Bandgap and lattice constant of GaInAsP as a function of alloy composition

Published data for the composition dependence of the room-temperature bandgap (E_g) and lattice constant (a_o) in the pseudobinary Ga_yIn_1-yAs, Ga_yIn_1-yP, GaAs_xP_l-x, and InAs_xP_l-x systems have been used to derive the following equations for the quaternary Ga_yIn_l-yAs_x P_l-x, alloys: $$\begin{gathered} a_o ({\AA}) = 5.87 + 0.18x - 0.42y + 0.02xy \hfill \\ E_g (eV) = 1.35 - x + 1.4y - 0.33xy - (0.758 - 0.28x)y(1 - y) \hfill \\ - (0.101 + 0.109y) x(1 - x). \hfill \\ \end{gathered} $$ Available experimental data are in excellent agreement with these equations.     

Some results concerning the abstract degenerate nonlinear equationD t Mu(t) +Lu(t)=f(t,Ku(t))

We apply some abstract existence results, proved in Sections 1 and 2 of the paper, to some cases of the following problem (P), formally stated as (P) $$\left\{ \begin{gathered} D_t \left( {Mu\left( t \right)} \right) + Lu\left( t \right) = f\left( {t,Ku\left( t \right)} \right) 0< t \leqslant \tau \hfill \\ Mu\left( t \right) \to u_0 as t \to 0 + \hfill \\ \end{gathered} \right.$$ whereK,L,M are linear and/is a nonlinear term. The unknown functionu is required to lie in various functional spaces.     

Assignment and frequency of C18O2 pumped fir laser lines in12CH3F using infrared diode laser spectroscopy

Optically pumped FIR laser lines in¹²CH₃F at 186.6 and 497.4μm have been assigned using high resolution diode laser spectroscopy. Accurate calibration of diode laser spectra of CH₃F using CO₂ laser lines yields the laser wavenumbers: $$\begin{gathered} 186.6 \mu m laser:53.5250cm^{ - 1} \hfill \\ 497.4 \mu m laser:20.1250cm^{ - 1} \hfill \\ \end{gathered}$$ These are in good agreement with values calculated from spectroscopic parameters by Arimondo and Inguscio and with a direct frequency measurement.     

A general factorization method for multivariable polynomials

The problem of factorizing a multivariable or multidimensional (m-D) polynomialf (z ₁,z ₂, ...,z _m ), with real or complex coefficients and independent variables, into a number of m-D polynomial factors that may involve any independent variable or combination of them is considered. The only restriction imposed is that all factors should be linear in one and the same variable (sayz ₁). This type of factorization is very near to the most general type: $$\begin{gathered} f(z_1 ,z_2 , \ldots ,z_m ) = \prod\limits_{i = 1}^{N_1 } {\lbrack {\mathop \sum \limits_{\epsilon _1 = 0}^{\epsilon _{i,1} } \cdots \mathop \sum \limits_{\epsilon _m = 0}^{\epsilon _{i,m} } a_{i;\epsilon _1 ,\epsilon _2 , \ldots ,\epsilon _m } z_1^{\epsilon _1 } \cdots z_m^{\epsilon _m } + c_i } \rbrack} \hfill \\ (\epsilon _1 , \ldots ,\epsilon _m ) \neq (0, \ldots ,0) \hfill \\ \end{gathered}$$ and appears to be the most general type available. The method is first briefly sketched for the convenience of the reader, and then is presented in detailed form through a number of theorems. These theorems provide a clear algorithmic way for the factorization, which may be automated via a suitable computer code. The factorization of m-D polynomials simplifies the stability analysis and the realization of m-D systems, as well as the solution of distributed parameters systems.     

On the Use of Symbolic Analyzers in Circuit Synthesis

In this paper several examples of circuits obtained with an automatic synthesis algorithm will be shown. The algorithm, described in a companion paper [1] and outlined here for clarity, has been implemented in the Mathematica language. We applied the new algorithm to classical problems of inmittance synthesis, obtaining well known topologies and also non-reported structures. When the algorithm is applied to challenging new problems, novel and practically useful inmittances are synthesized.     

