Some results of fuzzy BCK-filters

Let X be a bounded BCK-algebra and f a fuzzy set in X. If a fuzzy BCK-filter μ in X satisfies that (i) fμ, (ii) for any fuzzy BCK-filter ν in X, fν implies μν, then μ is said to be generated by f and denote μ by [f) for short. In the present paper, we give a procedure to construct the [f) by f. As applications of this result we prove that the set of all fuzzy BCK-filters in a bounded BCK-algebra forms a complete and infinitely distributive lattice.     

Immobilization of antibodies in micropatterns for cell detection by optical diffraction

Optical diffraction at biochemically microstructured surfaces has been investigated for the label-free in situ detection of cells. The new sensor concept is based on regular arrays of covalently coupled antibodies, which selectively bind cells from solution. Due to the adsorption process, changes are imposed on the intensity distribution of the diffracted light, which can serve to quantify the amount of adsorbed cells. For the formation of such microstructures, different classical film preparation techniques were transferred to a mesoscopic scale by the use of microcontact printing (μCP). Alternatively, receptors were functionalized with thiol groups prior to the immobilization process and directly printed onto the gold surface. Compared to imprinting of non-functionalized proteins on gold, a better replication of the micropatterns could be obtained. Additionally, a significantly lower amount of defects was observed than for the classical coupling techniques. Using such microstructures, first experiments on the detection of Escherichia coli bacteria were performed. Diffraction patterns have been observed for concentrations equal or higher than 10⁶ cells/ml. In time dependent experiments, diffraction spots occurred after 30 – 90 min or 10 – 20 min, depending on whether non-specific cell adsorption or specific binding to anti-E. coli IgG was studied. A first quantitative analysis of the diffraction patterns shows that the total amount of diffracted light increases with increasing incubation time.     

Self-containing reactant biochips for the electrochemiluminescent determination of glucose, lactate and choline

A multi-parametric biochip for glucose, lactate and choline has been developed based on luminol/hydrogen peroxide electrochemiluminescence (ECL). The sensing layers developed were composed of enzyme-bound beads co-entrapped in a photopolymer with luminol-charged beads and spotted at the surface of a glassy carbon electrode (GCE). Lactate oxidase, choline oxidase and luminol were immobilised via electrostatic interactions with DEAE (diethylaminoethyl)-Sepharose whereas glucose oxidase was immobilised, after modification with histidine, by chelation on nickel-charged IDA (imidodiacetic acid)-Sepharose. The luminol immobilisation enabled the achievement of micro-biosensors, present at the surface of the same GCE and free of lateral contamination between each spot by the other’s reaction product. After optimisation of the applied potential, the integration time and the luminol charge in the sensing layer, the electrochemiluminescent H₂O₂ sensor exhibited a detection limit of 2 μM and a working range from 2 μM to 0.5 mM.

The multi-biosensor enabled the concomitant detection of glucose, lactate and choline in the ranges 20 μM–2 mM, 2 μM–0.2 mM and 2 μM–0.2 mM, respectively. Glucose and lactate measurements in complex matrix such as human serum, were in good agreement with the reference methods, without internal calibration of the sample, demonstrating the absence of matrix interference with the present analytical system.     

Dispersion of single-walled carbon nanotubes in poly(diallyldimethylammonium chloride) for preparation of a glucose biosensor

Poly(diallyldimethylammonium chloride) (PDDA) was chosen to disperse single-walled carbon nanotubes (SWCNTs). The optimal conditions to prepare stable PDDA–SWCNTs aqueous dispersions were presented. Then, the positively charged PDDA–SWCNTs composite and negatively charged glucose oxidase (GOD) were employed to fabricate multilayer films on platinum (Pt) electrodes by layer-by-layer self-assembly technique. The consecutive growth of the multilayer films was confirmed by quartz crystal microbalance. Electrochemical measurements were used to study the properties of the proposed biosensor. Results demonstrated that SWCNTs were evenly dispersed within the PDDA films and efficiently improved the conductivity of the resulting films. Among the biosensors, the one based on seven layers of multilayer films got the best performance. It showed wide linear range of 0.05–12 mM, high sensitivity of 63.84 μA/(mM cm²), low detection limit of about 4 μM and small value of the apparent Michaelis–Menten constant, 8.46 mM. In addition, the biosensor also exhibited good suppression of interference and long-term operational stability. This protocol could be used to immobilize other enzymes to construct a range of biosensors.     

