Finite-dimensional algebras with smallest resolutions of simple modules

Let $X$ be a finitely generated left module over a left artinian ring $R$, and let $p(X)=\{l_i\}$ be the infinite sequence of nonnegative integers where $l_i$ is the length of the $i$-th term of the minimal projective resolution of $X$. We introduce a preorder relation $\le$ on the set $\{p(X)\}$ and characterize the elementary finite-dimensional algebras $\Lambda$ with the following property. Let $S$ be a simple $\Lambda$-module, and let $T$ be a finitely generated module over an arbitrary left artinian ring $R$. If the projective dimension of $S$ does not exceed the projective dimension of $T$, then $p(S)\le p(T)$. We characterize the indicated algebras by quivers with relations.Comment: Minor revisions, to appear in Journal of Algebr

A critique on the historical works of Ambedkar

Ambedkar was a learned scholar, an astute political statesman and a revolutionary social reformer who had written on varied issues concerning economy, history, society, polity, law, dalits, women and on education. One would see a gradual transformation in his writings with ever increasing involvement and confrontations that he had with his adversaries. From attempting to change the heart of the caste Hindus to the distruction of the sanctity behind the shastras, Ambedkar's writings shaped the characater and mind of the society that he lived in. The paper attempts to explore this transition in his writings and the reason for this transformation

Dr. B.R. Ambedkar as a Historian

Ambedkar was well versed in various disciples. Hence he was able to contribute with authority to various disciplines. Ambedkar‟s contribution to history is discussed in the present paper. He examines the various popular theories and their limitation in the understanding and unfolding of events related to history. The paper explores the problem of objectivity, imagination and interpretation as understood by Ambedkar

Order Parameter Measurements Of Dichroic Dyes Dissolved In Smectic Liquid Crystals That Tilt Without Layer Contraction

Measurements of the orientational order parameter of dissolved dichroic dyes are reported for two smectic-A liquid crystals that tilt in the presence of an in-plane electric field without any decrease in the layer spacing. The dye order parameter is determined by measuring the anisotropic absorption of linearly polarized light. Different dyes are used and measurements are also performed on a smectic liquid crystal that tilts with the expected layer contraction to check how closely the measurements reflect the order parameter of the liquid crystal. The variation of the dye order parameter with electric field is in accordance with the recently proposed model of azimuthal disorder of the tilt angle direction, but the surprising finding is that the local dye orientational order parameter is significantly lower than for the smectic liquid crystal that tilts with the expected layer contraction. This suggests that another mechanism might be contributing significantly to the smectic order, one possibility of which is the tendency for different parts of these siloxane-containing molecules to segregate within each layer. Another possible explanation is that the azimuthal disorder is due to a modulated phase with a high enough density of defects to decrease the value of the local order parameter

Orange-Brown Precipitate: A Threat to the Success of Endodontic Treatment – An In Vitro Study

AIM: The aim of the present study was to evaluate the effect of various intermediate irrigating solutions in the removal of orange-brown precipitate formed due to alternative use of sodium hypochlorite (NaOCl) and chlorhexidine (CHX) root canal irrigants. METHODS: The root canals of 50 mandibular premolars were prepared using ProTaper Universal Rotary instruments (Dentsply Maillefer, Ballaigues, Switzerland) up to size F3. The roots were randomly divided into five experimental groups specified by the intermediate irrigant used; Group 1: No intermediate irrigant used (control), Group 2: Saline, Group 3: 7% maleic acid (MA), Group 4: 4% sodium thiosulfate, and Group 5: 70% isopropyl alcohol (n = 10). After final irrigation with CHX, the specimens were evaluated for the presence/absence of orange-brown precipitate under stereomicroscope. RESULTS: Mean precipitate for all experimental groups was calculated using ANOVA F test which showed orange-brown precipitate (parachloroanaline) in all groups except Group 4 and Group 5 which were highly significant (p < 0.001) at all the levels of root canal. Intergroup pairwise comparison was done using Tukey’s post hoc test. CONCLUSION: About 7% MA is effective in minimizing the formation of orange-brown precipitate when used as intermediate irrigant between NaOCl and CHX. However, the precipitate was not observed with 4% sodium thiosulfate and 70% isopropyl alcohol

Antecedents of Leadership Agency : Understanding Leadership Development

This study aims to look into leadership development and the antecedents that are important for its development using Bandura’s Social Cognitive Theory. Specifically, the purpose of this study is threefold: 1) To develop and present a new construct called leadership agency, 2) to conduct a study to develop a self-reported measure of leadership agency, and finally 3) to create a framework that outlines the relationship between antecedents and leadership agency. Using an online survey tool, 36 freshmen students in the Emerging Leader Learning Community at Montclair State University, participated and completed surveys on the four components of leadership agency; leader mtentionality, leader forethought, leader self-reactiveness, leader self-reflectiveness and its hypothesized antecedents; behavioral, environmental and personal factors. Results indicated that leadership agency is construct that can be examined both as single and multi-faceted construct, depending on the situation. Furthermore, results from the regression analyses indicated that personal factors such as physiological state (resilience), goal orientation, and personality (conscientiousness, extroversion) as well as vicarious experience and individual’s perception of their past leadership experience had a significant impact on leadership agency. The implications of these results and how leadership agency can help understand leadership development are evaluated in the discussion section

REVISITING AMBEDKAR'S THOUGHTS ON PAKISTAN

Ambedkar's 'Thoughts on Pakistan' was taken up immediately after the passing of the Lahore Resolution on Pakistan. Perhaps Ambedkar's work is the earliest in the line of writings on Partition. It was actually a treatise submitted as a report to the Independent Labour Party which was subsequently published in the form of a book. The idea of Pakistan is bound to have diverse opinions in the Indian milieu. The question is undoubtedly controversial. This is definitely an arena of controversy based purely on sentiments. In this given situation anyone intending to comprehend it finds more stupefaction and less understanding of the subject. It is here that the writing of Ambedkar brings in a ray of hope in our understanding of the problem of Partition of India. The article tries to reflect the ideas as expressed by Ambedkar on the theme, in his work 'Thoughts on Pakistan' which eventually enables us to understand the issue without any prejudice over the subject of study

Meanings, Dimensions, and Categories of Mathematics Teacher Beliefs: A Navigation through the Literature

This paper aimed to discuss the meanings, dimensions, and categories of teacher beliefs about teaching and learning mathematics. I reviewed the relevant literature about teacher beliefs in general, beliefs about mathematics, and beliefs about mathematics teaching and learning in particular. Based on the review of the literature, I outlined the meanings of teacher beliefs and conceptualized three dimensions of teacher beliefs – affective dimension, cognitive dimension, and pedagogical dimension. Then, I discussed three viewpoints to observe teacher beliefs – relational, institutional, and praxis lenses. I utilized these lenses to categorize belief constructs into three classes of beliefs about mathematics, teaching mathematics, and learning mathematics. These classes’ included-instrumentalist, constructivist, and integral beliefs. I addressed the pedagogical implications of these categorical beliefs in the end