On the Stability and Solution Sensitivity of a Consumer Problem

We present a continuous-time generalization of the seminal research and development model of d’Aspremont and Jacquemin (Am Econ Rev 78(5):1133–1137, 1988) to examine the trade-off between the benefits of allowing firms to cooperate in research and the corresponding increased potential for product market collusion. We show the existence of a solution to the optimal investment problem using a combination of results from viscosity theory and the theory of planar dynamical systems. In particular, we show that there is a critical level of marginal cost at which firms are indifferent between doing nothing and starting to develop the technology. We find that colluding firms develop further a wider range of initial technologies, pursue innovations more quickly, and are less likely to abandon a technology. Product market collusion could thus yield higher total surplus.     

Novel route to size-controlled Fe-MIL-88B-NH2 metal-organic framework nanocrystals

A new approach for the synthesis of uniform metal-organic framework (MOF) nanocrystals with controlled sizes and aspect ratios has been developed using simultaneously the non-ionic triblock co-polymer F127 and acetic acid as stabilizing and deprotonating agents, respectively. The alkylene oxide segments of the triblock co-polymer can coordinate with metal ions and stabilize MOF nuclei in the early stage of the formation of MOF nanocrystals. Acetic acid can control the deprotonation of carboxylic linkers during the synthesis and, thus, enables the control of the rate of nucleation, leading to the tailoring of the size and aspect ratio (length/width) of nanocrystals. Fe-MIL-88B-NH(2), as an iron-based MOF crystal, was selected as a typical example to illustrate our approach. The results reveal that this approach is used for not only the synthesis of uniform nanocrystals but also the control of the size and aspect ratio of the materials. The size and aspect ratio of nanocrystals increase with an increase in the concentration of acetic acid in the synthetic mixture. The non-ionic triblock co-polymer F127 and acetic acid can be easily removed from the Fe-MIL-88B-NH(2) nanocrystal products by washing with ethanol, and thus, their amine groups are available for practical applications. The approach is expected to synthesize various nanosized carboxylate-based MOF members, such as MIL-53, MIL-89, MIL-100, and MIL-101.     

A-type cranberry proanthocyanidins inhibit the RANKL-dependent differentiation and function of human osteoclasts

This study investigated the effect of A-type cranberry proanthocyanidins (AC-PACs) on osteoclast formation and bone resorption activity. The differentiation of human pre-osteoclastic cells was assessed by tartrate-resistant acid phosphatase (TRAP) staining, while the secretion of interleukin-8 (IL-8) and matrix metalloproteinases (MMPs) was measured by ELISA. Bone resorption activity was investigated by using a human bone plate coupled with an immunoassay that detected the release of collagen helical peptides. AC-PACs up to 100 μg/mL were atoxic for osteoclastic cells. TRAP staining evidenced a dose-dependent inhibition of osteoclastogenesis. More specifically, AC-PACs at 50 μg/mL caused a 95% inhibition of RANKL-dependent osteoclast differentiation. This concentration of AC-PACs also significantly increased the secretion of IL-8 (6-fold) and inhibited the secretion of both MMP-2 and MMP-9. Lastly, AC-PACs (10, 25, 50 and 100 μg/ml) affected bone degradation mediated by mature osteoclasts by significantly decreasing the release of collagen helical peptides. This study suggests that AC-PACs can interfere with osteoclastic cell maturation and physiology as well as prevent bone resorption. These compounds may be considered as therapeutic agents for the prevention and treatment of periodontitis.     

Highly enantioselective Mannich reactions with α-aryl silyl ketene acetals and imines

Mannich reactions with chiral silicon Lewis acid activated acylhydrazones and α-aryl silyl ketene acetals and α-aryl,α-alkyl silyl ketene imines proceed efficiently and with good to excellent levels of both diastereoselectivity and enantioselectivity. The reactions provide access to α-aryl,β-hydrazido esters and α-aryl,α-alkyl,β-hydrazido nitriles, which are valuable analogs of β-amino acids.     

Electronic structures, vibrational and thermochemical properties of neutral and charged niobium clusters Nb(n), n = 7-12

Geometric and electronic structures, vibrational properties, and relative stabilities of niobium clusters Nb(n), n = 7-12, are studied using both DFT (BPW91 and M06 functionals) and CCSD(T) calculations with the cc-pVnZ-PP basis set. In each cluster, various lower-lying states are very close in energy in such a way that the ground state cannot be unambiguously established by DFT computations. Nb clusters tend to prefer the lowest possible spin state as the ground state, except for Nb(12) ((3)A(g)). The optimal structure of the cluster at a certain size does not simply grow from that of the smaller one by adding an atom randomly. Instead, the Nb clusters prefer a close-packed growth behavior. Nb(10) has a spherically aromatic character, high chemical hardness and large HOMO-LUMO gap. Electron affinities, ionization energies, binding energy per atom, and the stepwise dissociation energies are evaluated. Energetic properties exhibit odd-even oscillations. Comparison with experimental values shows that both BPW91 and M06 functionals are reliable in predicting the EA and IE values, but the BPW91 is deficient in predicting the binding and dissociation energies. We re-examine in particular the experimental far IR spectra previously recorded using the IR-MPD and free electron laser spectrometric techniques and propose novel assignments for Nb(7) and Nb(9) systems. The IR spectra of the anions are also predicted.     

QR methods and error analysis for computing Lyapunov and Sacker�CSell spectral intervals for linear differential-algebraic equations

In this paper, we propose and investigate numerical methods based on QR factorization for computing all or some Lyapunov or Sacker?CSell spectral intervals for linear differential-algebraic equations. Furthermore, a perturbation and error analysis for these methods is presented. We investigate how errors in the data and in the numerical integration affect the accuracy of the approximate spectral intervals. Although we need to integrate numerically some differential-algebraic systems on usually very long time-intervals, under certain assumptions, it is shown that the error of the computed spectral intervals can be controlled by the local error of numerical integration and the error in solving the algebraic constraint. Some numerical examples are presented to illustrate the theoretical results.     

Primitive symmetric designs with up to 2500 points

By this article we conclude the construction of all primitive ( v, k,λ ) symmetric designs with v < 2500 , up to a few unsolved cases. Complementary to the designs with prime power number of points published previously, here we give 55 primitive symmetric designs with v ≠ p ^m , p prime and m positive integer, together with the analysis of their full automorphism groups. The research involves programming and wide‐range computations. We make use of the software package GAP and the library of primitive groups which it contains. © 2011 Wiley Periodicals, Inc. J Combin Designs 19:463‐474, 2011     

Dynamic Picone's identity and its applications

We prove some Picone-type identities and inequalities for a class of first-order nonlinear dynamic systems and derive various weighted inequalities of Wirtinger type and Hardy type on time scales. As applications we study oscillatory and related properties of these systems including Reid's roundabout theorem on disconjugacy, Sturm's separation and comparison theorems, as well as a variational method in the oscillation theory.     

A simple spectral theory of polynomially bounded solutions and applications to differential equations

Semigroup Forum - In this paper we present a simple spectral theory of polynomially bounded functions on the half line, and then apply it to study the asymptotic behavior of solutions of fractional...