In this paper, we introduce a new generalization of weakly prime ideals called $I$-prime. Suppose $R$ is a commutative ring with identity and $I$ a fixed ideal of $R$. A proper ideal $P$ of $R$ is $I$-prime if for $a, b in R$ with $ab in P-IP$ implies either $a in P$ or $b in P$. We give some characterizations of $I$-prime ideals and study some of its properties.  Moreover, we give conditions  ...

We study 22 systems of variational inequalities which are only weakly elliptic; in particular, these systems are not necessarily monotone. The prototype diierential operator is the (vector-valued) p-Laplacian. We prove, under certain conditions, the existence of solutions to the unilateral obstacle problem. In addition, we address the question of determining function spaces on which the p-Lapla...

In this paper we investigate and refine Liu's procedure for the exploitation of the entropy inequality. We give a new-old proof of Liu's theorem. We shortly compare the Coleman-Noll and Liu techniques and call the attention to the proper application of the constraints in the procedure. As an example the Ginzburg-Landau equation and some variants are derived.

Modern deep learning models require large amounts of accurately annotated data, which is often difficult to satisfy. Hence, weakly supervised tasks, including object localization (WSOL) and detection (WSOD), have recently received attention in the computer vision community. In this paper, we motivate propose foreground (WSFL) task by showing that both WSOL WSOD can be greatly improved if ground...

In this paper we investigate and refine Liu's procedure for the exploitation of the entropy inequality. We give a new-old proof of Liu's theorem. We shortly compare the Coleman-Noll and Liu techniques and call the attention to the proper application of the constraints in the procedure. As an example the Ginzburg-Landau equation and some variants are derived.

The correlation between surface phenotype and function in subpopulations of murine thymocytes has been investigated using flow microfluorometry (FMF). C57BL/6 thymocytes stained with monoclonal antibodies directed against Lyt-2, H-2K(b), and Thy-l.2 and passed on an FACS II flow cytometer could be resolved into at least four distinct subpopulations on the basis of fluorescence and forward light...

In this note, we aim to present some properties of the space of all weakly fuzzy bounded linear operators, with the Bag and Samanta’s operator norm on Felbin’s-type fuzzy normed spaces. In particular, the completeness of this space is studied. By some counterexamples, it is shown that the inverse mapping theorem and the Banach-Steinhaus’s theorem, are not valid for this fuzzy setting. Also...