Projective Linear Groups as Galois Groups overQvia Modular Representations

We give an algorithm for the determination of the finitely many primes such that the image of the modular Galois representations attached to a weight 2 newform on Γ₀(N) without complex multiplication or inner twists may not be “as large as possible". We apply the algorithm to suitable newforms and we obtain the realization of the groups PSL(2,F_ℓ²),PGL (2,F_ℓ³) andPSL (2,F_ℓ⁴) as Galois groups overQfor high density sets of primes.     

Bounds on element order in rings Zm with divisors of zero

If p is a prime, integer ring Z_p has exactly ((p)) generating elements ω, each of which has maximal index I_p(ω) = (p) = p − 1. But, if m = Π^R_{J = 1} p^αJ_J is composite, it is possible that Z_m does not possess a generating element, and the maximal index of an element is not easily discernible. Here, it is determined when, in the absence of a generating element, one can still with confidence place bounds on the maximal index. Such a bound is usually less than (m), and in some cases the bound is shown to be strict. Moreover, general information about existence or nonexistence of a generating element often can be predicted from the bound.     

Direct amperometric determination of l-ascorbic acid (Vitamin C) at octacyanomolybdate-doped-poly(4-vinylpyridine) modified electrode in fruit juice and pharmaceuticals

The glassy carbon electrode (GCE) modified with Mo(CN)₈⁴⁻-incorporated-poly(4-vinylpyridine) (PVP/Mo(CN)₈⁴⁻), which has been recently shown to possess several attractive attributes as an efficient electrocatalytic electrode for l-ascorbic acid oxidation and its estimation, is used for l-ascorbic acid estimation directly in orange fruit juice and Celin tablet in a 0.1 M H₂SO₄ acid solution without any special treatment. Constant potential amperometry at 570 mV (saturated calomel electrode, SCE) in stirred solutions is used for this purpose. A good correlation is attained with the official titrametric method. To understand the possible electrocatalytic reaction mechanism for the electro-oxidation of l-ascorbic acid, calibration graphs over the range 1 × 10⁻⁵ to 1 × 10⁻² mol dm⁻³ l-ascorbic acid are compared for the three electrodes, ca. PVP/Mo(CN)₈⁴⁻, undoped PVP, and GCE; the curvature at high ascorbic acid concentration for the PVP/Mo(CN)₈⁴⁻ electrode is explained in terms of Michaelis–Menten (MM) saturation kinetics. The apparent MM constant (K_M), the maximum catalytic current (i_M), the complex decomposition rate constant (k_c), and the heterogeneous modified electrode rate constant (k^′_ME) are calculated from three different approaches. A reasonably high value of ≈1 × 10⁻² cm s⁻¹ is obtained for k^′_ME, indicating efficient l-ascorbic acid mediation at the PVP/Mo(CN)₈⁴⁻ electrode, thus accounting for quite a high sensitivity of this modified film electrode compared to several other modified electrodes.     

Electrochemical DNA biosensor for the detection of interaction between di[azino-di(5,6-azafluorene)-κ-NN′]dichlormanganous and DNA

A new Mn(II) complex of MnL₂Cl₂ (L = azino-di(5,6-azafluorene)-κ²-NN′) was synthesized and utilized as an electrochemical indicator for the determination of hepatitis B virus (HBV) based on its interaction with MnL₂Cl₂. The electrochemical behavior of interaction of MnL₂Cl₂ with salmon sperm DNA was investigated on glassy carbon electrode (GCE). In the presence of salmon sperm DNA, the peak current of [MnL₂]²⁺ was decreased and the peak potential was shifted positively without appearance of new peaks. The binding ratio between [MnL₂]²⁺ and salmon sperm DNA was calculated to be 2:1 and the binding constant was 3.72 × 10⁸ mol² L⁻². The extent of hybridization was evaluated on the basis of the difference between signals of [MnL₂]²⁺ with probe DNA before and after hybridization with complementary sequence. Control experiments performed with non-complementary and mismatch sequence demonstrated the good selectivity of the biosensor. With this approach, a sequence of the HBV could be quantified over the range from 1.76 × 10⁻⁸ to 1.07 × 10⁻⁶ mol L⁻¹, with a linear correlation of r = 0.9904 and a detection limit of 6.80 × 10⁻⁹ mol L⁻¹. Additionally, the binding mechanism was preliminarily discussed. The mode of interaction between MnL₂Cl₂ and DNA was found to be primary intercalation binding.     

