The Trans-Planckian Censorship Conjecture in Different Frameworks of Viable Inflation by Bruno Sanna, Lorenzo Sebastiani

“…We review the recently proposed <i>Trans-Planckian Censorship Conjecture</i> (TCC) that stems from the trans-Planckian problem of cosmological perturbations. …”
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On a conjecture of Chellali and Favaron regarding connected domination numbers by Phillip Mafuta

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A counterexample to a geometric Hales-Jewett type conjecture by Vytautas Gruslys

“…In this note we show that the conjecture is false for \(k, l \ge 3\).…”
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Tameness in least fixed-point logic and McColm's conjecture by Siddharth Bhaskar, Alex Kruckman

“…McColm's conjecture is known to be false in general. However, we show that McColm's conjecture is true for any family of finite structures whose limit theory is model-theoretically tame.…”
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Information Geometric Approach on Most Informative Boolean Function Conjecture by Albert No

“…We also show that the conjecture is true when the arithmetic and geometric mean coincide in a specific set of measures.…”
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On genus one mirror symmetry in higher dimensions and the BCOV conjectures by Dennis Eriksson, Gerard Freixas i Montplet, Christophe Mourougane

“…The mathematical physicists Bershadsky–Cecotti–Ooguri–Vafa (BCOV) proposed, in a seminal article from 1994, a conjecture extending genus zero mirror symmetry to higher genera. …”
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A Short Proof of the Maximum Conjecture in CR Dimension one by Masoud Sabzevari

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A conjectural variation approach to vertical integration in agricultural cooperatives by Yung-Chang WANG

“…Under the assumption that agricultural cooperative is a form of vertical integration, this paper, using conjectural variations, solves the profit-maximizing problem faced by the members in the multi-plant firm model in which they are vertically integrated with the agricultural cooperative. …”
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Shock Structures Using the OBurnett Equations in Combination with the Holian Conjecture by Ravi Sudam Jadhav, Amit Agrawal

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On a Conjecture for a Higher-Order Rational Difference Equation by Maoxin Liao, Xianhua Tang, Changjin Xu

“…Our main result generalizes several others in the recent literature and confirms a conjecture by Berenhaut et al., 2007.…”
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Eulerian Cycle Decomposition Conjecture for the line graph of complete graphs by R. Rajarajachozhan, R. Sampathkumar

“…This conjecture is verified for the line graph of the complete graph.…”
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ON THE INTEGRAL HODGE AND TATE CONJECTURES OVER A NUMBER FIELD by BURT TOTARO

“…Hassett and Tschinkel gave counterexamples to the integral Hodge conjecture among 3-folds over a number field. We work out their method in detail, showing that essentially all known counterexamples to the integral Hodge conjecture over the complex numbers can be made to work over a number field.…”
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Statistical approaches and the Bekenstein bound conjecture in Schwarzschild black holes by Everton M.C. Abreu, Jorge Ananias Neto

“…The Bekenstein-Hawking entropy of black holes satisfies the Bekenstein bound conjecture. In this paper we have shown that when we use important non-Gaussian entropies, like the ones of Barrow, Tsallis and Kaniadakis to describe the Schwarzschild black hole, then the Bekenstein bound conjecture seems to fail.…”
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On the Conjecture of Berry Regarding a Bernoulli Two-Armed Bandit by Jichen Zhang, Panyu Wu

“…We give an easily verifiable equivalent form of Berry’s conjecture and use it to prove that Berry’s conjecture holds when <i>R</i> and <i>L</i> are two-point distributions as well as when <i>R</i> and <i>L</i> are beta distributions and the number of trials <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>N</mi><mo>≤</mo><mfenced separators="" open="⌊" close="⌋"><mfrac><msub><mi>r</mi><mn>0</mn></msub><msubsup><mi>r</mi><mn>0</mn><mo>′</mo></msubsup></mfrac></mfenced><mo>+</mo><mn>1</mn></mrow></semantics></math></inline-formula>.…”
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Membranes in AdS4 orientifold vacua and their Weak Gravity Conjecture by Gonzalo F. Casas, Fernando Marchesano, David Prieto

“…They either contribute towards Q > T or Q < T depending on the 3-cycles separation, allowing to engineer 4d N $$ \mathcal{N} $$ = 0 vacua in tension with the Weak Gravity Conjecture for membranes.…”
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Cumulants of Jack symmetric functions and b-conjecture (extended abstract) by Maciej Dolega, Valentin Féray

“…We prove partially this conjecture, nowadays called b-conjecture, by showing that coefficients of ψ(x, y, z; t, 1 + β) are polynomials in β with rational coefficients. …”
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Two past forms inducing conjectural or non-intrusive questions by Kaneko Makoto

Subjects: “…conjectural or non-intrusive questions…”
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Solving Three Conjectures about Neutrosophic Quadruple Vector Spaces by Hasan Sankari, Mohammad Abobala

“…The aim of this paper is to answer Smarandache conjectures about neutrosophic quadruple vector spaces. …”
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The weak cosmic censorship conjecture in hairy Kerr black holes by Lai Zhao, Meirong Tang, Zhaoyi Xu

“…Abstract The weak cosmic censorship conjecture, since its proposal, has always been a controversial hypothesis, but its significance in astrophysics is undeniable. …”
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THE LOGARITHMICALLY AVERAGED CHOWLA AND ELLIOTT CONJECTURES FOR TWO-POINT CORRELATIONS by TERENCE TAO

“…Our arguments also extend to more general bounded multiplicative functions than the Liouville function $\unicode[STIX]{x1D706}$ , leading to a logarithmically averaged version of the Elliott conjecture in the two-point case. In a subsequent paper we will use this version of the Elliott conjecture to affirmatively settle the Erdős discrepancy problem.…”
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