Millisecond-order response measurement for fast oxygen gas sensors

A novel method for the evaluation of fast response of oxygen gas sensors in terms of milliseconds is developed. Using the method of modulating oxygen partial pressure by changing the total pressure inside the test chamber, the millisecond-order measurement was succeeded. For the 100 Hz sign-wave operation, the measurement system generated the pressure changes from 180 to 220 kPa, corresponding to the change of oxygen partial pressure from 36 to 44 kPa. Using both jump-method and pressure modulation method, the response of the resistive oxygen sensors of cerium oxide thick films were evaluated at 1173 K and the kinetic mechanism of gas sensing was discussed. Their response times of t₉₀ obtained by square-wave change were measured to be 37 and 22 ms for high-to-low oxygen partial pressure and vice versa transition, respectively. The log–log plot of resistance of sensor and the frequency, pressure modulation spectra, was also evaluated at the same time and the kinetics of oxygen sensing was suggested to be diffusion-limited.     

Analytic numerical solution of coupled semi-infinite diffusion problems

In this paper, we consider coupled semi-infinite diffusion problems of the form u_t(x, t)− A² u_xx(x,t) = 0, x> 0, t> 0, subject to u(0,t)=B and u(x,0)=0, where A is a matrix in , and u(x,t), and B are vectors in . Using the Fourier sine transform, an explicit exact solution of the problem is proposed. Given an admissible error and a domain D(x₀,t₀)={(x,t);0≤x≤x₀, t≥t₀ > 0, an analytic approximate solution is constructed so that the error with respect to the exact solution is uniformly upper bounded by in D(x₀, t₀).     

Optochemical hydrogen peroxide sensor based on oxygen detection

A novel hydrogen peroxide sensor based on an optochemical oxygen sensor is presented. An oxygen sensitive membrane is covered with an additional layer containing inorganic catalysts which decompose hydrogen peroxide to water and oxygen. The oxygen is detected in the underlying oxygen sensitive membrane via luminescence quenching. The investigated concentration range for the reported sensor was between 0.1 and 2 wt.% hydrogen peroxide in water. Several catalysts were tested for this application with manganese dioxide being the preferred material. In addition to this, it was shown that by coating the sensor with a proper polymer layer, the hydrogen peroxide sensitivity could be improved up to five times compared to an uncoated sensor. The response times of the sensors depends on the type of covering layer, with the shortest response times being similar to that of uncoated sensors (t₉₅ was approximately 1 min for a change from 0 to 0.2 wt.% hydrogen peroxide in water).     

Periodic solutions of a class of nonlinear difference equations via critical point method

In this paper, we obtain some new sufficient conditions for the existence of nontrivial m-periodic solutions of the following nonlinear difference equation

by using the critical point method, where f: Z × R → R is continuous in the second variable, m ≥ 2 is a given positive integer, p_n+m = p_n for any n  Z and f(t + m, z) = f(t, z) for any (t, z)  Z × R, (−1)^δ = −1 and δ > 0.     

Order-configuration functions: Mathematical characterizations and applications to digital signal and image processing

We call a function f in n variables an order-configuration function if for any x₁,…, x_n such that x_i1 … x_in we have f(x₁,…, x_n) = x_t, where t is determined by the n-tuple (i₁,…, i_n) corresponding to that ordering. Equivalently, it is a function built as a minimum of maxima, or a maximum of minima. Well-known examples are the minimum, the maximum, the median, and more generally rank functions, or the composition of rank functions. Such types of functions are often used in nonlinear processing of digital signals or images (for example in the median or separable median filter, min-max filters, rank filters, etc.). In this paper we study the mathematical properties of order-configuration functions and of a wider class of functions that we call order-subconfiguration functions. We give several characterization theorems for them. We show through various examples how our concepts can be used in the design of digital signal filters or image transformations based on order-configuration functions.     

Analytic-numerical solutions with a priori error bounds for time-dependent mixed partial differential problems

The aim of this paper is double. First, we point out that the hypothesis D(t₁)D(t₂) = D(t₂)D(t₁) imposed in [1] can be removed. Second, a constructive method for obtaining analytic-numerical solutions with a prefixed accuracy in a bounded domain Ω(t₀,t₁) = [0,p] × [t₀,t₁], for mixed problems of the type u_t(x,t) − D(t)u_xx(x,t) = 0, 0 < x < p, t> 0, subject to u(0,t) = u(p,t) = 0 and u(x,0) = F(x) is proposed. Here, u(x,t) and F(x) are r-component vectors, D(t) is a C^{r × r} valued analytic function and there exists a positive number δ such that every eigenvalue z of (1/2) (D(t) + D(t)^H) is bigger than δ. An illustrative example is included.     

