Thiele Rational Interpolation for the Numerical Computation of the Reversible Randles–Sevcik Function in Electrochemistry

This paper uses Thiele rational interpolation to derive a simple method for computing the Randles–Sevcik function ^1/2(x), with relative error at most 1.9 × 10^–5 for – < x < . We develop a piecewise approximation method for the numerical computation of ^1/2(x) on the union (–, –10) [–10, 10] (10, ). This approximation is particularly convenient to employ in electrochemical applications where four significant digits of accuracy are usually sufficient. Although this paper is primarily concerned with the approximation of the Randles–Sevcik function, some examples are included that illustrate how Thiele rational interpolation can be employed to generate useful approximations to other functions of interest in scientific work.     

Langages saturés et cônes décroissants langages et cônes bifidèles

Résumé C() (resp.C ^d (–),C ^f (–)) est la plus petite famille de langages contenant et fermée par homomorphisme (resp. homomorphisme alphabétique, homomorphisme non effaçant), homomorphisme inverse (resp. homomorphisme strictement alphabétique inverse, homomorphisme inverse) et par intersection rationnelle.C ^d (–) etC ^f (–) sont donc des cônes restreints deC(–). Nous donnons des relations entre cônes restreints deC(–) etC(–). Ce qui nous permet de construire une hiérarchie infinie de langages algébriques non effaçables (L est effaçable C({L})=C ^f ({L})).

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Saturated languages and decreasing cones bifaithful languages and bifaithful cones

Summary C() (resp.C ^d (–),C ^f (–)) is the smallest family of languages containing and closed under morphism (resp. alphabetic morphism, non erasing morphism), inverse morphism (resp. inverse alphabetic non erasing morphism, inverse morphism) and intersection with regular sets.C ^d (–) andC ^f (–) are restricted cones ofC(). We give relations between restricted cones ofC() andC(), that allows us to construct an infinite hierarchy of no-erasable context-fee languages (L is erasableC({L})=C ^f ({L}))

     

How to Pass a Turing Test

I advocate a theory of syntactic semantics as a way of understanding how computers can think (and how the Chinese-Room-Argument objection to the Turing Test can be overcome): (1) Semantics, considered as the study of relations between symbols and meanings, can be turned into syntax – a study of relations among symbols (including meanings) – and hence syntax (i.e., symbol manipulation) can suffice for the semantical enterprise (contra Searle). (2) Semantics, considered as the process of understanding one domain (by modeling it) in terms of another, can be viewed recursively: The base case of semantic understanding –understanding a domain in terms of itself – is syntactic understanding. (3) An internal (or narrow), first-person point of view makes an external (or wide), third-person point of view otiose for purposes of understanding cognition.     

An Auto-Adaptive Multidomain Spectral Technique for Linear Stability Analysis: Application to Viscous Compressible Flows

An auto-adaptive multidomain pseudo-spectral technique is considered in order to solve the linear stability problem of viscous compressible flows. Both the locations of the interfaces and the parameters of the mappings in each subdomain are adapted by minimizing the H ² -norm of the calculated solution. Such method provides automatically—this is the key point—the best polynomial interpolation of the basic state the stability of which is studied. It turns out that the whole procedure is needed to obtain reliable results. The method is first validated against results available in the literature (both viscous incompressible and inviscid compressible Rayleigh–Taylor configurations). The efficiency of the numerical method is illustrated with results on the linear stability of the compressible viscous diffusive Rayleigh–Taylor flow where no analytical or numerical results are available. New results showing the influence of stratification, viscosity, diffusity between species and thermal diffusivity are presented.     