Bases for projective modules in An(k)

Let A_n(k) be the Weyl algebra, with k a field of characteristic zero. It is known that every projective finitely generated left module is free or isomorphic to a left ideal. Let M be a left submodule of a free module. In this paper we give an algorithm to compute the projective dimension of M. If M is projective and rank(M)≥2 we give a procedure to find a basis.     

Application of m-CNTs/NaClO4/Ppy to a fast response, room working temperature ethanol sensor

A new blended material, m-CNTs/NaClO₄/Ppy, was developed as a gas sensor to detect ethanol concentrations at room temperature. The sensing material polypyrrole (Ppy) was synthesized in situ by UV-photo-polymerization. The multiwall carbon nanotubes (m-CNTs) added enhanced the short-term repeatability of the Ppy-sensing material. The relative resistance variation (R_ethanol/R_air) of m-CNTs/NaClO₄/Ppy was 1.193 when exposed to ethanol of 30,000 ppm. The sensor response and recovery times (both 20 s) were very short to this concentration. An unstable baseline of the sensor was explained by theoretical calculation of molecular dynamics made for ethanol adsorption on polypyrrole, which revealed formation of a new bond, N–HO. Adsorption energy decreased with increasing the number of ethanol molecules adsorbed and was 0.8 kcal/mol at eight adsorbed molecules. Sensor responses of three different Ppy samples were measured to ethanol concentrations of 18,000–40,000 ppm.     

Controlled synthesis and gas-sensing properties of hollow sea urchin-like α-Fe2O3 nanostructures and α-Fe2O3 nanocubes

Hollow sea urchin-like α-Fe₂O₃ nanostructures were successfully synthesized by a hydrothermal approach using FeCl₃ and Na₂SO₄ as raw materials, and subsequent annealing in air at 600 °C for 2 h. The hollow sea urchin-like α-Fe₂O₃ nanostructures with the diameters of 2–4.5 μm consist of well-aligned α-Fe₂O₃ nanorods with an average length of about 1 μm growing radially from the centers of the nanostructures, have a hollow interior with a diameter of about 2 μm. α-Fe₂O₃ nanocubes with a diameter of 700–900 nm were directly obtained by a hydrothermal reaction of FeCl₃ at 140 °C for 12 h. The response S_r (S_r = R_a/R_g) of the hollow sea urchin-like α-Fe₂O₃ nanostructures reached 2.4, 7.5, 5.9, 14.0 and 7.5 to 56 ppm ammonia, 32 ppm formaldehyde, 18 ppm triethylamine, 34 ppm acetone, and 42 ppm ethanol, respectively, which was excess twice that of the α-Fe₂O₃ nanocubes and the nanoparticle aggregations. Our results demonstrated that the hollow sea urchin-like α-Fe₂O₃ nanostructures were very promising for gas sensors for the detection of flammable and/or toxic gases with good-sensing characteristics.     

Rank Jumps in Codimension 2A-hypergeometric Systems

The holonomic rank of the A -hypergeometric systemH_A (β) is shown to depend on the parameter vector β when the underlying toric ideal I_Ais a non-Cohen–Macaulay codimension 2 toric ideal. The set of exceptional parameters is usually infinite.     

