Rapid polynomial approximation in L2L_2-spaces with Freud weights on the real line

The weights $W_\alpha(x)=\exp{(-|x|^{\alpha})}$ $(\alpha>1)$ form a subclass of Freud weights on the real line. Primarily from a functional analytic angle, we investigate the subspace of $L_2(\mathbb R, W_\alpha^2(x)\,dx)$ consisting of those elements that can be rapidly approximated by polynomials. This subspace has a natural Fr\'echet topology, in which it is isomorphic to the space of rapidly decreasing sequences. We show that it consists of smooth functions and obtain concrete results on its topology. For $\alpha=2$ there is a complete and elementary description of this topological vector space in terms of the Schwartz functions.Comment: 18 page

Surjective endomorphisms of projective surfaces -- the existence of infinitely many dense orbits

Let $f \colon X \to X$ be a surjective endomorphism of a normal projective surface. When $\operatorname{deg} f \geq 2$, applying an (iteration of) $f$-equivariant minimal model program (EMMP), we determine the geometric structure of $X$. Using this, we extend the second author's result to singular surfaces to the extent that either $X$ has an $f$-invariant non-constant rational function, or $f$ has infinitely many Zariski-dense forward orbits; this result is also extended to Adelic topology (which is finer than Zariski topology)

Situational Enterprise Services

The ability to rapidly find potential business partners as well as rapidly set up a collaborative business process is desirable in the face of market turbulence. Collaborative business processes are increasingly dependent on the integration of business information systems. Traditional linking of business processes has a large ad hoc character. Implementing situational enterprise services in an appropriate way will deliver the business more flexibility, adaptability and agility. Service-oriented architectures (SOA) are rapidly becoming the dominant computing paradigm. It is now being embraced by organizations everywhere as the key to business agility. Web 2.0 technologies such as AJAX on the other hand provide good user interactions for successful service discovery, selection, adaptation, invocation and service construction. They also balance automatic integration of services and human interactions, disconnecting content from presentation in the delivery of the service. Another Web technology, such as semantic Web, makes automatic service discovery, mediation and composition possible. Integrating SOA, Web 2.0 Technologies and Semantic Web into a service-oriented virtual enterprise connects business processes in a much more horizontal fashion. To be able run these services consistently across the enterprise, an enterprise infrastructure that provides enterprise architecture and security foundation is necessary. The world is constantly changing. So does the business environment. An agile enterprise needs to be able to quickly and cost-effectively change how it does business and who it does business with. Knowing, adapting to diffident situations is an important aspect of today’s business environment. The changes in an operating environment can happen implicitly and explicitly. The changes can be caused by different factors in the application domain. Changes can also happen for the purpose of organizing information in a better way. Changes can be further made according to the users' needs such as incorporating additional functionalities. Handling and managing diffident situations of service-oriented enterprises are important aspects of business environment. In the chapter, we will investigate how to apply new Web technologies to develop, deploy and executing enterprise services

The normalized Laplacian spectrum of subdivisions of a graph

Determining and analyzing the spectra of graphs is an important and exciting research topic in mathematics science and theoretical computer science. The eigenvalues of the normalized Laplacian of a graph provide information on its structural properties and also on some relevant dynamical aspects, in particular those related to random walks. In this paper, we give the spectra of the normalized Laplacian of iterated subdivisions of simple connected graphs. As an example of application of these results we find the exact values of their multiplicative degree-Kirchhoff index, Kemeny's constant and number of spanning trees.Postprint (published version

On the spectra of Markov matrices for weighted Sierpinski graphs

Relevant information from networked systems can be obtained by analyzing the spectra of matrices associated to their graph representations. In particular, the eigenvalues and eigenvectors of the Markov matrix and related Laplacian and normalized Laplacian matrices allow the study of structural and dynamical aspects of a network, like its synchronizability and random walks properties. In this study we obtain, in a recursive way, the spectra of Markov matrices of a family of rotationally invariant weighted Sierpinski graphs. From them we find analytic expressions for the weighted count of spanning trees and the random target access time for random walks on this family of weighted graphs.Postprint (published version

Forecasting and Evaluating Network Growth

This research assesses the implications of existing trends on future network investment, comparing alternative scenarios concerning budgets and investment rules across a variety of performance measures. The main scenarios compare 'stated decision rules';, processes encoded in flowcharts and weights developed from official documents or by discussion with agency staff, with 'revealed decision rules', weights estimated statistically based on observed historical behavior. This research specifies the processes necessary to run the network forecasting models with various decision rules. Results for different scenarios are presented including adding additional constraints for the transportation network expansion and calibration process details. We find that alternative decision rules make only small differences in overall system performance, though they direct investments to very different locations. However, changes in total budget can make a significant difference to system-wide performance.

Structural and Dynamical Properties of Galaxies in a Hierarchical Universe: Sizes and Specific Angular Momenta

We use a state-of-the-art semi-analytic model to study the size and the specific angular momentum of galaxies. Our model includes a specific treatment for the angular momentum exchange between different galactic components. Disk scale radii are estimated from the angular momentum of the gaseous/stellar disk, while bulge sizes are estimated assuming energy conservation. The predicted size--mass and angular momentum--mass relations are in fair agreement with observational measurements in the local Universe, provided a treatment for gas dissipation during major mergers is included. Our treatment for disk instability leads to unrealistically small radii of bulges formed through this channel, and predicts an offset between the size--mass relations of central and satellite early-type galaxies, that is not observed. The model reproduces the observed dependence of the size--mass relation on morphology, and predicts a strong correlation between specific angular momentum and cold gas content. This correlation is a natural consequence of galaxy evolution: gas-rich galaxies reside in smaller halos, and form stars gradually until present day, while gas-poor ones reside in massive halos, that formed most of their stars at early epochs, when the angular momentum of their parent halos is low. The dynamical and structural properties of galaxies can be strongly affected by a different treatment for stellar feedback, as this would modify their star formation history. A higher angular momentum for gas accreted through rapid mode does not affect significantly the properties of massive galaxies today, but has a more important effect on low-mass galaxies at higher redshift.Comment: 26 pages, 14 figures, 4 appendices. Accepted for publication in MNRA

The Evolution of Sizes and Specific Angular Momenta in Hierarchical Models of Galaxy Formation and Evolution

We extend our previous work focused at $z\sim0$, studying the redshift evolution of galaxy dynamical properties using the state-of-the-art semi-analytic model GAEA: we show that the predicted size-mass relation for disky/star forming and quiescent galaxies is in good agreement with observational estimates, up to $z\sim2$. Bulge dominated galaxies have sizes that are offset low with respect to observational estimates, mainly due to our implementation of disk instability at high redshift. At large masses, both quiescent and bulge dominated galaxies have sizes smaller than observed. We interpret this as a consequence of our most massive galaxies having larger gas masses than observed, and therefore being more affected by dissipation. We argue that a proper treatment of quasar driven winds is needed to alleviate this problem. Our model compact galaxies have number densities in agreement with observational estimates and they form most of their stars in small and low angular momentum high-$z$ halos. GAEA predicts that a significant fraction of compact galaxies forming at high-$z$ is bound to merge with larger structures at lower redshifts: therefore they are not the progenitors of normal-size passive galaxies at $z=0$. Our model also predicts a stellar-halo size relation that is in good agreement with observational estimates. The ratio between stellar size and halo size is proportional to the halo spin and does not depend on stellar mass but for the most massive galaxies, where AGN feedback leads to a significant decrease of the retention factor (from about 80 per cent to 20 per cent).Comment: Accepted for publication in MNRAS, 17 pages, 11 figure