Fabrication of microneedle array using LIGA and hot embossing process

We demonstrate a novel fabrication technology of the microneedle array applied to painless drug delivery and minimal invasive blood extraction. The fabrication technology consists of a vertical deep X-ray exposure and a successive inclined deep X-ray exposure with a deep X-ray mask whose pattern has a hollow triangular array. The vertical exposure makes triangular column array with a needle conduit. With the successive inclined exposure, the column array shapes into the microneedle array without deep X-ray mask alignment. Changing the inclined angle and the gap between the mask and PMMA (PolyMethylMetaAcrylic) substrate, different types of microneedle array are fabricated in 750–1000 m shafts length, 15^o–20^o tapered tips angle, and 190–300 m bases area. The masks are designed to 400–600 m triangles length, 70–100 m conduits diameter, 25–60EA/5 mm² arrays density, and various tip shapes such as triangular, rounded, or arrow-like features. In the medical application, the fabricated PMMA microneedle array fulfills the structural requirements such as three-dimensional sharp tapered tip, HAR (High-Aspect-Ratio) shafts, small invasive surface area, and out-of-plane structure. In the skin test, the microneedle array penetrates back of the hand skin with minimum pain and without tip break and blood is drawn after puncturing the skin. Hot embossing process and mold fabrication process are also investigated with silicon and PDMS mold. The processed tetrahedral PMMA structures are fabricated into the microneedle array by the additional deep X-ray exposure. With these processes, the microneedle array can be utilized as the mold base for electroplating process.The author thanks the staff in 9 C LIGA beamline, Pohang Light Source (PLS), Korea for their assistance on the fabrication process.     

Utilization Bounds for Multiprocessor Rate-Monotonic Scheduling

In this paper, we extend Liu and Layland's utilization bound for fixed priority scheduling on uniprocessors to homogeneous multiprocessor systems under a partitioning strategy. Assuming that tasks are pre-emptively scheduled on each processor according to fixed priorities assigned by the Rate-Monotonic policy, and allocated to processors by the First Fit algorithm, we prove that the utilization bound is (n–1)(2^1/2–1)+(m–n+1)(2^1/(m–n+1)–1), where m and n are the number of tasks and processors, respectively. This bound is valid for arbitrary utilization factors. Moreover, if all the tasks have utilization factors under a value , the previous bound is raised and the new utilization bound considering is calculated. Finally, simulation provides the average-case behavior.     

Visualizing Newton's method on fractional exponents

Newton's method for finding complex solutions of the equationz –1=0 is investigated for real values of . The bifurcations that occur, as the power varies are illuminated with computer graphics. In particular, the appearance of an attracting 2-cycle just below even powers is investigated.     

Randomness in interactive proofs

This paper initiates a study of the quantitative aspects of randomness in interactive proofs. Our main result, which applies to the equivalent form of IP known as Arthur-Merlin (AM) games, is a randomness-efficient technique for decreasing the error probability. Given an AM proof system forL which achieves error probability 1/3 at the cost of Arthur sendingl(n) random bits per round, and given a polynomialk=k(n), we show how to construct an AM proof system forL which, in the same number of rounds as the original proof system, achieves error 2 ^–k(n) at the cost of Arthur sending onlyO(l+k) random bits per round.Underlying the transformation is a novel sampling method for approximating the average value of an arbitrary functionf:{0,1} ^l [0,1]. The method evaluates the function onO(^–2 log ^–1) sample points generated using onlyO(l + log ^–1) coin tosses to get an estimate which with probability at least 1- is within of the average value of the function.     

Hydrogen sensors with double dipole layers using a Pd-mixture-Pd triple-layer sensing structure

This paper reports on new GaN sensors using a Pd-mixture-Pd triple-layer sensing structure to enhance their sensitivity to hydrogen at the tens of ppm level. The proposed hydrogen sensor biased with a constant voltage produced relatively high sensing responses of 4.84 × 10⁵% at 10,100 ppm and 8.7 × 10⁴% at 49.1 ppm H₂ in N₂. The corresponding barrier height variations are calculated to be 220 and 168 mV. When the sensor is biased by a constant current with maximum power consumption of 0.4 mW, a sensing voltage as an output signal showed a voltage shift of more than 17 V (the highest value ever reported) at 49.1 ppm H₂ in N₂. By comparison to Pd-deposited GaN sensors, the improvement in static-state performance is likely attributed to double dipole layers formed individually at the Pd–GaN interface and inside the mixture. Moreover, voltage transient response and current transient response to various hydrogen-containing gases were experimentally studied. The new finding is that the former response time is shorter than the latter one.     

