The McKay Conjecture and central isomorphic character triples

We refine the reduction theorem of the McKay Conjecture proved by Isaacs, Malle and Navarro. Assuming the inductive McKay condition, we obtain a strong version of the McKay Conjecture that gives central isomorphic character triples

Generalized Harish-Chandra theory for Dade's Conjecture

We prove new results in generalized Harish-Chandra theory providing a description of the so-called Brauer--Lusztig blocks in terms of the information encoded in the $\ell$-adic cohomology of Deligne--Lusztig varieties. Furthermore, we apply these results to obtain new progress towards the verification of the inductive condition for Dade's Conjecture in the case of groups of Lie type in non-defining characteristic

Projections of SDEs onto Submanifolds

In [AB16] the authors define three projections of $\mathbb R^d$-valued stochastic differential equations (SDEs) onto submanifolds: the Stratonovich, It\^o-vector and It\^o-jet projections. In this paper, after a brief survey of SDEs on manifolds, we begin by giving these projections a natural, coordinate-free description, each in terms of a specific representation of manifold-valued SDEs. We proceed by deriving formulae for the three projections in ambient $\mathbb R^d$-coordinates. We use these to show that the It\^o-vector and It\^o-jet projections satisfy respectively a weak and mean-square optimality criterion "for small t": this is achieved by solving constrained optimisation problems. These results confirm, but do not rely on the approach taken in [AB16], which is formulated in terms of weak and strong It\^o-Taylor expansions. In the final section we exhibit examples showing how the three projections can differ, and explore alternative notions of optimality

Monomial characters of finite solvable groups

We give new evidences to the fact that the structure of a solvable group can be controlled by irreducible monomial characters. In particular we inspect the role of monomial characters in Isaacs-Navarro-Wolf's conjecture and in Gluck's conjecture

The simplicial complex of Brauer pairs of a finite reductive group

In this paper we study the simplicial complex induced by the poset of Brauer pairs ordered by inclusion for the family of finite reductive groups. In the defining characteristic case, the homotopy type of this simplicial complex coincides with that of the Tits building thanks to a well-known result of Quillen. On the other hand, in the non-defining characteristic case, we show that the simplicial complex of Brauer pairs is homotopy equivalent to a simplicial complex determined by generalised Harish-Chandra theory. This extends earlier results of the author on the Brown complex and makes use of the theory of connected subpairs and twisted block induction developed by Cabanes and Enguehard

Simulazione energetica di un complesso di edifici ad uso commerciale e residenziale: confronto tra soluzioni tradizionali e unità ad acqua con produzione contemporanea di energia termica e frigorifera

Dopo la costruzione del modello degli edifici necessaria per conoscerne i fabbisogni energetici richiesti, si presentano alcune simulazione svolte considerando diverse tipologie di macchine per soddisfare i carichi calcolati. Tra queste sono presenti macchine tradizionali, come refrigeratori e caldaie, e macchine per la produzione contemporanea di energia termica e frigorifera con sorgente acqua, le quali vengono confrontate tra di loro per valutarne la convenienza, sia economica che energeticaope

Non-Geometric Rough Paths on Manifolds

We provide a theory of manifold-valued rough paths of bounded 3 > p-variation, which we do not assume to be geometric. Rough paths are defined in charts, and coordinate-free (but connection-dependent) definitions of the rough integral of cotangent bundle-valued controlled paths, and of RDEs driven by a rough path valued in another manifold, are given. When the path is the realisation of semimartingale we recover the theory of It\^o integration and SDEs on manifolds [\'E89]. We proceed to present the extrinsic counterparts to our local formulae, and show how these extend the work in [CDL15] to the setting of non-geometric rough paths and controlled integrands more general than 1-forms. In the last section we turn to parallel transport and Cartan development: the lack of geometricity leads us to make the choice of a connection on the tangent bundle of the manifold TM, which figures in an It\^o correction term in the parallelism RDE; such connection, which is not needed in the geometric/Stratonovich setting, is required to satisfy properties which guarantee well-definedness, linearity, and optionally isometricity of parallel transport. We conclude by providing numerous examples, some accompanied by numerical simulations, which explore the additional subtleties introduced by our change in perspective

Influence of pulsating flow on dispersion in helically coiled tubes and coiled flow inverters

