Right orthogonal class of pure projective modules over pure hereditary rings

Let $\mathcal{W}$ be the class of all pure projective modules. In this article, $\mathcal{W}$-injective modules is defined via the vanishing of cohomology of pure projective modules. First we show that every module has a $\mathcal{W}$-injective coresolution over an arbitrary ring and the class of all $\mathcal{W}$-injective modules is coresolving over a pure-hereditary ring. Further, we analyze the dimension of $\mathcal{W}$-injective coresolution over a pure-hereditary ring. It is shown that \Fcor_{\mathcal{W}^{\bot}}(R) = \sup\{\pd(G) \colon G is a pure projective $R$-module\} = \sup\{\cores_{\mathcal{W}^{\bot}}(M) \colon M is an $R$-module$\}.$ Finally, we give some equivalent conditions of $\mathcal{W}$-injective envelope with the unique mapping property. The dimension has desirable properties when the ring is semisimple artinian.Comment: 17 pages, 9 figure

Retrospective analysis of plagiaristic practices within a cinematic industry in india – a tip in the ocean of icebergs

Music plagiarism is defined as using tune, or melody that would closely imitate with another author’s music without proper attributions. It may occur either by stealing a musical idea (a melody or motif) or sampling (a portion of one sound, or tune is copied into a different song). Unlike the traditional music, the Indian cinematic music is extremely popular amongst the public. Since the expectations of the public for songs that are enjoyable are high, many music directors are seeking elsewhere to “borrow” tunes. Whilst a vast majority of Indian cinemagoers may not have noticed these plagiarised tunes, some journalists and vigilant music lovers have noticed these activities. This study has taken the initiative to investigate the extent of plagiaristic activities within one Indian cinematic music industry. A list of plagiarised songs was produced by using YouTube® searches for “comparative videos” made by the vigilant music lovers about accused/detected music plagiarism. Some of these individuals were also interviewed to understand their views on this. During the investigation, it was possible to identify a vast number of plagiarised tunes, snippets, or even the full songs. In fact, some of these examples’ dates to 1954, during the era when no one would have noticed plagiarism. The paper would highlight the similarities of these music files. It will also show some examples of the excuses/denial given by the composers and would try to highlight the attitudes of general public towards these types of activities.N/

A Power Efficient Server-to-Server Wireless Data Center Network Architecture Using 60 GHz Links

Data Centers have become the digital backbone of the modern society with the advent of cloud computing, social networking, big data analytics etc. They play a vital role in processing a large amount of information generated. The number of data centers and the servers present in them have been on the rise over the last decade. This has eventually led to the increase in the power consumption of the data center due to the power-hungry interconnect fabric which consists of switches, routers and switching fabric necessary for communication in the data center. Moreover, a major portion of the power consumed in a data center belongs to cooling infrastructure. The data center’s complex cabling prevents the heat dissipation by obstructing the air flow resulting in the need for a cooling infrastructure. Additionally, the complex cabling in traditional data centers poses design and maintenance challenges. In this work, these problems of traditional data centers are addressed by designing a unique new server-to-server wireless Data Center Network (DCN) architecture. The proposed design methodology uses 60GHz unlicensed millimeter-wave bands to establish direct communication links between servers in a DCN without the need for a conventional fabric. This will reduce the power consumption of the DCN significantly by getting rid of the power-hungry switches along with an increase in the independency in communication between servers. In this work, the previous traffic models of a data center network are studied and a new traffic model very similar to the actual traffic in a data center is modeled and used for simulating the DCN environment. It is estimated that the proposed DCN architecture’s power consumption is lowered by six to ten times in comparison to the existing conventional DCN architecture. Having established the power model of a server-to-server wireless DCN in terms of its power consumption, we demonstrate that such a power-efficient wireless DCN can sustain the traffic requirements encountered and provide data rates that are comparable to traditional DCNs. We have also compared the efficiency and performance of the proposed DCN architecture with some of the other novel DCN architectures like DCell, BCube with the same traffic

