L-correspondences: the inclusion Lp(μ,X)⊂Lq(ν,Y) by C. Bryan Dawson

“…After proving some basic theorems, we give characterizations of some types of L-correspondences and offer a conjecture that is similar to an equimeasurability theorem.…”
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Difference Equations and Sharing Values Concerning Entire Functions and Their Difference by Zhiqiang Mao, Huifang Liu

“…As its applications, we investigate the difference analogue of the Brück conjecture. We obtain some results on entire functions sharing a finite value with their difference operators. …”
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The incidence chromatic number of some graph by Liu Xikui, Li Yan

“…The concept of the incidence chromatic number of a graph was introduced by Brualdi and Massey (1993). They conjectured that every graph G can be incidence colored with Δ(G)+2 colors. …”
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On the Diophantine equation x2+2k=yn by S. Akhtar Arif, Fadwa S. Abu Muriefah

“…By factorizing the equation x2+2k=yn, n≥3, k-even, in the field Q(i), various theorems regarding the solutions of this equation in rational integers are proved. A conjecture regarding the solutions of this equation has been put forward and proved to be true for a large class of values of k and n.…”
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On the function TreH+itK by Mark Fannes, Dénes Petz

“…This shows that the Bessis-Moussa-Vilani conjecture holds for large random matrices in an asymptotic sense.…”
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On the recursive sequence xn+1=−1/xn+A/xn−1 by Stevo Stević

“…We give sufficient conditions under which every positive solution of this equation converges to a period two solution. This confirms a conjecture in the work of DeVault et al. (2000).…”
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Zero-One Law for Connectivity in Superposition of Random Key Graphs on Random Geometric Graphs by Y. Tang, Q. L. Li

“…For this class of random graphs, we establish a new version of a conjectured zero-one law for graph connectivity as the number of nodes becomes unboundedly large. …”
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On Some Symmetric Systems of Difference Equations by Josef Diblík, Bratislav Iričanin, Stevo Stević, Zdeněk Šmarda

“…Here we show that the main results in the papers by Yalcinkaya (2008), Yalcinkaya and Cinar (2010), and Yalcinkaya, Cinar, and Simsek (2008), as well as a conjecture from the last mentioned paper, follow from a slight modification of a result by G. …”
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The nonlinear cysteine redox dynamics in the i-space: A proteoform-centric theory of redox regulation by James N. Cobley, Panagiotis N. Chatzinikolaou, Cameron A. Schmidt

“…Monte Carlo simulations of the human protein PTP1B reveal extensive i-space sampling beyond site-centric models, supporting the “oxiform conjecture”. This conjecture posits that highly oxidised proteoforms, molecules bearing multiple oxidised cysteines, are central to redox regulation. …”
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Congruences involving F-partition functions by James Sellers

“…The primary goal of this note is to prove the congruence ϕ3(3n+2)≡0(mod3), where ϕ3(n) denotes the number of F-partitions of n with at most 3 repetitions. Secondarily, we conjecture a new family of congruences involving cϕ2(n), the number of F-partitions of n with 2 colors.…”
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Fourth Hankel Determinant for a Subclass of Starlike Functions Based on Modified Sigmoid by Wali Khan Mashwani, Bakhtiar Ahmad, Nazar Khan, Muhammad Ghaffar Khan, Sama Arjika, Bilal Khan, Ronnason Chinram

“…Further, we investigate the fourth-order Hankel determinant, Zalcman conjecture, and also evaluate the fourth-order Hankel determinants for 2-fold, 3-fold, and 4-fold symmetric starlike functions.…”
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Network Firewall Dynamics and the Subsaturation Stabilization of HIV by Bilal Khan, Kirk Dombrowski, Mohamed Saad, Katherine McLean, Samuel Friedman

“…In 2001, Friedman et al. conjectured the existence of a “firewall effect” in which individuals who are infected with HIV, but remain in a state of low infectiousness, serve to prevent the virus from spreading. …”
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Finite Groups of Order p2qr in which the Number of Elements of Maximal Order Is p3q∗ by Qingliang Zhang, Liang Xu

“…This topic involves Thompson’s conjecture. In this paper, we classify the finite groups of order p2qr in which the number of elements of maximal order is p3q, where p<q<r are different primes.…”
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Finite Groups with the Same Order and the Same Number of Elements of Maximal Order as the Projective Special Linear Group L2q by Qingliang Zhang

“…This subject is related to Thompson’s conjecture. In the present paper, we give a complete classification of the groups with the same order and the same number of elements of maximal order as L2q, where q=7,17.…”
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Twisted holography by Kevin Costello, Davide Gaiotto

“…The duality relates the B-model on certain Calabi-Yau three-folds to two-dimensional chiral algebras defined as gauged βγ systems. The duality conjecturally captures a topological sector of more familiar AdS5/CFT4 holographic dualities.…”
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Local newforms for generic representations of unramified even unitary groups I: Even conductor case by Hiraku Atobe

“…To do this, we use the local Gan–Gross–Prasad conjecture, the local Rankin–Selberg integrals and the local theta correspondence.…”
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On Constructing Two-Point Optimal Fourth-Order Multiple-Root Finders with a Generic Error Corrector and Illustrating Their Dynamics by Young Ik Kim, Young Hee Geum

“…The relevant optimal order satisfies Kung-Traub conjecture made in 1974. Numerical experiments performed for various test equations demonstrate convergence behavior agreeing with theory and the basins of attractions for several examples are presented.…”
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On the difference of values of the kernel function at consecutive integers by Jean-Marie De Koninck, Florian Luca

“…Given a fixed integer k≠±1, we establish that if the ABC-conjecture holds, then the equation γ(n+1)−γ(n)=k has only finitely many solutions. …”
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Properties of the function f(x)=x/π(x) by Panayiotis Vlamos

“…We study the expression 2f(x+y)−f(x)−f(y) for integers x,y≥2 and as an application we make several remarks in connection with the conjecture of Hardy and Littlewood.…”
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Large N limit of the Yang–Mills measure on compact surfaces II: Makeenko–Migdal equations and the planar master field by Antoine Dahlqvist, Thibaut Lemoine

“…We prove that this conjecture holds true whenever it does for the restricted class of loops of the main theorem. …”
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