1,486 research outputs found

    Finite-dimensional algebras with smallest resolutions of simple modules

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    Let XX be a finitely generated left module over a left artinian ring RR, and let p(X)={li}p(X)=\{l_i\} be the infinite sequence of nonnegative integers where lil_i is the length of the ii-th term of the minimal projective resolution of XX. We introduce a preorder relation ≤\le on the set {p(X)}\{p(X)\} and characterize the elementary finite-dimensional algebras Λ\Lambda with the following property. Let SS be a simple Λ\Lambda-module, and let TT be a finitely generated module over an arbitrary left artinian ring RR. If the projective dimension of SS does not exceed the projective dimension of TT, then p(S)≤p(T)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

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    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

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    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

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    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

    REVISITING AMBEDKAR'S THOUGHTS ON PAKISTAN

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    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

    Murugesam pillay - A champion of the oppressed

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    Princely Mysore in colonial parlance was called a ‘Model State’. For a long time it was under the western influence although not under their sway. Tipu sultan the erstwhile ruler of Mysore had adopted technological modernity in so far as his army was concerned. Ever since the fall of Tipu in the battle of Srirangapatna in 1799, the state of Mysore and its rulers came under the direct influence of the British. The rulers of Mysore in their endevour to be free from the hold of the British worked in conformity with them. This eventually paved way for liberal western outlook amongst its rulers. This earned them the title of being a ‘Model State’ in comparison with the other princely states that existed in India. However, the orthodox mindset of the Maharaja and its people who were reluctant to change needed effective catalysts. This was provided by the myride luminaries who were in the service of the princely government like the many efficient Dewans and men like C.R. Reddy, K.T. Bashyam, H.C. Dasappa, Kamalamma, H. Dasappa, P. Subbarama Chetty and P. Murugesam Pillai, to name only a few. These people were the torch bearers in bringing about a change in the mindset of the Maharaja as well as in the people of the state. These and a number of other intellectual dignitaries contributed immensely in evolving a favourable environment. It is in this context that the study of Murugesam Pillai becomes relevant as a person who championed the cause of the down trodden in Mysore

    Ambedkar's Ideology as a Source for the Study of Dalits

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    In modern times, history in order to be understood as a science was perceived to be based on facts. Facts were to be found in the documents. Therefore, Langlois and Seignobos had come to the conclusion that documents were the be all and end all of history. However, historians have realized that this statement of history has grave limitation as it documents only the elites. To overcome the limitation imposed by the documents historians today have resorted to alternative sources which are based on traditions, folklore, ballads, which give a contrary picture to that of official one. In this context since the history related to the dalits was rarely recorded, writing their history proved to be a challenge. Today, in the writing of dalit history there are alternative sources that are available for the historian. Dr. B.R Ambedkar has provided many leads to the issue and the statistics that he has generated over the course of his study has rendered any research on dalits a starting point in the understanding of their history

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

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    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
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