Primordial vorticity and gradient expansion

The evolution equations of the vorticities of the electrons, ions and photons in a pre-decoupling plasma are derived, in a fully inhomogeneous geometry, by combining the general relativistic gradient expansion and the drift approximation within the Adler-Misner-Deser decomposition. The vorticity transfer between the different species is discussed in this novel framework and a set of general conservation laws, connecting the vorticities of the three-component plasma with the magnetic field intensity, is derived. After demonstrating that a source of large-scale vorticity resides in the spatial gradients of the geometry and of the electromagnetic sources, the total vorticity is estimated to lowest order in the spatial gradients and by enforcing the validity of the momentum constraint. By acknowledging the current bounds on the tensor to scalar ratio in the (minimal) tensor extension of the $\Lambda$CDM paradigm the maximal comoving magnetic field induced by the total vorticity turns out to be, at most, of the order of $10^{-37}$ G over the typical comoving scales ranging between 1 and 10 Mpc. While the obtained results seem to be irrelevant for seeding a reasonable galactic dynamo action, they demonstrate how the proposed fully inhomogeneous treatment can be used for the systematic scrutiny of pre-decoupling plasmas beyond the conventional perturbative expansions.Comment: 36 page

Nucleon structure functions in noncommutative space-time

In the context of noncommutative space-time, we investigate the nucleon structure functions which plays an important role to identify the internal structure of nucleons. We use the corrected vertices and employ new vertices that appear in two approaches of noncommutativity and calculate the proton structure functions in terms of noncommutative tensor \theta_{\mu\nu}. To check our result, we plot the nucleon structure function (NSF), F_2(x), and compare it with experimental data and the result coming out from the GRV, GJR and CT10 parametrization models. We show that new vertex which is arising the noncommutativity correction will lead us to better consistency between theoretical result and experimental data for NSF. This consistency would be better at small values of x-Bjorken variable. To indicate and confirm the validity of our calculations, we also act conversely and obtain an lower bound for the numerical values of \Lambda_{NC} scale which are corresponding to the recent reports.Comment: 28 pages, 5 figure

The Study of the Relationship between Managers' Transformational and Transactional Leadership Styles and School Effectiveness in Secondary Schools in Iran

The purpose of this paper is to study the relationship between secondary school managers' transformational and transactional leadership styles and school effectiveness and also to study the possibility of school effectiveness based on secondary school managers' transformational and transactional leadership styles in Iran. The participants were selected among managers, teachers, students and parents from Shiraz City, Iran. The Multifactor Leadership Questionnaire (MLQ-5X) and School Effectiveness Questionnaire (SEQ) were used to measure secondary school managers' leadership styles and school effectiveness respectively. Correlation coefficient (Pearson Correlation) and linear regression were used to analyze the data based on the designed hypotheses for this research. Based on the results of this research, there was a positive correlation with school effectiveness in secondary schools in Shiraz City as the higher the scores in transformational leadership style of managers, the higher the scores were in school effectiveness. Finally, leadership style can be a good and tenable predictor for school effectiveness in Shiraz City. Thus, the findings of the study indicated that managers should practice transformational leadership style for improving the school quality and effectiveness