Tetrakis(alkylthio)-substituted lutetium bisphthalocyanines for sensing NO2 and O3

In this study, the nitrogen dioxide (NO₂) and ozone (O₃) sensing properties of a series bis[tetrakis(alkylthio) phthalocyaninato] lutetium(III) complexes [(C_nH_2n+1S)₄Pc]₂Lu(III) (n = 6, 10, 16) are investigated as a function of concentration in the temperature range between 25 °C and 150 °C. The concentration ranges were 1–10 ppm for NO₂, and 50 ppb–1 ppm for O₃. The response time and the sensor response to NO₂ are measured for approximately 1 min and 100% ppm⁻¹, respectively, for compound 1 at room temperature. At room temperature, all compounds are in the solid phase. The response time decreases to a few seconds with increasing operation temperature to 150 °C. At this temperature, all compounds are in the liquid crystal phase. The fastest response to oxidizing gases is observed at the liquid crystal phase of the Pcs. It has also been observed that the response time and the sensor response depend on the alkyl chain lengths of the Pcs. The doping effect of oxygen has been determined under high purity nitrogen N₂ flow, after exposure to dry air, at a different period of time and after annealing. It has been found that the conductivities of [(C_nH_2n+1S)₄Pc]₂Lu(III) thin films increased after exposure to dry air and the conduction mechanism also changed from ohmic behavior to space-charge-limited conduction.     

Computing Homomorphisms Between HolonomicD-modules

Let K C be a subfield of the complex numbers, and let D be the ring of K -linear differential operators on R = K [ x₁, . . . , x_n]. If M and N are holonomic left D -modules we present an algorithm that computes explicit generators for the finite dimensional vector space _D(M, N). This enables us to answer algorithmically whether two given holonomic modules are isomorphic. More generally, our algorithm can be used to get explicit generators for _Dⁱ(M, N) for any i in the sense of Yoneda.     

Fliess operators on Lp spaces: convergence and continuity

Fliess operators as input–output mappings are particularly useful in a number of fundamental problems concerning nonlinear realization theory. In the classical analysis of these operators, certain growth conditions on the coefficients in their series representations insure uniform and absolute convergence, provided every input is uniformly bounded by some fixed upperbound. In some emerging applications, however, it is more natural to consider other classes of inputs. In this paper, L_p function spaces are considered. In particular, it is shown that the classic growth conditions also provide sufficient conditions for convergence and continuity when the admissible inputs are from a ball in L_p[t₀,t₀+T], where T is bounded and p1. In addition, stronger global growth conditions are given that apply even for the case where T is unbounded. When the coefficients of a Fliess operator have a state space representation, it is shown that the state space model will always locally realize the corresponding input–output map on L_p[t₀,t₀+T] for sufficiently small T>0. If certain well-posedness conditions are satisfied then the state space model will globally realized the input–output mapping for unbounded T when the coefficients satisfy the global growth condition.     

Explicit Comparison Theorems for D -modules

We prove in an explicit way a duality formula between two A₂-modulesM andM associated to a plane curve and we give an application of this duality to the comparison between M and theA₂ -module of rational functions along the curve. We treat the analytic case as well.     

Polypyrrole functionalized with FePcTSA for NO2 sensor application

The nitrogen dioxide (NO₂) sensing capability of polypyrrole (PPy) was enhanced dramatically after functionalized with iron(III)phthalocyanine-4,4′,4″,4-tetrasulfonic acid monosodium salt (FePcTSA). The incorporated phthalocyanine was confirmed by different characterization techniques such as UV–vis spectroscopy, FTIR, GFAAS, EDAX, etc. The resistance of the functionalized PPy decreased spontaneously during exposure to NO₂ gas at room temperature. This material exhibited excellent stability, reversibility, and reproducibility. The lowest response time (t₅₀) thus obtained is 47 s with a highest response factor (ΔR/R₀ × 100) of 50.25.     