Narrow Residence Time Distribution (RTD) is a desirable characteristic for many chemical engineering processes. However, when flow devices operate at low Reynolds number (characteristic for micro and millifluidic devices), significant fluid dispersion can occur. Narrowing RTD, while maintaining long space time, is currently a challenge. In this work, we addressed this by a combination of passive and active mixing techniques similar to those found in arterial flow. In the biomedical literature, plug flow is often assumed due to low axial dispersion in blood flow [1]. By reviewing this literature, we identified that the reduction in axial dispersion in arteries can be attributed to two factors, curvature of the blood vessels (Dean number in arteries reaches 260) [2] and pulsation of the flow [3]. Flow in curved geometries leads to formation of Dean vortices due to centrifugal force and is a well-established passive mixing technique [4]. At the same time, the introduction of a periodic variation in the flow rate (later on referred to as pulsation for simplicity) is an active technique which was first described in the fluid dynamics literature in the early 1960s [5]; however, it is yet to be utilized to its full potential within the millifluidic community. In process engineering, each of these techniques has been shown separately to have a positive effect and here we investigate the effect of utilizing both of these techniques simultaneously for narrowing RTD. The effect of two key dimensionless pulsation parameters, amplitude ratio (, dimensionless amplitude of pulsation) and Strouhal Number (St, dimensionless frequency of pulsation), on RTDs was studied in Helically Coiled Tubes (HCTs) and Coiled Flow Inverters (CFIs). Additionally, the contribution of tube elasticity was also considered, since arteries are less rigid than the hard walled channels typically used in chemical engineering processes. An experimental system was developed to conduct RTD experiments via step injection of tracer at the tube inlet and measurement of tracer concentration via UV-Vis spectroscopy at the tube outlet. Experiments without pulsation were also conducted for comparison. The results showed that in the presence of pulsation narrower RTDs are achievable. Furthermore, both increase in amplitude and frequency of pulsation have a positive effect on reducing dispersion. Separately, pulsation and curved geometries could achieve a maximum reduction of vessel dispersion number (dimensionless parameter that measures the extent of axial dispersion) from 190 to 110 and 125, respectively. When tube curvature and flow pulsation are combined, the vessel dispersion number was reduced by an order of magnitude (from 190 to 20). Numerical simulations supported the experimental results and showed that in the presence of pulsation there is a significant enhancement of radial mixing. Further consideration included the effect of tube elasticity on RTD. It was found that reduction in the RTD width in a harder material is more pronounced than that in a softer material. Overall, the results show a promising technique for reducing the RTD, which can benefit a variety of fields including process intensification, particle synthesis and continuous manufacturing. [1] R.B. Buxton, L.R. Frank, E.C. Wong, B. Siewert, S. Warach, R.R. Edelman, “A general kinetic model for quantitative perfusion imaging with arterial spin labeling”, Magn. Reson. Med. 40 (1998) 383 [2] D. N. Ku, “Blood Flow in Arteries”, Ann. Rev. of Fl. Mech. 29 (1997) 399 [3] M.D. Ford, N. Alperin, S.H. Lee, D.W. Holdsworth, D.A. Steinman, “Characterization of volumetric flow rate waveforms in the normal internal carotid and vertebral arteries, Physiol. Meas. 26 (2005) 477 [4] W. R. Dean, “Note on the motion of fluid in a curved pipe”, Phil. Mag., 4 (20) (1928) 208-223 [5] R. Aris, “On the dispersion of a solute in pulsating flow through a tube,” Proc. R. Soc. A Math. Phys. Eng. Sci., 259 (1960) 370–37

Application of a smart dynamic scale for measuring live-fish biomass in aquaculture

— The need of measuring the fish biomass, either for in-land facilities or offshore cages, drove recently to develop a cheap dynamic scale (by MEGA Materials srl), based on a board of the Arduino family, suitable to measure live-fish weights. Via a Bluetooth transmitter and a specific app the communication with smartphones is allowed. The estimation of live-fish biomass is extremely relevant to precisely quantify the daily dose of feed to be supplied and to avoid a reduction of fish growth. We present the comparison between ‘static’ and ‘dynamic’ weight measures of seabream juveniles reared in tanks