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.     

Existence of solutions for lower semicontinuous quasi-equilibrium problems

In this paper, we deal with the following quasi-equilibrium problem: given a nonempty subset C of a topological vector space X, a nonempty set D, two functions T : C → D, f : X × D → R and a multifunction S : C → 2^X, find such that , and for all . Such a problem, recently introduced in [1], extends and unifies several variational inequality problems, generalized complementarity problems and Nash equilibrium problems. We prove several existence results in which the upper semicontinuity of the multifunction S is not assumed.     

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.     

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.     

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.     

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.     

Ti–W–O sputtered thin film as n- or p-type gas sensors

We present some recent trends about research on gas sensors based on semiconducting thin films together with a discussion on the development of novel nanostructured materials such as TiO, TiO₂, and WO₃ in single phase or as mixed oxides. The films, deposited by RF reactive sputtering from a composite target of W and Ti at two different abundances, are investigated through scanning and transmission electron microscopy (SEM and TEM) techniques for structural characterisation and by volt-amperometric technique for electrical and gas-sensing properties. All of the layers were capable to sense NO₂, no effect of poisoning of the surface was recorded, and recovery of the resistance was complete. A concentration as low as 0.5 ppm was detected with a relative change in the resistance ΔR/R about 1400% and as short a response time as 2 min. A detection limit lower than 100 ppb of NO₂ is expected.     

A mathematical model with finite-element analysis of recessed dissolved-oxygen cathode array

A mathematical model of recessed dissolved-oxygen cathode array sensors is described. A three-dimensional cylindrical coordinate (R, θ Z) finite-element analysis with a trigonal ring element has been developed for analysing the complex geometry of the recessed cathode plain array. Some priorities to estimate sensitivity, response time, stability, diffusion cross-talk and flow independence concurrently are provided. It is found that a microhole with a vertical wall is more effective in limiting the diffusion field than those with different wall slope, given the same depth/diameter (H/D) ratio. In order to avoid cross-talk between the diffusion fields of two microholes, their centres must be more than 1.9D apart. A new microhole cathode array three-electrode oxygen sensor has been developed using the result of the model.     

Discontinuous quasivariational-like inequalities

In this note, we deal with the following problem: given X Rⁿ, a multification gG : X → 2^X, two (single-valued) maps f : X → Rⁿ, η : X × X → Rⁿ, find a point x* X such that x* Γ (x*) and f(x*), η(x,x*) ≥ 0 for all x Γ(x*). We prove an existence theorem in which, in particular, the function f is not supposed to be continuous.     

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.     

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.     

An asymptotic theory for recurrence relations based on minimization and maximization

We derive asymptotic approximations for the sequence f(n) defined recursively by f(n)=min_1j<n {f(j)+f(n−j)}+g(n), when the asymptotic behavior of g(n) is known. Our tools are general enough and applicable to another sequence F(n)=max_1j<n {F(j)+F(n−j)+min{g(j),g(n−j)}}, also frequently encountered in divide-and-conquer problems. Applications of our results to algorithms, group testing, dichotomous search, etc. are discussed.     

Thermodynamics of the cao-si02 system

In order to maintain consistency, analytical expressions for the free energy of mixing of phases should reproduce not only the phase diagrams but also the experimentally determined activities. Information on the partial molar free energies and the phase boundaries, in turn, can be used to estimate the free energy of formation of compounds.

An examination of thermochemical data in the CaO-SiO₂ system showed that ΔGδf values for -Ca₂Si0₄, which are stable at temperatures above 1710°K, are limited a maximum of 1800°K. The free energy of formation in a temperature range from about 1700 to 2400°K was estimated from the phase boundary and the activity of silica to be as follows:

2Ca0(s) + Si0₂(cristo.) = Ca2Si0₄() ΔG°f = −86303.50 − 34.338 Tjoules

An analytical expression for the free energy of mixing of the liquid phase was obtained for the entire composition range in the CaO-Si0₂ system. Confidence in the estimated G‡f for -Ca₂Si0₄ was demonstrated by good agreement of the calculated phase diagram and the experimentally determined activity of silica.     

Repetitiveness of languages generated by morphisms

We study the repetition of subwords in languages generated by morphisms. Fundamental to our approach is the notion of quasi-repetitive elements. Using these elements we present a new characterization for repetitive morphisms, from which we derive a simple proof for the fact that a D0L-language is repetitive if and only if it is strongly repetitive (Ehrenfeucht and Rozenberg, Inform. and Control 59 (1983) 13–35). From this proof we obtain a structurally simple polynomial-time algorithm for deciding whether such a language is repetitive. From further results on quasi-repetitive elements we obtain as a consequence a complete characterization for all those morphisms on a two-letter alphabet that are repetitive, a result which is closely related to a result of Séébold (Bull. EATCS 36 (1988) 137–151) on the D0L periodicity problem. Finally, we characterize those morphisms f on a two-letter alphabet, for which the language L(f) generated by f or the language SL(f) of subwords of L(f) are context-free or even regular.     

