Enumeration of surfaces containing an elliptic quartic curve

A very general surface of degree at least four in projective space of dimension three contains no curves other than intersections with surfaces. We find a formula for the degree of the locus of surfaces of degree at least five which contain some elliptic quartic curve. We also compute the degree of the locus of quartic surfaces containing an elliptic quartic curve, a case not covered by that formula.Comment: Minor typos corrected. To appear on Proceedings of the American Mathematical Societ

Floquet time crystal in the Lipkin-Meshkov-Glick model

In this work we discuss the existence of time-translation symmetry breaking in a kicked infinite-range-interacting clean spin system described by the Lipkin-Meshkov-Glick model. This Floquet time crystal is robust under perturbations of the kicking protocol, its existence being intimately linked to the underlying $\mathbb{Z}_2$ symmetry breaking of the time-independent model. We show that the model being infinite-range and having an extensive amount of symmetry breaking eigenstates is essential for having the time-crystal behaviour. In particular we discuss the properties of the Floquet spectrum, and show the existence of doublets of Floquet states which are respectively even and odd superposition of symmetry broken states and have quasi-energies differing of half the driving frequencies, a key essence of Floquet time crystals. Remarkably, the stability of the time-crystal phase can be directly analysed in the limit of infinite size, discussing the properties of the corresponding classical phase space. Through a detailed analysis of the robustness of the time crystal to various perturbations we are able to map the corresponding phase diagram. We finally discuss the possibility of an experimental implementation by means of trapped ions.Comment: 14 pages, 12 figure

Quantum clock models with infinite-range interactions

We study the phase diagram, both at zero and finite temperature, in a class of $\mathbb{Z}_q$ models with infinite range interactions. We are able to identify the transitions between a symmetry-breaking and a trivial phase by using a mean-field approach and a perturbative expansion. We perform our analysis on a Hamiltonian with $2p$-body interactions and we find first-order transitions for any $p>1$; in the case $p=1$, the transitions are first-order for $q=3$ and second-order otherwise. In the infinite-range case there is no trace of gapless incommensurate phase but, when the transverse field is maximally chiral, the model is in a symmetry-breaking phase for arbitrarily large fields. We analytically study the transtion in the limit of infinite $q$, where the model possesses a continuous $U(1)$ symmetry

Definindo a camada de gestão operacional de cursos das plataformas de eLearning com base numa ontologia de domínio

O presente artigo pretende descrever o processo que tem sido seguido no sentido da obtenção de um referencial para a camada de gestão on-line dos processos de e-learning. Tal camada deverá ser desenvolvida por forma a poder integrar-se no todo que constiui uma qualquer plataforma de ensino/aprendizagem utilizando tecnologias de informação e comunicação, nomeadamente aquelas que assentam o seu funcionamento nos serviços da Internet. Esta integração será viabilizada a partir da utilização de de uma abordagem comum àquela que já se verifica, relativamente à especificação das restantes camadas, em particular no âmbito do projecto SCORM. Existem diversas abordagens capazes de permitir a obtenção destes objectivos, isto é, de permitirem a obtenção dos metadados necessários à completa caracterização da camada de gestão operacional de cursos em plataformas de e-Learning. Para levar a cabo este trabalho, recorremos à escrita de uma ontologia de domínio, aplicável a este caso concreto. Tal abordagem, para além de conjugar em si todas as caratecrísticas de formalismo e rigor desejáveis, permite ainda um entendimento muito fácil do modelo desenvolvido. Para além disso, a sua tradução para XML pode ser também obtida com um mínimo de esforço, possibilitando a divulgação do documento num formato de utilização universal na Web

Improving energy and material efficiency in distribution transformers: Assessing the impact of stricter minimum energy performance standards on cost and material use

The EU ecodesign regulation for power transformers is currently under revision. While no option for reducing energy losses can be ignored in light of the European Green Deal, there are concerns about what impact stricter minimum energy performance standards could have on costs and material use. To what extent do alternative design strategies or a systems approach to material use change how this subject is viewed? And how far will a decline in energy losses compensate for the extra capital investment? The European Copper Institute (ECI) conducted a quantitative comparison between various scenarios and design strategies

