Structural Theory and Classification of 2D Adinkras by Kevin Iga, Yan X. Zhang

“…In this paper, we classify all 2D Adinkras, confirming a conjecture of T. Hübsch. Along the way, we obtain other structural results, including a simple characterization of Hübsch’s even-split doubly even codes.…”
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Relaxation Oscillations and Dynamical Properties in Two Time-Delay Slow-Fast Modified Leslie-Gower Models by Yufeng Wang, Youhua Qian, Bingwen Lin

“…For the second system, we put forward a conjecture that the relaxation oscillation of the system is unique. …”
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Optimal $L^2$ Extensions of Openness Type and Related Topics by Xu, Wang, Zhou, Xiangyu

“…We describe a different approach to the Suita conjecture and its generalizations, which is based on a log-concavity for certain minimal $L^2$ integrals.…”
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An inductive approach to generalized abundance using nef reduction by Chaudhuri, Priyankur

“…We use the canonical bundle formula for parabolic fibrations to give an inductive approach to the generalized abundance conjecture using nef reduction. In particular, we observe that generalized abundance holds for a klt pair $(X,B)$ if the nef dimension $n(K_X+B+L)=2$ and $K_X+B \ge 0$ or $n(K_X+B+L)=3$ and $\kappa (K_X+B)>0$.…”
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On Generalization Based on Bi et al. Iterative Methods with Eighth-Order Convergence for Solving Nonlinear Equations by Taher Lotfi, Alicia Cordero, Juan R. Torregrosa, Morteza Amir Abadi, Maryam Mohammadi Zadeh

“…Consequently, it satisfies Kung and Traub’s conjecture relevant to construction optimal methods without memory. …”
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Computational proofs of congruences for 2-colored Frobenius partitions by Dennis Eichhorn, James A. Sellers

“…In 1994, the following infinite family of congruences was conjectured for the partition function cΦ2(n) which counts the number of 2-colored Frobenius partitions of n: for all n≥0 and α≥1, cΦ2(5αn+λα)≡0(mod5α), where λα is the least positive reciprocal of 12 modulo 5α. …”
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On the Nonexistence of Order Isomorphisms between the Sets of All Self-Adjoint and All Positive Definite Operators by Lajos Molnár

“…We prove that there is no bijective map between the set of all positive definite operators and the set of all self-adjoint operators on a Hilbert space with dimension greater than 1 which preserves the usual order (the one coming from the concept of positive semidefiniteness) in both directions. We conjecture that a similar assertion is true for general noncommutative C*-algebras and present a proof in the finite dimensional case.…”
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On the Singular Spectrum for Adiabatic Quasiperiodic Schrödinger Operators by Magali Marx, Hatem Najar

“…In the energy intervals where this happens, we obtain an asymptotic formula for the Lyapunov exponent and show that the spectrum is purely singular. This result was conjectured and proved in a particular case by Fedotov and Klopp (2005).…”
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On Erdős sums of almost primes by Gorodetsky, Ofir, Lichtman, Jared Duker, Wong, Mo Dick

“…According to a 2013 conjecture of Banks and Martin, the sums $f_k$ are predicted to decrease monotonically in $k$. …”
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A Note on Edge-Group Choosability of Planar Graphs without 5-Cycles by Amir Khamseh

“…In this paper, we study an edge-group choosability version of Vizing conjecture for planar graphs without 5-cycles and for planar graphs without noninduced 5-cycles (2010 Mathematics Subject Classification: 05C15, 05C20).…”
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Density of systoles of hyperbolic manifolds by Douba, Sami, Huang, Junzhi

“…In particular, the Salem conjecture holds if and only if the systoles of closed arithmetic hyperbolic manifolds in some (any) dimension fail to be dense in $(0, +\infty )$.…”
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A note on the exact formulas for certain $2$-color partitions by Guadalupe, Russelle

“…Our results partially extend the work of Mauth, who proved the asymptotic formula for $\log a_2(n)$ conjectured by Banerjee et al.…”
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A survey on the positive mass theorem for asymptotically flat initial data sets by Huang, Lan-Hsuan

“…Originating from a conjecture in general relativity regarding the ADM mass, the positive mass theorem has significantly influenced geometry and analysis over the past four decades and continued to inspire new connections. …”
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Cybernetics, semiotics and meaning in the cinema by Keyan Tomaselli

“…The paper ends with some conjecture on how the cyber- semiotic theory developed can be combined with Lacanian psychoanalysis and Marxist approaches developed by the scholars contributing to the British journal Screen. …”
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Economic Growth, Markets and the Rule of Law: Brief Considerations on the Brazilian Case by Alexandre B. Cunha

“…Therefore, it is reasonable to expect a positive relationship to exist between income per capita and adhesion to the rule of law. This conjecture is corroborated here in a sample of 110 countries in 2016. …”
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An interesting family of curves of genus 1 by Andrew Bremner

“…In the former case, all integral solutions are determined; in the latter case, computation in the range 1≤t≤999 shows large ranks are common, giving a particularly simple example of curves which (admittedly over a small range) apparently contradict the once held belief that the rank under specialization will tend to have minimal rank consistent with the parity predicted by the Selmer conjecture.…”
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The vanishing of anticyclotomic $\mu $-invariants for non-ordinary modular forms by Hatley, Jeffrey, Lei, Antonio

“…We study signed Selmer groups for non-ordinary modular forms over the anticyclotomic $\mathbb{Z}_p$-extension of $K$, showing that one inclusion of an Iwasawa main conjecture involving the $p$-adic $L$-function of Bertolini–Darmon–Prasanna implies that their $\mu $-invariants vanish. …”
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On permutation polynomials over finite fields by R. A. Mollin, C. Small

“…We also give some results bearing on a conjecture of Carlitz which says essentially that for any even integer m, the cardinality of finite fields admitting permutation polynomials of degree m is bounded.…”
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Analysis of the Fault Attack ECDLP over Prime Field by Mingqiang Wang, Tao Zhan

“…The runtime bound relies on heuristics conjecture about smooth numbers similar to the ones used by Lenstra, 1987.…”
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Left Baire-1 Compositors and Continuous Functions by Jonald P. Fenecios, Emmanuel A. Cabral

“…This answers a characterization problem posed in the work by Zhao (2007, page 550) and settles in the affirmative the conjecture in the work by Fenecios and Cabral (2012, page 43). …”
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