Constructible functions in cellular automata and their applications to hierarchy results

We investigate time-constructible functions in one-dimensional cellular automata (CA). It is shown that (i) if a function t(n) is computable by an O(t(n)−n)-time Turing machine, then t(n) is time constructible by CA and (ii) if two functions are time constructible by CA, then the sum, product, and exponential functions of them are time constructible by CA. As an application, it is shown that if t₁(n) and t₂(n) are time constructible functions such that lim_n→∞ t₁(n)/t₂(n) = 0 and t₁(n)n, then there is a language which can be recognized by a CA in t₂(n) time but not by any CA in t₁(n) time.     

Blossoms are polar forms

Consider the functions H(t):=t² and h(u,v):=uv. The identity H(t)=h(t,t) shows that h is the restriction of h to the diagonal u=v in the uv-plane. Yet, in many ways, a bilinear function like h is simpler than a homogeneous quadratic function like H. More generally, if F(t) is some n-ic polynomial function, it is often helpful to study the polar form of F, which is the unique symmetric, multiaffine function ƒ(u_1,…u_n) satisfying the identity F(t)=f(t,…,t). The mathematical theory underlying splines is one area where polar forms can be particularly helpful, because two pieces F and G of an n-ic spline meet at a point r with C^k parametric continuity if and only if their polar forms ƒ and g agree on all sequences of n arguments that contain at least n-k copies of r.

The polar approach to the theory of splines emerged in rather different guises in three independent research efforts: Paul de Faget Casteljau called it ‘shapes through poles’; Carl de Boor called it ‘B-splines without divided differences’; and Lyle Ramshaw called it ‘blossoming’. This paper reviews the work of de Casteljau, de Boor, and Ramshaw in an attempt to clarify the basic principles that underly the polar approach. It also proposes a consistent system of nomenclature as a possible standard.     

Nonnegative solutions of singular boundary value problems with sign changing nonlinearities

The paper presents sufficient conditions for the existence of positive solutions of the equation x″(t) + q(t)f(t,x(t),x′(t)) = 0 with the Dirichlet conditions x(0) = 0, x(1) = 0 and of the equation (p(t)x′(t))′ + p(t)q(t)f(t,x(t),p(t)x′(t)) = 0 with the boundary conditions lim_t→o⁺ p(t)x′(t) = 0, x(1) = 0. Our nonlinearity f is allowed to change sign and f may be singular at x = 0. The proofs are based on a combination of the regularity and sequential techniques and the method of lower and upper functions.     

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.     

Robust H∞ control design for systems with structured parameter uncertainty

In a recent paper a unification of the H₂ (LQG) and H_∞ control-design problems was obtained in terms of modified algebraic Riccati equations. In the present paper these results are extended to guarantee robust H₂ and H_∞ performance in the presence of structured real-valued parameter variiations (ΔA, ΔB, ΔC) in the state space model. For design flexibility the paper considers two distinct types of uncertainty bounds for both full- and reduced-order dynamic compensation. An important special case of these results generates H₂/H_∞ controller designs with guaranteed gain margins.     

Bisector curves of planar rational curves

This paper presents a simple and robust method for computing the bisector of two planar rational curves. We represent the correspondence between the foot points on two planar rational curves C₁(t) and C₂(r) as an implicit curve (t,r)=0, where (t,r) is a bivariate polynomial B-spline function. Given two rational curves of degree m in the xy-plane, the curve (t,r)=0 has degree 4m−2, which is considerably lower than that of the corresponding bisector curve in the xy-plane.     

NOx sensing properties of In2O3 nanoparticles prepared by metal organic chemical vapor deposition

In₂O₃ nanoparticles were deposited by low-temperature metal organic chemical vapor deposition. The response of 10-nm thick In₂O₃ particle containing layers to NO_x and O₂ gases is investigated. The lowest detectable NO_x concentration is 200 ppb and the sensor performance is strongly dependent on the gas partial pressure as well as on the operating temperature. The sensor response towards 200 ppm of NO_x is found to be above 10⁴. Furthermore, the cross-sensitivity against O₂ is very low, demonstrating that the In₂O₃ nanoparticles are very suitable for the selective NO_x detection.     

