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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Transcendentality of ABJM two-point functions by Marco S. Bianchi

“…The result exhibits uniform transcendentality empirically, which we conjecture to hold at all orders. We leverage this property to streamline the reconstruction of the dimensional regularization expansion of master integrals in terms of bases of Euler sums of uniform transcendental weight.…”
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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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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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Primitive polynomials and word oriented linear feedback shift registers by ZENG Guang, YANG Yang, HAN Wen-bao, FAN Shu-qin

“…Through a large number of experiments, an explicit formula was proposed for the number of primitive σ-LFSRs over finite field, which generalized a known formula for the number of primitive LFSRs over finite field, and also was the extension of the number of primitive polynomial.Utilizing the given methods to distinguish the primitive σ-LFSR, the conjecture in three special cases was proved and a preliminary analysis for the general case was given.…”
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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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