Area law for fixed points of rapidly mixing dissipative quantum systems

We prove an area law with a logarithmic correction for the mutual information for fixed points of local dissipative quantum system satisfying a rapid mixing condition, under either of the following assumptions: the fixed point is pure, or the system is frustration free.Comment: 17 pages, 1 figure. Final versio

Effect of Mn and Fe contents on the microstructural evolution of two twin roll caster Al-Fe-Mn-Si alloys

Com o crescimento constante da utilização do processo twin roll caster para a obtenção de chapas de alumínio, torna-se cada vez mais necessário um melhor conhecimento das características das chapas obtidas por este processo. Foram estudadas, nesse trabalho, duas ligas não tratáveis termicamente, 3003 (1,2%Mn; 0,6%Fe) e 8106 (0,4%Mn; 1,5%Fe). As amostras foram retiradas de chapas com 7 mm de espessura a partir de bobinas brutas de fundição e após tratamento térmico de homogeneização de 500°C por 12 horas. As técnicas utilizadas para a caracterização das amostras foram: microscopia óptica com auxílio de luz polarizada, ensaio de microdureza, além dos ensaios de condutividade elétrica.The continuous growth in the usage of the twin roll caster process for aluminum plate production demands a better understanding of the plate's final characteristics. In this work two non-heat treatable largely-used aluminum alloys, namely 3003 (1.2%Mn; 0.6%Fe) and 8106 (0.4%Mn; 1.5% Fe), have been studied. Samples were obtained from 7mm thick plates stemming from rolls in the as-cast condition and after 500°C/12h homogenizing heat treatment. The techniques employed in the sample characterization included: polarized light optical microscopy, microhardness and electrical conductivity tests

Computation of energy exchanges by combining information theory and a key thermodynamic relation: Physical applications

Abstract By considering a simple thermodynamic system, in thermal equilibrium at a temperature T and in the presence of an external parameter A , we focus our attention on the particular thermodynamic (macroscopic) relation d U = T d S + δ W . Using standard axioms from information theory and the fact that the microscopic energy levels depend upon the external parameter A , we show that all usual results of statistical mechanics for reversible processes follow straightforwardly, without invoking the Maximum Entropy principle. For the simple system considered herein, two distinct forms of heat contributions appear naturally in the Clausius definition of entropy, T d S = δ Q ( T ) + δ Q ( A ) = C A ( T ) d T + C T ( A ) d A . We give a special attention to the amount of heat δ Q ( A ) = C T ( A ) d A , associated with an infinitesimal variation d A at fixed temperature, for which a "generalized heat capacity", C T ( A ) = T ( ∂ S / ∂ A ) T , may be defined. The usefulness of these results is illustrated by considering some simple thermodynamic cycles

Pengaruh Instagram Marketing di Instagram ZAP Clinic terhadap Customer Engagement: Survei terhadap Pengikut Instagram @zapcoid Selama Pandemi COVID-19

Industri kecantikan diekspektasikan bertumbuh pesat di Indonesia bertahun-tahun ke depan. Klinik estetika menjadi satu kegiatan bisnis yang merasakan perkembangan industri ini. Namun, masuknya pandemi COVID-19 di Indonesia membuat kegiatan yang memiliki kontak fisik, seperti klinik estetika, harus berhenti total. Klinik estetika seperti ZAP Clinic harus memutar cara untuk mempertahankan bisnisnya, dengan memanfaatkan Instagram Marketing. Sayangnya, engaement rate dari Instagram @zapcoid terpantau rendah dibandingkan klinik estetika lain. Penelitian ini ingin melihat apakah Instagram Marketing berpengaruh terhadap customer engagement. Penelitian dilakukan terhadap 308 responden dari populasi yaitu pengikut Instagram @zapcoid, dengan pendekatan kuantitatif eksplanatif, berparadigma positivisme, serta melakukan survei dengan instrumen kuesioner. Penelitian ini menemukan bahwa terdapat pengaruh antara Instagram marketing terhadap customer engagement dengan korelasi di tingkat sedang. Melalui uji regresi linear sederhana, Instagram Marketing memiliki pengaruh sebanyak 29,5% terhadap customer engagament sedangkan 70,5% faktor lain tidak ada di penelitian ini. Didapatkan persamaan Y=-0,393+0,425(X) yang berarti hubungan mengarah positif. Selain itu, Instagram Marketing memiliki pengaruh yang signifikan terhadap customer engagement