Enhanced H2S sensing characteristics of SnO2 nanowires functionalized with CuO

The CuO-functionalized SnO₂ nanowire (NW) sensors were fabricated by depositing a slurry containing SnO₂ NWs on a polydimethylsiloxane (PDMS)-guided substrate and subsequently dropping Cu nitrate aqueous solution. The CuO coating increased the gas responses to 20 ppm H₂S up to 74-fold. The R_a/R_g value of the CuO-doped SnO₂ NWs to 20 ppm H₂S was as high as 809 at 300 °C, while the cross-gas responses to 5 ppm NO₂, 100 ppm CO, 200 ppm C₂H₅OH, and 100 ppm C₃H₈ were negligibly low (1.5–4.0). Moreover, the 90% response times to H₂S were as short as 1–2 s at 300–400 °C. The selective detection of H₂S and enhancement of the gas response were attributed to the uniform distribution of the sensitizer (CuO) on the surface of the less agglomerated network of the SnO₂ NWs.     

Semigroup generation and stabilization by A-bounded feedback perturbations

Let A be a generator of a strongly continuous semigroup of operators, and assume that C and H are operators such that A + CH generates a strongly continuous semigroup S_H(t) on X. Let λ₀ be a real number in the resolvent set of A, and let ε [−1, 1]. Then there are some fairly unrestrictive conditions under which A+(λ₀ − A)CH(λ₀ − A)⁻ also generates a strongly continuous semigroup S_K(t) on X which has the same exponential growth rate as S_H(t). Given an input operator B, we can use this to identify a class of feedback perturbations K such that A + BK generates a strongly continuous semigroup. We can also use this result to identify classes of feedbacks which can and cannot uniformly stabilize a system. For example, we show that if the control on a cantilever beam in the state space H₀²[0, 1] × L²[0, 1] is a moment force on the free end, then we cannot stabilize the beam with an A^−1/2-bounded feedback, but we can find an A^−1/4-bounded feedback, for any > 0, which does stabilize the beam.     

Decomposition of Polynomials with Respect to the Cyclic Group of Orderm

Given a polynomial solution of a differential equation, its m -ary decomposition, i.e. its decomposition as a sum of m polynomials P^{[ j ]}(x)  = ∑_kα_j,kx^{λ_{j, k}}containing only exponentsλ_{j, k} with λ_{j,k  + 1} − λ_j,k = m, is considered. A general algorithm is proposed in order to build holonomic equations for the m -ary parts P^{[ j ]}(x) starting from the initial one, which, in addition, provides a factorized form of them. Moreover, these differential equations are used to compute expansions of the m -ary parts of a given polynomial in terms of classical orthogonal polynomials. As illustration, binary and ternary decomposition of these classical families are worked out in detail.     

Environmentally friendly disposable sensors with microfabricated on-chip planar bismuth electrode for in situ heavy metal ions measurement

This paper presents an environmentally friendly disposable heavy metal ion sensor for in situ and online monitoring in the nature and physiological systems. The miniaturized sensor chip consists of a non-toxic microfabricated bismuth (Bi) working electrode that replaces the conventional mercury electrodes, an integrated Ag/AgCl reference electrode, a gold counter electrode, and microfluidic channels. In this work, the electrochemical behavior of the Bi working electrode was characterized in several non-deaerated buffer solutions using cyclic voltammetry. The detection and quantification of Pb (II) and Cd (II) were statically performed using anodic stripping voltammetry inside the microchannels, in the Pb (II) concentration range of 25–400 ppb (R² = 0.991) with limit of detection of 8 ppb for 60 s deposition, and in the Cd (II) concentration range of 28–280 ppb (R² = 0.986) with limit of detection of 9.3 ppb for 90 s deposition. Particularly, the applications of this sensor chip have been reported with the examples of in situ measurement of Cd (II) concentration in soil pore and ground water and online direct measurement of Cd (II) concentration in cell culture media in its native environment.     