On the stability of real exponential polynomials with interval-valued delays

We consider the family ? of exponential polynomials. $$f_T (z): = f_0 (z) + f_1 (z)e^{ - zT_1 } + f_2 (z)e^{ - T_2 } + \cdots + f_n (z)e^{ - zT_n } ,T : = T_1 \times T_2 \times \cdots \times T_n ,$$ where thef _k(z),k=0(1)n, are real polynomials under the degree restriction deg(f ₀)>deg(f _k),k=1(1)n, and theT _k,k=1(1)n, are intervals inR ₊. The functions in ? are characteristic functions of linear, retarded dynamical systems with constant coefficients and finitely many interval-valued discrete delays. A stability criterion for ? is expounded; ? is stable if (a) ? contains a stable member and (b) a certain functionalT:S(y) →; {0, 1} vanishes fory in a compact interval inR ₊. Here,S(y) is the boundary of a circular are regionS(y) in the complex plane derived fromf _T. Tools needed for a computer implementation are compiled.     

Approximating linearizations for nonlinear systems

Given a nonlinear control system $$\dot x(t) = f(x(t)) + \sum\limits_{i = 1}^m {u_i (t)g_i (x(t))}$$ on ? ⁿ and a pointx ₀ in ? ⁿ , we want to approximate the system nearx ₀ by a linear system. Of course, one approach is to use the usual Taylor series linearization. However, the controllability properties of both the nonlinear and linear systems depend on certain Lie brackets of the vector field under consideration. This suggests that we should construct a linear approximation based on Lie bracket matching atx ₀. In general, the linearizations based on the Taylor method and the Lie bracket approach are different. However, under certain mild assumptions, we show that there is a coordinate system for ? ⁿ nearx ₀ in which these two types of linearizations agree. We indicate the importance of this agreement by examining the time responses of the nonlinear system and its linear approximation and comparing the lower-order kernels in Volterra expansions of each.     

Structure theorems for nonlinear systems

One of the main results is a proposition to the effect that under some typically mild conditions finite sums of the form $$\sum\limits_\ell {K_\ell \sigma } \left[ {\sum\limits_m {\eta _{\ell m} Q_m (\cdot) + \rho _\ell } } \right]$$ are dense in an important sense in the set of shift-invariant approximately-finite-memory mapsG(·) that take a certain type of subsetU ofR intoR, whereR is the set of real-valued functions defined onR ⁿ orZ ⁿ . Here theQ _m (·) are linear, σ is any element of a certain set of nonlinear maps fromR toR, and the κ_?, ρ_?, and η_?m are real constants. Approximate representations comprising only affine elements and lattice nonlinearities are also presented.     

Four-Dimensional Gallant–Lambert–Vanstone Scalar Multiplication

The GLV method of Gallant, Lambert, and Vanstone (CRYPTO 2001) computes any multiple kP of a point P of prime order n lying on an elliptic curve with a low-degree endomorphism Φ (called GLV curve) over $\mathbb{F}_{p}$ as $$kP = k_1P + k_2\varPhi(P) \quad\text{with } \max \bigl\{ |k_1|,|k_2| \bigr\} \leq C_1\sqrt{n} $$ for some explicit constant C ₁>0. Recently, Galbraith, Lin, and Scott (EUROCRYPT 2009) extended this method to all curves over $\mathbb{F}_{p^{2}}$ which are twists of curves defined over $\mathbb{F}_{p}$ . We show in this work how to merge the two approaches in order to get, for twists of any GLV curve over $\mathbb{F}_{p^{2}}$ , a four-dimensional decomposition together with fast endomorphisms Φ,Ψ over $\mathbb{F}_{p^{2}}$ acting on the group generated by a point P of prime order n, resulting in a proven decomposition for any scalar k∈[1,n] given by $$kP=k_1P+ k_2\varPhi(P)+ k_3\varPsi(P) + k_4\varPsi\varPhi(P) \quad \text{with } \max_i \bigl(|k_i| \bigr)< C_2\, n^{1/4} $$ for some explicit C ₂>0. Remarkably, taking the best C ₁,C ₂, we obtain C ₂/C ₁<412, independently of the curve, ensuring in theory an almost constant relative speedup. In practice, our experiments reveal that the use of the merged GLV–GLS approach supports a scalar multiplication that runs up to 1.5 times faster than the original GLV method. We then improve this performance even further by exploiting the Twisted Edwards model and show that curves originally slower may become extremely efficient on this model. In addition, we analyze the performance of the method on a multicore setting and describe how to efficiently protect GLV-based scalar multiplication against several side-channel attacks. Our implementations improve the state-of-the-art performance of scalar multiplication on elliptic curves over large prime characteristic fields for a variety of scenarios including side-channel protected and unprotected cases with sequential and multicore execution.     

