A diophantine equation for sums of consecutive like powers

We show that the diophantine equation $n^\ell+(n+1)^\ell + ...+ (n+k)^\ell=(n+k+1)^\ell+ ...+ (n+2k)^\ell$ has no solutions in positive integers $k,n \ge 1$ for all $\ell \ge 3$.Comment: History of the problem adde

Has HIV evolved to induce immune pathogenesis?

Human immunodeficiency virus (HIV) induces a chronic generalized activation of the immune system, which plays an important role in the pathogenesis of AIDS. This ability of the virus might either be an evolved (adaptive) trait or a coincidental side effect of jumping to a new host species. We argue that selection favours the ability of HIV to induce immune activation at the local sites of infection (e.g. lymph follicles) but not at the systemic level. Immune activation increases the supply of susceptible target cells; however, mutations that increase systemic immune activation benefit all virus variants equally and are therefore selectively neutral. We thus conclude that the generalized immune acti- vation that is probably responsible for pathogenesis is probably not directly under selection

Constraining cometary ejection models from meteor storm observations

Modelling and observations of the Leonids have shown that maxima in the meteor storm activity can be identified as due to particles released from the comet during certain perihelion passages. If the particles originating from a certain perihelion passage can be identified, the next obvious question to ask is what information can be gained about the ejection process of particles from a cometary nucleus. We have developed a method to calculate the set of all possible dust trajectories that reach the Earth at some given time. The method involves numerical integration of a few dust particles only and is applied to the Leonid activity in the year 2000. We show that particles of different sizes entering the Earth's atmosphere at the same time were released from the comet at different heliocentric distances. Therefore one has to make assumptions about the activity of the comet with heliocentric distance in order to derive the cometary mass distribution from an observed meteor mass distribution. However, we outline how lower limits on the ejection velocity of the observed particles can be derived

East African topography and volcanism explained by a single, migrating plume

Anomalous topographic swells and Cenozoic volcanism in east Africa have been associated with mantle plumes. Several models involving one or more fixed plumes beneath the northeastward migrating African plate have been suggested to explain the space-time distribution of magmatism in east Africa. We devise paleogeographically constrained global models of mantle convection and, based on the evolution of flow in the deepest lower mantle, show that the Afar plume migrated southward throughout its lifetime. The models suggest that the mobile Afar plume provides a dynamically consistent explanation for the spatial extent of the southward propagation of the east African rift system (EARS), which is difficult to explain by the northeastward migration of Africa over one or more fixed plumes alone, over the last ≈45 Myrs. We further show that the age-progression of volcanism associated with the southward propagation of EARS is consistent with the apparent surface hotspot motion that results from southward motion of the modelled Afar plume beneath the northeastward migrating African plate. The models suggest that the Afar plume became weaker as it migrated southwards, consistent with trends observed in the geochemical record

The new ecosystem of the digital age: Impact of blockchain technology on the accounting environment and financial statement fraud detection

The agency theory is an underlying framework for the installation of corporate governance roles in business enterprises. Their function to shield from financial statement fraud remains a shield with lacks that allow the occurrence of unsolved and intrinsic misbehaviour in business conduct. Technological developments have not been able to solve this issue, still waiting for a liberator from these well-known chains. One is seen in the use of Blockchain technology, the framework that builds trust among untrusting participants in networks such as Bitcoin or Ethereum. Since its mainstreaming popularity, researchers, corporations, and advocates foresee a great impact on the accounting industry that stems from the use of Blockchain. Taking this opportunity, this work investigates on these assumptions by reviewing literature on the domain, using case studies of former financial statement frauds to frame the fraudster’s profile, and applying it in the suggested scenario of blockchain-based accounting. By doing so, the use of permissioned blockchains raises doubt in a scenario that is shaped by management override activities, causing severe adversely affections to tiers in an ecosystem that trusts a technology and its “immutable” records.A teoria da agência é um quadro subjacente para a instalação de funções de governação empresarial em empresas comerciais. A sua função de protecção contra a fraude de declarações financeiras continua a ser um escudo com carências que permitem a ocorrência de comportamentos incorrectos não resolvidos e intrínsecos na conduta empresarial. Os desenvolvimentos tecnológicos não foram capazes de resolver esta questão, ainda à espera de um libertador destas bem conhecidas cadeias. Vê-se na utilização da tecnologia Blockchain, a estrutura que gera confiança entre os participantes não confiantes em redes como a Bitcoin ou a Ethereum. Desde a sua popularidade de mainstreaming, investigadores, empresas e defensores prevêem um grande impacto na indústria da contabilidade que resulta da utilização da Blockchain. Aproveitando esta oportunidade, este trabalho investiga estes pressupostos através da revisão da literatura sobre o domínio, utilizando estudos de caso de antigas fraudes em demonstrações financeiras para enquadrar o perfil do fraudador e aplicando-o no cenário sugerido de contabilidade baseada em cadeias de bloqueio. Ao fazê-lo, a utilização sugerida de cadeias de bloqueio autorizadas levanta dúvidas num cenário que é moldado por actividades de substituição da gestão, causando graves afecções negativas a camadas num ecossistema que confia numa tecnologia e nos seus registos "imutáveis"