Mathematical aspects of the Heisenberg uncertainty principle within local fractional Fourier analysis

In this paper, we discuss the mathematical aspects of the Heisenberg uncertainty principle within local fractional Fourier analysis. The Schrödinger equation and Heisenberg uncertainty principles are structured within local fractional operators.

Self-similarity principle: the reduced description of randomness

A new general fitting method based on the Self-Similar (SS) organization of random sequences is presented. The proposed analytical function helps to fit the response of many complex systems when their recorded data form a self-similar curve. The verified SS principle opens new possibilities for the fitting of economical, meteorological and other complex data when the mathematical model is absent but the reduced description in terms of some universal set of the fitting parameters is necessary. This fitting function is verified on economical (price of a commodity versus time) and weather (the Earth’s mean temperature surface data versus time) and for these nontrivial cases it becomes possible to receive a very good fit of initial data set. The general conditions of application of this fitting method describing the response of many complex systems and the forecast possibilities are discussed.

The application of the controllability principle in Electricidade dos Açores, SA

A Work Project, presented as part of the requirements for the Award of a Masters Degree in Management from the NOVA – School of Business and Economics

Res Publica: Citizenship and Political Representation in Portugal, 1820-1926

The term res publica (literally “thing of the people”) was coined by the Romans to translate the Greek word politeia, which, as we know, referred to a political community organised in accordance with certain principles, amongst which the notion of the “good life” (as against exclusively private interests) was paramount. This ideal also came to be known as political virtue. To achieve it, it was necessary to combine the best of each “constitutional” type and avoid their worst aspects (tyranny, oligarchy and ochlocracy). Hence, the term acquired from the Greeks a sense of being a “mixed” and “balanced” system. Anyone that was entitled to citizenship could participate in the governance of the “public thing”. This implied the institutionalization of open debate and confrontation between interested parties as a way of achieving the consensus necessary to ensure that man the political animal, who fought with words and reason, prevailed over his “natural” counterpart. These premises lie at the heart of the project which is now being presented under the title of Res Publica: Citizenship and Political Representation in Portugal, 1820-1926. The fact that it is integrated into the centenary commemorations of the establishment of the Republic in Portugal is significant, as it was the idea of revolution – with its promise of rupture and change – that inspired it. However, it has also sought to explore events that could be considered the precursor of democratization in the history of Portugal, namely the vintista, setembrista and patuleia revolutions. It is true that the republican regime was opposed to the monarchic. However, although the thesis that monarchy would inevitably lead to tyranny had held sway for centuries, it had also been long believed that the monarchic system could be as “politically virtuous” as a republic (in the strict sense of the word) provided that power was not concentrated in the hands of a single individual. Moreover, various historical experiments had shown that republics could also degenerate into Caesarism and different kinds of despotism. Thus, when absolutism began to be overturned in continental Europe in the name of the natural rights of man and the new social pact theories, initiating the difficult process of (written) constitutionalization, the monarchic principle began to be qualified as a “monarchy hedged by republican institutions”, a situation in which not even the king was exempt from isonomy. This context justifies the time frame chosen here, as it captures the various changes and continuities that run through it. Having rejected the imperative mandate and the reinstatement of the model of corporative representation (which did not mean that, in new contexts, this might not be revived, or that the second chamber established by the Constitutional Charter of 1826 might not be given another lease of life), a new power base was convened: national sovereignty, a precept that would be shared by the monarchic constitutions of 1822 and 1838, and by the republican one of 1911. This followed the French example (manifested in the monarchic constitution of 1791 and in the Spanish constitution of 1812), as not even republicans entertained a tradition of republicanism based upon popular sovereignty. This enables us to better understand the rejection of direct democracy and universal suffrage, and also the long incapacitation (concerning voting and standing for office) of the vast body of “passive” citizens, justified by “enlightened”, property- and gender-based criteria. Although the republicans had promised in the propaganda phase to alter this situation, they ultimately failed to do so. Indeed, throughout the whole period under analysis, the realisation of the potential of national sovereignty was mediated above all by the individual citizen through his choice of representatives. However, this representation was indirect and took place at national level, in the hope that action would be motivated not by particular local interests but by the common good, as dictated by reason. This was considered the only way for the law to be virtuous, a requirement that was also manifested in the separation and balance of powers. As sovereignty was postulated as single and indivisible, so would be the nation that gave it soul and the State that embodied it. Although these characteristics were common to foreign paradigms of reference, in Portugal, the constitutionalization process also sought to nationalise the idea of Empire. Indeed, this had been the overriding purpose of the 1822 Constitution, and it persisted, even after the loss of Brazil, until decolonization. Then, the dream of a single nation stretching from the Minho to Timor finally came to an end.

