Let $R$ be an infinite ring. Here we prove that if $0_R$ belongs to ${x_1x_2cdots x_n ;|; x_1,x_2,dots,x_nin X}$ for every infinite subset $X$ of $R$, then $R$ satisfies the polynomial identity $x^n=0$. Also we prove that if $0_R$ belongs to ${x_1x_2cdots x_n-x_{n+1} ;|; x_1,x_2,dots,x_n,x_{n+1}in X}$ for every infinite subset $X$ of $R$, then $x^n=x$ for all $xin R$.

root ofplumbago indica linn is used in ayurveda and siddha medicine for the treatment of colic inflammations bronchitis, helminthiasis, hemorrhoids, elephantiasis, hepatosplenomegaly, amenorrhea, odontalgia, piles, and diabetes. the present study aims to investigate the anatomical characters of thin and thick root and to confirm the physicochemical characters of the root. anatomical studies and...

Subset Interconnection Design is an NP −hard problem which draws its motivation from various applications, such as the design of scalable overlay networks, the inference of inter-molecular protein connectivity, the design of vacuum systems and several other problems in the industry. In that problem, we are given a set of vertices V and a collection S of subsets of V and we want to find an edge ...

This paper presents the governing equations on the rectangular plate with the variation of material stiffness through their thick using higher order shear deformation theory (HSDT). The governing equations are obtained by using Hamilton's principle with regard to variation of Young's modulus in through their thick with regard sinusoidal variation of the displacement field across the thickness. ...

Satellites are useful for monitoring climatological parameters over large domains. They are especially useful for measuring various cloud microphysical and radiative parameters where ground-based instruments are not available. The geostationary operational environmental satellite (GOES) has been used to retrieve cloud and radiative properties over an extended domain centered on the Atmospheric ...

A flat transducer was constructed, using a 9-microm-thick PVDF (polyvinylidene fluoride) film for generation and detection of high-frequency ultrasonic waves, and used for measurements of the phase velocity of longitudinal waves traveling along the thickness direction in a very thin material. The transducer has a useful wideband frequency characteristic extending from 10 MHz to over 150 MHz. Me...

Tetragenococcus halophilus is known to flourish in extreme salt environments. Recently, this halophilic bacterium also appeared as the dominant microflora during storage of sugar thick juice, an intermediate product of beet sugar production. Although T. halophilus can cause degradation of thick juice, dominance of this bacterium does not always result in degradation. In this study T. halophilus...