Unified Analysis of Viscoelasticity and Viscoplasticity Using the Onsager Variational Principle by Kwang Soo Cho

“…This paper shows that this conjecture is correct by using the Onsager variational principle.…”
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Uniform Lipschitz-connectedness and metric convexity by Paranjothi Pillay, Dharmanand Baboolal

“…We provide some examples to corroborate our conjecture.…”
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On a question of permutation groups acting on the power set by Li Jinbao, Yang Yong, You Mengxi

“…In this work, we settle a conjecture about the number of set-orbits of permutation group acting on the power set.…”
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Co-convexial reflector curves with applications by Abdallah M. Al-Rashed, Neyamat Zaheer

“…Though, in the said paper, certain convex compact sets (e.g. closed discs, closed line segments and the ones with polygonal boundaries) were shown to be of reflecting type, it was only conjectured that all convex compact sets are likewise. …”
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Note on Quasi-Numerically Positive Log Canonical Divisors by Shigetaka Fukuda

“…We propose a subconjecture that implies the semiampleness conjecture for quasi-numerically positive log canonical divisors and prove the ampleness in some elementary cases.…”
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The Pinchuk example revisited by Fernandes, Filipe, Jelonek, Zbigniew

“…In this note we provide two special counterexamples to the strong real Jacobian Conjecture; the first one is surjective, the second one has non-dense image.…”
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New proof and generalization of some results on translated sums over k-almost primes by Laib, Ilias

“…In 2019, Laib et al. proved that the analogous conjecture of Erdős $f(\mathcal{A},h)\le f(\mathbb{N}_{1},h)$ is false for $h\ge 81$ on a sequence of semiprimes. …”
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Unicity of Entire Functions concerning Shifts and Difference Operators by Dan Liu, Degui Yang, Mingliang Fang

“…The corollary of the theorem confirms the conjecture posed by Li and Gao (2011).…”
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On Satnoianu-Wu’s Inequality by Bo-Yan Xi

“…By applying techniques in the theory of convex functions and Schur-geometrically convex functions, the author investigates a conjecture of Satnoianu on an algebraic inequality and generalizes some known results in recent years.…”
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Almost convex metrics and Peano compactifications by R. F. Dickman

“…In an earlier paper, the author conjectured that if a space (X,d) has a Peano compactification, then it must be S-metrizable. …”
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Towards tree Yang-Mills and Yang-Mills-scalar amplitudes with higher-derivative interactions by Kang Zhou, Chang Hu

“…All results are represented as universal expansions to appropriate basis. We also conjecture a compact general formula for tree YM amplitudes with higher mass dimension, which allows us to generate them from ordinary YM amplitudes, and discuss the consistent factorizations of the conjectured formula.…”
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The Diophantine equation x2+2k=yn, II by J. H. E. Cohn

“…These support a previous conjecture, without providing a complete proof.…”
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Splaying a search tree in preorder takes linear time by R. Chaudhuri, H. Höft

“…This is a special case of the splay tree traversal conjecture of Sleator and Tarjan.…”
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A class of gap series with small growth in the unit disc by L. R. Sons, Zhuan Ye

“…In this paper, investigations concerning this conjecture are discussed. For example, we prove that limsupr→1−(logL(r)/logM(r))=1 and limsupr→1−(L(r)/M(r))=0 when ak=kα(1+β).…”
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An Improvement of the Lower Bound on the Maximum Number of Halving Lines for Sets in the Plane with an Odd Number of Points by Javier Rodrigo, Mariló López, Danilo Magistrali, Estrella Alonso

“…With respect to this problem, it is conjectured that, for all <i>n</i> multiples of 3, there are 3-symmetric sets of <i>n</i> points for which the rectilinear crossing number is attained.…”
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Energy Conservation for 3D Tropical Climate Model in Periodic Domains by Hui Zhang

“…Our results are similar to Onsager’s conjecture which is on energy conservation for weak solutions of Euler equations.…”
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On Almost Orthogonal Frames by Virender, A. Zothansanga, S. K. Kaushik

“…It has been proved that a bounded almost orthogonal frame satisfies Feichtinger conjecture. Also, we prove that a bounded almost orthogonal frame contains a Riesz basis.…”
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Rigidity of symmetric simplicial complexes and the lower bound theorem by James Cruickshank, Bill Jackson, Shin-ichi Tanigawa

“…Our result implies that Stanley’s lower bound theorem for centrally symmetric polytopes extends to pseudomanifolds with a free simplicial automorphism of order 2, thus verifying (the inequality part of) another conjecture of Klee, Nevo, Novik and Zheng. Both results actually apply to a much larger class of simplicial complexes – namely, the circuits of the simplicial matroid. …”
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The Rank-One property for free Frobenius extensions by Bellamy, Gwyn, Thiel, Ulrich

“…A conjecture by the second author, proven by Bonnafé–Rouquier, says that the multiplicity matrix for baby Verma modules over the restricted rational Cherednik algebra has rank one over $\mathbb{Q}$ when restricted to each block of the algebra.In this paper, we show that if $H$ is a prime algebra that is a free Frobenius extension over a regular central subalgebra $R$, and the centre of $H$ is normal Gorenstein, then each central quotient $A$ of $H$ by a maximal ideal $\mathfrak{m}$ of $R$ satisfies the rank-one property with respect to the Cartan matrix of $A$. …”
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Global Attractivity of a Family of Max-Type Difference Equations by Xiaofan Yang, Wanping Liu, Jiming Liu

“…Through some numerical results of other cases, we finally pose a generic conjecture.…”
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