A few neuroinformatics databases now exist that record results from neuroimaging studies in the form of brain coordinates in stereotaxic space. The Brede Toolbox was originally developed to extract, analyze and visualize data from one of them - the BrainMap database. Since then the Brede Toolbox has expanded and now includes its own database with coordinates along with ontologies for brain regi...

The general form of the Smoluchowski equation in two reaction coordinates is obtained as the diffusion limit of a random walk on an infinite square grid using transition probabilities that satisfy detailed balance at thermodynamic equilibrium. The diffusion limit is then used to construct a generalization of the single-particle model to two reaction coordinates. The state space includes a squar...

We consider a version of Kaluza-Klein theory where the cylinder condition is not imposed. We replace this condition with the requirement that physics in four-dimensional spacetime should remain invariant under changes of coordinates in the five-dimensional bulk. This invariance does not eliminate physical effects from the extra dimension but separates them from spurious geometrical ones. We all...

New four coordinates are introduced which are related to the usual space-time coordinates. For these coordinates, the Euclidean four dimensional length squared is equal to the interval squared of the Minkowski space. The Lorentz transformation, for the new coordinates, becomes an SO(4) rotation. New scalars (invariants) are derived. A second approach to the Lorentz transformation is presented. ...

Iterated local search (ILS) is used to construct the optimal experimental designs for multi-dimensional constrained spaces, in which inner loop based on stochastic coordinate-exchange (SCE) algorithm. Every time a solution found by SCE algorithm, perturbation operator applied it, and then new explored areas where exchange of coordinates may produce improvement, so as retain features attributes ...

Let B={Bt}t≥0 be a one-dimensional standard Brownian motion and denote by At,t≥0, the quadratic variation of semimartingale eBt,t≥0. The celebrated Bougerol’s identity in law (1983) asserts that, if β={βt}t≥0 is another independent B, then βAt has same as sinhBt for every fixed t>0. Bertoin, Dufresne Yor (2013) obtained two-dimensional extension involving, second coordinates, local times B β at...

OVERVIEW In the automated embroidery business, the ability to present a client with a tangible design prototype is highly desirable. However, the cost of materials involved with creating such prototypes increases sharply when one takes into consideration the thousands of possible combinations of thread types and colors, stitch patterns, and applications of a particular embroidery design. I defi...

Mixing tanks equipped with mechanical stirrer are broadly applied in chemical and petrochemical industries, due to their variety of industrial process requirements. In this study, helical single blade mixer was designed applying CATIA and then mixing of fluid and solid particles, in a tank with this agitator was examined by OpenFOAM. For velocity distribution in the mixing tank, continuity, mom...