1.1 Topology Let us first recall some basic Euclidean topology. For x0 = (x0, y0, z0) ∈ R3 and r > 0 we define the open ball of radius r > 0 centered at x0 to be B(x0, r) = {x ∈ R | ‖x− x0‖ < r}. Recall that ‖x‖ = √ x2 + y2 + z2 is the Euclidean norm, or length, of the vector x. Definition 1 (Open set). We say a set D ⊂ R3 is open if for every x0 ∈ D, there exists a radius r > 0 such that B(x0,...

Measurements of individual wheel speeds and absolute position from a global navigation satellite system (GNSS) are used for high-precision estimation of vehicle tire radii in this work. The radii deviation from its nominal value is modeled as a Gaussian process and included as noise components in a vehicle model. The novelty lies in a Bayesian approach to estimate online both the state vector o...

Huygens’ principle states that the solution of the wave equation radiated by a bounded source can be represented outside the source region as a superposition of spherical ‘Huygens wavelets’ radiated by secondary point-sources on a surface enclosing the primary source. This was originally proposed as a geometrical explanation of wave propagation, but as such it is conceptually problematic becaus...

Most works on Support Vector Regression (SVR) focus kernel or loss functions, with the corresponding support vectors obtained using a fixed-radius [Formula: see text]-tube, affording good predictive performance datasets. However, fixed radius limitation prevents adaptive selection of according to data distribution characteristics, compromising SVR-based methods. Therefore, this study proposes a...

Of primary concern with the integration of Hall thrusters on conventional satellite designs is the possible damaging effect of high-energy exhaust ions impinging upon spacecraft surfaces. This paper reports on measurements of plasma ion-energy distributions within the plume of an SPT-100 Hall thruster using a custom-designed molecular beam mass spectrometer. With this instrument ion energy was ...

A dressed-quark core contribution to nucleon electromagnetic form factors is calculated. It is defined by the solution of a Poincaré covariant Faddeev equation in which dressed-quarks provide the elementary degree of freedom and correlations between them are expressed via diquarks. The nucleonphoton vertex involves a single parameter; i.e., a diquark charge radius. It is argued to be commensura...

Clinical signs of paediatric pulmonary tuberculosis (TB) include stenosis and deformation of the airways. This paper presents two methods to analyse airway shape and detect airway pathology from CT images. Features were extracted using (1) the principal components of the airway surface mesh and (2) branch radius and orientation features. These methods were applied to a dataset of 61 TB and non-...

As an alternative approach to the infinite-array description of dense matter in the Skyrme model, we report about the properties of a single skyrmion on a compact 3-sphere of finite radius. The density of this matter can be increased by decreasing the hypersphere radius. As in the array calculations one encounters a transition to a distinct high density phase characterized by a delocalization i...

C = 1 2 log2 (1 + SNR) where SNR = PX σ N . Shannon showed that in the limit of using long block length n, generating 2 i.i.d. N (0, PX) codewords and averaging across all codebooks is a capacity-achieving strategy: with high likelihood the power constraint will be satisfied and the average probability of error under ML decoding tends to 0 as n → ∞. This result can be derived geometrically as w...

The modiied quark-meson coupling model, which features a density dependent bag constant and bag radius in nuclear matter, is checked against the EMC eeect within the framework of dynamical rescaling. Our emphasis is on the change in the average bag radius in nuclei, as evaluated in a local density approximation, and its implication for the rescaling parameter. We nd that when the bag constant i...