Search results for "Mathematica"

Geometric mean and triangles inscribed in a semicircle in Banach spaces

2008

AbstractWe consider the triangles with vertices x, −x and y where x,y are points on the unit sphere of a normed space. Using the geometric means of the variable lengths of the sides of these triangles, we define two geometric constants for Banach spaces. These constants are closely related to the modulus of convexity of the space under consideration, and they seem to represent a useful tool to estimate the exact values of the James and Jordan–von Neumann constants of some Banach spaces.

Solutions to the 1-harmonic flow with values into a hyper-octant of the N-sphere

2013

Abstract We announce existence results for the 1-harmonic flow from a domain of R m into the first hyper-octant of the N -dimensional unit sphere, under homogeneous Neumann boundary conditions. The arguments rely on a notion of “geodesic representative” of a BV-vector field on its jump set.

THE 1-HARMONIC FLOW WITH VALUES IN A HYPEROCTANT OF THE N-SPHERE

2014

We prove the existence of solutions to the 1-harmonic flow — that is, the formal gradient flow of the total variation of a vector field with respect to the [math] -distance — from a domain of [math] into a hyperoctant of the [math] -dimensional unit sphere, [math] , under homogeneous Neumann boundary conditions. In particular, we characterize the lower-order term appearing in the Euler–Lagrange formulation in terms of the “geodesic representative” of a BV-director field on its jump set. Such characterization relies on a lower semicontinuity argument which leads to a nontrivial and nonconvex minimization problem: to find a shortest path between two points on [math] with respect to a metric w…

Rotationally symmetric p -harmonic maps fromD2toS2

2013

We consider rotationally symmetric p-harmonic maps from the unit disk D2⊂R2 to the unit sphere S2⊂R3, subject to Dirichlet boundary conditions and with 1<p<∞. We show that the associated energy functional admits a unique minimizer which is of class C∞ in the interior and C1 up to the boundary. We also show that there exist infinitely many global solutions to the associated Euler–Lagrange equation and we completely characterize them.

Unitary transformations depending on a small parameter

2011

We formulate a unitary perturbation theory for quantum mechanics inspired by the LieDeprit formulation of canonical transformations. The original Hamiltonian is converted into a solvable one by a transformation obtained through a Magnus expansion. This ensures unitarity at every order in a small parameter. A comparison with the standard perturbation theory is provided. We work out the scheme up to order ten with some simple examples.

Implementation and performance of the ATLAS second level jet trigger

2008

ATLAS is one of the four major LHC experiments, designed to cover a wide range of physics topics. In order to cope with a rate of 40 MHz and 25 interactions per bunch crossing, the ATLAS trigger system is divided in three different levels. The first one (LVL1, hardware based) identifies signatures in 2 microseconds that are confirmed by the the following trigger levels (software based). The Second Level Trigger (LVL2) only looks at a region of the space around the LVL1 signature (called Region of Interest or ROI), confirming/rejecting the event in about 10 ms, while the Event Filter (Third Level Trigger, EF) has potential full event access and larger processing times, of the order of 1 s. T…

The Upgrade of the ATLAS Level-1 Central Trigger Processor

2013

The ATLAS Level-1 Central Trigger Processor (CTP) combines information from calorimeter and muon trigger processors as well as other sources and makes the final Level-1 Accept (L1A) decision. Due to the increasing luminosity of the LHC and the growing demands of physics and monitoring placed on the ATLAS Level-1 trigger system, the current CTP has reached its design limits. Therefore and in order to provide some margin for future operation, the CTP will be upgraded during the LHC shutdown of 2013/14.

Performance of the ATLASPix1 pixel sensor prototype in ams aH18 CMOS technology for the ATLAS ITk upgrade

2019

Olive oil intake and cancer risk: A systematic review and meta-analysis

2022

Background Research evidence has established the beneficial effects of diet in cancer prevention; various epidemiological studies have suggested that olive oil component could play a role in decreasing cancer risk. This systematic review and meta-analysis aims to investigate the association between olive oil consumption, cancer risk and prognosis. Methods A systematic search was conducted in PubMed, EMBASE and Google Scholar databases (end-of-search: May 10, 2020). Pooled relative risk (RR) and 95% confidence intervals (95% CIs) were estimated with random-effects (DerSimonian-Laird) models. Subgroup analyses, sensitivity analyses and meta-regression analysis were also performed. Results 45…

IKT LIETOJUMA IESPĒJAS MATEMĀTIKAS MĀCĪŠANĀ SKOLĀ

2013

Elektroniskā versija nesatur pielikumus