The singularity problem and phase-space noncanonical noncommutativity

The Wheeler-DeWitt equation arising from a Kantowski-Sachs model is considered for a Schwarzschild black hole under the assumption that the scale factors and the associated momenta satisfy a noncanonical noncommutative extension of the Heisenberg-Weyl algebra. An integral of motion is used to factorize the wave function into an oscillatory part and a function of a configuration space variable. The latter is shown to be normalizable using asymptotic arguments. It is then shown that on the hypersufaces of constant value of the argument of the wave function's oscillatory piece, the probability vanishes in the vicinity of the black hole singularity.Comment: 4 pages, revtex

A Discretization of the Hadamard fractional derivative

We present a new discretization for the Hadamard fractional derivative, that simplifies the computations. We then apply the method to solve a fractional differential equation and a fractional variational problem with dependence on the Hadamard fractional derivative

Emerging startup studios in Portugal : organizational characteristics of Portuguese startup studios

There is an emerging trend in the entrepreneurial landscape which promises to become revolutionary: Startup Studios. This emerging incubation model is generally characterized by the development of internally generated ideas and the creation of its own cohort of startups, supported by internal resources and a multidisciplinary team. Despite the Startup Studio model being already highly implemented in bigger and more developed entrepreneurial ecosystems, the infancy of the underlying concept and the diverging way each Startup Studio organizes itself, combined with the lack of academic research on this topic leaves an unclear definition of the Startup Studio concept. This thesis aims to clarify the definition of the Startup Studio concept and its characteristics. Moreover, it focuses on the implementation of the studio incubator model in smaller and emerging entrepreneurial ecosystems to understand if it can be a viable alternative to foster innovation and prompt economic development. Thus, two case studies of Startup Studios in Portugal were conducted. The findings of this analysis revealed that elements like funding, type of founders and exit strategy will be context specific, differing from Startup Studios in bigger economies. However, elements like ideation process, equity distribution, operations and team set up of Startup Studios in smaller and emerging entrepreneurial ecosystem will be like the ones found in more developed entrepreneurial ecosystem. Based on this evidence, a definition for the Startup Studios is suggested as well as the proposition of the possible implication of the studio incubator model in smaller economies.Tem-se observado uma tendência emergente que promete revolucionar o panorama de empreendedorismo: os Startup Studios. Este modelo de incubação emergente é geralmente caracterizado pelo desenvolvimento de ideias geradas internamente e pela criação do seu próprio grupo de startups incubadas, suportado pela utilização de recursos internos e por uma equipa multidisciplinar. Apesar deste modelo já estar largamente implementado em ecossistemas de empreendedorismo mais desenvolvidos, a infância do conceito subjacente e a forma como cada Startup Studio se organiza, em conjunto com a falta de investigação académica sobre este tópico deixa uma definição pouco clara do conceito. Esta tese tem como objetivo esclarecer a definição do conceito do Startup Studio e suas características. Além disso, concentra-se na implementação deste modelo de incubação em ecossistemas de empreendedorismo menores e emergentes, para entender se o mesmo pode ser considerado uma alternativa viável para promover inovação e o desenvolvimento económico destes ecossistemas. Assim, foi conduzido um estudo de caso com dois Startup Studios em Portugal. Os resultados desta análise revelaram que elementos como financiamento, tipo de fundadores e estratégia de saída são específicos ao contexto e diferentes dos observados em Startup Studios em economias mais desenvolvidas. No entanto, elementos como processo de ideação, distribuição de capital, operações e a configuração da equipa nos Startup Studios em ecossistemas de empreendedorismo emergentes serão semelhantes aos encontrados em ecossistemas de empreendedorismo mais desenvolvidos. Com base nestas evidências, sugere-se uma definição para o conceito de Startup Studio, bem como as possíveis implicações que este modelo terá em economias menores

An approximation formula for the Katugampola integral

The objective of this paper is to present an approximation formula for the Katugampola fractional integral, that allows us to solve fractional problems with dependence on this type of fractional operator. The formula only depends on first-order derivatives, and thus converts the fractional problem into a standard one. With some examples, we show the accuracy of the method, and then we present the utility of the method by solving a fractional integral equation