Results 11 to 20 of about 528,533 (276)
The Interplay of Curvature, Geometry, and Topology Shapes Tissue Organisation in Epithelial Shells. [PDF]
Adv Sci (Weinh)Purely geometric 3D Voronoi models predict the organisation of epithelial shells. The interplay of curvature, geometry, and topology enriches the number of pentagons in shells with lower number of cells. Small MDCK cysts and Mouse embryos match the top polygonal configurations in a compactness‐based ranking derived from the Voronoi model. In conclusion,
Morato L +9 more
europepmc +2 more sources
From Displacement to Angle: Diamond-Based 3D Rotation Sensing for High-Precision Cellular Force Measurement. [PDF]
Adv Sci (Weinh)Cellular forces are traditionally inferred from displacement measurements, which lack rotational information and are constrained by linear model assumptions. This work replaces displacement with rotational angle for the fundamental mechanical readout.
Ma L +8 more
europepmc +2 more sources
GENERALIZATION OF EULER’S FORMULA
Grail of ScienceFactorial powers allow generalizing various mathematical studies. The publication proposes new functions and which are analogs of classical functions and The functions and are constructed using power series and factorial powers. Graphs of these functions are plotted, some properties and formulas connecting them are established.
Oleksandr Makhnei, Roman Zatorsky
openaire +2 more sources
, 2016 Educação Superior::Ciências Exatas e da Terra::MatemáticaLet the number of vertices, edges, and faces of a polyhedron be V, E, and F. The Euler characteristic, V+F-E, is always 2 for convex polyhedra. This Demonstration shows Euler's polyhedral formula V+
Zenil, Hector
core +5 more sources
De Moivre’s and Euler Formulas for Matrices of Hybrid Numbers
Axioms, 2021 It is known that the hybrid numbers are generalizations of complex, hyperbolic and dual numbers. Recently, they have attracted the attention of many scientists.
Mücahit Akbıyık +3 more
doaj +1 more source
Integral inequalities via harmonically h-convexity
Moroccan Journal of Pure and Applied Analysis, 2021 In this paper, we establish some estimates of the left side of the generalized Gauss-Jacobi quadrature formula for harmonic h-preinvex functions involving Euler’s beta and hypergeometric functions.
Merad Meriem +2 more
doaj +1 more source
The Desymmetrized PSL(2, Z) Group; Its ‘Square-Box’ One-Cusp Congruence Subgroups
Computer Sciences & Mathematics Forum, 2023 In this paper, the desymmetrized PSL(2, Z) group is studied. The Fourier coefficients of the non-holomorphic one-cusp Eisenstein series expansion are summed, and as a further result, a new dependence on the Euler’s γ constant is found.
Orchidea Maria Lecian
doaj +1 more source
Euler's Polyhedron Formula [PDF]
Formalized Mathematics, 2008 where V , E, and F are, respectively, the number of vertices, edges, and faces of p. The formula was first stated in print by Euler in 1758 [11]. The proof given here is based on Poincare’s linear algebraic proof, stated in [17] (with a corrected proof in [18]), as adapted by Imre Lakatos in the latter’s Proofs and Refutations [15].
openaire +1 more source
Unification Theories: Means and Generalized Euler Formulas
Axioms, 2020 The main concepts in this paper are the means and Euler type formulas; the generalized mean which incorporates the harmonic mean, the geometric mean, the arithmetic mean, and the quadratic mean can be further generalized.
Radu Iordanescu +2 more
doaj +1 more source
On a generalization of Euler's constant [PDF]
Surveys in Mathematics and its Applications, 2021 A one parameter generalization of Euler's constant γ from [Numer. Algorithms 46(2) (2007) 141--151] is investigated, and additional expressions for γ are derived.
Stephen Kaczkowski
doaj