Results 71 to 80 of about 2,569 (239)
Известия Иркутского государственного университета: Серия "Математика"The paper proposes a matrix implementation of the collocation method for constructing a solution to Volterra integral equations of the second kind using systems of orthogonal Chebyshev polynomials of the first kind and Legendre polynomials. The integrand
O.V. Germider, V. N. Popov
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New AI‐Assisted Approach for Expanding the Solution Space: Application to Lattice Structure Design
Advanced Engineering Materials, EarlyView.This work introduces an innovative framework for designing structured materials by ex panding the design space through reparameterization of qualitative variables into continuous structural descriptors. Combined with machine‐learning‐based prediction and multi‐objective optimization, the approach enables the discovery of novel lattice architectures ...
G. H. Gahimbare +5 more
wiley +1 more source
Advanced Engineering Materials, EarlyView.Digitalizing electroplating requires both domain knowledge and interoperability. This work introduces PlatOn, a domain ontology for trivalent chromium plating and coating characterization, and a hybrid pipeline that aligns it to a mid‐level reference ontology by combining eight similarity metrics with language model reasoning. Expert‐validated mappings
Janik Harter +10 more
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Sum-product type estimates for subsets of finite valuation rings
Acta Arithmetica, 2018 Let $R$ be a finite valuation ring of order $q^r.$ Using a point-plane incidence estimate in $R^3$, we obtain sum-product type estimates for subsets of $R$. In particular, we prove that for $A\subset R$, $$|AA+A|\gg \min\left\{q^{r}, \frac{|A|^3}{q^{2r-1}}\right\}.$$ We also show that if $|A+A||A|^{2}>q^{3r-1}$, then $$|A^2+A^2||A+A|\gg q^{\frac{r ...
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Finite Sums and Products involving Special Functions
, 2023 Various product and sum relationships are established using special functions, specifically involving Special functions. These relationships are derived from formulas inspired by the finite sum that incorporates the Hurwitz-Lerch zeta function.
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ON SUM OF PRODUCTS AND THE ERDŐS DISTANCE PROBLEM OVER FINITE FIELDS [PDF]
Bulletin of the Australian Mathematical Society, 2011 AbstractFor a prime powerq, let 𝔽qbe the finite field ofqelements. We show that 𝔽*q⊆d𝒜2for almost every subset 𝒜⊂𝔽qof cardinality ∣𝒜∣≫q1/d. Furthermore, ifq=pis a prime, and 𝒜⊆𝔽pof cardinality ∣𝒜∣≫p1/2(logp)1/d, thend𝒜2contains both large and small residues. We also obtain some results of this type for the Erdős distance problem over finite fields.
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High‐Resolution Corrosion Fingerprinting of Alloy Libraries via Microdroplet Spectroelectrochemistry
Advanced Engineering Materials, EarlyView.Ionic‐liquid microdroplet spectroelectrochemistry enables stable, localized electrochemical measurements over extended timescales. By coupling impedance spectroscopy, wetting analysis, finite‐element simulations, and operando Raman spectroscopy, it disentangles geometrical and electrochemical effects, opening new opportunities for rapid corrosion ...
Ekaterina Kurchavova +3 more
wiley +1 more source
The distribution function inequality for a finite sum of finite products of Toeplitz operators
Journal of Functional Analysis, 2005 The authors consider the problem of when a finite sum of finite products of Toeplitz operators is a compact perturbation of a Toeplitz operator. The authors introduce a generalized area function associated with a finite sum of finite products of Toeplitz operators and establish a distribution function inequality for the area function.
Guo, Kunyu, Zheng, Dechao
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Advanced Engineering Materials, EarlyView.Different Al/Al bimetals with a single engineered interface reveal how mechanical mismatch governs fatigue crack growth under cyclic loading. Additionally, loading–unloading–reloading tests link the microyielding behavior to the fatigue crack growth resistance, while crack‐path analysis reveals toughening mechanisms at the interface, highlighting ...
Sebastian Vollath +2 more
wiley +1 more source
Advanced Engineering Materials, EarlyView.We apply a foundational machine‐learning interatomic potential based on the graph atomic cluster expansion (GRACE) to simulate the commercial Ni‐based single‐crystal superalloy CMSX‐4. Hybrid Monte‐Carlo/molecular dynamics sampling resolves short‐range order in the γ phase and L12 sublattice occupancies in the γ’ phase and connects them to stacking ...
Aditya Vishwakarma +4 more
wiley +1 more source