Coarsening of the Sn-Pb solder microstructure in constitutive model-based predictions of solder joint thermal mechanical fatigue

An expression for the coarsening rate of the Pb-rich phase particles was determined through isothermal aging experiments and comparative literature data as:

Influence of a strong longitudinal static electric field on free carrier faraday effect in an n-type InSb at room temperature at submillimeter wave frequencies

The expression for free carrier Faraday rotation θ and for ellipticity Δ, as the function of the applied parallel static electric field \(\mathop {E_0 }\limits_ \to \) and static magnetic field \(\mathop {B_0 }\limits_ \to \) for a given value of wave angular frequency and electron concentration N₀, are obtained and theoretically analyzed with the aid of one-dimensional linearized wave theory and Kane's non-parabolic isotropic dispersion law. It is shown that the maximum Faraday rotation occurs near the cyclotron resonance condition, which can be expressed as \(\chi \omega = \omega _{ce} \) , where \(\chi = 1{1 \mathord{\left/ {\vphantom {1 {\sqrt {1 - ({{v_0 } \mathord{\left/ {\vphantom {{v_0 } {v_c }}} \right. \kern-0em} {v_c }})^2 } }}} \right. \kern-0em} {\sqrt {1 - ({{v_0 } \mathord{\left/ {\vphantom {{v_0 } {v_c }}} \right. \kern-0em} {v_c }})^2 } }}\) , \(v_c = \sqrt {{{\varepsilon _g } \mathord{\left/ {\vphantom {{\varepsilon _g } {2m}}} \right. \kern-0em} {2m}}} *\) , and \(\omega _{ce} = ({{eB_0 } \mathord{\left/ {\vphantom {{eB_0 } {m*}}} \right. \kern-0em} {m*}})\) . Here m^* and e denote the effective mass and charge of electron, respectively. ?_g is the forbidden bandgap of semiconductor. v₀ is the carrier drift velocity, which is a non-linear function of E₀ in high field condition. A possibility of a simple way of determining the non-linear “v₀ vs E₀” characteristics of semiconductors by the measurement of Faraday rotation is also discussed.     

Linear systems in a saturated mode and convergence as gain becomes large of asymptotically stable equilibrium points of neural nets

We study solutions of the linear system in a saturated mode

Mixed-Mode Oscillations in a Modified Chua’s Circuit

We consider a singularly perturbed system of differential equations of the form ε u′=g(u,v,λ), v′=f(u,v,λ), where (u,v)∈R ³, 0<ε?1, and λ is a set of parameters. Such a system describes a modified Chua’s circuit with mixed-mode oscillations (MMOs). MMOs consist of a series of small-amplitude oscillations (canard solutions) and large-amplitude relaxations. In the paper we provide a series of both numerical and analytical analyses of the singularly perturbed system for the modified Chua’s circuit with nonlinear f and g. In particular, we analyze the occurrence of the Farey sequence $\it L^{s}$ , where $\it L$ and $\it s$ are the numbers of large and small oscillations, respectively.     

Hydride Vapor-Phase Epitaxy of c-Plane AlGaN Layers on Patterned Sapphire Substrates

Growth of Al _x Ga_1?x N layers by hydride vapor-phase epitaxy on patterned sapphire substrates is investigated. The pattern consists of honeycombs which by their orientation and size promote the formation of coalesced c-plane-oriented Al _x Ga_1?x N layers with reduced crack density. The orientation of parasitic crystallites in the honeycomb openings is investigated using scanning electron microscopy and electron back-scatter diffraction. Crystallites with their [ $ \bar{1} $ $ \bar{1} $ .0] and [52.3] directions parallel to the vertical growth direction of the Al_0.3Ga_0.7N layer are observed and successfully overgrown by a 20-μm-thick fully coalesced c-plane-oriented layer.     

