Very recently Pascal Koiran introduced in [10] a model of computation that comes from a modification of the cost notion of the real Turing machine of [2]. This new model —that following Koiran will be called weak— drops the unit cost assumption for the arithmetical operations and only allows a “moderate use of multiplication” ([11]). The main result of [10] states that when restricted to Boolea...

We investigate the information processing of a linear mixture of independent sources of different magnitudes. In particular we consider the case where a number m of the sources can be considered as "strong" as compared to the other ones, the "weak" sources. We find that it is preferable to perform blind source separation in the space spanned by the strong sources, and that this can be easily do...

The traditional weak signal chaotic detection system still restricts some technical issues in the situation of the signal with noise, such as poor denoising ability and low detection precision. In this paper, we propose a novel weak signal chaotic detection system based on an improved wavelet transform algorithm. First, the traditional wavelet transform algorithm domain variables have been tran...

The semantics of concurrent programs is now defined by a weak memory model, determined either by the programming language (e.g., in the case of C/C++11 or Java) or by the hardware architecture (e.g., for assembly and legacy C code). Since most work in concurrent software verification has been developed prior to weak memory consistency, it is natural to ask how these models affect formal reasoni...

The authors present a generalized theory of microphase separation for charged-neutral diblock copolymer melt. The stability limit of the disordered phase for salt-free melt has been calculated using random phase approximation (RPA) and self-consistent-field theory (SCFT). Explicit analytical free energy expressions for different classical ordered microstructures (lamellar, cylinder, and sphere)...

These notes give a summary of results that everyone who does work in functional analysis should know about the weak topology on locally convex topological vector spaces and the weak-* topology on their dual spaces. The most striking of the results we prove is Theorem 9, which shows that a subset of a locally convex space is bounded if and only if it is weakly bounded. It is straightforward to p...

The novel nanocomposite membranes were successfully prepared by the incorporation of different concentrations (5, 10, and 15 wt%) of montmorillonite (MMT) as a nanoadditive into a blend of chitosan/polystyrene (CS/PS) at a ratio of 3:1 on the basis of solution-casting method and they were subsequently used for the separation of phenol, p-chlorophenol, and 2,4-dichlorophenol from water through p...

This work is devoted to examining inverse vector variational inequalities with constraints by means of a prominent nonlinear scalarizing functional. We show that inverse vector variational inequalities are equivalent to multiobjective optimization problems with a variable domination structure. Moreover, we introduce a nonlinear function based on a well-known nonlinear scalarization function. We...

Dynamic ordinal analysis is ordinal analysis for weak arithmetics like fragments of bounded arithmetic. In this paper we will define dynamic ordinals – they will be sets of number theoretic functions measuring the amount of sΠb1(X) order induction available in a theory. We will compare order induction to successor induction over weak theories. We will compute dynamic ordinals of the bounded ari...

The aim of this work is to prove the global-in-time existence weak solutions for a viscoelastic phase separation model in three space dimensions. To end, we apply relative energy concept provided by [7]. We consider case regular polynomial-type potentials and positive mobilities, as well degenerate with logarithmic potential vanishing mobility.