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 $xin r$.

Abstract Cellular structures are a favorite selection for the design of lightweight components and energy absorption applications due to several advantages such as their customizable stiffness strength. In this investigation, functionally graded (FG) triply periodic minimal surfaces, Schoen-IWP (SIWP), Schwarz primitive (SPrim) cellular were fabricated by masked stereolithography (MSLA) techniq...

Eruptive sequences can be used as windows into the thermal and chemical evolution of magma chambers. We examined a continuous vertical section of the Baichahe basalt flow associated with the late Cenozoic Chifeng flood basalt in Inner Mongolia, North China. From oldest to youngest, MgO increases, K2O, light rare earths and other incompatible elements decrease, and Nb/La and radiogenic Pb isotop...

The disposition of the Anlage fields of the neural plate and the intraembryonic mesoblast in the upper layer of the chicken blastoderm was studied at the primitive streak stage prior to the regression of Hensen's node (stages 5V to 6V, L. Vakaet (1970) Arch. Biol. 81, 387-426). Chicken blastoderms were cultured by New's technique on a mixture of thin egg white and agar. The anterior half of the...

Geochemical observations place several constraints on geophysical processes in the mantle, including a requirement to maintain several distinct reservoirs. Geophysical constraints limit plausible physical locations of these reservoirs to a thin basal layer, isolated deep 'piles' of material under large-scale mantle upwellings, high-viscosity blobs/plums or thin strips throughout the mantle, or ...