Development of principle culture medium formulations for Saccharomyces cerevisiae

Saccharomyces cerevisiae as well as other microorganisms are frequently used in industry with the purpose of obtain different kind of products that can be applied in several areas (research investigation, pharmaceutical compounds, etc.). In order to obtain high yields for the desired product, it is necessary to make an adequate medium supplementation during the growth of the microorganisms. The higher yields are typically reached by using complex media, however the exact formulation of these media is not known. Moreover, it is difficult to control the exact composition of complex media, leading to batch-to-batch variations. So, to overcome this problem, some industries choose to use defined media, with a defined and known chemical composition. However these kind of media, many times, do not reach the same high yields that are obtained by using complex media. In order to obtain similar yield with defined media the addition of many different compounds has to be tested experimentally. Therefore, the industries use a set of empirical methods with which it is tried to formulate defined media that can reach the same high yields as complex media. In this thesis, a defined medium for Saccharomyces cerevisiae was developed using a rational design approach. In this approach a given metabolic network of Saccharomyces cerevisiae is divided into a several unique and not further decomposable sub networks of metabolic reactions that work coherently in steady state, so called elementary flux modes. The EFMtool algorithm was used in order to calculate the EFM’s for two Saccharomyces cerevisiae metabolic networks (amino acids supplemented metabolic network; amino acids non-supplemented metabolic network). For the supplemented metabolic network 1352172 EFM’s were calculated and then divided into: 1306854 EFM’s producing biomass, and 18582 EFM’s exclusively producing CO2 (cellular respiration). For the non-supplemented network 635 EFM’s were calculated and then divided into: 215 EFM’s producing biomass; 420 EFM’s producing exclusively CO2. The EFM’s of each group were normalized by the respective glucose consumption value. After that, the EFMs’ of the supplemented network were grouped again into: 30 clusters for the 1306854 EFMs producing biomass and, 20 clusters for the 18582 EFM’s producing CO2. For the non-supplemented metabolic network the respective EFM’s of each metabolic function were grouped into 10 clusters. After the clustering step, the concentrations of the other medium compounds were calculated by considering a reasonable glucose amount and by accounting for the proportionality between the compounds concentrations and the glucose ratios. The approach adopted/developed in this thesis may allow a faster and more economical way for media development.

The Zariski-Lefschetz principle for higher homotopy groups of nongeneric pencils

We prove a general Zariski-van Kampen-Lefschetz type theorem for higher homotopy groups of generic and nongeneric pencils on singular open complex spaces.

A note on the separability principle in economies with single-peaked

We consider the problem of allocating an infinitely divisible commodity among a group of agents with single-peaked preferences. A rule that has played a central role in the analysis of the problem is the so-called uniform rule. Chun (2001) proves that the uniform rule is the only rule satisfying Pareto optimality, no-envy, separability, and continuity (with respect to the social endowment). We obtain an alternative characterization by using a weak replication-invariance condition, called duplication-invariance, instead of continuity. Furthermore, we prove that Pareto optimality, equal division lower bound, and separability imply no-envy. Using this result, we strengthen one of Chun's (2001) characterizations of the uniform rule by showing that the uniform rule is the only rule satisfying Pareto optimality, equal división lower bound, separability, and either continuity or duplication-invariance.

The Taylor Principle and (In-) Determinacy in a New Keynesian Model with hiring Frictions and Skill Loss

We introduce duration dependent skill decay among the unemployed into a New-Keynesian model with hiring frictions developed by Blanchard/Gali (2008). If the central bank responds only to (current, lagged or expected future) inflation and quarterly skill decay is above a threshold level, determinacy requires a coefficient on inflation smaller than one. The threshold level is plausible with little steady-state hiring and firing ("Continental European Calibration") but implausibly high in the opposite case ("American calibration"). Neither interest rate smoothing nor responding to the output gap helps to restore determinacy if skill decay exceeds the threshold level. However, a modest response to unemployment guarantees determinacy. Moreover, under indeterminacy, both an adverse sunspot shock and an adverse technology shock increase unemployment extremely persistently.

The Liberal Ethics of Non-Interference and the Pareto Principle

We analyse the liberal ethics of non-interference applied to social choice. A liberal principle capturing noninterfering views of society and inspired by John Stuart Mill s conception of liberty, is examined. The principle captures the idea that society should not penalise agents after changes in their situation that do not a¤ect others. An impossibility for liberal approaches is highlighted: every social decision rule that satis es unanimity and a general principle of noninterference must be dictatorial. This raises some important issues for liberal approaches in social choice and political philosophy.