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ON A DIFFERENTIAL EQUATION RELATED WITH DIFFERENTIAL GEOMETRY

Memoirs of the Faculty of Science, Kyusyu University. Series A, Mathematics, 1993
The paper is a survey of the works of the author on the nonlinear ordinary differential equation \(nx(1- x^ 2) {d^ 2 x\over dt^ 2}+\Bigl({dx\over dt}\Bigr)^ 2+ (1- x^ 2)(nx^ 2- 2)= 1\), where \(n\) is a real constant, which occurs in differential geometry.
openaire   +2 more sources

Does Long‐Term Lower Extremity Strength Training in Adults With Knee Osteoarthritis and Varus Alignment Reduce Knee Joint Loading During Gait?

Arthritis Care &Research, EarlyView.
Objective We examined whether 18 months of strength training in individuals with knee varus alignment and medial tibiofemoral osteoarthritis (OA) reduced knee joint loads during walking compared to an attention control group. Methods This study was a secondary analysis of a randomized clinical trial that compared the effects of strength training to a ...
Stephen P. Messier, Matthew N. Vigliotti, Paige E. Rice, Brian Pietrosimone, Shannon L. Mihalko, Edward H. Ip, Richard F. Loeser, David J. Hunter, Ali Guermazi, Ryan Hill, Santiago Saldana, Kim L. Bennell, Paul DeVita   +12 more
wiley   +1 more source

Affine differential geometry of osculating hypersurfaces

Lietuvos Matematikos Rinkinys, 2012
Osculating surfaces of second order have been studied in classical affine differential geometry [1].  In this article we generalize this notion to osculating hypersurfaces of higher order of hypersurfaces in Euclidean n-space.
Kazimieras Navickis
doaj   +1 more source

Thermoreflectance Detection of Point Defects Resulting from Focused Ion Beam Milling

Advanced Engineering Materials, Volume 28, Issue 11, 3 June 2026.
Focused ion beam (FIB) milling is a common tool for nanoscale material processing, however irradiation damage, redeposition, and contamination can occur. We use several characterization tools to show FIB‐induced effects beyond 1 mm from the milled area.
Thomas W. Pfeifer, Eric R. Hoglund, Anton V. Ievlev, Patrick E. Hopkins   +3 more
wiley   +1 more source

Differential Geometry of Microlinear Frolicher Spaces II [PDF]

, 2010
In this paper, as the second in our series of papers on differential geometry of microlinear Frolicher spaces, we study differenital forms. The principal result is that the exterior differentiation is uniquely determined geometrically, just as grad (ient)
Nishimura, Hirokazu
core   +1 more source

Characterization of Defect Distribution in an Additively Manufactured AlSi10Mg as a Function of Processing Parameters and Correlations with Extreme Value Statistics

Advanced Engineering Materials, EarlyView.
Predicting extreme defects in additive manufacturing remains a key challenge limiting its structural reliability. This study proposes a statistical framework that integrates Extreme Value Theory with advanced process indicators to explore defect–process relationships and improve the estimation of critical defect sizes. The approach provides a basis for
Muhammad Muteeb Butt, Varma Kvvssn, Hossein Laieghi, Zia Uddin, Peyman Ansari, E. Kıvanç Sadak, Can Barış Toprak, Hüseyin Kızıl, Enrico Salvati   +8 more
wiley   +1 more source

Experimental Evaluation of 100Cr6 Steel Microindented Surfaces Under Lubricated Nonconformal Point Contacts

Advanced Engineering Materials, EarlyView.
The tribological behavior of 100Cr6 steel spheres textured via Vickers microindentation is evaluated under lubricated sliding by varying both dimple size and density. Fine and dense textures significantly reduce friction across all lubrication regimes, while large dimples increase it.
Farideh Davoodi, Pasquale Guglielmi, Gianfranco Palumbo, Giuseppe Carbone   +3 more
wiley   +1 more source

Geometric Aspects of Mixed Quantum States Inside the Bloch Sphere

Quantum Reports
When studying the geometry of quantum states, it is acknowledged that mixed states can be distinguished by infinitely many metrics. Unfortunately, this freedom causes metric-dependent interpretations of physically significant geometric quantities such as
Paul M. Alsing, Carlo Cafaro, Domenico Felice, Orlando Luongo   +3 more
doaj   +1 more source

Heat Kernel Embeddings, Differential Geometry and Graph Structure

Axioms, 2015
In this paper, we investigate the heat kernel embedding as a route to graph representation. The heat kernel of the graph encapsulates information concerning the distribution of path lengths and, hence, node affinities on the graph; and is found by ...
Hewayda ElGhawalby, Edwin R. Hancock
doaj   +1 more source

Laser Powder Bed Fusion of Alumina: Effects of Scanning Strategies on External and Internal Defects

Advanced Engineering Materials, EarlyView.
This study investigates how scanning strategies affect pure alumina in laser powder bed fusion. Linear 45° scanning yields uniform surfaces but high porosity, while the island‐concentric strategy provides higher density with through‐holes favorable for infiltration. Findings highlight pathways toward optimizing defect‐free alumina parts.
Mohamed Abdelmoula, Gökhan Küçüktürk, Duran Kaya, David Grossin, Christophe Tenailleau, Benjamin Duployer, Enrique Juste, Fabrice Petit   +7 more
wiley   +1 more source