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Search Results: 1 - 10 of 11308 matches for " George Chailos "
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The Index of Invariant Subspaces of Bounded below Operators on Banach Spaces  [PDF]
George Chailos
Advances in Pure Mathematics (APM) , 2012, DOI: 10.4236/apm.2012.22018
Abstract: For an operator on a Banach space , let be the collection of all its invariant subspaces. We consider the index function on and we show, amongst others, that if is a bounded below operator and if , , then If in addition are index 1 invariant subspaces of , with nonzero intersection, we show that . Furthermore, using the index function, we provide an example where for some , holds .
Mathematical Interpretation of Plato's Third Man Argument
George Chailos
Mathematics , 2014,
Abstract: The main aim of this article is to defend the thesis that Plato apprehended the structure of incommensurable magnitudes in a way that these magnitudes correspond in a unique and well defined manner to the modern concept of the "Dedekind cut". Thus, the notion of convergence is consistent with Plato's apprehension of mathematical concepts, and in particular these of "density" of magnitudes and the complete continuum in the sense that they include incommensurable cuts. For this purpose I discuss and interpret, in a new perspective, the mathematical framework and the logic of the Third Man Argument (TMA) that appears in Plato's "Parmenides" as well as mathematical concepts from other Platonic dialogues. I claim that in this perspective the apparent infinite sequence of F-Forms, that it is generated by repetitive applications of the TMA, converges (in a mathematical sense) to a unique F-Form for the particular predicate. I also claim and prove that within this framework the logic of the TMA is consistent with that of the Third Bed Argument (TBA) as presented in Plato's "Republic". This supports Plato's intention for assuming a unique Form per Predicate; that is, the Uniqueness thesis.
The notion of Infinity within the Zermelo system and its relation to the Axiom of Countable Choice
George Chailos
Mathematics , 2015,
Abstract: In this article we consider alternative definitions-descriptions of a set being Infinite within the primitive Axiomatic System of Zermelo.
Venture Capital and Innovation in Europe  [PDF]
George Geronikolaou, George Papachristou
Modern Economy (ME) , 2012, DOI: 10.4236/me.2012.34058
Abstract: In this paper we search for evidence signifying whether VC activity is demand or supply stimulated. Namely, we examine whether innovation and entrepreneurship are fostered by Venture Capital (VC) investments or whether innovative entrepreneurship is a precondition of a VC involvement. Based on a European panel of VC investments, we test the direction of causality between VC and innovation (proxied by annual patent applications at the European Patents Office). We present evidence indicating that causality runs from patents to VC suggesting that, in Europe, innovation seems to create a demand for VC and not VC a supply of innovation. In this sense, innovative ideas seem to lack more than funds in Europe. We explain our findings on the basis of information asymmetry issues and irreversibility considerations of VC investments.
General Markowitz Optimization Problems  [PDF]
George Stoica
Applied Mathematics (AM) , 2012, DOI: 10.4236/am.2012.312A281

We solve two Markowitz optimization problems for the one-step financial model with a finite number of assets. In our results, the classical (inefficient) constraints are replaced by coherent measures of risk that are continuous from below. The methodology of proof requires optimization techniques based on functional analysis methods. We solve explicitly both problems in the important case of Tail Value at Risk.

A Spectral Integral Equation Solution of the Gross-Pitaevskii Equation  [PDF]
George Rawitscher
Applied Mathematics (AM) , 2013, DOI: 10.4236/am.2013.410A3009

The Gross-Pitaevskii equation (GPE), that describes the wave function of a number of coherent Bose particles contained in a trap, contains the cube of the normalized wave function, times a factor proportional to the number of coherent atoms. The square of the wave function, times the above mentioned factor, is defined as the Hartree potential. A method implemented here for the numerical solution of the GPE consists in obtaining the Hartree potential iteratively, starting with the Thomas Fermi approximation to this potential. The energy eigenvalues and the corresponding wave functions for each successive potential are obtained by a spectral method described previously. After approximately 35 iterations a stability of eight significant figures for the energy eigenvalues is obtained. This method has the advantage of being physically intuitive, and could be extended to the calculation of a shell-model potential in nuclear physics, once the Pauli exclusion principle is allowed for.