Classical and Quantum Complexity of the Sturm–Liouville Eigenvalue Problem

We study the approximation of the smallest eigenvalue of a Sturm–Liouville problem in the classical and quantum settings. We consider a univariate Sturm–Liouville eigenvalue problem with a nonnegative function q from the class C² ([0,1]) and study the minimal number n() of function evaluations or queries that are necessary to compute an -approximation of the smallest eigenvalue. We prove that n()=(^–1/2) in the (deterministic) worst case setting, and n()=(^–2/5) in the randomized setting. The quantum setting offers a polynomial speedup with bit queries and an exponential speedup with power queries. Bit queries are similar to the oracle calls used in Grovers algorithm appropriately extended to real valued functions. Power queries are used for a number of problems including phase estimation. They are obtained by considering the propagator of the discretized system at a number of different time moments. They allow us to use powers of the unitary matrix exp((1/2) iM), where M is an n× n matrix obtained from the standard discretization of the Sturm–Liouville differential operator. The quantum implementation of power queries by a number of elementary quantum gates that is polylog in n is an open issue. In particular, we show how to compute an -approximation with probability (3/4) using n()=(^–1/3) bit queries. For power queries, we use the phase estimation algorithm as a basic tool and present the algorithm that solves the problem using n()=(log ^–1) power queries, log ^2–1 quantum operations, and (3/2) log ^–1 quantum bits. We also prove that the minimal number of qubits needed for this problem (regardless of the kind of queries used) is at least roughly (1/2) log ^–1. The lower bound on the number of quantum queries is proven in Bessen (in preparation). We derive a formula that relates the Sturm–Liouville eigenvalue problem to a weighted integration problem. Many computational problems may be recast as this weighted integration problem, which allows us to solve them with a polylog number of power queries. Examples include Grovers search, the approximation of the Boolean mean, NP-complete problems, and many multivariate integration problems. In this paper we only provide the relationship formula. The implications are covered in a forthcoming paper (in preparation).PACS: 03.67.Lx, 02.60.-x.     

Stability of a Class of Differential Inclusions

Stability of differential inclusions F(x(t)) is studied by using minorant and majorant mappings F ^– and F ⁺, F ^–(x)F(x)F ⁺(x). Properties of F ^–,F ⁺ are developed in terms of partial orderings, with the condition that F ^–, F ⁺ are either heterotone or pseudoconcave. The main results concern asymptotically stable absorbing sets, including the case of a single equilibrium point, and are illustrated by examples of control systems.     

