$$\mathcal {H}^+$$-multivalued contractions and their application to homotopy theory

Kikkawa and Suzuki (Nonlinear Anal 69:2942–2949, 2008) and Kikkawa and Suzuki (Fixed Point Theory Appl, 2008, Art. ID 649749) proved some fixed point results that are generalizations of Kannan’s, Nadler’s and Suzuki’s fixed point theorems. Here, we present fixed point results of this kind for multivalued mappings in the setting of \(\mathcal {H}^+\)-metric spaces. The theorems provided allow upgrading of some known results which is shown by examples. Moreover, we give a homotopy result as an application of our main theorem.     

Thermodynamics of water entry in hydrophobic channels of carbon nanotubes

Experiments and computer simulations demonstrate that water spontaneously fills the hydrophobic cavity of a carbon nanotube. To gain a quantitative thermodynamic understanding of this phenomenon, we use the recently developed two phase thermodynamics method to compute translational and rotational entropies of confined water molecules inside single-walled carbon nanotubes and show that the increase in energy of a water molecule inside the nanotube is compensated by the gain in its rotational entropy. The confined water is in equilibrium with the bulk water and the Helmholtz free energy per water molecule of confined water is the same as that in the bulk within the accuracy of the simulation results. A comparison of translational and rotational spectra of water molecules confined in carbon nanotubes with that of bulk water shows significant shifts in the positions of the spectral peaks that are directly related to the tube radius.     

Unexpected phenol production from arylboronic acids under palladium-free conditions; organocatalyzed air oxidation

An intriguing class of quinones that efficiently catalyze the air oxidation (overall hydroxylation) of arylboronic acids to the corresponding phenol is reported. Autocatalysis in the parent system is particularly efficient and leads to rapid, quantitative synthesis of quinones such as 4 from boronic acid 1 at room temperature using air as stoichiometric oxidant. The efficiency results from a balance between two-stage conjugate addition and migration with each step driven by aromatization of a naphthalene fragment.     

微极流体蠕动泵经由滑移边界管道输送的Stokes流动

计及管道边界条件滑移的影响,研究微极流体蠕动泵,经由圆柱形管道输运的Stokes流动.壁面运动的控制方程为正弦波方程.使用润滑理论,得到了轴向速度、微转动向量、流函数、压力梯度、摩擦力和机械效率的解析数值解.用图形表示出构成参数,如像耦合参数、微极参数和表征蠕流泵特性的滑移参数、摩擦力和俘获现象的影响.数值计算表明,当耦合参数较大时,需要蠕动泵的压力更大,而微极参数和滑移参数正相反.俘获团块的大小随耦合参数和微极参数的减小而缩小,而随滑移参数的增大而缩小.     

Further studies of intramolecular Michael reactions of nitrosoalkenes for construction of functionalized bridged ring systems

A wide variety of stabilized carbanions have been found to participate as nucleophiles in intramolecular Michael-type conjugate additions to in situ generated nitrosoalkenes to form bridged carbocyclic systems. The vinylnitroso platforms for these cyclizations have been prepared via two key steps involving ring-closing metathesis of vinyl chlorides and regioselective conversion of vinyl chlorides to α-chloroketones with sodium hypochlorite in glacial acetic acid/acetone. An alternative approach to preparation of some cyclization substrates has involved use of more reactive enol ethers as precursors to the requisite α-chloroketones. A sulfonamide anion has also been found to be an effective nucleophile in this type of reaction, leading to formation of a 6-azabicyclo[3.2.1]octane.     

On the integration of data and mathematical modeling languages

This paper examines ways in which the addition of data modeling features can enhance the capabilities of mathematical modeling languages. It demonstrates how such integration is achieved as an application of the embedded languages technique proposed by Bhargava and Kimbrough [4]. Decision-making, and decision support systems, require the representation and manipulation of both data and mathematical models. Several data modeling languages as well as several mathematical modeling languages exist, but they have different sets of these capabilities. We motivate with a detailed example the need for the integration of these capabilities. We describe the benefits that might result, and claim that this could lead to a significant improvement in the functionality of model management systems. Then we present our approach for the integration of these languages, and specify how the claimed benefits can be realized.The author's work on this paper was performed in conjunction with research funded by the Naval Postgraduate School.     

Pricing under quality of service uncertainty: Market segmentation via statistical QoS guarantees

This article examines how performance-contingent pricing schemes with long-term statistical performance guarantees can be applied to many IT services. We study two forms of performance-contingent pricing, with rebate proportional to failure rate and fixed rebate for below-threshold performance. We show that threshold-performance contingency pricing can increase both profits and fairness (customers who receive higher benefits pay higher effective price) relative to standard pricing. But an even better solution is to offer a menu of performance guarantees: this can increase the firm’s profit and segment the market. Only service providers whose performance level is sufficiently better than the industry standard can benefit from this pricing mechanism.     

Practical synthesis of chiral 9,9'-spirobixanthene-1,1'-diol

A concise four-step synthesis of 9,9'-spirobixanthene-1,1'-diol is reported, featuring a practical preparation at large scale without the use of column chromatography purification. Co-crystallization with N-benzylcinchonidinium chloride and N-benzylquininium chloride rendered the optically pure product in both enantiomers.     

Aryl trihydroxyborates: easily isolated discrete species convenient for direct application in coupling reactions

A conceptually and practically simple alternative approach to the use of arylboron species as the organometallic component in cross-coupling processes is described whereby trihydroxyborate salts are isolated and directly employed. The protocol derives practical benefit from the ease and convenience of the isolation and subsequent use of the discrete borate salts, eliminates the need for additional base, and aids the use of correct reaction stoichiometry.     

The Conjugacy Class Number k(G): A Different Perspective

For a finite group G, let m(G) denote the least positive integer such that the union of any m(G) distinct nontrivial conjugacy classes of G together with the identity of G is a subgroup of G. We prove that m(G) = k(G) ?1 for all m(G) ≥2.