A smooth embedding of a closed $3$-manifold $M$ in $\mathbb{R}^4$ may generically be composed with projection to the fourth coordinate determine Morse function on and hence Heegaard splitting $M=X\cup_\Sigma Y$. However, starting splitting, we find an obstruction coming from geometry curve complex $C(\Sigma)$ realizing corresponding $M\hookrightarrow \mathbb{R}^4$.

By frame of reference transformations, an input variable in one coordinate system is transformed into an output variable in a different coordinate system depending on another input variable. If the variables are represented as neural population codes, then a sigma–pi network is a natural way of coding this transformation. By multiplying two inputs it detects coactivations of input units, and by...

It is shown how derived brackets naturally arise in sigma-models via Poissonor antibracket, generalizing a recent observation by Alekseev and Strobl. On the way to a precise formulation of this relation, an explicit coordinate expression for the derived bracket is obtained. The generalized Nijenhuis tensor of generalized complex geometry is shown to coincide up to a de-Rham closed term with the...

We study the diffusion of charm quarks in early stage high energy nuclear collisions at RHIC and LHC. The main novelty present is introduction color current carried by heavy that propagate evolving glasma (EG), which responsible loss via polarization medium. compute transverse momentum broadening, ${\ensuremath{\sigma}}_{p}$, prethermalization stage, impact on modification factor nucleus-nucleu...

This paper describes the dynamical part of a global, hydrostatic grid point model developed from models described in Mesinger et al. (1988) and Wyman (1996). The model described here solves the same set of dynamical equations but has a modified vertical and horizontal grid. The vertical grid is a hybrid sigma-pressure coordinate system, sigma coordinate surfaces in the lower model levels may gr...

The domain of analysis and conception of Decisional Information System (DIS) is, highly, applying new techniques and methods to succeed the process of the decision and minimizing the time of conception. Our objective in this paper is to define a group of patterns to ensure a systematic reuse of our approach to analyse a DIS’s business requirements. We seek, through this work, to guide the disco...

A coupled 3D-baroclinic hydrodynamic and cohesive sediment transport model applied to the Western Scheldt estuary is presented. The use of the two-fold sigma coordinate considerably improves the results on intertidal zones. The simulations provide an insight into the effetcs of stratification and its tidal asymmetry into the sediment transport. The calculated density current show an intensity t...

The space R comes with its standard topology which we denote byO (that is, O is the collection of open sets in R). It comes also with its Borel sigma algebra which we denote by B. The Borel sigma algebra is the smallest one containing all open sets (i.e., the sigma algebra generated by O). Let I be an arbitrary non-empty set (finite, countable or uncountable). For x ∈ I, the coordinate function...