Liquid–solid equilibria in quinary system Na,Mg/Cl,SO4,NO3–H2O at 298.15 K

In order to develop the nitrate deposits found close to Lop Nur in the Xinjiang region in China, the solubilities of the system Na⁺,Mg²⁺/Cl⁻,SO₄²⁻, NO₃⁻–H₂O and its subsystems, the quaternary systems Na⁺,Mg²⁺/SO₄²⁻,NO₃⁻–H₂O and Mg²⁺/Cl⁻,SO₄²⁻,NO₃⁻–H₂O, were studied at 298.15 K. The phase diagrams were plotted according to the solubilities achieved. In the equilibrium phase diagram of Mg²⁺/Cl⁻,SO₄²⁻,NO₃⁻–H₂O, there are two invariant points, five univariant curves and four regions of crystallization: Mg(NO₃)₂6H₂O,MgCl₂6H₂O,MgSO₄7H₂O and MgSO₄(1–6)H₂O. In the equilibrium phase diagram of Na⁺,Mg²⁺/SO₄²⁻, NO₃⁻–H₂O, there are five invariant points, eleven univariant curves and seven regions of crystallization: Na₂SO₄,Na₂SO₄10H₂O,NaNO₃,MgSO₄Na₂SO₄4H₂O,NaNO₃Na₂SO₄2H₂O,Mg(NO₃)₂6H₂O and MgSO₄7H₂O. In the equilibrium phase diagram of the Na⁺, Mg²⁺/Cl⁻,SO₄²⁻,NO₃⁻–H₂O system, there are six invariant points, and ten regions of crystallization: NaCl, NaNO₃,Na₂SO₄,Na₂SO₄10H₂O,MgSO₄Na₂SO₄4H₂O, NaNO₃Na₂SO₄2H₂O,MgCl₂6H₂O,Mg(NO₃)₂6H₂O, MgSO₄(1–6)H₂O and MgSO₄7H₂O.     

An implicit enthalpy scheme for one-phase Stefan problems

A compact finite-difference scheme to solve one-phase Stefan problems in one dimension is described. Numerical experiments indicate that the moving interface is obtained withO(t) accuracy when 3–4 iterations per time step are used to solve the nonlinear implicit scheme. The scheme can be adapted to ADI methods in higher dimensions.     

Stochastic Routh-Hurwitz problem

The stochastic Routh—Hurwitz problem is considered, i.e., the probability of stability is obtained for a polynomial xⁿ + a₁x^n–1 + + a_n with random coefficients.Translated from Kibernetika i Sistemnyi Analiz, No. 4, pp. 61–70, July–August, 1991.     

Analysis of interface states of metal–insulator–semiconductor photodiode with n-type silicon by conductance technique

A metal–insulator–semiconductor photodiode (MIS-PD) as active layer with n-type silicon as interdigitated Schottky electrodes has been fabricated. The current–voltage characteristics, density of interface states and photovoltaic properties of the MIS-PD diode have been investigated. The diode has a metal–insulator–semiconductor configuration with ideality factor higher than unity. The electronic parameters (ideality factor, series resistance and barrier height) of the diode were found to be 1.94, 2.23 × 10⁴ Ω and 0.74, respectively. At voltages between 0.13 and 0.50 V, the charge transport mechanism of the diode is controlled by space charge-limited current mechanism. The interface state density of the diode was found to vary from 5.54 × 10¹² to 5.67 × 10¹² eV⁻¹ cm⁻² with bias voltage. The Au/SiO₂/n-Si/Al device shows a photovoltaic behavior with a maximum open circuit voltage V_oc of 97.7 mV and short-circuit current I_sc of 17.4 μA under lower illumination intensities. The obtained electronic parameters confirm that the Au/SiO₂/n-Si/Al diode is a MIS type photodiode.     

A relationship between difference hierarchies and relativized polynomial hierarchies

Chang and Kadin have shown that if the difference hierarchy over NP collapses to levelk, then the polynomial hierarchy (PH) is equal to thekth level of the difference hierarchy over ₂ ^p . We simplify their poof and obtain a slightly stronger conclusion: if the difference hierarchy over NP collapses to levelk, then PH collapses to (P _(k–1) ^NP )^NP, the class of sets recognized in polynomial time withk – 1 nonadaptive queries to a set in NP^NP and an unlimited number of queries to a set in NP. We also extend the result to classes other than NP: For any classC that has _m ^p -complete sets and is closed under _conj ^p -and _m ^NP -reductions (alternatively, closed under _disj ^p -and _m ^co-NP -reductions), if the difference hierarchy overC collapses to levelk, then PH ^C = (P _(k–1)–tt ^NP ) ^C . Then we show that the exact counting class C_P is closed under _disj ^p - and _m ^co-NP -reductions. Consequently, if the difference hierarchy over C_P collapses to levelk, then PH^PP(= PH^C_P) is equal to (P _(k–1)–tt ^NP )^PP. In contrast, the difference hierarchy over the closely related class PP is known to collapse.Finally we consider two ways of relativizing the bounded query class P _k–tt ^NP : the restricted relativization P _k–tt ^{NP C} and the full relativization (P _k–tt ^NP ) ^C . IfC is NP-hard, then we show that the two relativizations are different unless PH ^C collapses.Richard Beigel was supported in part by NSF Grants CCR-8808949 and CCR-8958528. Richard Chang was supported in part by NSF Research Grant CCR 88-23053. This work was done while Mitsunori Ogiwara was at the Department of Information Science, Tokyo Institute of Technology, Tokyo, Japan.     

