The Webster Scalar Curvature and Sharp Upper and Lower Bounds for the First Positive Eigenvalue of the Kohn-Laplacian on Real Hypersurfaces

Let(M, θ) be a compact strictly pseudoconvex pseudohermitian manifold which is CR embedded into a complex space. In an earlier paper, Lin and the authors gave several sharp upper bounds for the first positive eigenvalue λ_1 of the Kohn-Laplacian □_b on(M, θ). In the present paper, we give a sharp upper bound for λ_1, generalizing and extending some previous results. As a corollary, we obtain a Reilly-type estimate when M is embedded into the standard sphere. In another direction, using a Lichnerowicz-type estimate by Chanillo, Chiu, and Yang and an explicit formula for the Webster scalar curvature, we give a lower bound for λ_1 when the pseudohermitian structure θ is volume-normalized.     

Fredholm operators,evolution semigroups,and periodic solutions of nonlinear periodic systems

Let X be a Banach space and L the generator of the evolution semigroup associated with the τ  -periodic evolutionary process _{{U(t,s)}t≥s}${\{U(t,s)\}}_{t\ge s}$ on the space _Pτ(X)$P_{\tau }(X)$ of all τ-periodic continuous X  -valued functions. We give criteria for the existence of periodic solutions to nonlinear systems of the form Lp=−?F(p,?)$Lp=-?F(p,?)$ under the condition that 1 is a normal eigenvalue of the monodromy operator U(τ,0)$U(\tau ,0)$. The proof is based on a new decomposition of the space _Pτ(X)$P_{\tau }(X)$ by constructing a right inverse of L.     

Convergence analysis of a new mixed finite element method for Biot's consolidation model

In this article, we propose a mixed finite element method for the two‐dimensional Biot's consolidation model of poroelasticity. The new mixed formulation presented herein uses the total stress tensor and fluid flux as primary unknown variables as well as the displacement and pore pressure. This method is based on coupling two mixed finite element methods for each subproblem: the standard mixed finite element method for the flow subproblem and the Hellinger–Reissner formulation for the mechanical subproblem. Optimal a‐priori error estimates are proved for both semidiscrete and fully discrete problems when the Raviart–Thomas space for the flow problem and the Arnold–Winther space for the elasticity problem are used. In particular, optimality in the stress, displacement, and pressure has been proved in when the constrained‐specific storage coefficient is strictly positive and in the weaker norm when is nonnegative. We also present some of our numerical results.Copyright © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 1189–1210, 2014     

A genetic design of linguistic terms for fuzzy rule based classifiers

The determination of fuzzy information granules including the estimation of their membership functions play a significant role in fuzzy system design as well as in the design of fuzzy rule based classifiers (FRBCSs). However, although linguistic terms are fundamental elements in the process of elucidating expert’s knowledge, the problem of linguistic term design along with their fuzzy-set-based semantics has not been fully addressed, since term-sets of attributes have not been interpreted as a formalized structure. Thus, the essential relationship between linguistic terms, as syntax, and the constructed fuzzy sets, as their quantitative semantics, or in other words, the problem of the natural semantics of terms behind the linguistic literal has not been addressed. In this paper, we introduce the problem of the design of optimal linguistic terms and propose a method of the design of FRBCSs which may incorporate with the design of linguistic terms to ensure that the presence of linguistic literals are supported not only by data but also by their natural semantics. It is shown that this problem plays a primordial role in enhancing the performance and the interpretability of the designed FRBCSs and helps striking a better balance between the generality and the specificity of the desired fuzzy rule bases for fuzzy classification problems. A series of experiments concerning 17 Machine Learning datasets is reported.     

Characterizations of linear Volterra integral equations with nonnegative kernels

We first introduce the notion of positive linear Volterra integral equations. Then, we offer a criterion for positive equations in terms of the resolvent. In particular, equations with nonnegative kernels are positive. Next, we obtain a variant of the Paley-Wiener theorem for equations of this class and its extension to perturbed equations. Furthermore, we get a Perron-Frobenius type theorem for linear Volterra integral equations with nonnegative kernels. Finally, we give a criterion for positivity of the initial function semigroup of linear Volterra integral equations and provide a necessary and sufficient condition for exponential stability of the semigroups.     

Bonding and impedance matching of acoustic transducers using silver epoxy

Silver epoxy was selected to bond transducer plates on glass substrates. The properties and thickness of the bonding medium affect the electrical input impedance of the transducer. Thus, the thickness of the silver epoxy bonding layer was used as a design parameter to optimize the structure for the transducer input impedance to match the 50 Ω output impedance of most radio frequency (RF) generators. Simulation and experimental results show that nearly perfect matching is achieved without using any matching circuit. At the matching condition, the transducer operates at a frequency band a little bit below the half-wavelength resonant frequency of the piezoelectric plate. In experiments, lead titanate (PT) piezoelectric plates were employed. Both full-size, 11.5 mm × 2 mm × 0.4 mm, and half-size, 5.75 mm × 2 mm × 0.4 mm, can be well matched using optimal silver epoxy thickness. The transducer assemblies demonstrate high efficiency. The conversion loss from electrical power to acoustic power in soda-lime glass is 4.3 dB. This loss is low considering the fact that the transducers operate at off-resonance by 12%. With proper choice of silver epoxy thickness, the transducer can be matched at the fundamental, the 3rd and 5th harmonic frequencies. This leads to the possible realization of triple-band transducers. Reliability was assessed with thermal cycling test according to Telcordia GR-468-Core recommendation. Of the 30 transducer assemblies tested, none broke until 2900 cycles and 27 have sustained beyond 4050 cycles.     

Multiferroic characteristics of the strained epitaxial Bi0.9Ho0.1FeO3 thin film

We fabricated high quality epitaxial Bi_0.9Ho_0.1FeO₃ thin films which exhibited the tetragonally stained structure with a c/a ratio of about 1.04. The Bi_0.9Ho_0.1FeO₃ thin film showed a good ferroelectric property with the high remanent polarization (P_r) of about 80 μC/cm². The ferromagnetic hysteresis loop with a clear remanent magnetization was shown. The coercive field and the remanent magnetization of the Bi_0.9Ho_0.1FeO₃ film are 6200 Oe and 1.7 emu/g, respectively. The abrupt conduction due to space charge limited (SCL) was revealed in leakage current density versus electric field.     

Catalytic one-pot synthesis of [5.5.5.6]fenestrane systems via a dicobalt octacarbonyl-catalyzed tandem cycloaddition of dienediynes

Catalytic one-pot synthesis of fenestrane derivatives from dienediynes was developed: fenestranes were synthesized in high yields by a dicobalt octacarbonyl-catalyzed tandem cycloaddition of dienediynes.     

Catalytic one-pot synthesis of N-phenyl alkyl amides from alkene and aniline in the presence of cobalt on charcoal under carbon monoxide

N-Phenyl alkyl amides were synthesized by the cobalt on charcoal-catalyzed one-pot reaction of alkene and aniline under carbon monoxide; this is the first heterogeneous catalytic formation of N-phenyl alkyl amides.