Wonderful asymptotics of matrix coefficient D-modules

Beilinson-Bernstein localization realizes representations of complex reductive Lie algebras as monodromic $D$-modules on the "basic affine space" $G/N$, a torus bundle over the flag variety. A doubled version of the same space appears as the horocycle space describing the geometry of the reductive group $G$ at infinity, near the closed stratum of the wonderful compactification $\overline{G}$, or equivalently in the special fiber of the Vinberg semigroup of $G$. We show that Beilinson-Bernstein localization for $U\mathfrak g$-bimodules arises naturally as the specialization at infinity in $\overline{G}$ of the $D$-modules on $G$ describing matrix coefficients of Lie algebra representations. More generally, the asymptotics of matrix coefficient $D$-modules along any stratum of $\overline{G}$ are given by the matrix coefficient $D$-modules for parabolic restrictions. This provides a simple algebraic derivation of the relation between growth of matrix coefficients of admissible representations and $\mathfrak n$-homology. The result is an elementary consequence of the compatibility of localization with the degeneration of affine $G$-varieties to their asymptotic cones; analogous results hold for the asymptotics of the equations describing spherical functions on symmetric spaces.Comment: Preliminary version, comments welcome

A fractal approach to the rheology of concentrated cell suspensions

Results on the rheological behavior of novel CHO cell suspensions in a large range of concentrations are reported. The concentration dependent yield stress and elastic plateau modulus are formalized in the context of fractal aggregates under shear, and quite different exponents are found as compared to the case of red blood cell suspensions. This is explained in terms of intrinsic microscopic parameters such as the cell-cell adhesion energy and cell elasticity but also the cell individual dynamic properties, found to correlate well with viscoelastic data at large concentrations (phi>0.5).Comment: 4 pages, 5 figure

Entrepreneurial Developments and Challenges in the Sud Muntenia Region of Romania

Entrepreneurship is crucial for the economic development of a region. Using entropy, cluster and shift-share analysis techniques, the authors present a detailed picture of the entrepreneurial milieu of the Sud Muntenia region of Romania, pointing both towards the presence of an overall development process, and also to inter-county and intra-county sectoral imbalances, evolutionary discrepancies and lack of adequate use of territorial resources. Policy recommendations are proposed to address the future challenges for the balanced development of the Sud Muntenia region of Romania. Keywords: entrepreneurship, territorial development, regional business demography, sectoral structure, regional policy JEL Classification: O18, R11, R12, R30

Modeling of residence time distribution : application to a three-phase inverse fluidized bed based on a Mellin transform

The study is focused on modeling of gas and liquid residence time distribution in an aerated liquid system of an inverse fluidized bed bioreactor. Two opposite strategies are currently available: the use of powerful complex computational fluid dynamics (CFD) simulation and the phenomenological semi-empirical models. In this work, a specific methodology is proposed, as follows: the reactor is modeled as a reactor network containing a combination of zones with basic ideal flow patterns such as perfect mixed flow (PMF) and plug flow (PF). The approach is based on a Mellin-modification of the Laplace transformation over the relevant equations. The method allows zero-time solutions for identification analysis. The study shows that the increase of the gas flowrate leads to higher mixing intensity of the gas phase. Decreasing the gas velocity, the inverse fluidized bed tends to perform as a plug flow reactor. The liquid phase performs closer to disperse plug flow

Groups of a Square-Free Order

Hölder\u27s formula for the number of groups of a square-free order is an early advance in the enumeration of finite groups. This paper gives a structural proof of Hölder\u27s result that is accessible to undergraduates. We introduce a number of group theoretic concepts such as nilpotency, the Fitting subgroup, and extensions. These topics, which are usually not covered in undergraduate group theory, feature in the proof of Hölder\u27s result and have wide applicability in group theory. Finally, we remark on further results and conjectures in the enumeration of finite groups