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

Growth performance, recovery rate and fish yield of GIFT strain at various water depths under rice-fish culture systems

Effect of water depth on recovery rate, growth performance and fish yield of GIFT in the rice-fish production systems was studies in experimental plots of 123 m2 with a pond refuge of I meter deep which covered 10% of the total land area. Mortality rate of fish was very low ranging from 0.81-1.63%. However, at harvest, recovery rate ranged from 76.69-82.93% with the highest recovery at 11-15 em of water depth. Significantly the highest absolute growth (99.97) and specific growth rate (2.42%) were found at 21-25 cm water depth. The same treatment also produced significantly higher fish yield (909.76 kg/ha) although statistically similar to the fish yield (862.60 kg/ha) obtained at ll-15 em of water depth. Results also suggested that higher water depth can produce bigger fish but no significant effects of water depth was found on fish yield in the treatments 11-15 cm and 21-25 cm water depths of this experiment

The Effect of Web Reinforcement on the Shear Capacity of Brick Aggregate Concrete Beams

Shear capacity of reinforced brick aggregate concrete beams without any web reinforcement and with varying ratio of web reinforcement was studied in this investigation. Deflections of beams and cracks during the progress of loading were recorded. Brick aggregate concrete beams with web reinforcement and two layers of tensile reinforcement were found to have increased cracking shear stress by a considerable amount. Equations for cracking and ultimate shear stresses were suggested within the scope of this study. The experimental values of ultimate shear strength of beams were compared with the values obtained by equations proposed by ACI and other researchers. The equations proposed herein were found to represent the test results better than those of other researchers while remaining on the conservative side. It is hoped that the equations developed herein will provide a rational and basic point of departure from the prevailing concept and will help towards the formulation of a suitable code to provide web reinforcement for brick aggregate concrete beams

Quantum memory assisted entropic uncertainty and entanglement dynamics: Two qubits coupled with local fields and Ornstein Uhlenbeck noise

Entropic uncertainty and entanglement are two distinct aspects of quantum mechanical procedures. To estimate entropic uncertainty relations, entropies are used: the greater the entropy bound, the less effective the quantum operations and entanglement are. In this regard, we analyze the entropic uncertainty, entropic uncertainty lower bound, and concurrence dynamics in two non-interacting qubits. The exposure of two qubits is studied in two different qubit-noise configurations, namely, common qubit-noise and independent qubit-noise interactions. To include the noisy effects of the local external fields, a Gaussian Ornstein Uhlenbeck process is considered. We show that the rise in entropic uncertainty gives rise to the disentanglement in the two-qubit Werner type state and both are directly proportional. Depending on the parameters adjustment and the number of environments coupled, different classical environments have varying capacities to induce entropic uncertainty and disentanglement in quantum systems. The entanglement is shown to be vulnerable to current external fields; however, by employing the ideal parameter ranges we provided, prolonged entanglement retention while preventing entropic uncertainty growth can be achieved. Besides, we have also analyzed the intrinsic behavior of the classical fields towards two-qubit entanglement without any imperfection with respect to different parameter

Application of blend fuels in a diesel engine

AbstractExperimental study has been carried out to analyze engine performance and emissions characteristics for diesel ngine using different blend fuels without any engine modifications. A total of four fuel samples, such as DF (100% iesel fuel), JB5 (5% jatropha biodiesel and 95% DF), JB10 (10% JB and 90% DF) and J5W5 (5% JB, 5% waste ooking oil and 90% DF) respectively were used in this study. Engine performance test was carried out at 100% load eeping throttle 100% wide open with variable speeds of 1500 to 2400rpm at an interval of 100rpm. Whereas, mission tests were carried out at 2300rpm at 100% and 80% throttle position. As results of investigations, the erage torque reduction compared to DF for JB5, JB10 and J5W5 was found as 0.63%, 1.63% and 1.44% and verage power reduction was found as 0.67%, 1.66% and 1.54% respectively. Average increase in bsfc compared to F was observed as 0.54%, 1.0% JB10 and 1.14% for JB5, JB10 and J5W5 respectively. In case of engine exhaust as emissions, compared to DF average reduction in HC for JB5, JB10 and J5W5 at 2300rpm and 100% throttle osition found as 8.96%, 11.25% and 12.50%, whereas, at 2300 and 80% throttle position, reduction was as 16.28%, 0.23% and 31.98% respectively. Average reduction in CO at 2300rpm and 100% throttle position for JB5, JB10 and 5W5 was found as 17.26%, 25.92% and 26.87%, whereas, at 80% throttle position, reduction was observed as 0.70%, 33.24% and 35.57%. Similarly, the reduction in CO2 compared to DF for JB5, JB10 and J5W5 at 2300rpm nd 100% throttle position was as 12.10%, 20.51% and 24.91%, whereas, at 80% throttle position, reductions was bserved as 5.98%, 10.38% and 18.49% respectively. However, some NOx emissions were increased for all blend els compared to DF. In case of noise emission, sound level for all blend fuels was reduced compared to DF. It can e concluded that JB5, JB10 and J5W5 can be used in diesel engines without any engine modifications However, 5B5 produced some better results when compared to JB10

Marigold Blooming Maturity Levels Classification Using Machine Learning Algorithms

Image processing is swiftly progressive in the area of computer science and engineering. Image classification is a fascinating task in image processing. In this study, we have classified the marigold blooming maturity levels like a marigold bud, partial blooming marigold, and fully blooming marigold. To classify the marigold blooming maturity levels are a tough and time-consuming task for human beings. Hence, an automatic marigold maturity levels classification tool is very adjuvant even for experience humans to classify the huge number of marigolds. For the sake of that, we have deliberated a novel system to classify automatically marigold blooming maturity levels image data by using machine learning algorithms. There are three types of machine learning models namely Artificial Neural Network(ANN), Convolutional Neural Network(CNN), and Support Vector Machine(SVM) that are used to automatically classify marigold maturity levels. Hence, we have preprocessed the image at first. Then we extract the various features from the marigold images. After that, these features have fed into Machine Learning(ML) models and classify these images into the category. From the experiment, we observed that the Convolutional Neural Network (CNN) model provides a high accuracy compared to other Artificial Neural Network(ANN) and Support Vector Machine(SVM) algorithms. The Convolutional Neural Network(CNN) models performed the best among all two classifiers with an overall accuracy of 93.9%. Our proposed system is efficiently classifying marigold maturity levels