Takeuti's proof theory in the context of the Kyoto School

Gaisi Takeuti (1926–2017) is one of the most distinguished logicians in proof theory after Hilbert and Gentzen. He extensively extended Hilbert's program in the sense that he formulated Gentzen's sequent calculus, conjectured that cut-elimination holds for it (Takeuti's conjecture), and obtained several stunning results in the 1950–60s towards the solution of his conjecture. Though he has been known chiefly as a great mathematician, he wrote many papers in English and Japanese where he expressed his philosophical thoughts. In particular, he used several keywords such as "active intuition" and "self-reflection" from Nishida's philosophy. In this paper, we aim to describe a general outline of our project to investigate Takeuti's philosophy of mathematics. In particular, after reviewing Takeuti's proof-theoretic results briefly, we describe some key elements in Takeuti's texts. By explaining these texts, we point out the connection between Takeuti's proof theory and Nishida's philosophy and explain the future goals of our project

To what extent financial development is important in promoting economic growth in OECD countries

This paper revisits the relationship between economic growth and the main determinants of financial development in The Organisation for Economic Co-operation and Development (OECD) countries during the period 1990-2016. Using a random effects model, we provide empirical evidence of different aspects of financial development in order to show which of these characteristics of financial development help to explain economic growth in OEDC countries in terms of finances through a panel data model for the period examined. We pay special attention to the main determinants of the financial system and verify their influence on economic growth even when we control for other key country-level factors relating to economic growth. Results show that an increase in domestic credit provided by financial-sector, in market capitalization and in the turnover ratio of domestic shares entails a significant positive effect on the Gross Domestic Product (GDP) per capita. Among other socioeconomic determinants related to economic growth, expenditure in education, the inflation and unemployment rates appear highly significant in the economic growth of the analysed countries.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

On the relationship between plane and solid geometry

Traditional geometry concerns itself with planimetric and stereometric considerations, which are at the root of the division between plane and solid geometry. To raise the issue of the relation between these two areas brings with it a host of different problems that pertain to mathematical practice, epistemology, semantics, ontology, methodology, and logic. In addition, issues of psychology and pedagogy are also important here. To our knowledge there is no single contribution that studies in detail even one of the aforementioned area

Financial development and economic growth: a study for OECD countries in the context of crisis

The aim of this paper is to study the relationship between economic growth and the main determinants of financial development in developed countries during the period 1990-2016. Using a random effects model, we provide empirical evidence of different aspects of financial development in order to show which of these characteristics of financial development help to explain economic growth in developed countries, particularly in OEDC countries in terms of finances through a panel data model and a dynamic model for the period examined. Paying special attention to the main determinants of the financial system and verify their influence on economic growth even when we control for other key country-level factors relating to economic growth. We conclude that an increase in domestic credit provided by financial-sector, in market capitalization and in the turnover ratio of domestic shares entails a significant positive effect on the GDP per capita. Among other socioeconomic determinants related to economic growth, expenditure in education, the inflation and unemployment rates seem highly significant in the economic growth of the analysed countries.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

Endogenous Growth and Comparative Standards of Living between Mexico and the US

This paper calibrates an AK model of growth for Mexico. Investment financing is modeled considering the domestic savings ratio as well as net factorial income and capital inflows of the balance of payments. Productivity A and the rate of depreciation of capital are found using econometric techniques. According to this model, actual parameters determining growth in Mexico are compatible with a sustained long run rate of growth of about 3.6%. At the same time, under these circumstances the ratio of the Mexican GDP to US GDP would be growing in time. The model is very sensible to the parameters and depends strongly of Mexicans living in the US and transferring remittances to Mexico, nonetheless. If remittances were eliminated, the actual rate of domestic savings would not be compatible with positive growth in the long run, which implies that relatively speaking the domestic savings rate in Mexico is very low. The paper concludes that to assure a positive growth that improves standards of living and the relative size of Mexico with respect to the US, it is necessary to implement policies oriented to increase the domestic savings rate and productivity. Otherwise there are high risks of macroeconomic crises in the future.

Series active variable geometry suspension application to comfort enhancement

This paper explores the potential of the Series Active Variable Geometry Suspension (SAVGS) for comfort and road holding enhancement. The SAVGS concept introduces significant nonlinearities associated with the rotation of the mechanical link that connects the chassis to the spring-damper unit. Although conventional linearization procedures implemented in multi-body software packages can deal with this configuration, they produce linear models of reduced applicability. To overcome this limitation, an alternative linearization approach based on energy conservation principles is proposed and successfully applied to one corner of the car, thus enabling the use of linear robust control techniques. An H∞ controller is synthesized for this simplified quarter-car linear model and tuned based on the singular value decomposition of the system's transfer matrix. The proposed control is thoroughly tested with one-corner and full-vehicle nonlinear multi-body models. In the SAVGS setup, the actuator appears in series with the passive spring-damper and therefore it would typically be categorized as a low bandwidth or slow active suspension. However, results presented in this paper for an SAVGS-retrofitted Grand Tourer show that this technology has the potential to also improve the high frequency suspension functions such as comfort and road holding

New Constraints on General Slepton Flavor Mixing

We explore the phenomenological implications on charged lepton flavor violating (LFV) processes from slepton flavor mixing within the Minimal Supersymmetric Standard Model. We work under the model-independent hypothesis of general flavor mixing in the slepton sector, being parametrized by a complete set of dimensionless delta^AB_ij (A,B = L,R; i,j = 1, 2, 3) parameters. The present upper bounds on the most relevant LFV processes, together with the requirement of compatibility in the choice of the MSSM parameters with the recent LHC and (g-2) data, lead to updated constraints on all slepton flavor mixing parameters. A comparative discussion of the most effective LFV processes to constrain the various generation mixings is included.Comment: 42 pages, 19 figures. Minor changes, version to appear in PR