Gapped phases with non-invertible symmetries: (1+1)d by Lakshya Bhardwaj, Lea E. Bottini, Daniel Pajer, Sakura Schafer-Nameki

“…This set-up provides computational power to determine the number of vacua, the symmetry breaking pattern, and the action of the symmetry on the vacua. …”
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Recent Developments of Hilbert-Type Discrete and Integral Inequalities with Applications by Lokenath Debnath, Bicheng Yang

“…Included are numerous generalizations, extensions, and refinements of Hilbert-type inequalities involving many special functions such as beta, gamma, logarithm, trigonometric, hyper-bolic, Bernoulli's functions and Bernoulli's numbers, Euler's constant, zeta function, and hypergeometric functions with many applications. …”
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Controlled Roof Collapse during Secondary Mining in Coal Mines by Ashleigh Hutchinson

“…The roof rock between the pillar, which is the working face, and the snook is modelled as an Euler-Bernoulli beam acted on at each end by a horizontal force and by its weight per unit length. …”
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Riemann–Roch for the ring $\mathbb{Z}$ by Connes, Alain, Consani, Caterina

“…The formula equates the (integer valued) Euler characteristic of an Arakelov divisor with the sum of the degree of the divisor (using logarithms with base 2) and the number $1$, thus confirming the understanding of the ring $\mathbb{Z}$ as a ring of polynomials in one variable over the absolute base $\mathbb{S}$, namely $\mathbb{S}[X], 1+1=X+X^2$.…”
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Certain Properties of Generalized M-Series under Generalized Fractional Integral Operators by D. L. Suthar, Fasil Gidaf, Mitku Andualem

“…The corresponding assertions in terms of Euler and Laplace transform methods are presented. …”
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Image Enhancement of Cross-Border E-Commerce Logistics Video Surveillance Based on Partial Differential Equations by Xiaosheng Yu, Peili Wu

“…By introducing the heat equation, the direct solution of Euler’s equation is converted into an iterative form, which greatly reduces the amount of calculation. …”
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Stability Analysis and Simulation of Diffusive Vaccinated Models by Mohammed M. Al-Shamiri, N. Avinash, P. Chellamani, Manal Z. M. Abdallah, G. Britto Antony Xavier, V. Rexma Sherine, M. Abisha

“…Here, we demonstrate that the endemic equilibrium is worldwide asymptotic stable when the basic reproductive number is greater than 1, and the disease-free equilibrium is globally asymptotic stable whenever the basic reproductive number is less than 1. …”
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Fitted Tension Spline Scheme for a Singularly Perturbed Parabolic Problem With Time Delay by Sisay Ketema Tesfaye, Gemechis File Duressa, Tekle Gemechu Dinka, Mesfin Mekuria Woldaregay

“…Classical numerical methods cause spurious nonphysical oscillations unless an unacceptable number of mesh points is considered, which requires a large computational cost. …”
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Spatial and Temporal Dynamics of a Viral Infection Model with Two Nonlocal Effects by Xiaoyan Wang, Yuming Chen, Junyuan Yang

“…First, the semigroup theory and the classical renewal process are adopted to compute the basic reproduction number R0 as the spectral radius of the next-generation operator. …”
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Compensated integrability on tori; a priori estimate for space-periodic gas flows by Serre, Denis

“…We obtain a weighted estimate of the average number of collisions per unit time, provided that the “linear density” $Na/L$ ($N$ particles of radius $a$) is smaller than some threshold.…”
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Epidemiological Characteristics of Generalized COVID-19 Deterministic Disease Model by Shuo Li, Nasir Hussain, Ihsan Ullah Khan, Amjid Hussain, Shewafera Wondimagegnhu Teklu

“…The basic reproduction number is obtained which is a key factor in defining the nonlinear dynamics of biological and physical obstacles in the study of mathematical models of COVID-19 disease. …”
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Free Vibrations of a Reddy-Bickford Multi-Span Beam Carrying Multiple Spring-Mass Systems by Yusuf Yesilce

“…The literature regarding the free vibration analysis of Bernoulli-Euler and Timoshenko single-span beams carrying a number of spring-mass system and multi-span beams carrying multiple spring-mass systems are plenty, but the free vibration analysis of Reddy-Bickford multi-span beams carrying multiple spring-mass systems has not been investigated by any of the studies in open literature so far. …”
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Explicit inverse of the Pascal matrix plus one by Sheng-liang Yang, Zhong-kui Liu

“…This paper presents a simple approach to invert the matrix Pn+In by applying the Euler polynomials and Bernoulli numbers, where Pn is the Pascal matrix.…”
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A Note on Eulerian Polynomials by D. S. Kim, T. Kim, W. J. Kim, D. V. Dolgy

“…We study Genocchi, Euler, and tangent numbers. From those numbers we derive some identities on Eulerian polynomials in connection with Genocchi and tangent numbers.…”
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Elastodynamic modeling and analysis of a 4SRRR overconstrained parallel robot by B. Wang, Y. Zhao, C. Yang, X. Hu, Y. Zhao

“…Further increasing the number of rod divisions results in diminishing reductions in the error.…”
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Multiplicities of Representations in Algebraic Families by Cai, Li, Fan, Yangyu

“…In this short notes, we consider multiplicities of representations in general algebraic families, especially the upper semi-continuity of homological multiplicities and the locally constancy of Euler–Poincaré numbers. This generalizes the main result of Aizenbud–Sayag for unramified twisting families.…”
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Symmetry Fermionic 𝑝-Adic 𝑞-Integral on ℤ𝑝 for Eulerian Polynomials by Daeyeoul Kim, Min-Soo Kim

“…They studied some identities on the Eulerian polynomials in connection with the Genocchi, Euler, and tangent numbers. In this paper, by applying the symmetry of the fermionic p-adic q-integral on ℤ𝑝, defined by Kim (2008), we show a symmetric relation between the q-extension of the alternating sum of integer powers and the Eulerian polynomials.…”
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Below the Schwinger critical magnetic field value, quantum vacuum and gamma-ray bursts delay by Iver H. Brevik, Moshe M. Chaichian, Anca Tureanu

“…For the latter, we also give a corresponding estimate for the number of the magnetars along the trajectory and also for the delay. …”
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Formulation of Equations of Motion for a Simply Supported Bridge under a Moving Railway Freight Vehicle by Ping Lou, Qing-yuan Zeng

“…The bridge deck, together with railway track resting on bridge, is modelled as a simply supported Bernoulli-Euler beam and its deflection is described by superimposing modes. …”
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Simulation Study on Dynamics of Hydraulic Turbines Used in Drilling Engineering by Yijin Zeng, Jin Wang, Shidong Ding, Haobo Zhou, Yanbin Zang, Fangtao Li

“…Using the CFD (computational fluid dynamics) method, based on the realizable k-ɛ turbulence model and Euler multiphase flow model, the effects of different external loads, blade numbers, blade installation angles, and flow rates on the force condition of turbine and the influence of different solid contents, particle sizes, and densities on turbine performance were studied. …”
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