Confluent general-factorial difference and derivative operators and polynomial-exponential interpolation

A previous application of the Newton divided difference series of the displacement function E^z = (1 + Δ)^z = e ^Dz, where the operators Δ and D are the variables, to purely exponential interpolation employing general-factorial differences and derivatives, {Pi;^m_i=0 (Δ - S_i)}f(0) and {Pi;^m_i=0 (D - t_i)}f(0), in which the s_i's and t_i's are distinct[1], is here extended to mixed polynomial-exponential interpolation where the s_i's and t_i's are no longer distinct.     

Integral averages and oscillation of second-order nonlinear differential equations

We present some criteria for the oscillation of the second-order nonlinear differential equation

Full-size image

where a ε C¹([t₀, ∞)) is a nonnegative function, q ε C ([t₀, ∞)) are allowed to change sign on [t₀, ∞), ψ, f ε C¹ , ψ(x) > 0, xf(x) > 0, f′(x) ≥ 0 for x ≠ 0. These criteria are obtained by using a general class of the parameter functions H(t,s) in the averaging techniques and represent extension, as well as improvement of known oscillation criteria of Philos and Purnaras for the generalized Emden-Fowler equation.     

On the sensitivity of camera calibration

The orientation position errors of an object's coordinate frame are determined when the offset of image centre and lens distortion are not included in the calibration process. The orientation and position errors are [(u₀)² + (v₀)²]^0.5/f and [(u²₀+v²₀)T²_z + (u²₀T²_z + v²₀T_y²)]^0.5/f, respectively, where f is the focal length, (u₀, v₀) is the offset of image centre and (T_x T_y T_z) is the position of an object. We also obtain the following conclusions: (a) The offset of image centre has little effect on the determinations of the position and orientation of a coordinate frame; (b) the lens distortion will not dramatically change the position and orientation of a coordinate frame; (c) the scale factor has a great effect on the position of a coordinate frame, and on the accuracy of measurement; (d) the offset of image centre is more sensitive than the lens distortion on the determinations of the position and orientation of a coordinate frame. Finally, some experimental results are given to demonstrate the theoretical analysis given in this paper.     

Infinite words and biprefix codes

Let A be an alphabet and ƒ be a right infinite word on A. If ƒ is not ultimately periodic then there exists an infinite set {v_ii0} of (finite) words on A such that ƒ=v₀v₁…v_i…, {v_ii1} is a biprefix code and v_i≠v_j for positive integers i≠j.     

Continuous monitoring of gastric carbon dioxide with optical fibres

An optical fibre sensor for the continuous monitoring of gastric carbon dioxide is described, based on the utilisation of a sensing layer, in which the colour of the layer is dependent on the CO₂ concentration. The CO₂-sensitive layer consists basically of a dye/quaternary ammonium ion pair, dissolved in a thin layer of ethylcellulose. The sensor was thoroughly characterised in laboratory and its performances were compared with those of Tonocap, the instrument based on gastric tonometry, which is the present method for detecting partial pressure of gastric carbon dioxide. Its measurement range, 0–150 h Pa, its accuracy, ±2.5 h Pa, and its response time, less than 1 min, were capable of satisfying the physicians’ requirements for clinical application. The clinical tests, carried out on volunteers and on intensive care patients, showed that the developed sensor is definitely superior to the sensor that is at present available on the market: thanks to its short response time, the optical fibre sensor is able to detect rapid changes in pCO₂, currently unknown because of the lack of a tool with which to measure them.     

A fast algorithm for parametric curve plotting

In parametric curve plotting by means of line segments, a curve r = r(t), t[t₀, t_u] is given, and a set of ordered points r(t_i, iN, t_ie[t₀, t_u] is specified as the vertices of an inscribed polygon of the curve. There are several, analytical, numerical or intuitive ways to derive these vertices obtaining a smooth polygonal approximation. The methods, which can be found in the literature, either belong to some special curves or involve a considerable waste of computing time.

In this paper, we consider an algorithm that appears as a subroutine in the whole program. The subroutine allows the main program to space points as a function of a distance interval for any parametric curve. The design of the routine for performing this spacing is outlined and two examples are shown.     

On the error in Padé approximations for functions defined by Stieltjes integrals

Consdier I(z) = ∫^b_a w(t)f(t, z) dt, f(t, z) = (1 + t/z)⁻¹. It is known that generalized Gaussian quadrature of I(z) leads to approximations which occupy the (n, n + r − 1) positions of the Padé matrix table for I(z). Here r is a positive integer or zero. In a previous paper the author developed a series representation for the error in Gaussian quadrature. This approach is now used to study the error in the Padé approximations noted. Three important examples are treated. Two of the examples are generalized to the case where f(t, z) = (1 + t/z)^−v.