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

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

Biological relationship of Bean common mosaic virus (BCMV) infecting cowpea with leguminous plant species

Bean common mosaic virus (BCMV) associated with cowpea mechanically inoculated to different legumi-nous plants. Out of nineteen including cowpea Var.C-152, the virus was easily transferred to ten different legumi-nous hosts. All other hosts assessed for the presence of BCMV were found to be uninfected. The number of days taken for symptom expression and symptoms were varied within plant species. Pole bean expressed mosaic symp-tom after long incubation period (15-18 days) whereas, shorter incubation period was observed in common bean and rice bean (7- 10 days). BCMV produced chlorosis, mosaic, leaf distortion, puckering, vein banding, vein clearing and vein netting on cowpea(C-152). A typical virus symptom, mosaic was observed in green gram, common bean, lime bean, rice bean and yard long bean, whereas, leaf rolling and leaf distortion was observed in black gram, pole bean and snap bean. The virus-host relationship was confirmed by back inoculation test to C. amaranticolor. Further symptomatic plants were subjected for Reverse Transcriptase polymerase chain reaction (RT-PCR) for molecular confirmation using BCMV coat protein (CP) specific primer pair. A PCR fragment size of 439bp was amplified for the symptomatic plants. The results generated indicated the ability of a plant to support virus expression and host speci-ficity of BMCV within the leguminous plant species

Evaluation of pigeonpea genotypes for resistance to pigeonpea sterility Mmsaic Vvrus - B Isolate

Pigeonpea genotypes (89) were evaluated for resistance to Pigeonpea sterility mosaic virus Bangalore isolate (PPSMV-B). Of these, three genotypes, ICP 7035, MAL 14 and MAL 19, were found resistant, and two genotypes, ICP 6997 and ICP 8862, were tolerant to PPSMV-B. All the resistant lines tested negative to virus in enzyme-linked immunosorbent assay (ELISA) using PPSMV polyclonal antiserum. The resistant lines can be used in breeding programme for developing PPSMV-resistant high yielding cultivar

The relationship between stimulus intensity and response amplitude for the photopic negative response of the flash electroretinogram

The aim of this study was to investigate the relationship between stimulus intensity and response amplitude for the photopic negative response (PhNR) of the flash ERG. Specific aims were (i) to determine whether a generalized Naka-Rushton function provided a good fit to the intensity-response data and (ii) to determine the variability of the parameters of the best-fitting Naka-Rushton models. Electroretinograms were recorded in 18 participants, on two occasions, using both DTL fibre and skin active electrodes, in response to Ganzfeld red stimuli (Lee filter "terry red") ranging in stimulus strength from -1.30 to 0.53 log cd.s.m(-2) (0.28-2.11 log phot td.s) presented over a steady blue background (Schott glass filter BG28; 3.9 log scot td). PhNR amplitude was measured from b-wave peak and from pre-stimulus baseline. The Naka-Rushton function was fitted to all intensity-response data, and parameters, 'n', 'Vmax' and 'K' were obtained. Coefficients of variation (CoV), and inter-ocular and inter-session limits of agreement (LoA) were calculated for both Naka-Rushton parameters. A generalized Naka-Rushton function was found to provide a good fit to the intensity-response data, except at the highest stimulus intensity, where a reduction in amplitude occurred in many individuals. The 'Vmax' parameter was less variable than 'K' for all intensity-response data. Variability was lower for DTL than skin electrodes, and for peak-to-trough PhNR measurements, compared to baseline-to-trough. This study has demonstrated for the first time that the Naka-Rushton model provides a useful means of quantifying the intensity-response relationship of the PhNR