Fabrication of carbon nanotubes/poly(1,2-diaminobenzene) nanoporous composite via multipulse chronoamperometric electropolymerization process and its electrocatalytic property toward oxidation of NADH

A novel method was proposed for fabrication of a carbon nanotubes/poly(1,2-diaminobenzene) nanoporous composite based electrode. The poly(1,2-diaminobenzene) was deposited onto the surface of a glassy carbon electrode (GCE) modified with multi-wall carbon nanotubes (MWNTs) via multipulse chronoamperometric electropolymerization (MCE) process. Compared with the composite prepared by conventional electropolymerization (CE), the electronic and ionic transport capacity of the MCE-based composite were significantly improved due to its unique nanoporous structure. The surface of the composite-modified GCE was characterized with scanning electron microscopy (SEM) and cyclic voltammetry (CV). The nanoporous MCE-based electrode was applied to determination of NADH at a much low potential of 70 mV, and a linear range from 2.0 μM to 4.0 mM was observed with fast response (within 5 s) and a lower detection limit of 0.5 μM (based on S/N = 3). In comparison, a narrow linear range from 5.0 μM to 2.0 mM, slower response (up to 15 s) and a higher detection limit of 3.0 μM (based on S/N = 3) was obtained with the electrode prepared by CE. The wider linear range, lower detection limit and fast response of the MCE-based electrode implies that the new method proposed can provide more excellent platforms for sensitive electrochemical sensing and biosensing.     

Intersection of finitely generated congruences over term algebra

We show that it is decidable for any given ground term rewrite systems R and S if there is a ground term rewrite system U such that ↔_U^*=↔_R^*∩↔_S^*. If the answer is yes, then we can effectively construct such a ground term rewrite system U. In other words, for any given finitely generated congruences ρ and τ over the term algebra, it is decidable if ρ∩τ is a finitely generated congruence. If the answer is yes, then we can effectively construct a ground term rewrite system U such that ↔_U^*=ρ∩τ.     

Simulation and fabrication of piezoresistive membrane type MEMS strain sensors

Two piezoresistive (n-polysilicon) strain sensors on a thin Si₃N₄/SiO₂ membrane with improved sensitivity were successfully fabricated by using MEMS technology. The primary difference between the two designs was the number of strips of the polysilicon patterns. For each design, a doped n-polysilicon sensing element was patterned over a thin 3 μm Si₃N₄/SiO₂ membrane. A 1000×1000 μm² window in the silicon wafer was etched to free the thin membrane from the silicon wafer. The intent of this design was to fabricate a flexible MEMS strain sensor similar in function to a commercial metal foil strain gage. A finite element model of this geometry indicates that strains in the membrane will be higher than strains in the surrounding silicon. The values of nominal resistance of the single strip sensor and the multi-strip sensor were 4.6 and 8.6 kΩ, respectively. To evaluate thermal stability and sensing characteristics, the temperature coefficient of resistance [TCR=(ΔR/R₀)/ΔT] and the gage factor [GF=(ΔR/R₀)/] for each design were evaluated. The sensors were heated on a hot plate to measure the TCR. The sensors were embedded in a vinyl ester epoxy plate to determine the sensor sensitivity. The TCR was 7.5×10⁻⁴ and 9.5×10⁻⁴/°C for the single strip and the multi-strip pattern sensors. The gage factor was as high as 15 (bending) and 13 (tension) for the single strip sensor, and 4 (bending) and 21 (tension) for the multi-strip sensor. The sensitivity of these MEMS sensors is much higher than the sensitivity of commercial metal foil strain gages and strain gage alloys.     

A new optical sensing reaction for nitric oxide

Based on the reaction between the Cu(II) complex of Eriochrome cyanine R (ECR) and nitric oxide (NO) in phosphate buffer (pH 7.4), a new colorimetric method for the determination of NO concentration has been developed. The linear calibration range for NO was 0–60 μM with a detection limit of 1.24 μM. This reaction was then used as the basis in the development of a fibre optic chemical sensor for NO gas. The copper complex was incorporated into silicone rubber membranes and exposed to NO gas after incubating the films in phosphate buffer (pH 7.4). A linear calibration for NO gas between 0 and 6 ppm was obtained with a detection limit of 0.227 ppm (1 μM 0.031 ppm NO in solution). The sensor response was shown to be reproducible and reversible (2.77%, R.S.D., n=4) upon exposure to aqueous phosphate buffer (pH 7.4). The sensor response was also found to be pH independent between 7 and 10.     

