Non-commutative geometry of 4-dimensional quantum Hall droplet

We develop the description of non-commutative geometry of the 4-dimensional quantum Hall fluid's theory proposed recently by Zhang and Hu. The non-commutative structure of fuzzy $S^{4}$ appears naturally in this theory. The fuzzy monopole harmonics, which are the essential elements in this non-commutative geometry, are explicitly constructed and their obeying the matrix algebra is obtained. This matrix algebra is associative. We also propose a fusion scheme of the fuzzy monopole harmonics of the coupling system from those of the subsystems, and determine the fusion rule in such fusion scheme. By products, we provide some essential ingredients of the theory of SO(5) angular momentum. In particular, the explicit expression of the coupling coefficients, in the theory of SO(5) angular momentum, are given. It is discussed that some possible applications of our results to the 4-dimensional quantum Hall system and the matrix brane construction in M-theory.Comment: latex 22 pages, no figures. some references added. some results are clarifie

Unusual Thermodynamics on the Fuzzy 2-Sphere

Higher spin Dirac operators on both the continuum sphere($S^2$) and its fuzzy analog($S^2_F$) come paired with anticommuting chirality operators. A consequence of this is seen in the fermion-like spectrum of these operators which is especially true even for the case of integer-spin Dirac operators. Motivated by this feature of the spectrum of a spin 1 Dirac operator on $S_F^2$, we assume the spin 1 particles obey Fermi-Dirac statistics. This choice is inspite of the lack of a well defined spin-statistics relation on a compact surface such as $S^2$. The specific heats are computed in the cases of the spin $\frac{1}{2}$ and spin 1 Dirac operators. Remarkably the specific heat for a system of spin $\frac{1}{2}$ particles is more than that of the spin 1 case, though the number of degrees of freedom is more in the case of spin 1 particles. The reason for this is inferred through a study of the spectrums of the Dirac operators in both the cases. The zero modes of the spin 1 Dirac operator is studied as a function of the cut-off angular momentum $L$ and is found to follow a simple power law. This number is such that the number of states with positive energy for the spin 1 and spin $\frac{1}{2}$ system become comparable. Remarks are made about the spectrums of higher spin Dirac operators as well through a study of their zero-modes and the variation of their spectrum with degeneracy. The mean energy as a function of temperature is studied in both the spin $\frac{1}{2}$ and spin 1 cases. They are found to deviate from the standard ideal gas law in 2+1 dimensions.Comment: 19 pages, 7 figures. The paper has been significantly modified. Main results are unchange

How Valid Are Measures of Children’s Self-Concept/ Self-Esteem? Factors and Content Validity in Three Widely Used Scales

Children’s self-esteem/self-concept, a core psychological construct, has been measured in an overwhelming number of studies, and the widespread use of such measures should indicate they have well-established content validity, internal consistency and factor structures. This study, sampling a demographically representative cohort in late childhood/early adolescence in Dublin, Ireland (total n = 651), examined three major self-esteem/self-concept scales designed for late childhood/early adolescence: Piers-Harris Self-Concept Scale for Children 2 (Piers et al. 2002), Self-Description Questionnaire I (Marsh 1992) and Self-Perception Profile for Children (Harter 1985). It also examined findings in light of the salient self factors identified by participants in a linked mixed-methods study. The factor structure of Piers-Harris Self-Concept Scale was not replicated. The Self-Description Questionnaire I and Self-Perception Profile for Children were replicated only in part although in similar ways. In all three scales, a global/ appearance self evaluation factor accounted for the largest variance in factor analyses. Sport/athletic ability, school ability, school enjoyment, maths and reading ability/enjoyment, behaviour, peer popularity, and parent factors were also identified but did not always reflect existing scale structures. Notably, the factors extracted, or items present in these scales, often did not reflect young people’s priorities, such as friendship over popularity, the importance of family and extended family members, and the significance of incremental personal mastery in activities rather than assessing oneself as comparatively good at preferred activities. The findings raise questions about how self-esteem/self-concept scales are used and interpreted in research with children and young people

Classification of All 1/2 BPS Solutions of the Tiny Graviton Matrix Theory

The tiny graviton matrix theory [hep-th/0406214] is proposed to describe DLCQ of type IIB string theory on the maximally supersymmetric plane-wave or AdS_5xS^5 background. In this paper we provide further evidence in support of the tiny graviton conjecture by focusing on the zero energy, half BPS configurations of this matrix theory and classify all of them. These vacua are generically of the form of various three sphere giant gravitons. We clarify the connection between our solutions and the half BPS configuration in N=4 SYM theory and their gravity duals. Moreover, using our half BPS solutions, we show how the tiny graviton Matrix theory and the mass deformed D=3, N=8 superconformal field theories are related to each other.Comment: 40 pages, 12 figures, v

