New Expansion Formulas for a Family of the λ

We derive several new expansion formulas for a new family of the λ-generalized Hurwitz-Lerch zeta functions which were introduced by Srivastava (2014). These expansion formulas are obtained by making use of some important fractional calculus theorems such as the generalized Leibniz rules, the Taylor-like expansions in terms of different functions, and the generalized chain rule. Several (known or new) special cases are also considered

Applying different methods to model dry and wet spells at daily scale in a large range of rainfall regimes across Europe

The modelling of the occurrence of rainfall dry and wet spells (ds and ws, respectively) can be jointly conveyed using the inter-arrival times (it). While the modelling of it has the advantage of requiring a single fitting for the description of all rainfall time characteristics (including wet and dry chains, an extension of the concept of spells), the assumption on the independence and identical distribution of the renewal times it implicitly imposes a memoryless property on the derived ws, which may not be true in some cases. In this study, two different methods for the modelling of rainfall time characteristics at station scale have been applied: i) a direct method (DM) that fits the discrete Lerch distribution to it records, and then derives ws and ds (as well as the corresponding chains) from the it distribution; and ii) an indirect method (IM) that fits the Lerch distribution to the ws and ds records separately, relaxing the assumptions of the renewal process. The results of this application over six stations in Europe, characterized by a wide range of rainfall regimes, highlight how the geometric distribution does not always reasonably reproduce the ws frequencies, even when it are modelled by the Lerch distribution well. Improved performances are obtained with the IM, thanks to the relaxation of the assumption on the independence and identical distribution of the renewal times. A further improvement on the fittings is obtained when the datasets are separated into two periods, suggesting that the inferences may benefit for accounting for the local seasonality.Comment: 28 pages, 11 figure

New Expansion Formulas for a Family of the -Generalized Hurwitz-Lerch Zeta Functions

We derive several new expansion formulas for a new family of the -generalized Hurwitz-Lerch zeta functions which were introduced by Srivastava (2014). These expansion formulas are obtained by making use of some important fractional calculus theorems such as the generalized Leibniz rules, the Taylor-like expansions in terms of different functions, and the generalized chain rule. Several (known or new) special cases are also considered

Zeta Function Methods and Quantum Fluctuations

A review of some recent advances in zeta function techniques is given, in problems of pure mathematical nature but also as applied to the computation of quantum vacuum fluctuations in different field theories, and specially with a view to cosmological applications.Comment: 17 pages, Talk given at the Conference ``Quantum Theory and Symmetries - 5'', Valladolid (Spain), July 22 - 28, 200

Inside UMaine, vol. 3, no. 11

Inside UMaine was the employee newsletter issued starting in 2005. The newsletter was published once each month during the academic year. The intent was to complement the university\u27s other communication vehicles, including the UMaine Today magazine, UMaine Today Online and various other online Information Services, such as the university\u27s Web-based calendar. The newsletter took over where the Maine Perspective left off to promote professional achievement and stories about campus events and advancements

Age of Information in Multi-Hop Connections with Tributary Traffic and no Preemption

Age of Information (AoI) has gained significant attention from the research community because of its applications to Internet of Things (IoT) monitoring and control. In this work, we treat multihop connections over queuing networks with tributary flows and non-preemptive service: packets cannot be discarded because they are utilized for other system objectives, such as data analytics. Without preemption, the key tool for optimizing AoI is then the scheduling policy between the different data flows at each intermediate node. This is the subject of our analysis, along with the impact of packet erasure on the age. We derive upper and lower bounds for the average AoI considering several queuing policies in arbitrary network topologies, and present the results in different scenarios. Network topology, tributary traffic load, and link characteristics such as packet erasure generate complex trade-offs, which affect the optimal operation point and the age performance. The scheduling strategy at each node can also affect performance and fairness among users, particularly at critical bottleneck links, which have a significant impact on the overall performance of the whole network.acceptedVersionPeer reviewe