Comparative study and advantages of laparoscopic ventral hernia mesh repair Versus conventional open mesh repair

BACKGROUND: An incisional hernia develops in 7% to 11% of laparotomy incisions. Laparoscopic repair was applied to the ventral hernias, with the expectation of earlier recovery, fewer postoperative complications, and decreased recurrence rates. This prospective study was performed to compare the outcomes after open and laparoscopic ventral hernia repair. METHODS: It is prospective study involved 55 patients with ventral hernia, were subjected either to repair by laparoscopy or to open repair. The open surgical operations were performed by onlay mesh repair, whereas the laparoscopic repairs were performed using the intra-peritoneal dual mesh IPOM repair technique. RESULTS: The mean surgery durations were significantly lower in laparoscopic repair when compared to open repair (p < 0.001). The mean duration of post-operative analgesics used in laparoscopic group is 4.3+ 0.50 days as compared to open ventral hernia repair 6.48 ±0.15 days (p < 0.001) which is significant. The mean postoperative stay in hospital was shorter for the laparoscopic group than for the open hernia group (6.3 versus 11.06 days; p < 0.001). Antibiotics used in laparoscopy group is for 5.85±0.50 days as compared to open repair 6.48±0.50 days (p <0.001). Return to the activity or normal daily work is significantly low in laparoscopic group as compared to open repair of hernia (2.2 versus 4.34 days; p <0.001). There were fewer post-operative complications in laparoscopy. CONCLUSIONS: The findings demonstrate that laparoscopic ventral hernia repair in our experience was safe and resulted in shorter operative time, fewer complications; shorter hospital stays, and earlier returns to daily activity. Hence, it should be considered as the procedure of choice for ventral hernia repair

MICROCONTROLLER BASED SPEED CONTROL OF SINUSOIDAL PWM INVERTER FED THREE PHASE INDUCTION MOTOR

This paper is concerned with Microcontroller based speed control of Sinusoidal PWM Inverter fed three phase Induction Motor. The Work involves design and fabrication of a variable frequency PWM inverter using MOSFETs, operating from a DC source. The objective is to implement variable frequency sinusoidal PWM inverter in order to control the speed of the Induction Motor using Microcontroller. When it is required to provide wide range of speed control covering about 600rpm to 1500rpm, normal three phase supply at 50Hz with voltage control alone is not successful due to the unstable region in the Torque-Slip characteristics of the motor. Hence it is necessary to go in for variable voltage and variable frequency mode of operation. The main focus of the this paper is the design and fabrication of variable voltage and variable frequency sinusoidal PWM inverter for speed control operation of Induction Motor. This drive system is simulated in MATLAB/Simulink and the simulation results are presented. After integrating the hardware and software the whole setup is tested for satisfactory operation. It is found that the three phase Induction motor is capable of running over a speed range from 600rpm to 1500rpm while driving a fixed load

On the Hochschild homology of singularity categories

Let $k$ be an algebraically closed field and $A$ a finite-dimensional $k$-algebra. In this note, we determine complexes which compute the Hochschild homology of the canonical dg enhancement of the bounded derived category of $A$ and of the canonical dg enhancement of the singularity category of $A$. As an application, we obtain a new approach to the computation of Hochschild homology of Leavitt path algebras

On the Hochschild homology of singularity categories

Let $k$ be an algebraically closed field and $A$ a finite-dimensional $k$-algebra. In this note, we determine complexes which compute the Hochschild homology of the canonical dg enhancement of the bounded derived category of $A$ and of the canonical dg enhancement of the singularity category of $A$. As an application, we obtain a new approach to the computation of Hochschild homology of Leavitt path algebras

MALAYALAM LETTER LL

At that time we did not pay any particular attention to the suitability of names from the user community. The feedback on the [email protected] list indicates there can be potential user confusion between the non-Chillu form and the consonant+Chandrakala forms just from the names. To avoid such potential confusion it is proposed to modify the names of the above characters as follows