Fractal Interpolation on a Torus

A very general method of fractal interpolation on T ¹ is proposed in the first place. The approach includes the classical cases using trigonometric functions, periodic splines, etc. but, at the same time, adds a diversity of fractal elements which may be more appropriate to model the complexity of some variables. Upper bounds of the committed error are provided. The arguments avoid the use of derivatives in order to handle a wider framework. The Lebesgue constant of the associated partition plays a key role. The procedure is proved convergent for the interpolation of specific functions with respect to some nodal bases. In a second part, the approximation is then extended to bidimensional tori via tensor product of interpolation spaces. Some sufficient conditions for the convergence of the process in the Fourier case are deduced.      

A nonparametric approach to 3D shape analysis from digital camera images — I

This article for the first time develops a nonparametric methodology for the analysis of projective shapes of configurations of landmarks on real 3D objects from their regular camera pictures. A fundamental result in computer vision, emulating the principle of human vision in space, claims that, generically, a finite 3D configuration of points can be retrieved from corresponding configurations in a pair of camera images, up to a projective transformation. Consequently, the projective shape of a 3D configuration can be retrieved from two of its planar views, and a projective shape analysis can be pursued from a sample of images. Projective shapes are here regarded as points on projective shape manifolds. Using large sample and nonparametric bootstrap methodology for extrinsic means on manifolds, one gives confidence regions and tests for the mean projective shape of a 3D configuration from its 2D camera images. Two examples are given: an example of testing for accuracy of a simple manufactured object using mean projective shape analysis, and a face identification example. Both examples are data driven based on landmark registration in digital images.     

A sensor based on electrodes supported on ion-exchange membranes for the flow-injection monitoring of sulphur dioxide in wines and grape juices

A sensitive and fast responding electrochemical sensor is described for the determination of free and total sulphur dioxide in wines and grape juices which prevents interferences coming from ethanol and other natural components. It consists of a cell provided with a porous gold working electrode supported on one face of an ion-exchange membrane, acting as a solid polymer electrolyte (SPE), which allows gaseous electroactive analytes to be detected. This sensor was used as an amperometric detector for a flow injection system in which controlled volumes of headspace equilibrated with samples were injected. This approach was adopted to make also possible the determination of total SO₂, avoiding drawbacks caused by the high relative humidity generated by the sample heating resulting from the neutralization reaction of excess NaOH, whose addition was required to release sulphur dioxide from its combined forms. Factors affecting the detection process were examined and optimised. Under the identified optimal conditions, SO₂ detection resulted in sharp peaks which allowed to infer detection limits for a signal-to-noise ratio of 3, referred to liquid samples, of 0.04 and 0.02 mg L⁻¹ for free and total SO₂ which were determined at 20 and 35 °C, respectively. Moreover, the responses were found to be characterized by good repeatability (±2% and ±4%, respectively) and linear dependence on the SO₂ concentration over a wide range (0.2-500 mg L⁻¹ for both free and total SO₂). Finally, the long-term stability of the sensor turned out to be totally satisfactory in that responses changed of ±9% alone even after long periods of continuous use. The application to some commercial wines and grape juices is also presented.     

Sulfonated polyaniline/vanadate composite as anode material and its electrochemical property in microbial fuel cells on ocean floor

A unique sulfonated polyaniline/vanadate composite was synthesized and utilized as a composite anode in microbial fuel cells on ocean floor (BMFCs). X-ray diffraction (XRD) and thermogravimetric analysis (TGA) were employed to characterize its chemical composition and morphology. Wettability of the composite anodes decreases due to the addition of polytetrafluoroethylene (PTFE). The electrochemical behavior of the composite anodes was investigated by means of linear sweep voltammetry and Tafel plot measurem...     

A generalized h-fractional Gronwall's inequality and its applications for nonlinear h-fractional difference systems with ‘maxima’

ABSTRACT

This paper gives a generalized h-fractional Gronwall's inequality. Applying this result, we prove the uniqueness and give bounds on solutions for a nonlinear h-fractional difference system with ‘maxima’. Finally, we give an example to illustrate one of our main results.     

Groups with π-maximal and π-layer maximal conditions

By analogy with π-minimal, π-layer minimal, primary minimal, and layer minimal conditions, similar maximal conditions are introduced and studied. Translated fromMatematicheskie Zametki, Vol. 68, No. 2, pp. 311–320, August, 2000.     

A Probabilistic Approach to the Problem of the Defects of Admissible Sets in a Lattice

New estimates for the defect of the admissible set in a lattice are obtained for a sufficiently large class of sequences.     

The quasi order of graphs on an ordinal

For α an ordinal, a graph with vertex set α may be represented by its characteristic function, f:[α]²→2, where f({γ,δ})=1 if and only if the pair {γ,δ} is joined in the graph. We call these functions α-colorings.We introduce a quasi order on the α-colorings (graphs) by setting f≤g if and only if there is an order-preserving mapping t:α→α such that f({γ,δ})=g({t(γ),t(δ)}) for all {γ,δ}∈[α]². An α-coloring f is an atom if g≤f implies f≤g.We show that for α=ω^ω below every coloring there is an atom and there are continuum many atoms. For α<ω^ω below every coloring there is an atom and there are finitely many atoms.