The Hopf bifurcation theorem for quasilinear differential-algebraic equations

We prove a generalization of the Hopf bifurcation theorem for quasilinear differential equations (DAEs), i.e. equations of the form A(μ, χ)χ = G(μ, χ) where the matrix A(χ, μ) has constant but not full rank and hence the system cannot be made into an explicit ODE. The paper includes an appendix by J. Ernsthausen addressing the numerical calculation of the Hopf points in the DAE setting.     

A note on measuring in P

We revisit the problem of generalising Lutz's resource-bounded measure to small complexity classes, and propose a definition of a random-based on , which we argue as being a good generalisation to of Lutz's . We cannot unconditionally prove the existence of such a measure, but we give sufficient and necessary conditions for its existence. We also revisit μ_τ, an for defined by Strauss [Inform. Comput. 136(1) (1997) 1], and correct an erroneous claim concerning the relations between μ_τ and random sets. A correction to this mistake is then proposed, which is a less powerful but accurate relation between μ_τ and random sets.

In order to obtain these results, we introduce a mathematical structure called a measuring system, which is a general setting that can be used to compare different s on any fixed complexity class through a partial ordering relation.     

3-D silicon vector sensor based on a novel parallel-field Hall microdevice

A single-chip 3-D silicon vector sensor for magnetic-field measurement is presented. This triaxial device functionally integrates in a common transducer region two novel five-contacts parallel-field Hall elements for in-plane components B_x and B_y and four cross-coupled orthogonal triple Hall elements for the B_z component, perpendicular to the chip surface. The effective sensor volume is 150 μm×150 μm×100 μm. The main advantage of this 3-D vector magnetometer is the strongly reduced (with about 45%) channel cross-sensitivities. This is achieved by amperometric output mode of operation using an original read-out circuitry, keeping equal voltage conditions on the top of the chip with and without magnetic field. The sensitivities per channel reaches S_A(B_x)=S_A(B_y)=356 μA/T and S_A(B_z)=260 μA/T at a supply current 10 mA, the measured equivalent offsets of the three channel outputs are 25/35 mT and the low frequency noise is mainly a 1/f. The lowest detected magnetic induction of the three output channels is about 15/20 μT in the range 1≤f≤ 10² Hz and the frequency response of the 3-D device together with the read-out electronics is at least 30 kHz.     

Time division multiplexed strain sensing system by the use of dual-wavelength fiber Bragg gratings

The dual-wavelength fiber Bragg gratings (DWFBGs) accompanying with dual-wavelength pulsed laser source for strain measurement in a time division multiplexed (TDM) sensing system have been demonstrated. The accuracy up to 2.3 μ in a ±50 μ range has been achieved.     

Plasma-polymerized coatings for bio-MEMS applications

Coatings that provide either hydrophobic, hydrophilic, cell adhesive or cell non-adhesive functionalities have been deposited using three-phase low energy plasma-polymerization. The cell adhesive/non-adhesive coatings were tested using E. coli k-12. The four plasma-polymerized coatings are: para-xylene (PX), 1-vinyl-2-pyrrolidinone (VP), polyvinyldifluoride (PVDF) and phosphorous glass (SiPOC), respectively. In addition, micropatterning of PX and VP has been performed on the same silicon substrate. Feature sizes down to 2 μm and precise alignment were obtained using lift-off and cleanroom photolithography techniques. The patterning process used did not influence the wetability of the coatings. The simplicity of the lift-off technique and the sturdiness and versatility of the plasma-polymerized coatings, make this ideal for MEMS, bio-MEMS and microfluidic applications, where patterned surfaces with different functionalities are required on for instance the same microchip.     

Thin-film thermocouples of Ge doped with Au and B

High thermoelectric power (S300 μV K⁻¹;ρ10⁻⁴ Ω m) has been achieved for germanium layers doped with gold deposited by evaporation. The relative simplicity and good reproducibility of the method seems to be promising for thermopiles in some types of microsensors.     