Soft X-ray Absorption and Photoemission Spectroscopy Study of Cobalt-Based Thermoelectric Oxides: \hbox{Ca}_3\hbox{Co}_4\hbox{O}_9, \hbox{Ca}_3\hbox{Co}_2\hbox{O}_6, and \hbox{Bi}_{2}\hbox{Sr}_{2}\hbox{Co}_2\hbox{O}_{y}

The electronic structures of Co-based potential thermoelectric (TE) oxides, including $\hbox{Ca}_3\hbox{Co}_4\hbox{O}_9$ and $\hbox{Bi}_{2}\hbox{Sr}_{2}\hbox{Co}_2\hbox{O}_{y}$ (y = 8 + δ) single crystals and polycrystalline $\hbox{Ca}_3\hbox{Co}_2\hbox{O}_6$ , have been investigated by employing soft x-ray absorption spectroscopy (XAS) and photoemission spectroscopy (PES). Co 2p XAS measurements show that Co ions are nearly trivalent ( $\hbox{Co}^{3+}$ ) in all of these Co-based TE oxides with a small mixture of $\hbox{Co}^{4+}$ ions in $\hbox{Bi}_{2}\hbox{Sr}_{2}\hbox{Co}_2\hbox{O}_{y}$ . Valence-band PES and O 1s XAS measurements show that the occupied Co 3d states are located at the top of the valence bands and that the lowest unoccupied states have the primarily Co 3d character, respectively. These findings suggest the importance of the Co 3d electronic structures in determining TE properties of these Co-based oxides.     

On the robust control of nonlinear systems

In this paper we consider robust stabilization of the class of nonlinear plants of the form $$\dot x = f(x) + \sum\limits_{i = 1}^m {g_i } (x)u_i (t),$$ which are equivalent, under smooth state space coordinate transformations and nonlinear state feedback, to controllable systems. This approach is very sensitive for unknown parameters' values. Parameter adaptation may be used as a technique to robustify minimum-phase systems [3]. We give an example of a locally stable adaptive tracking system in which the last assumption is weakened. The minimum-phase plant considered in the paper is a current-controlled squirrel cage induction motor.     

Precise Control of Na Content in the Layered Cobaltate <Emphasis Type="Italic">γ</Emphasis>-Na<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>CoO<Subscript>2</Subscript>

We have developed a preparation method for precisely controlling the Na content x of a γ-Na_0.7CoO₂ precursor by a halogen oxidation technique in the range 0.50 ≤ x ≤ 0.70. The Na content of the precursor was reduced in a concentration-controlled I₂-CH₃CN solution. The magnetic susceptibility of γ-Na _x CoO₂ shows Curie–Weiss (CW)-type paramagnetism (x ≈ 0.70) or Pauli-type paramagnetism (x ≈ 0.50). The boundary of the CW and Pauli paramagnetic phases was identified at x ≈ 0.61. The content and temperature for a disorder–order transition from the γ phase to a \(\sqrt{7}a_0 \times \sqrt{7}a_0\) superstructure were accurately elucidated by differential scanning calorimetry (DSC) measurement. A phase transition for the 0.52 ≤ x ≤ 0.54 sample was observed at 250 K by DSC measurements. The heat absorption of the 0.52 ≤ x ≤ 0.54 samples was of the same order of magnitude as that of the transition from the γ phase to the \(\sqrt{7}a_0 \times \sqrt{7}a_0\) phase.     