Rethinking the Formal Methodology (II): Cognitive Content of Relativity (On the Centenary of General Relativity)  [PDF]
George Kirakosyan
International Journal of Astronomy and Astrophysics (IJAA) , 2016, DOI: 10.4236/ijaa.2016.61004
Abstract: An attempt to epistemological completion of formal-math theories of relativity is presented. Causal interpretations of SR and GR are suggested. The problem to physical gist of gravity is explained as a contradiction of cognition vs. intuition. Gravity phenomena are represented as unexplored peculiarity of basic particles. The gravity constant is deduced from the known parameters of the electron.
Small Scale Contractors in Africa’s Emerging Markets: The Case of South Africa  [PDF]
George Hove
Open Journal of Business and Management (OJBM) , 2016, DOI: 10.4236/ojbm.2016.44065
Abstract: In South Africa, the development of Small scale emerging contractors (SSECs) has become vital to bring about economic prosperity and the government has prioritised the advancement of SSECs as the vehicle towards achieving economic growth, development and job creation for previously disadvantaged people. This paper reviewed related construction studies on small scale contractors and highlighted unique roles and challenges as they relate to emerging construction businesses. The paper established that the main challenges affecting SSECs included finance, skills shortage, enabling environment and competition. Based on data analysis, it is imperative for the South African government to develop a clear and more comprehensive small business contracting policies that would enhance growth and profitability of Small scale emerging contractors.
Left Atrial Volume Index in Patients with Dilated Cardiomyopathy—Correlation with Left Ventricular Function  [PDF]
Stanley George
World Journal of Cardiovascular Diseases (WJCD) , 2016, DOI: 10.4236/wjcd.2016.69035
Abstract: Background: The aim of this study was to determine the relation of left atrial (LA) volume and LA volume index with left ventricular function and to determine the association of duration of symptoms and left atrial volume index in patients with dilated cardiomyopathy. Materials and Methods: This was an observational, single centre study conducted in India. A total of 50 patients who were admitted to department of cardiology from July, 2008 to February, 2009 with diagnosis of dilated cardiomyopathy and an ejection fraction of <40% were included. Results: Of the 50 patients, 34 (68%) were males. 27 (54%) patients were in NYHA class II and 23 (46%) patients were in NYHA class III. LA volume was found to be ≥40 ml in all patients. LV function and LA volume were found to be correlated (r = -0.789, p < 0.01). Similarly, there was a correlation between LV function and LA volume index (r = -0.826, p < 0.01). There was no correlation between LA volume index and duration of symptoms (r = 0.04). Conclusion: It can be concluded that there is a strong inverse correlation between LA volume and left ventricular function and also between LA volume index and left ventricular function. The patients with NYHA class III were having larger left atrial volume than those with NYHA class II. Moreover, the duration of symptoms has no correlation with left atrial volume index.
Angiographic Profile and Treadmill Test Relationship of Women with Chest Pain Suggestive of Coronary Artery Disease  [PDF]
Stanley George
World Journal of Cardiovascular Diseases (WJCD) , 2017, DOI: 10.4236/wjcd.2017.78021
Abstract: Aim: The aim of present study was to analyze the prevalence and pattern of coronary artery disease (CAD) among women who underwent coronary angiography (CAG) and Treadmill Test (TMT). Methods: A total of 100 consecutive women patients for coronary angiogram were studied at Department of Cardiology, Government Medical College, Kottayam, Kerala, India on over a period of 6 months from February 2008. Total 65 women completed TMT stress test. The patients were subjected to CAG and TMT. Data were analyzed by using SPSS 20.0 software. Results: A total of 100 women patients were included. Among that 66% patients had hypertension and 47% patients had diabetes mellitus. The CAG revealed the presence of 17%, 13% and 15% of single vessel disease, double vessel disease, and triple vessel disease respectively. Vessel involvements were notably higher in positive TMT values during stress test. The sensitivity and specificity of TMT for detecting coronary artery disease in women were 61% and 69% respectively. Conclusion: It is concluded that, the findings of the present study effectively demonstrated higher predictive value of TMT in women with chest pain suggestive of CAD.
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