Optimal strategies against a liar

We consider the following scenario: There are two individuals, say Q (Questioner) and R (Responder), involved in a search game. Player R chooses a number, say x, from the set S={1,…,M}. Player Q has to find out x by asking questions of type: “which one of the sets A₁,A₂,…,A_q, does x belong to?”, where the sets A₁,…,A_q constitute a partition of S. Player R answers “i” to indicate that the number x belongs to A_i. We are interested in the least number of questions player Q has to ask in order to be always able to correctly guess the number x, provided that R can lie at most e times. The case e=0 obviously reduces to the classical q-ary search, and the necessary number of questions is [log_qM]. The case q=2 and e1 has been widely studied, and it is generally referred to as Ulam's game. In this paper we consider the general case of arbitrary q2. Under the assumption that player R is allowed to lie at most twice throughout the game, we determine the minimum number of questions Q needs to ask in order to successfully search for x in a set of cardinality M=qⁱ, for any i1. As a corollary, we obtain a counterexample to a recently proposed conjecture of Aigner, for the case of an arbitrary number of lies. We also exactly solve the problem when player R is allowed to lie a fixed but otherwise arbitrary number of times e, and M=qⁱ, with i not too large with respect to q. For the general case of arbitrary M, we give fairly tight upper and lower bounds on the number of the necessary questions.     

Pulsed laser deposited Y-doped BaZrO3 thin films for high temperature humidity sensors

Pulsed laser deposited (PLD) Y-doped BaZrO₃ thin films (BaZr_1-xY_xO_3-y/2, x = 0.2, y > 0), were investigated as to their viability for reliable humidity microsensors with long-term stability at high operating temperatures (T > 500 °C) as required for in situ point of source emissions control as used in power plant combustion processes. Defect chemistry based models and initial experimental results in recent humidity sensor literature [1] and [2]. indicate that bulk Y-doped BaZrO₃ could be suitable for use in highly selective, high temperature compatible humidity sensors. In order to accomplish faster response and leverage low cost batch microfabrication technologies we have developed thin film deposition processes, characterized layer properties, fabricated and tested high temperature humidity micro sensors using these thin films. Previously published results on sputtering Y-doped BaZrO₃ thin films have confirmed the principle validity of our approach [3]. However, the difficulty in controlling the stoichiometry of the films and their electrical properties as well as mud flat cracking of the films occurring either at films thicker than 400 nm or at annealing temperature above 800 °C have rendered sputtering a difficult process for the fabrication of reproducible and reliable thin film high temperature humidity microsensors, leading to the evaluation of PLD as alternative deposition method for these films.X-ray Photoelectron Spectroscopy (XPS) data was collected from as deposited samples at the sample surface as well as after 4 min of Ar⁺ etching. PLD samples were close to the desired stoichiometry. X-ray diffraction (XRD) spectra from all as deposited BaZrO₃:Y films show that the material is polycrystalline when deposited at substrate temperatures of 800 °C. AFM results revealed that PLD samples have a particle size between 32 nm and 72 nm and root mean square (RMS) roughness between 0.2 nm and 1.2 nm. The film conductivity increases as a function of temperature (from 200 °C to 650 °C) and upon exposure to a humid atmosphere, supporting our hypothesis of a proton conduction based conduction and sensing mechanism. Humidity measurements are presented for 200–500 nm thick films from 500 °C to 650 °C at vapor pressures of between 0.05 and 0.5 atm, with 0.03–2% error in repeatability and 1.2–15.7% error in hysteresis during cycling for over 2 h. Sensitivities of up to 7.5 atm⁻¹ for 200 nm thick PLD samples at 0.058 atm partial pressure of water were measured.     

A Better Constant-Factor Approximation for Selected-Internal Steiner Minimum Tree

The selected-internal Steiner minimum tree problem is a generalization of original Steiner minimum tree problem. Given a weighted complete graph G=(V,E) with weight function c, and two subsets R ^′ ⊊ R⊆V with |R−R ^′|≥2, selected-internal Steiner minimum tree problem is to find a minimum subtree T of G interconnecting R such that any leaf of T does not belong to R ^′. In this paper, suppose c is metric, we obtain a (1+ρ)-approximation algorithm for this problem, where ρ is the best-known approximation ratio for the Steiner minimum tree problem.