Results 41 to 50 of about 349,838 (276)
Unification of all hyperbolic tangent function methods
Open Physics, 2016 Over the last twenty years, several “different” hyperbolic tangent function methods have been proposed to search solutions for nonlinear partial differential equations (NPDEs).
Gözükızıl Ömer Faruk +2 more
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Micro tangent sets of continuous functions [PDF]
Mathematica Bohemica, 2003 Summary: Motivated by the concept of tangent measures and by H. Fürstenberg's definition of microsets of a compact set \(A\) we introduce micro tangent sets and central micro tangent sets of continuous functions. It turns out that the typical continuous function has a rich (universal) micro tangent set structure at many points.
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Evaluating Energy Absorption Performance of Filled Lattice Structures
Advanced Engineering Materials, EarlyView.Maximum stress must be considered to robustly evaluate energy absorber designs. This approach was applied to compare all types of absorbers in a single Ashby diagram and determine the utility of filling lattice voids with a second material. High‐performance fillers can improve the performance of lattices that are limited by buckling or catastrophic ...
Christian Bonney +2 more
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High school students’ learning trajectories of the concept of tangent line
Enseñanza de las Ciencias, 2018 The goal of this research is to characterize high school students’ learning trajectories of the concept of tangent line in a teaching experiment. The experiment considers a model of learning progression of the concept of tangent line using the local ...
Abilio Orts Muñoz +2 more
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Multiple tangent zeta function and tangent polynomials of higher order
Advanced Studies in Theoretical Physics, 2014 In this paper, we introduce Tangent numbers T (k) n and Tangent polynomials T (k) n (x) of higher order. Finally, we obtain interesting properties of these numbers and polynomials.
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Phase Field Failure Modeling: Brittle‐Ductile Dual‐Phase Microstructures under Compressive Loading
Advanced Engineering Materials, EarlyView.The approach by Amor and the approach by Miehe and Zhang for asymmetric damage behavior in the phase field method for fracture are compared regarding their fitness for microcrack‐based failure modeling. The comparison is performed for the case of a dual‐phase microstructure with a brittle and a ductile constituent.
Jakob Huber, Jan Torgersen, Ewald Werner
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The tangent function and power residues modulo primes
Czechoslovak Mathematical Journal, 2023 Let $p$ be an odd prime, and let $a$ be an integer not divisible by $p$. When $m$ is a positive integer with $p\equiv1\pmod{2m}$ and $2$ is an $m$th power residue modulo $p$, we determine the value of the product $\prod_{k\in R_m(p)}\tanπ\frac{ak}p$, where $$R_m(p ...
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Weak tangent and level sets of Takagi functions [PDF]
Monatshefte für Mathematik, 2020 AbstractIn this paper, we study some properties of Takagi functions and their level sets. We show that for Takagi functions $$T_{a,b}$$Ta,b with parameters a, b such that ab is a root of a Littlewood polynomial, there exist large level sets. As a consequence, we show that for some parameters a, b, the Assouad dimension of graphs of $$T_{a,b}$$Ta,b is ...
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Numerical Exploration of Thermal Shock Resistance in MgO–C Refractories
Advanced Engineering Materials, EarlyView.A mesostructure‐resolved numerical framework is developed to evaluate the thermal shock resistance of MgO–C refractories. By modeling interface debonding under rapid temperature changes and introducing a modified thermal shock parameter that accounts for mesocracks, the study shows how graphite content and aggregate size influence thermal shock ...
Jishnu Vinayak Gopi +3 more
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Coefficient Inequalities of q-Bi-Univalent Mappings Associated with q-Hyperbolic Tangent Function
Fractal and Fractional, 2023 The present study introduces a new family of analytic functions by utilizing the q-derivative operator and the q-version of the hyperbolic tangent function.
Timilehin Gideon Shaba +5 more
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