Band gaps and defect modes in periodically structured waveguides

This work examines a simple one-dimensional acoustic band gap system made from a diameter-modulated waveguide. Experimental and theoretical results are presented on perfectly periodic waveguide arrays showing the presence of band gaps--frequency intervals in which the transmission of sound is forbidden. The introduction of defects in the perfect periodicity leads to narrow frequency transmission bands--defect states--within the forbidden band gaps. The circular cross-section waveguide system is straightforward to simulate theoretically and experimental results demonstrate good agreement with theory. The experimental transmission of the periodic waveguide arrays is measured using an impulse response technique.     

Bond orders and atomic properties of the highly deformed halogenated fullerenes C60F18 and C60Cl30 derived from their charge densities

The experimental charge densities of the halogenated C(60) fullerenes C(60)F(18) and C(60)Cl(30) were determined from high-resolution X-ray data sets measured with conventional Mo(Kalpha) radiation at 20 K for C(60)Cl(30) and with synchrotron radiation at 92 K for the fluorine compound. Bond topological and atomic properties were analyzed by using Bader's AIM theory. For the different C--C bonds, which vary in lengths between 1.35 and 1.70 A bond orders n between n=2 and significantly below n=1 were calculated from the bond topological properties at the bond critical points (BCP's). The low bond orders are seen for 5/6 bonds with each contributing carbon carrying a halogen atom. By integration over Bader's zero flux basins in the electron density gradient vector field atomic properties were also obtained. In contrast to free C(60), in which all carbon atoms have a uniform volume of 11 A(3) and zero charge, atomic volumes vary roughly between 5 and 10 A(3) in the halogenated compounds. Almost zero atomic charges are also found in the Cl derivative but a charge separation up to +/-0.8 e exists between C and F in C(60)F(18) due to the higher fluorine electronegativity, which is also seen in the electrostatic potential for which the electronegativity difference between carbon and fluorine, and the addition to one hemisphere of the fullerene cage leads to a strong potential gradient along the C(60)F(18) molecule. From the summation over all atomic volumes it follows that the halogen addition does not only lead to a dramatic distortion of the C(60) cage but also to a significant shrinkage of its volume.     

Pricing and advertisement in a manufacturer–retailer supply chain

We use a game theoretical approach to study pricing and advertisement decisions in a manufacturer–retailer supply chain when price discounts are offered by both the manufacturer and retailer. When the manufacturer is the leader of the game, we obtained Stackelberg equilibrium with manufacturer’s local allowance, national brand name investment, manufacturer’s preferred price discount, retailer’s price discount, and local advertising expense. For the special case of two-stage equilibrium when the manufacturer’s price discount is exogenous, we found that the retailer is willing to increase local advertising expense if the manufacturer increases local advertising allowance and provides deeper price discount, or if the manufacturer decreases its brand name investment. When both the manufacturer and retailer have power, Nash equilibrium in a competition game is obtained. The comparison between the Nash equilibrium and Stackelberg equilibrium shows that the manufacturer always prefers Stackelberg equilibrium, but there is no definitive conclusion for the retailer. The bargaining power can be used to determine the profit sharing between the manufacturer and the retailer. Once the profit sharing is determined, we suggest a simple contract to help the manufacturer and retailer obtain their desired profit sharing.     

Piecewise linear prewavelets over type-2 triangulations

In this article, we study the construction of piecewise linear prewavelets over type-2 triangulations. Different from a so-called semi-prewavelet approach, we investigate the orthogonal conditions directly and obtain parameterized prewavelets with a smaller support. The conditions for parameterized prewavelet basis on the parameters are also given.     

Partial information systems and the Smyth powerdomain

The dual of the join semilattice of proper compact Scott open subsets of a domain D is called the Smyth powerdomain of D. The Smyth powerdomain is used in programming semantics as a model for demonic nondeterminism. In this paper, we introduce the concept of partial information systems; and, as an application, show that the Smyth powerdomain of any domain can be realized in terms of the sub partial information systems of the domain??s corresponding information system.     

Optimal rates for spectral algorithms with least-squares regression over Hilbert spaces

In this paper, we study regression problems over a separable Hilbert space with the square loss, covering non-parametric regression over a reproducing kernel Hilbert space. We investigate a class of spectral/regularized algorithms, including ridge regression, principal component regression, and gradient methods. We prove optimal, high-probability convergence results in terms of variants of norms for the studied algorithms, considering a capacity assumption on the hypothesis space and a general source condition on the target function. Consequently, we obtain almost sure convergence results with optimal rates. Our results improve and generalize previous results, filling a theoretical gap for the non-attainable cases.     

Maximum matchings in regular graphs

It was conjectured by Mkrtchyan, Petrosyan and Vardanyan that every graph $G$ with $\Delta \left(G\right)?\delta \left(G\right)\le 1$ has a maximum matching $M$ such that any two $M$-unsaturated vertices do not share a neighbor. The results obtained in Mkrtchyan et al. (2010), Petrosyan (2014) and Picouleau (2010) leave the conjecture unknown only for $k$-regular graphs with $4\le k\le 6$. All counterexamples for $k$-regular graphs $(k\ge 7)$ given in Petrosyan (2014) have multiple edges. In this paper, we confirm the conjecture for all $k$-regular simple graphs and also $k$-regular multigraphs with $k\le 4$.     

C(1)-Phenethyl Derivatives of [closo-1-CB11H12]− and [closo-1-CB9H10]− Anions: Difunctional Building Blocks for Molecular Materials

C(1)-vinylation of [closo-1-CB₉H₁₀]⁻ ( A ) and [closo-1-CB₁₁H₁₂]⁻ ( B ) with 4-benzyloxystyryl iodide followed by hydrogenation of the double bond and reductive deprotection of the phenol functionality led to C(1)-(4-hydroxyphenethyl) derivatives. The phenol functionality was protected as the acetate. The esters were then treated with PhI(OAc)₂ and the resulting isomers were separated kinetically (for derivatives of anion A ) or by chromatography (for derivatives of anion B ) giving the difunctionalized building blocks in overall yields of 9 % and 50 %, respectively. A similar series of reactions was performed starting with anions A and B and 4-methoxystyryl bromide and iodide. Significant differences in the reactivity of derivatives of the two carborane anions were rationalized with DFT computational results. Application of the difunctionalized carboranes as building blocks was demonstrated through preparation of two ionic liquid crystals. The extensive synthetic work is accompanied by single crystal XRD analysis of six derivatives.     

Competitive exclusion in a nonlocal reaction–diffusion–advection model of phytoplankton populations

We continue our study on the global dynamics of a nonlocal reaction–diffusion–advection system modeling the population dynamics of two competing phytoplankton species in a eutrophic environment, where both populations depend solely on light for their metabolism. In our previous work, we proved that system (1.1) is a strongly monotone dynamical system with respect to a non-standard cone related to the cumulative distribution functions, and further determined the global dynamics when the species have either identical diffusion rate or identical advection rate. In this paper, we study the trade-off of diffusion and advection and their joint influence on the outcome of competition. Two critical curves for the local stability of two semi-trivial equilibria are analyzed, and some new competitive exclusion results are obtained. Our main tools, besides the theory of monotone dynamical system, include some new monotonicity results for the principal eigenvalues of elliptic operators in one-dimensional domains.