Preparation of BST ferroelectric thin film by metal organic decomposition for infrared sensor

Barium strontium titanate (Ba_1−xSr_xTiO₃) ferroelectric thin films have been prepared by metal organic decomposition (MOD) on Pt/Ti/SiO₂/Si and on micromachined wafer with an aim to fabricate dielectric bolometer type infrared (IR) sensor. The XRD pattern and D–V hysteresis curve of the film have been measured in order to investigate the effects of the final annealing temperature and annealing time on the property of the film. The results show that the films annealed at 700 °C or 800 °C all have good perovskite structure, while the film annealed at 800 °C has better ferroelectric loops. Films annealed at 800 °C with different annealing time from 5 to 60 min show a similar perovskite structure, among which films annealed at 30 and 60 min condition have the better ferroelectric loops. Temperature coefficient of dielectric constant (TCD) of the MOD made BST thin film on micromachined substrate is about 1%/K. The uniformity of the BST film on micromachined Si wafer also has been confirmed to be good enough for operation of sensor array. Chopperless operation has been attained and infrared response evaluation of the fabricated sensor also has been carried out with R_v of 0.4 kV/W and D^* of 1.0×10⁸ cm Hz^1/2/W, respectively.     

New bounds for multi-label interval routing

Interval routing (IR) is a space-efficient routing method for computer networks. For longest routing path analysis, researchers have focused on lower bounds for many years. For any n-node graph G of diameter D, there exists an upper bound of 2D for IR using one or more labels, and an upper bound of for IR using or more labels. We present two upper bounds in the first part of the paper. We show that for every integer i>0, every n-node graph of diameter D has a k-dominating set of size for . This result implies a new upper bound of for IR using or more labels, where i is any positive integer constant. We apply the result by Kutten and Peleg [8] to achieve an upper bound of (1+)D for IR using O(n/D) or more labels, where is any constant in (0,1). The second part of the paper offers some lower bounds for planar graphs. For any M-label interval routing scheme (M-IRS), where , we derive a lower bound of [(2M+1)/(2M)]D−1 on the longest path for , and a lower bound of [(2(1+δ)M+1)/(2(1+δ)M)]D, where δ(0,1], for . The latter result implies a lower bound of on the number of labels needed to achieve optimality.     

Sensitive PAT gene sequence detection by nano-SiO2/p-aminothiophenol self-assembled films DNA electrochemical biosensor based on impedance measurement

Nano-SiO₂/p-aminothiophenol (PATP) film was fabricated by self-assembly and electrodeposition methods. The immobilization and hybridization of DNA on the nano-SiO₂/PATP film were characterized by cyclic voltammetry (CV) and electrochemical impedance spectroscopy (EIS). EIS was applied to label-free detection of the target DNA according to the increase of the electron transfer resistance (R_et) of the electrode surface after the hybridization of the probe DNA with the target DNA. This DNA electrochemical biosensor showed its own performance of simplicity, good stability, fine selectivity and high sensitivity, and was successfully applied to the detection of the PAT gene sequences by a label-free EIS method. The dynamic detection range was from 1.0 × 10⁻¹¹ to 1.0 × 10⁻⁶ mol/L 20-base sequence of the PAT gene, with the detection limit of 1.5 × 10⁻¹² mol/L. This DNA sensor has a good ability of recognizing single- or double-base mismatched DNA sequence with the complementary DNA sequence.     

Minimizing the distance to one evader while chasing another

To approach a simple game Δ² of P and E = {E₁, E₂} with no a priori evaders' role assignment and the payoff equal to the distance to one evader at an instant of catching another, we introduce a concept of casting and study the games Δ_1,2 and Δ_2,1 for preassigned and Δ_p² for open-loop casting procedures. Since Δ_p² is reduced to Δ_1,2 or Δ_2,1 which, in turn, are distinguished only by their notations, we focus attention mainly on Δ_1,2. According to the tenet of transition, Δ_1,2 is divided into a concatenation of Δ_1,2^b (basic) and Δ_1,2^a (auxiliary) games that model the problem before and after the first instant of E₁ capture. The games Δ_1,2^a, Δ_1,2^b, Δ_1,2 are studied one after another with use of the Isaacs' approach extended by Berkowitz, Breakwell, Bernhard et al.     

Efficient enumeration of all minimal separators in a graph

This paper presents an efficient algorithm for enumerating all minimal a-b separators separating given non-adjacent vertices a and b in an undirected connected simple graph G = (V, E), Our algorithm requires O(n³R_ab) time, which improves the known result of O(n⁴R_ab) time for solving this problem, where ¦V¦= n and R_ab is the number of minimal a-b separators. The algorithm can be generalized for enumerating all minimal A-B separators that separate non-adjacent vertex sets A, B < V, and it requires O(n²(n − n_A − n_b)R_AB) time in this case, where n_a = ¦A¦, n_B = ¦B¦ and r_AB is the number of all minimal A−B separators. Using the algorithm above as a routine, an efficient algorithm for enumerating all minimal separators of G separating G into at least two connected components is constructed. The algorithm runs in time O(n³R⁺_Σ + n⁴R_Σ), which improves the known result of O(n⁶R_Σ) time, where R_σ is the number of all minimal separators of G and R_ΣR⁺_Σ = ∑_1i, v_j) ER_vivj n − 1)/2 − m)R_Σ. Efficient parallelization of these algorithms is also discussed. It is shown that the first algorithm requires at most O((n/log n)R_ab) time and the second one runs in time O((n/log n)R⁺_Σ+n log nR_Σ) on a CREW PRAM with O(n³) processors.     

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.