Leavitt path algebras: Graded direct-finiteness and graded Σ\Sigma-injective simple modules

In this paper, we give a complete characterization of Leavitt path algebras which are graded $\Sigma$-$V$ rings, that is, rings over which a direct sum of arbitrary copies of any graded simple module is graded injective. Specifically, we show that a Leavitt path algebra $L$ over an arbitrary graph $E$ is a graded $\Sigma$-$V$ ring if and only if it is a subdirect product of matrix rings of arbitrary size but with finitely many non-zero entries over $K$ or $K[x,x^{-1}]$ with appropriate matrix gradings. We also obtain a graphical characterization of such a graded $\Sigma$-$V$ ring $L$% . When the graph $E$ is finite, we show that $L$ is a graded $\Sigma$-$V$ ring $\Longleftrightarrow L$ is graded directly-finite $\Longleftrightarrow L$ has bounded index of nilpotence $\Longleftrightarrow$ $L$ is graded semi-simple. Examples show that the equivalence of these properties in the preceding statement no longer holds when the graph $E$ is infinite. Following this, we also characterize Leavitt path algebras $L$ which are non-graded $\Sigma$-$V$ rings. Graded rings which are graded directly-finite are explored and it is shown that if a Leavitt path algebra $L$ is a graded $\Sigma$-$V$ ring, then $L$ is always graded directly-finite. Examples show the subtle differences between graded and non-graded directly-finite rings. Leavitt path algebras which are graded directly-finite are shown to be directed unions of graded semisimple rings. Using this, we give an alternative proof of a theorem of Va\v{s} \cite{V} on directly-finite Leavitt path algebras.Comment: 21 page

How and Why Decision Models Influence Marketing Resource Allocations

We study how and why model-based Decision Support Systems (DSSs) influence managerial decision making, in the context of marketing budgeting and resource allocation. We consider several questions: (1) What does it mean for a DSS to be "good?"; (2) What is the relationship between an anchor or reference condition, DSS-supported recommendation and decision quality? (3) How does a DSS influence the decision process, and how does the process influence outcomes? (4) Is the effect of the DSS on the decision process and outcome robust, or context specific? We test hypotheses about the effects of DSSs in a controlled experiment with two award winning DSSs and find that, (1) DSSs improve users' objective decision outcomes (an index of likely realized revenue or profit); (2) DSS users often do not report enhanced subjective perceptions of outcomes; (3) DSSs, that provide feedback in the form of specific recommendations and their associated projected benefits had a stronger effect both on the decision making process and on the outcomes.Our results suggest that although managers actually achieve improved outcomes from DSS use, they may not perceive that the DSS has improved the outcomes. Therefore, there may be limited interest in managerial uses of DSSs, unless they are designed to: (1) encourage discussion (e.g., by providing explanations and support for the recommendations), (2) provide feedback to users on likely marketplace results, and (3) help reduce the perceived complexity of the problem so that managers will consider more alternatives and invest more cognitive effort in searching for improved outcomes.marketing models;resource allocation;DSS;decision process;decision quality

Cytological Effects of Paper Mills Effluents on Somatic Cells of Allium Cepa

The cytological effects of paper mills effluents on somatic cells of Allium cepa were presented. The cytological effect decreased by decreasing the concentration of the effluents. Disturbed metaphase, anaphase and telophase, occurrence of binucleate and tetranucleate cells comprised the most dominant types of abnormalities. Clumping of chromosomes, contracted chromosomes, pleiomorphic and micronuclei formation, cell vacuolation and polyploid cells are found less frequently. The c-mitotic effect and other abnormalities may be due to the action of alkalies, acids and bleaching agents present in the paper mill effluents

Experimental Study of Perforated Pin Fins with Perforations around the Circumference of the Fins

Nine fins with inline arrangement and eight fins in staggered arrangement with each fin having the diameter of 16 mm and the perforation diameter of 3 mm are modeled to study the heat transfer performance. The Nusselt number for staggered perforated fins is obtained in the range of 90 to 235 while for solid pin fins in the similar arrangement, obtained in the range of 80 to 220 with Reynolds number in the range of 15000 to 82,000. The convective heat transfer coefficient in case of perforated fins with staggered arrangement is obtained in the range of 25 to 60 W/m2K while for solid pin fins, it in the range of 20 to 50 W/m2K. Overall analysis showed perforated pin fins with staggered arrangement performed better in terms of heat transfer as compared sold pin fins

Hirayama disease: a rare neurological condition of cervical cord pathology

The disease is characterized by a progressive muscle weakness and wasting of distal upper limb muscles sparing brachioradialis. The pathology is in the lower cervical cord due to forward displacement of dural sac and spinal cord by neck flexion. Repeated neck flexion may result in ischemia of the lower cervical anterior horns. The diagnosis can be confirmed by MRI, EMG. It requires a high degree of suspicion in a young patient presenting with unilateral upper limb distal muscle weakness with no sensory involvement, as early diagnosis will help in preventing the progression of the disease by employing simple measures like usage of a cervical collar. We report a case of a 25 year old man presenting with progressive distal upper limb muscle wasting, on investigating further diagnosed to have Hirayama disease