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1.
A previous application of the Newton divided difference series of the displacement function Ez = (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; mi=0 (Δ - Si)} f(0) and {Pi; mi=0 ( D - ti)} f(0), in which the si's and ti's are distinct[1], is here extended to mixed polynomial-exponential interpolation where the si's and ti's are no longer distinct. 相似文献
2.
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. 相似文献
3.
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, pn+m = pn for any n Z and f( t + m, z) = f( t, z) for any ( t, z) Z × R, (−1) δ = −1 and δ > 0. 相似文献
4.
Two piezoresistive ( n-polysilicon) strain sensors on a thin Si 3N 4/SiO 2 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 Si 3N 4/SiO 2 membrane. A 1000×1000 μm 2 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=(Δ R/ R0)/Δ T] and the gage factor [GF=(Δ R/ 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. 相似文献
5.
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, yt) = 0, for t ε [0,1], y( t) -β y′( t) =η( t), for t ε [−τ,0], −γ y( t) + Δ y′( 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. 相似文献
6.
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. 相似文献
7.
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, TiO 2, and WO 3 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 NO 2, 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 Δ R/ R about 1400% and as short a response time as 2 min. A detection limit lower than 100 ppb of NO 2 is expected. 相似文献
8.
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 1.9 D apart. A new microhole cathode array three-electrode oxygen sensor has been developed using the result of the model. 相似文献
9.
In this note, we deal with the following problem: given X R n, a multification gG : X → 2 X, two (single-valued) maps f : X → R n, η : X × X → R n, 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. 相似文献
10.
Consdier I( z) = ∫ ba w( t) f( t, z) d t, 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. 相似文献
11.
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 ut( x, t) − D( t) uxx( 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 Cr × 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. 相似文献
12.
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. 相似文献
13.
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. 相似文献
14.
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. 相似文献
15.
Barium strontium titanate (Ba 1−xSr xTiO 3) ferroelectric thin films have been prepared by metal organic decomposition (MOD) on Pt/Ti/SiO 2/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 Rv of 0.4 kV/W and D* of 1.0×10 8 cm Hz 1/2/W, respectively. 相似文献
16.
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 2 D 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 [(2 M+1)/(2 M)] 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. 相似文献
17.
Nano-SiO 2/ p-aminothiophenol (PATP) film was fabricated by self-assembly and electrodeposition methods. The immobilization and hybridization of DNA on the nano-SiO 2/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 ( Ret) 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. 相似文献
18.
To approach a simple game Δ 2 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 1,2b (basic) and Δ 1,2a (auxiliary) games that model the problem before and after the first instant of E1 capture. The games Δ1,2a, Δ 1,2b, Δ 1,2 are studied one after another with use of the Isaacs' approach extended by Berkowitz, Breakwell, Bernhard et al. 相似文献
19.
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( n3Rab) time, which improves the known result of O( n4Rab) time for solving this problem, where ¦ V¦= n and Rab 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 − nA − nb) RAB) time in this case, where na = ¦ A¦, nB = ¦ B¦ and rAB 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 + n4RΣ), which improves the known result of O( n6RΣ) time, where Rσ is the number of all minimal separators of G and RΣR+Σ = ∑ 1i, v j) ER vivj (n( n − 1)/2 − m) RΣ. Efficient parallelization of these algorithms is also discussed. It is shown that the first algorithm requires at most O(( n/ log n) Rab) time and the second one runs in time O(( n/ log n) R+Σ+ n log nRΣ) on a CREW PRAM with O( n3) processors. 相似文献
20.
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. 相似文献
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