MEDIATING EFFECT OF WORK ENVIRONMENT OF SCHOOL HEADS ON THE RELATIONSHIP BETWEEN ETHICAL LEADERSHIP AND SCHOOL CULTURE

This study sought to ascertain the role that the workplace environment played in mediating the link between ethical leadership and school climate. Data were collected from 300 respondents who are elementary public school teachers of the public elementary schools in the province of Davao Oriental using a quantitative, non-experimental design using a correlational approach. For data gathering, the researcher used an online survey and stratified random sampling. Additionally, the researcher used the Pearson r, Med graph employing the Sobel z-test and mean statistical methods. According to the study's findings, there are very high levels of mean scores for ethical leadership, a high level for school culture, and a high level for work environment. Additionally, the findings showed a substantial association between ethical leadership and work environment, a large relationship between work environment and school culture, and a substantial relationship between ethical leadership and both. Additionally, it was discovered that the relationship between ethical leadership and school culture was somewhat mediated by the workplace.  Article visualizations

Spatially embedded random networks

Many real-world networks analyzed in modern network theory have a natural spatial element; e.g., the Internet, social networks, neural networks, etc. Yet, aside from a comparatively small number of somewhat specialized and domain-specific studies, the spatial element is mostly ignored and, in particular, its relation to network structure disregarded. In this paper we introduce a model framework to analyze the mediation of network structure by spatial embedding; specifically, we model connectivity as dependent on the distance between network nodes. Our spatially embedded random networks construction is not primarily intended as an accurate model of any specific class of real-world networks, but rather to gain intuition for the effects of spatial embedding on network structure; nevertheless we are able to demonstrate, in a quite general setting, some constraints of spatial embedding on connectivity such as the effects of spatial symmetry, conditions for scale free degree distributions and the existence of small-world spatial networks. We also derive some standard structural statistics for spatially embedded networks and illustrate the application of our model framework with concrete examples

Central limit theorem for multiplicative class functions on the symmetric group

Hambly, Keevash, O'Connell and Stark have proven a central limit theorem for the characteristic polynomial of a permutation matrix with respect to the uniform measure on the symmetric group. We generalize this result in several ways. We prove here a central limit theorem for multiplicative class functions on symmetric group with respect to the Ewens measure and compute the covariance of the real and the imaginary part in the limit. We also estimate the rate of convergence with the Wasserstein distance.Comment: 23 pages; the mathematics is the same as in the previous version, but there are several improvments in the presentation, including a more intuitve name for the considered function

Visualizing Spacetime Curvature via Gradient Flows I: Introduction

Traditional approaches to the study of the dynamics of spacetime curvature in a very real sense hide the intricacies of the nonlinear regime. Whether it be huge formulae, or mountains of numerical data, standard methods of presentation make little use of our remarkable skill, as humans, at pattern recognition. Here we introduce a new approach to the visualization of spacetime curvature. We examine the flows associated with the gradient fields of invariants derived from the spacetime. These flows reveal a remarkably rich structure, and offer fresh insights even for well known analytical solutions to Einstein's equations. This paper serves as an overview and as an introduction to this approach.Comment: 10 pages twocolumn revtex 4-1 two figures. Final form to appear in Phys Rev

Quantum mechanics on a circle: Husimi phase space distributions and semiclassical coherent state propagators

We discuss some basic tools for an analysis of one-dimensionalquantum systems defined on a cyclic coordinate space. The basic features of the generalized coherent states, the complexifier coherent states are reviewed. These states are then used to define the corresponding (quasi)densities in phase space. The properties of these generalized Husimi distributions are discussed, in particular their zeros.Furthermore, the use of the complexifier coherent states for a semiclassical analysis is demonstrated by deriving a semiclassical coherent state propagator in phase space.Comment: 29 page

Markovian Master Equations: A Critical Study

We derive Markovian master equations of single and interacting harmonic systems in different scenarios, including strong internal coupling. By comparing the dynamics resulting from the corresponding Markovian master equations with exact numerical simulations of the evolution of the global system, we precisely delimit their validity regimes and assess the robustness of the assumptions usually made in the process of deriving the reduced dynamics. The proposed method is sufficiently general to suggest that the conclusions made here are widely applicable to a large class of settings involving interacting chains subject to a weak interaction with an environment.Comment: 40 pages, 14 figures, final versio

Harmonic Sums and Mellin Transforms up to two-loop Order

A systematic study is performed on the finite harmonic sums up to level four. These sums form the general basis for the Mellin transforms of all individual functions $f_i(x)$ of the momentum fraction $x$ emerging in the quantities of massless QED and QCD up to two--loop order, as the unpolarized and polarized splitting functions, coefficient functions, and hard scattering cross sections for space and time-like momentum transfer. The finite harmonic sums are calculated explicitly in the linear representation. Algebraic relations connecting these sums are derived to obtain representations based on a reduced set of basic functions. The Mellin transforms of all the corresponding Nielsen functions are calculated.Comment: 44 pages Latex, contract number adde

Counting and effective rigidity in algebra and geometry

The purpose of this article is to produce effective versions of some rigidity results in algebra and geometry. On the geometric side, we focus on the spectrum of primitive geodesic lengths (resp., complex lengths) for arithmetic hyperbolic 2-manifolds (resp., 3-manifolds). By work of Reid, this spectrum determines the commensurability class of the 2-manifold (resp., 3-manifold). We establish effective versions of these rigidity results by ensuring that, for two incommensurable arithmetic manifolds of bounded volume, the length sets (resp., the complex length sets) must disagree for a length that can be explicitly bounded as a function of volume. We also prove an effective version of a similar rigidity result established by the second author with Reid on a surface analog of the length spectrum for hyperbolic 3-manifolds. These effective results have corresponding algebraic analogs involving maximal subfields and quaternion subalgebras of quaternion algebras. To prove these effective rigidity results, we establish results on the asymptotic behavior of certain algebraic and geometric counting functions which are of independent interest.Comment: v.2, 39 pages. To appear in Invent. Mat

Spherical Universe topology and the Casimir effect

The mode problem on the factored 3--sphere is applied to field theory calculations for massless fields of spin 0, 1/2 and 1. The degeneracies on the factors, including lens spaces, are neatly derived in a geometric fashion. Vacuum energies are expressed in terms of the polyhedral degrees and equivalent expressions given using the cyclic decomposition of the covering group. Scalar functional determinants are calculated and the spectral asymmetry function treated by the same approach with explicit forms on one-sided lens spaces.Comment: 33 pages, 1 figure. Typos corrected and one reference adde

Special Functions Related to Dedekind Type DC-Sums and their Applications

In this paper we construct trigonometric functions of the sum T_{p}(h,k), which is called Dedekind type DC-(Dahee and Changhee) sums. We establish analytic properties of this sum. We find trigonometric representations of this sum. We prove reciprocity theorem of this sums. Furthermore, we obtain relations between the Clausen functions, Polylogarithm function, Hurwitz zeta function, generalized Lambert series (G-series), Hardy-Berndt sums and the sum T_{p}(h,k). We also give some applications related to these sums and functions