Exponentially Accurate Approximations to Periodic Lipschitz Functions Based on Fourier Series Partial Sums

The problem of accurately reconstructing a piecewise smooth. 2-periodic function f and its first few derivatives, given only a truncated Fourier series representation of f, is studied and solved. The reconstruction process is divided into two steps. In the first step, the first 2N + 1 Fourier coefficients of f are used to approximate the locations and magnitudes of the discontinuities in f and its first M derivatives. This is accomplished by first finding initial estimates of these quantities based on certain properties of Gibbs phenomenon, and then refining these estimates by fitting the asymptotic form of the Fourier coefficients to the given coefficients using a least-squares approach. The locations of the singularities are approximated to within O(N ^–M–2), and the associated jump of the kth derivative of f is approximated to within O(N ^–M–1+k ), as N , and the method is robust. These estimates are then used with a class of singular basis functions, which have certain built-in singularities, to construct a new sequence of approximations to f. Each of these new approximations is the sum of a piecewise smooth function and a new Fourier series partial sum. When N is proportional to M, it is shown that these new approximations, and their derivatives, converge exponentially in the maximum norm to f, and its corresponding derivatives, except in the union of a finite number of small open intervals containing the points of singularity of f. The total measure of these intervals decreases exponentially to zero as M . The technique is illustrated with several examples.     

QFT template generation for time-delay plants based on zero-inclusion test

Plant template generation is the key step in applying quantitative feedback theory (QFT) to design robust control for uncertain systems. In this paper we propose a technique for generating plant templates for a class of linear systems with an uncertain time delay and affine parameter perturbations in coefficients. The main contribution lies in presenting a necessary and sufficient condition for the zero inclusion of the value set f(T,Q)={f(τ,q): τT[τ⁻,τ⁺], qQ∏_k=0^m−1[q_k⁻,q_k⁺]}, where f(τ,q)=g(q)+h(q)e^−jτω*, g(q) and h(q) are both complex-valued affine functions of the m-dimensional real vector q, and ω^* is a fixed frequency. Based on this condition, an efficient algorithm which involves, in the worst case, evaluation of m algebraic inequalities and solution of m2^m−1 one-variable quadratic equations, is developed for testing the zero inclusion of the value set f(T,Q). This zero-inclusion test algorithm allows one to utilize a pivoting procedure to generate the outer boundary of a plant template with a prescribed accuracy or resolution. The proposed template generation technique has a linear computational complexity in resolution and is, therefore, more efficient than the parameter gridding and interval methods. A numerical example illustrating the proposed technique and its computational superiority over the interval method is included.     

Signal Representation by Adaptive Biased Wavelet Expansions

This paper reviews a technique of adaptive wavelet expansions and introduces the novel concept of “biased wavelets.” These are functions that are localized in time and in frequency but, unlike conventional wavelets, have an adjustable nonzero mean component. Under mild conditions, it is shown that a conventional mother wavelet can be used to construct a family of biased wavelets which spans the set of finite-energy functions L²( ). Numerical tests suggest that the introduction of the adjustable “bias” considerably improves the representation capabilities of wavelet expansions. A problem of electrocardiographic data compression is used for illustration purposes. Test signals were extracted from the MIT–BIH ECG Compression Test Database.