Abstract:
We introduce the concept of a weak nil clean ring, a generalization of nil clean ring, which is nothing but a ring with unity in which every element can be expressed as sum or difference of a nilpotent and an idempotent. Further if the idempotent and nilpotent commute the ring is called weak* nil clean. We characterize all $n\in \mathbb{N}$, for which $\mathbb{Z}_n$ is weak nil clean but not nil clean. We show that if $R$ is a weak* nil clean and $e$ is an idempotent in $R$, then the corner ring $eRe$ is also weak* nil clean. Also we discuss $S$-weak nil clean rings and their properties, where $S$ is a set of idempotents and show that if $S=\{0, 1\}$, then a $S$-weak nil clean ring contains a unique maximal ideal. Finally we show that weak* nil clean rings are exchange rings and strongly nil clean rings provided $2\in R$ is nilpotent in the later case. We have ended the paper with introduction of weak J-clean rings.

Abstract:
The commuting probability of a finite ring $R$, denoted by $\Pr(R)$, is the probability that any two randomly chosen elements of $R$ commute. In this paper, we obtain several bounds for $\Pr(R)$ through a generalization of $\Pr(R)$. Further, we define ${\Z}$-isoclinism between two pairs of rings and show that the generalized commuting probability, defined in this paper, is invariant under ${\Z}$-isoclinism between two pairs of finite rings.

Abstract:
In this paper, we compute the number of distinct centralizers of some classes of finite rings. We then characterize all finite rings with $n$ distinct centralizers for any positive integer $n \leq 5$. Further we give some connections between the number of distinct centralizers of a finite ring and its commutativity degree.

Abstract:
Let $R$ be a finite ring and let $\Cent(R)$ denote the set of all distinct centralizers of $R$. $R$ is called an $n$-centralizer ring if $|Cent(R)| = n$. In this paper, we characterize $n$-centralizer finite rings for $n \leq 7$.

Abstract:
The recent deployment of complex and capital intensiveequipment in mines has resulted in increased interest in themaintenance and operational reliability of these equipments.This is because random equipment failure has consequencesthat influence the total operating cost of this system. Thiscase study analyses the reliability of a fleet of load hauldump machines in a Coal India mine situated in NagpurThere are three goals of this case study: To estimate theoperational reliability of these machines secondly to Locateitems or assemblies that need improvement in design toenhance the reliability. Thirdly to decide whether preventivemaintenance should be applied. Failure data of one year ofload haul dump (LHD) machines are analyzed and otheranalytical methods are used in the analysis.

Theory of
“Relativity of speed of light with speed of universe expansion” explains relation
of speed of light with speed of universe expansion. This theory provides an evidence
that the time cannot be relative as stated by Theory of General Relativity. Theory
of Special Relativity and Theory of General Relativity were based on two fundamental
propositions i.e. constancy of speed of
light and independence of physical laws (especially the constancy of speed of light)
from the choice of inertial system. However, postulate of these theories is not
correct. Theory of “Relativity of speed of light with speed of universe expansion”
answers fundamental propositions i.e.
constancy of speed of light and independence of physical laws in logical manner.
This theory also explains real reason behind E = mc^{2}.

Abstract:
Lightning strikes can affect photovoltaic generators and their exposed installation sites as well as the sensitive electronics of the inverter. Therefore, it is necessary, to estimate the risk by lightning strikes, and to take these results into account for the design. IEC (EN) 62305-2 states procedures and data for the calculation of the risk resulting from lightning strikes into structures and for the choice of lightning protection systems. Actually, the technical guidelines for installation suggest protecting with SPD’s (surge protective device) both the DC and AC sides of the PV plant. The aim of this paper is to estimate voltages due to lightning discharges and to determine the effective need of lightning protection measures on the basis of the risk analysis and the protection costs.

Abstract:
Modern probability theory studies chance processes for which theknowledge of previous outcomes influence predictions for future experiments. In principle, when a sequence of chance experiments, all of the past outcomes could influence the predictions for the next experiment. In Markov chain type of chance, the outcome of a given experiment can affect the outcome of the next experiment. The system state changes with time and the state X and time t are two random variables. Each of these variables can be either continuous or discrete. Various degradation on photovoltaic (PV) systems can be viewed as different Markov states and further degradation can be treated as the outcome of the present state. The PV system is treated as a discrete state continuous time system with four possible outcomes, namely, s1 : Good condition, s2 : System with partial degradation failures and fully operational, s3 : System with major faults and partially working and hence partial output power, s4 : System completely fails. The calculation of the reliability of the photovoltaic system is complicated since the system have elements or subsystems exhibiting dependent failures and involving repair and standby operations. Markov model is a better technique that has much appeal and works well when failure hazards and repair hazards are constant. The usual practice of reliability analysis techniques include FMEA((failure mode and effect analysis), Parts count analysis, RBD ( reliability block diagram ), FTA( fault tree analysis ) etc. These are logical, boolean and block diagram approaches and never accounts the environmental degradation on the performance of the system. This is too relevant in the case of PV systems which are operated under harsh environmental conditions. This paper is an insight into the degradation of performance of PV systems and presenting a Markov model of the system by means of the different states and transitions between these states.

Abstract:
The paper is concerned with the study of criticality analysis of components of Gas Turbine Power Plant Systems (GTPPS) and the failures occurring in the plant. Failure mode and effect and criticality analysis (FMECA) is carried out to estimate the criticality number for different components and failure modes. In addition the failure effects, higher effects and end effectsare incorporated in the final FMECA sheet. The criticality resultscompensating provision will highlight possible ways to tackle thefailures economically. The findings in this Paper are (1) criticality index of the components (2) Critical failures (3) compensating provision of critical failure.

A field experiment was conducted to
study the growth and productivity of wheat as affected by row spacing and
direction of sowing at Rampur, Chitwan, Nepal during the 2007-2008 wheat growing
season. The experiment was carried out in 3-factors factorial randomized
complete block design comprising two varieties (Gautam and BL-2800), three row
spacings (15, 20 and25 cm)
and two row directions of sowing (east-west and north-south). The effects of
variety and row direction of sowing on grain yield were significant (p < 0.05), but the grain yield was
not affected by the row spacing treatment. BL-2800 variety produced higher grain yield (3.53 t·ha^{-}^{1}) as compared to Gautam (3.11 t·ha^{-}^{1}). Both wheat varieties yielded about 11% higher (p <
0.05) grain in the north-south sowing as compared to the eastwest
sowing.