Results 61 to 70 of about 745,915 (284)
The First Mean Value Theorem for Integrals [PDF]
Formalized Mathematics, 2008 For simplicity, we use the following convention: X is a non empty set, S is a σ-field of subsets of X, M is a σ-measure on S, f , g are partial functions from X to R, and E is an element of S. One can prove the following three propositions: (1) If for every element x of X such that x ∈ dom f holds f(x) ≤ g(x), then g − f is non-negative.
Keiko Narita +2 more
openaire +1 more source
Advanced Optical Materials, EarlyView.Hexagonal arrays of silicon nanodisks are proposed to control 1.5 µm emission of Er3+ ions. Toroidal dipole resonance of the nanodisk array generates accessible magnetic hot spots at the surface, leading to enhanced and highly directional magnetic dipole emission along the surface‐normal direction via the magnetic Purcell effect.
Keisuke Moriasa +3 more
wiley +1 more source
Mean values of Dirichlet polynomials and applications to linear equations with prime variables
, 2004 We prove a new mean-value theorem for Dirichlet polynomials with coefficients given by the von Mangoldt function. We then use our theorem to derive new estimates for certain exponential sums over primes.
Angel V. Kumchev +2 more
core +2 more sources
Continuum Mechanics Modeling of Flexible Spring Joints in Surgical Robots
Advanced Robotics Research, EarlyView.A new mechanical model of a tendon‐actuated helical extension spring joint in surgical robots is built using Cosserat rod theory. The model can implicitly handle the unknown contacts between adjacent coils and numerically predict spring shapes from straight to significantly bent under actuation forces.
Botian Sun +3 more
wiley +1 more source
Waveguide Photoactuators: Materials, Fabrication, and Applications
Advanced Robotics Research, EarlyView.Waveguide photoactuators convert guided light into mechanical motion. Their tethered‐flexible design enables minimally invasive surgery and confined‐space robotics. This review aims to guide materials selection, device design, and system integration, accelerating the transition of waveguide photoactuators from laboratory prototypes to versatile ...
Minjie Xi +4 more
wiley +1 more source
Some fundamental theorems in the interval-valued functions and time scales [PDF]
Journal of Mahani Mathematical ResearchThis research investigates the topological structure of the space of interval-valued functions equipped with an order relation defined by open balls. The aim is to establish analogues of fundamental theorems in calculus, including Bolzano’s theorem, the ...
Tahere Shokoohi +2 more
doaj +1 more source
Near-optimal mean value estimates for multidimensional Weyl sums
, 2012 We obtain sharp estimates for multidimensional generalisations of Vinogradov's mean value theorem for arbitrary translation-dilation invariant systems, achieving constraints on the number of variables approaching those conjectured to be the best possible.
G.I. Arkhipov +17 more
core +1 more source
Consensus Formation and Change are Enhanced by Neutrality
Advanced Science, EarlyView.Neutral agents are shown to enhance both the formation and overturning of consensus in collective decision‐making. A general mathematical model and experiments with locusts and humans reveal that neutrality enables robust consensus via simple interactions and accelerates consensus change by reducing effective population size.
Andrei Sontag +3 more
wiley +1 more source
On Weyl sums for smaller exponents [PDF]
, 2010 We present a hybrid approach to bounding exponential sums over kth powers via Vinogradov's mean value theorem, and derive estimates of utility for exponents k of intermediate ...
D. Wooley, Kent D. Boklan, Trevor
core
Solution-free sets for sums of binary forms
, 2011 We obtain quantitative estimates for the asymptotic density of subsets of the two-dimensional integer lattice which contain only trivial solutions to an additive equation involving binary forms.
Prendiville, Sean
core +2 more sources