Methodological Developments in Human Development Literature

The present paper is a review of methodological advancements in human development literature starting from 1990 till date. While highlighting the contribution of UNDP to the concept of human development and construction of HDI it mentions that the introduced concept and method of measurement is a huge qualitative improvement over the earlier concept of growth and per capita GDP measurement. Although the human development report started with a poor methodology, thanks to the galaxy of scholars for their untiring efforts and invaluable contributions in the successive years that enabled UNDP in refining its methodology to a large extent. There is no denying fact that there is no end to refinements, the purpose for which Mahbub ul Haq struggled in his entire life has been served

Cross-divisional innovation in large, multi-divisional firms: Economic relevance and managerial actions

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Fuzzy Sphere Dynamics and Non-Abelian DBI in Curved Backgrounds

We consider the non-Abelian action for the dynamics of $N Dp'$-branes in the background of $M Dp$-branes, which parameterises a fuzzy sphere using the SU(2) algebra. We find that the curved background leads to collapsing solutions for the fuzzy sphere except when we have $D0$ branes in the $D6$ background, which is a realisation of the gravitational Myers effect. Furthermore we find the equations of motion in the Abelian and non-Abelian theories are identical in the large $N$ limit. By picking a specific ansatz we find that we can incorporate angular momentum into the action, although this imposes restriction upon the dimensionality of the background solutions. We also consider the case of non-Abelian non-BPS branes, and examine the resultant dynamics using world-volume symmetry transformations. We find that the fuzzy sphere always collapses but the solutions are sensitive to the combination of the two conserved charges and we can find expanding solutions with turning points. We go on to consider the coincident $NS$5-brane background, and again construct the non-Abelian theory for both BPS and non-BPS branes. In the latter case we must use symmetry arguments to find additional conserved charges on the world-volumes to solve the equations of motion. We find that in the Non-BPS case there is a turning solution for specific regions of the tachyon and radion fields. Finally we investigate the more general dynamics of fuzzy $\mathbb{S}^{2k}$ in the $Dp$-brane background, and find collapsing solutions in all cases.Comment: 49 pages, 3 figures, Latex; Version to appear in JHE

Factor Analysis vs. Fuzzy Sets Theory: Assessing the Influence of Different Techniques on Sen's Functioning Approach

This paper explores a couple of specific operational interpretations of Sen's approach in view of assessing the extent to which the results originated by the implementation of Sen's concepts are influenced by the choice of the specific technique. By means of a survey based on a representative sample of Belgian individuals, seven achieved functioning's are identified via each technique and subsequently confronted. To structure the information and to facilitate comparisons, standard multivariate analysis is performed, while at the same time considering in more detail the sub-group of the most deprived individuals. In this way, a substantial accordance - yet no perfect equivalence - is uncovered in the general patterns of functionings' achievements.

Factor Analysis vs Fuzzy Sets Theory: Assessing the Influence of Different Techniques on Sen's Functioning Approach.

This paper explores a couple of specific operational interpretations of Sen's approach in view of assessing the extent to which the results originated by the implementation of Sen's concepts are influenced by the choice of the specific technique. By means of a survey based on a representative sample of Belgian individuals, seven achieved functioning's are identified via each technique and subsequently confronted. To structure the information and to facilitate comparisons, standard multivariate analysis is performed, while at the same time considering in more detail the sub-group of the most deprived individuals. In this way, a substantial accordance - yet no perfect equivalence - is uncovered in the general patterns of functioning's' achievements.

The impact of initial planning activities on project success: Some evidence from a study of Japanese companies

The domain of New Product Development (NPD) is subject to considerable uncertainties. However, companies are required to manage the innovation process as efficiently as possible. The resulting conflicting demands often leave companies struggling to achieve both, efficiency as well as flexibility due to their often opposing implications for organizing and managing NPD projects. In this context, planning plays a central role. This study tries to develop a deeper understanding of the influences of project planning, the degree of technological newness and both their effects on project success. Our analysis is based on project planning of in combination with New Product Development projects in 497 electrical and mechanical engineering companies. --