Autonomous agile teams: Challenges and future directions for research

According to the principles articulated in the agile manifesto, motivated and empowered software developers relying on technical excellence and simple designs, create business value by delivering working software to users at regular short intervals. These principles have spawned many practices. At the core of these practices is the idea of autonomous, self-managing, or self-organizing teams whose members work at a pace that sustains their creativity and productivity. This article summarizes the main challenges faced when implementing autonomous teams and the topics and research questions that future research should address

The fundamental plane of evolving red nuggets

We present an exploration of the mass structure of a sample of 12 strongly lensed massive, compact early-type galaxies at redshifts $z\sim0.6$ to provide further possible evidence for their inside-out growth. We obtain new ESI/Keck spectroscopy and infer the kinematics of both lens and source galaxies, and combine these with existing photometry to construct (a) the fundamental plane (FP) of the source galaxies and (b) physical models for their dark and luminous mass structure. We find their FP to be tilted towards the virial plane relative to the local FP, and attribute this to their unusual compactness, which causes their kinematics to be totally dominated by the stellar mass as opposed to their dark matter; that their FP is nevertheless still inconsistent with the virial plane implies that both the stellar and dark structure of early-type galaxies is non-homologous. We also find the intrinsic scatter of their FP to be comparable to the local value, indicating that variations in the stellar mass structure outweight variations in the dark halo in the central regions of early-type galaxies. Finally, we show that inference on the dark halo structure -- and, in turn, the underlying physics -- is sensitive to assumptions about the stellar initial mass function (IMF), but that physically-motivated assumptions about the IMF imply haloes with sub-NFW inner density slopes, and may present further evidence for the inside-out growth of compact early-type galaxies via minor mergers and accretion.Comment: 10 pages, 3 figures, 3 tables; submitted to MNRA

Dynamics of Fractal Solids

We describe the fractal solid by a special continuous medium model. We propose to describe the fractal solid by a fractional continuous model, where all characteristics and fields are defined everywhere in the volume but they follow some generalized equations which are derived by using integrals of fractional order. The order of fractional integral can be equal to the fractal mass dimension of the solid. Fractional integrals are considered as an approximation of integrals on fractals. We suggest the approach to compute the moments of inertia for fractal solids. The dynamics of fractal solids are described by the usual Euler's equations. The possible experimental test of the continuous medium model for fractal solids is considered.Comment: 12 pages, LaTe

Red nuggets grow inside-out: evidence from gravitational lensing

We present a new sample of strong gravitational lens systems where both the foreground lenses and background sources are early-type galaxies. Using imaging from HST/ACS and Keck/NIRC2, we model the surface brightness distributions and show that the sources form a distinct population of massive, compact galaxies at redshifts $0.4 \lesssim z \lesssim 0.7$, lying systematically below the size-mass relation of the global elliptical galaxy population at those redshifts. These may therefore represent relics of high-redshift red nuggets or their partly-evolved descendants. We exploit the magnifying effect of lensing to investigate the structural properties, stellar masses and stellar populations of these objects with a view to understanding their evolution. We model these objects parametrically and find that they generally require two S\'ersic components to properly describe their light profiles, with one more spheroidal component alongside a more envelope-like component, which is slightly more extended though still compact. This is consistent with the hypothesis of the inside-out growth of these objects via minor mergers. We also find that the sources can be characterised by red-to-blue colour gradients as a function of radius which are stronger at low redshift -- indicative of ongoing accretion -- but that their environments generally appear consistent with that of the general elliptical galaxy population, contrary to recent suggestions that these objects are predominantly associated with clusters.Comment: 21 pages; accepted for publication in MNRA

Weyl Quantization of Fractional Derivatives

The quantum analogs of the derivatives with respect to coordinates q_k and momenta p_k are commutators with operators P_k and $Q_k. We consider quantum analogs of fractional Riemann-Liouville and Liouville derivatives. To obtain the quantum analogs of fractional Riemann-Liouville derivatives, which are defined on a finite interval of the real axis, we use a representation of these derivatives for analytic functions. To define a quantum analog of the fractional Liouville derivative, which is defined on the real axis, we can use the representation of the Weyl quantization by the Fourier transformation.Comment: 9 pages, LaTe

Transport Equations from Liouville Equations for Fractional Systems

We consider dynamical systems that are described by fractional power of coordinates and momenta. The fractional powers can be considered as a convenient way to describe systems in the fractional dimension space. For the usual space the fractional systems are non-Hamiltonian. Generalized transport equation is derived from Liouville and Bogoliubov equations for fractional systems. Fractional generalization of average values and reduced distribution functions are defined. Hydrodynamic equations for fractional systems are derived from the generalized transport equation.Comment: 11 pages, LaTe

Spectral Asymptotics of Eigen-value Problems with Non-linear Dependence on the Spectral Parameter

We study asymptotic distribution of eigen-values $\omega$ of a quadratic operator polynomial of the following form $(\omega^2-L(\omega))\phi_\omega=0$, where $L(\omega)$ is a second order differential positive elliptic operator with quadratic dependence on the spectral parameter $\omega$. We derive asymptotics of the spectral density in this problem and show how to compute coefficients of its asymptotic expansion from coefficients of the asymptotic expansion of the trace of the heat kernel of $L(\omega)$. The leading term in the spectral asymptotics is the same as for a Laplacian in a cavity. The results have a number of physical applications. We illustrate them by examples of field equations in external stationary gravitational and gauge backgrounds.Comment: latex, 20 page

Fractional Generalization of Gradient Systems

We consider a fractional generalization of gradient systems. We use differential forms and exterior derivatives of fractional orders. Examples of fractional gradient systems are considered. We describe the stationary states of these systems.Comment: 11 pages, LaTe

Fractional Derivative as Fractional Power of Derivative

Definitions of fractional derivatives as fractional powers of derivative operators are suggested. The Taylor series and Fourier series are used to define fractional power of self-adjoint derivative operator. The Fourier integrals and Weyl quantization procedure are applied to derive the definition of fractional derivative operator. Fractional generalization of concept of stability is considered.Comment: 20 pages, LaTe

Nonholonomic Constraints with Fractional Derivatives

We consider the fractional generalization of nonholonomic constraints defined by equations with fractional derivatives and provide some examples. The corresponding equations of motion are derived using variational principle.Comment: 18 page