Let $mathcal{H}$ and $mathcal{K}$ be infinite dimensional Hilbert spaces, while $mathcal{B(H)}$ and $mathcal{B(K)}$ denote the algebras of all linear bounded operators on $mathcal{H}$ and $mathcal{K}$, respectively. We characterize the forms of additive mappings from $mathcal{B(H)}$ into $mathcal{B(K)}$ that preserve the nonzero idempotency of either Jordan products of operators or usual produc...

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Let R be a commutative ring and M and N be R-modules. (We always work with rings having a multiplicative identity and modules are assumed to be unital: 1 ·m = m for all m ∈M .) The direct sum M ⊕N is an addition operation on modules. We introduce here a product operation M ⊗RN , called the tensor product. We will start off by describing what a tensor product of modules is supposed to look like....

conclusions l. innocua is not a pathogen, but the presence of the bacterium could be an indicator of probable contamination with l. monocytogenes. moreover, there is a potential risk to public health from the consumption of raw or undercooked burgers, which may increase the possibility of the acquisition of resistance to antibiotics. objectives the aim of this study was to evaluate the occurren...

introduction: heavy metals are types of elements naturally present in soil or enter into soil as a result of human activities. the most important route of exposure to heavy metals is daily intake of food. crops grown in contaminated soil (due to mining activities, industrial operations and agriculture) may contain high concentrations of heavy metals. also closeness to cities and industrial cent...

formaldehyde in small quantities is commonly analyzed by spectrophotometric methods. one of the most-commonly used spectrophotometric techniques for this purpose is based on the reaction with chromotropic acid. because of its simplicity, sensitivity, selectivity and its low cost, it is still widely used. investigations for replacing the concentrated sulfuric acid with other acids or using more ...