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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A Note on Normal Families of Meromorphic Functions Concerning Shared Values by Yuan Wenjun, Wei Jinjin, Lin Jianming

“…We study the normality of families of meromorphic functions related to a Hayman conjecture. We consider whether a family of meromorphic functions ℱ is normal in D if, for every pair of functions f and g in ℱ, f′−afn and g′−agn share the value b for n=1,2, and 3, where a and b≠0 are two finite complex numbers. …”
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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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A Family of Derivative-Free Methods with High Order of Convergence and Its Application to Nonsmooth Equations by Alicia Cordero, José L. Hueso, Eulalia Martínez, Juan R. Torregrosa

“…Also, numerical examples are used to show the performance of the presented methods, on smooth and nonsmooth equations, and to compare with other derivative-free methods, including some optimal fourth-order ones, in the sense of Kung-Traub’s conjecture.…”
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Holographic Description of Noncommutative Schwinger Effect by Udit Narayan Chowdhury

“…Using Maldacena’s holographic conjecture, the threshold electric field for pair production is computed from the quark/antiquark potential for noncommutative theories. …”
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Some results on value distribution concerning Hayman's alternative by Zhuang Xinyu, Zheng Ruilin, He Zhiying, Fang Mingliang

“…We extend and improve some results due to Zhu [A far-reaching form of Hayman’s inequality; fixed points of meromorphic functions and their derivatives, Kexue Tongbao (Chinese) 31 (1986), no. 11, 801–804], Hua and Chuang [On a conjecture of Hayman, Acta Math. Sinica (N.S.) 7 (1991), no. 2, 119–126], and Charak and Singh [A value distribution result related to Hayman’s alternative, Commun. …”
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On the acyclic point-connectivity of the n-cube by John Banks, John Mitchem

“…We show that the upper bound is obtained for n≤8 and conjecture that it is obtained for all n.…”
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A reaction-diffusion system modeling the spread of resistance to an antimalarial drug by Nicolas Bacaër, Cheikh Sokhna

“…Based on a linearization study and on numerical simulations,an expression for the speed at which resistancespreads is conjectured. It dependson the ratio of the two basic reproduction numbers,on a coefficient representing the diffusion of mosquitoes,on the death rate of mosquitoes infected by resistant parasites,and on the recovery rate of nonimmune humans infected by resistant parasites.…”
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Qu’est-ce qu’un « mauvais » théâtre de science-fiction (avant 1920) ? by Florence Fix

“…Nevertheless, “bad” theatre is a way to explore science fiction before science fiction theory : is conjectural science in dramas by Becque, Feydeau or Curel to be seen as a genre, a pattern or a tonality ?…”
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