Development of a bienzyme system based on sugar–lectin biospecific interactions for amperometric determination of phenols and aromatic amines

Bienzyme electrode with horseradish peroxidase (HRP) and glucose oxidase (GOD) multilayers was constructed based on sugar–lectin biospecific interactions for amperometric determination of phenolic compounds and aromatic amines. Atomic force microscopy (AFM) was applied to monitor the uniform layer-by-layer assembly of concanavalin A (Con A) and HRP or GOD on polyelectrolyte precursor film-modified Au electrode. Substituted phenolic compounds and aromatic amines could be determined with in situ generation of H₂O₂ by GOD-catalyzed oxidation of glucose. The parameters of the biosensor including the number of assembled HRP and GOD layer, and the concentrations of glucose were optimized. The linear range for the determination of catechol and p-phenyldiamine was 6.0–60.0 μmol L⁻¹ and 7.6–68.4 μmol L⁻¹ with detection limit of 0.9 μmol L⁻¹ and 0.4 μmol L⁻¹, respectively. The biosensor possessed high sensitivity and fast response for phenolic compounds and 95% of the maximum response could be reached in about 3 s. Glucose, ascorbic acid, tartaric acid, citric acid and starch exhibited no interference for the detection. The biosensor presented high stability due to the design for in situ generation of H₂O₂ with bienzyme system.     

Paired-domination in inflated graphs

The inflation G_I of a graph G with n(G) vertices and m(G) edges is obtained from G by replacing every vertex of degree d of G by a clique K_d. A set S of vertices in a graph G is a paired dominating set of G if every vertex of G is adjacent to some vertex in S and if the subgraph induced by S contains a perfect matching. The paired domination number γ_p(G) is the minimum cardinality of a paired dominating set of G. In this paper, we show that if a graph G has a minimum degree δ(G)2, then n(G)γ_p(G_I)4m(G)/[δ(G)+1], and the equality γ_p(G_I) = n(G) holds if and only if G has a perfect matching. In addition, we present a linear time algorithm to compute a minimum paired-dominating set for an inflation tree.     

Existence of multiple positive solutions for functional differential equations

In this paper, the existence of at least three positive solutions for the boundary value problem (BVP) of second-order functional differential equation with the form y″(t) + f(t, y^t) = 0, for t ε [0,1], y(t) -βy′(t) =η(t), for t ε [−τ,0], −γy(t) + Δy′(t) = ζ(t), for t ε [1, 1 + a], is studied. Moreover, we investigate the existence of at least three partially symmetric positive solutions for the above BVP with Δ = βγ.     

A wireless, remote-query sensor for real-time detection of Escherichia coli O157:H7 concentrations

This paper describes the real-time detection of Escherichia coli O157:H7 concentrations using a remote-query (wireless, passive) magnetoelastic sensor. The resonance frequency of a liquid immersed magnetoelastic sensor, measured through magnetic field telemetry, changes mainly in response to bacteria adhesion to the sensor and the liquid properties (viscosity, density, elasticity, etc.) of the culture medium. In the described application, during its growth and reproduction we find E. coli consumes nutrients from a liquid culture medium that decreases the solution viscosity, and in turn changes the resonance frequency of the medium-immersed magnetoelastic sensor. Using the described technique we are able to directly quantify E. coli O157:H7 concentrations of 2 × 10² to 3 × 10⁶ cells ml⁻¹, and quantify the effect of gentamycin sulfate injection (GSI) on proliferation of the bacteria. The lack of any physical connections between the sensor and the monitoring electronics facilitates aseptic operation, and makes the sensor platform ideally suited for monitoring bacteria from within, for example, sealed food containers.     

Scattering on a ring of processors

In this note, we prove that the complexity of scattering in an oriented ring of p processors is (p - 1) (β + Lτ) where L is the length of the messages, β the communication startup, and τ the elemental propagation time.     

McClellan transformation and the construction of biorthogonal wavelet bases of LR

Bidimensional wavelet bases are constructed by means of McClellan's transformation applied to a pair of one-dimensional biorthogonal wavelet filters. It is shown that under some conditions on the transfer function F(ω₁,ω₂) associated to the McClellan transformation and on the dilation matrix D, it is possible to construct symmetric compactly supported biorthogonal wavelet bases of L²(R²). Finally, the construction method is illustrated by means of numerical examples.