δ-Bit serial binary addition with linear threshold networks

In this paper we investigate δ-bit serial addition in the context of feed-forward linear threshold gate based networks. We show that twon-bit operands can be added in $2\left\lceil {\sqrt n } \right\rceil $ overall delay with a feed-forward network constructed with $\left\lceil {\sqrt n } \right\rceil + 1$ linear threshold gates and $\frac{1}{2}\left( {5\left\lceil {\sqrt n } \right\rceil ^2 + 9\left\lceil {\sqrt n } \right\rceil } \right) + 2$ latches. The maximum weight value is $2^{\left\lceil {\sqrt n } \right\rceil } $ and the maximum fan-in is $3\left\lceil {\sqrt n } \right\rceil + 1$ . We also investigate the implications our scheme have to the performance and the cost under small weights and small fan-in requirements. We deduce that if the weight values are to be limited by a constantW, twon-bit operands can be added in $\left[ {\log W} \right] + \tfrac{n}{{\left[ {\log W} \right]}}$ overall delay with a feed-forward network that has the implementation cost [logW]+1, in terms of linear threshold gates, $\tfrac{1}{2}(5[\log W]^2 + 9[\log W]) + 2$ in terms of latches and a maximum fan-in of 3[logW]+1. We also prove that, if the fan-in values are to be limited by a constantF+1, twon-bit operands can be added in $[\tfrac{F}{3}] + \tfrac{n}{{[\tfrac{F}{3}]}}$ overall delay with a feed-forward network that has the implementation cost $[\tfrac{F}{3}] + 1$ , in terms of linear threshold gates, $\tfrac{1}{2}(5[\tfrac{F}{3}]^2 + 9[\tfrac{F}{3}]) + 2$ in terms of latches, and a maximum weight value of $2^{[\tfrac{F}{3}]} $ . An asymptotic bound of $O(\tfrac{n}{{\log n}})$ is derived for the addition overall delay in the case that the weight values have to be linearly bounded, i.e., in the order ofO(n). The implementation cost in this case is in the order ofO(logn), in terms of linear threshold gates, and in the order ofO(log² n), in terms of latches. The maximum fan-in is in the order ofO(logn). Finally, a partition technique, that substantially reduces the overall cost of the implementation for all the schemes in terms of delay, latches, weights, and fan-in with some few additional threshold gates, is also presented.     

Basis arrays and successive packing for M-D interleaving

In this paper, we first present a novel concept of 2-D basis interleaving array (also referred to as basis array for short). That is, an m × m interleaved array is said to be a basis array if the shortest distance among all pairs of elements in each of the so-called m-equivalent sets within the m × m array reaches the maximum. It is shown that this maximum is given by ${\lfloor \sqrt{2m} \rfloor}$ and an m × m basis array can be constructed by using a simple cyclic translation method. The previously developed concept of successive packing is then generalized in the sense that it can be applied to any basis array to generate an interleaved array with a larger size. Except that optimality cannot be guaranteed, the concept of basis arrays and successive packing are extended to M-D cases. It is shown that for any M ?? 2, the proposed technique can spread any error burst of block size ${m_{1}^{k} \times m_{2}^{k} \times \cdots \times m_{M}^{k}}$ within an ${ m_{1}^{n} \times m_{2}^{n} \times \cdots \times m_{M}^{n}}$ array (1 ?? k ?? n?1) so effectively that the error burst can be corrected with some simple random error-correcting code (provided the error-correcting code is available). It is shown that important prior results in M-D interleaving such as the t-interleaved array based approach by Blaum et al. and the successive packing approach by Shi and Zhang now become special cases of the framework based on basis arrays and successive packing, proposed in this paper.     

Formation of a Buffer Layer for Graphene on C-Face SiC{0001}

Graphene films prepared by heating the SiC $ (000\bar{1}) $ surface (the C-face of the {0001} surface) in a Si-rich environment have been studied using low-energy electron diffraction (LEED) and low-energy electron microscopy. Upon graphitization, an interface with $ \sqrt {43} \times \sqrt {43} - R \pm 7.6^\circ $ symmetry is observed by in situ LEED. After oxidation, the interface displays $ \sqrt 3 \times \sqrt 3 - R 30^\circ $ symmetry. Electron reflectivity measurements indicate that these interface structures arise from a graphene-like “buffer layer” that forms between the graphene and the SiC, similar to that observed on Si-face SiC. From a dynamical LEED structure calculation for the oxidized C-face surface, it is found to consist of a graphene layer sitting on top of a silicate (Si₂O₃) layer, with the silicate layer having the well-known structure as previously studied on bare SiC $ (000\bar{1}) $ surfaces. Based on this result, the structure of the interface prior to oxidation is discussed.