Chaotic convergence of the decision-directed blind equalization algorithm

Classically, adaptive equalization algorithms are analyzed in terms of two possible steady state behaviors: convergence to a fixed point and divergence to infinity. This twofold scenario suits well the modus operandi of linear supervised algorithms, but can be rather restrictive when unsupervised methods are considered, as their intrinsic use of higher-order statistics gives rise to nonlinear update expressions. In this work, we show, using different analytical tools belonging to dynamic system theory, that one of the most emblematic and studied unsupervised approaches – the decision-directed algorithm – is potentially capable of presenting behaviors, like convergence to limit-cycles and chaos, that transcend the aforementioned dichotomy. These results also indicate theoretical possibilities concerning step-size selection and initialization.     

Generic conformally flat hypersurfaces and surfaces in 3-sphere

Science China Mathematics - The aim of this paper is to verify that the study of generic conformally flat hypersurfaces in 4-dimensional space forms is reduced to a surface theory in the standard...     

Chemical recycling of networked polystyrene derivatives using subcritical water in the presence of an aminoalcohol

Subcritical water is a benign and effective media for polymer degradation. On subcritical water treatment in the presence of an aminoalcohol, unsaturated polyesters crosslinked with styrene were decrosslinked, and a linear polystyrene derivative bearing hydroxy-terminated side-chains was recovered. After modification of the hydroxy groups with maleic anhydride, the polystyrene derivative was re-crosslinked with styrene to form a networked structure again. The resulting solid was degradable by subcritical water treatment in the presence of the aminoalcohol to give another polystyrene derivative bearing hydroxy groups. These processes could be repeated successfully, demonstrating the applicability as a novel recycling system of thermosetting resins. The polystyrene derivative was also re-crosslinked again on heating with an alternative copolymer of styrene and maleic anhydride due to the formation of linkage between the hydroxy groups and carboxylic anhydride moieties.     

Bezout equations over bivariate polynomial matrices related by an entire function

This study addresses Bezout equations over bivariate polynomial matrices, where the relationship between two variables is described by a real entire function. This paper proposes a solution method that makes optimal use of minor primeness to reduce such Bezout equations to simple equations over univariate scalar polynomials. The proposed solution method requires only matrix calculations, thus making it very useful, especially in the absence of modern computer algebra systems.     

Smoothing out negative tension brane

We propose an extension of the five-dimensional gravitational action with an external source in order to allow arbitrary smoothing of the negative tension brane in the Randall–Sundrum model. This extended action can be derived from a model with an auxiliary four form field coupled to the gravity. We point out a further generalization of our model in relation to tachyon condensation. A possible mechanism for radion stabilization in our model is also discussed.     

Formation of multiple aerial LED signs in multiple lanes formed with AIRR by use of two beam splitters

Optical Review - We propose multiple aerial imaging system by use of two beam splitters in the optical system of aerial imaging by retro-reflection (AIRR). The AIRR optical system consists of a...     

Analysis and fabrication for the dimensional expansion of arc 3D display to cone-shaped display

Optical Review - This paper successfully describes the analysis between 3D image location in air and arc-shaped scratches on cone-shaped arc 3D display. The arc 3D display is typically flat and its...     

Occlusion of transition metal ions by new adsorbents synthesized from plant polyphenols and animal fibrous proteins

Removing and collecting heavy and rare metal ions from industrial effluents and waste aqueous solutions are improtant problems. Our previous studies showed that animal fibrous proteins (AFPs) such as hen eggshell membrane, chicken feather (CF), wool, and silk were stable and insoluble proteins and had an excellent ability to bind not only hard (Mn²⁺ and Fe³⁺) but alsosoft (Ag⁺, Au⁺, Pd²⁺, Pt²⁺, and Hg²⁺) acids from aqueous solutions. In this study, we syntheszed some adsorbents for transition (Cr⁶⁺, Mn²⁺, Co²⁺, Ni²⁺, and Cu²⁺) and heavy (Cd²⁺) metalions from AFPs (gelatin, CF, and wool) and plant polyphenols (lignin and tannin) by heating a mixture of AFPs and plant polyphenols under acidic conditions. In batch experiments, pH profile, time dependency, and isotherm analysis were performed to determine binding properties of adsorbents for transition and heavy metal ions. Columnexperiments were also performed to removecopper ion from aqueous solution. The results showed that the new adsorbents were effective for collecting and removing transition and heavy metal ions from aqueous solutions.     

Remarks on toric manifolds whose Chern characters are positive

Abstract

We show that the second Chern character of any projective toric manifold of Picard number three is not positive. In connection with this result, we give various examples of the positivity of higher Chern characters of projective toric manifolds.

Communicated by Stephen L. Kleiman