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In a recent letter, new representations were proposed for the pair of sequences ($\gamma,\delta$), as defined formally by Bailey in his famous lemma. Here we extend and prove this result, providing pairs ($\gamma,\delta$) labelled by the…

We provide a formula for the $n^{th}$ term of the $k$-generalized Fibonacci-like number sequence using the $k$-generalized Fibonacci number or $k$-nacci number, and by utilizing the newly derived formula, we show that the limit of the ratio…

A sequence $S$ is potentially $K_{m}-H$-graphical if it has a realization containing a $K_{m}-H$ as a subgraph. Let $\sigma(K_{m}-H, n)$ denote the smallest degree sum such that every $n$-term graphical sequence $S$ with $\sigma(S)\geq…

The available experimental data on shell evolution indicate that the strength of the spin-orbit (SO) single-particle potential may be enhanced in neutron-rich nuclei. We observe that such a simple scheme destroys the Harmonic Oscillator…

We investigate the ascending Loewy socle series of Leavitt path algebras $L_K(E)$ for an arbitrary graph $E$ and field $K$. We classify those graphs $E$ for which $L_K(E)=S_{\lambda}$ for some element $S_{\lambda}$ of the Loewy socle…

The spectral gap of a Markov chain can be bounded by the spectral gaps of constituent "restriction" chains and a "projection" chain, and the strength of such a bound is the content of various decomposition theorems. In this paper, we…

We consider a generalized Takagi function for beta-expansions with the base $1<\beta\leq2$, motivated by multifractal analysis for digit frequency sets of beta-expansions [20]. We show that it is pointwise $\alpha$-H\"older continuous for…

A well-known conjecture of Vizing is that $\gamma(G \square H) \ge \gamma(G)\gamma(H)$ for any pair of graphs $G, H$, where $\gamma$ is the domination number and $G \square H$ is the Cartesian product of $G$ and $H$. Suen and Tarr,…

We present an approximate gap equation for different crystalline structures of the LOFF phase of high density QCD at T=0. This equation is derived by using an effective condensate term obtained by averaging the inhomogeneous condensate over…

The compact fourth-order finite-difference scheme for solving the 1d wave equation is studied. New error bounds of the fractional order $\mathcal{O}(h^{4(\lambda-1)/5})$ are proved in the mesh energy norm in terms of data, for two initial…

We apply the spectral energy distribution (SED) fitting code ProSpect to multiwavelength imaging for $\sim$7,000 galaxies from the GAMA survey at $z<0.06$, in order to extract their star formation histories. We combine a parametric…

Let $\pi(x;\gamma_1,\gamma_2)$ denote the number of primes $p$ with $p\leqslant x$ and $p=\lfloor n^{1/\gamma_1}_1\rfloor=\lfloor n^{1/\gamma_2}_2\rfloor$, where $\lfloor t\rfloor$ denotes the integer part of $t\in\mathbb{R}$ and…

A famous conjecture of P\'osa from 1962 asserts that every graph on $n$ vertices and with minimum degree at least $2n/3$ contains the square of a Hamilton cycle. The conjecture was proven for large graphs in 1996 by Koml\'os, S\'ark\"ozy…

We consider a spin-1/2 ladder with a ferromagnetic rung coupling J_\perp and inequivalent chains. This model is obtained by a twist (\theta) deformation of the ladder and interpolates between the isotropic ladder (\theta=0) and the SU(2)…

The classic string indexing problem is to preprocess a string S into a compact data structure that supports efficient pattern matching queries. Typical queries include existential queries (decide if the pattern occurs in S), reporting…

Genome rearrangements can be modeled as $k$-breaks, which break a genome at k positions and glue the resulting fragments in a new order. In particular, reversals, translocations, fusions, and fissions are modeled as $2$-breaks, and…

This is the first of a series of papers that will introduce a user-friendly, detailed, and modular GALactic Chemical Evolution Model, GalCEM, that tracks isotope masses as a function of time in a given galaxy. The list of tracked isotopes…

We present the first complete high-precision QCD corrections to the inclusive decay width $\mathrm{\Gamma}_t$, the $W$-helicity fractions $f_{\mathrm{L,R,0}}$ and semi-inclusive distributions for the top-quark decay process $t \rightarrow b…

We study the structure of the set of all maximal green sequences of a finite-dimensional algebra. There is a natural equivalence relation on this set, which we show can be interpreted in several different ways, underscoring its…

The rare exclusive decay of the Higgs boson $H \to J/\psi + \gamma$ is an important channel for measuring the Yukawa coupling of the charm quark. In this article, we analyze the process by employing the Principle of Maximum Conformality…