$\varLambda $$ Λ CDM model against gravity-thermodynamics conjecture: observational constraints after DESI 2024 by N. Shahhoseini, M. Malekjani, A. Khodam-Mohammadi

“…Abstract In the context of the gravity-thermodynamics conjecture based on the Tsallis entropy-area relation, we investigate the standard $$\varLambda $$ Λ CDM cosmology and examine some potential deviations from it. …”
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Weak gravity conjecture validation with photon spheres of quantum corrected Reissner–Nordstrom–AdS black holes in Kiselev spacetime by Mohammad Reza Alipour, Mohammad Ali S. Afshar, Saeed Noori Gashti, Jafar Sadeghi

“…Abstract In this study, we investigate the Weak Gravity Conjecture (WGC) in the context of quantum-corrected Reissner–Nordstrom–AdS (RN-AdS) black holes within Kiselev spacetime. …”
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Contribution of M. Maknys to number theory by Antanas Laurinčikas

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When the Future Becomes no Longer a Threat but, More, an Opportunity by Terry Trickett

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On the calculation of integer sequences, associated with twin primes by Igoris Belovas, Martynas Sabaliauskas, Paulius Mykolaitis

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