Results 71 to 80 of about 4,592,487 (264)
A theta function identity and its implications [PDF]
Transactions of the American Mathematical Society, 2004 In this paper we prove a general theta function identity with four parameters by employing the complex variable theory of elliptic functions. This identity plays a central role for the cubic theta function identities. We use this identity to re-derive some important identities of Hirschhorn, Garvan and Borwein about cubic theta ...
openaire +1 more source
On the equivalence of two fundamental theta identities [PDF]
, 2014 Two fundamental theta identities, a three-term identity due to Weierstrass and a five-term identity due to Jacobi, both with products of four theta functions as terms, are shown to be equivalent. One half of the equivalence was already proved by R.
Koornwinder, T.H.; id_orcid
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On two 10th order mock theta identities [PDF]
, 2016 We give short proofs of conjectural identities due to Gordon and McIntosh involving two 10th order mock theta ...
Lovejoy, Jeremy +3 more
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Time‐Dependent Oxidation and Scale Evolution of a Wrought Co/Ni‐Based Superalloy
Advanced Engineering Materials, EarlyView.This study shows how a new wrought Co/Ni‐based superalloy resists oxidation at 800 ∘$^\circ$C. The oxide scale changes from rough, fast‐growing spinel to a dense, protective chromia–alumina layer. Atom probe analysis reveals tiny refractory‐rich bubbles at the interface that mark the transition to long‐term, diffusion‐controlled protection ...
Cameron Crabb +6 more
wiley +1 more source
Karl Popper and the Mechanisms of Hydrogen Embrittlement
Advanced Engineering Materials, EarlyView.Representation of the beginning of loss of ductility rather than embrittlement. Small concentrations of hydrogen in a diffusible form within iron are well‐established to harm the mechanical integrity of steels. There are theories that attempt to explain the pernicious role of hydrogen.
H. K. D. H. Bhadeshia
wiley +1 more source
Theta-modulated place-by-direction cells in the hippocampal formation in the rat [PDF]
, 2004 We report the spatial and temporal properties of a class of cells termed theta-modulated place-by-direction (TPD) cells recorded from the presubicular and parasubicular cortices of the rat. The firing characteristics of TPD cells in open-field enclosures
Wills, TJ +4 more
core
Advanced Engineering Materials, EarlyView.We develop a data‐driven method to derive the mathematical expressions of the Flory–Huggins interaction parameter χ for the swelling behavior of temperature–responsive hydrogels. Starting from initial assumptions of χ, our workflow combines Bayesian optimization, Flory–Rehner theory, and symbolic regression to generate candidate χ expressions.
Yawen Wang +2 more
wiley +1 more source
A New Class of Theta-Function Identities Originating in Ramanujan′s Notebooks
, 1994 In the unorganized pages of his second notebook, Ramanujan offers two new theta-function identities that have a form different from other identities found in the literature.
Zhang, L.C., Berndt, B.C.
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Increased mesiotemporal delta activity characterizes virtual navigation in humans [PDF]
, 2013 Hippocampal theta or rhythmic slow activity (RSA) occurring during exploratory behaviors and rapid-eye-movement (REM) sleep is a characteristic and well-identifiable oscillatory rhythm in animals.
Janszky, József +9 more
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Advanced Engineering Materials, EarlyView.A two‐dimensional multiscale finite element analysis framework was established for the first‐generation MoSiBTiC alloy, and the mechanical and fracture‐related parameters of the constituent phases were calibrated through experiments and simulations. The framework provides a basis for analyzing crack propagation behavior in its complex microstructure ...
Junfeng Du +4 more
wiley +1 more source