In this paper, we study a generalization of z-ideals in the ring C(X) of continuous real valued functions on a completely regular Hausdorff space X. The notion of a weak ideal and naturally a weak z-ideal and a prime weak ideal are introduced and it turns out that they behave such as z-ideals in C(X).

Non-statistical weak measurements yield weak values that are outside the range of eigenvalues and are not rare, suggesting that weak values are a property of every preand-post-selected ensemble. They also extend the applicability and valid regime of weak values.

The aim of this paper is to analyze a viscoelastic phase separation model. We derive suitable notion the relative energy taking into account nonconvex nature law for separation. This allows us prove weak–strong uniqueness principle. will provide estimates full model in two space dimensions. For reduced model, we present three dimensions and conditional estimates.

To separate proteins with a wide distribution of pIs under the conditions compatible to online tryptic digestion (with preferable pH=8.0), weak anion and cation exchange chromatography (WAX/WCX) mixed-bed microcolumn has been developed. With a mixture of five proteins with pIs ranging from 4.2 to 11.4, the effect of WAX/WCX ratio on the separation performance was investigated, and an optimum pa...

Current understanding of the critical outbreak condition on temporal networks relies on approximations (time scale separation, discretization) that may bias the results. We propose a theoretical framework to compute the epidemic threshold in continuous time through the infection propagator approach. We introduce the weak commutation condition allowing the interpretation of annealed networks, ac...

In this paper, we propose a novel method of blind signal separation using a new performance criterion with nonlinear separating functions, and derive an adaptive algorithm. The criterion consists of nonlinear mappings of output signals and their cumulants for independence of the signals. We show that our method requires a weak condition for stable separation through the ODE analysis. Simulation...

We study the 1D extended Hubbard model with a weak repulsive short-range interaction in the non-half-filled band case, using non-perturbative Renormalization Group methods and Ward Identities. At the critical temperature, T = 0, the response functions have anomalous power-law decay with multiplicative logarithmic corrections. The critical exponents, the susceptibility and the Drude weight verif...