Fractional Hardy–Hénon equations on exterior domains

In this paper, we consider the fractional Hardy–Hénon equations with an isolated singularity. If the isolated singularity is located at the origin, we give a classification of solutions to this equation. If the isolated singularity is located at infinity, in the case of exterior domains, we provide decay estimates of solutions and their gradients at infinity. Our results are an extension of the classical work by Caffarelli, Gidas et al.     

On the Cegrell Classes Associated to a Positive Closed Current

The aim of this paper is to study the operatoron■ on some classes of plurisubharmonic (psh) functions, which are not necessary bounded, where T is a positive closed current of bidimension (q, q) on an open set ? of C~n. The author introduces two classes F_p~T (?) and■ and shows first that they belong to the domain of definition of the operator■. Then the author proves that all functions that belong to these classes are C_T-quasi-continuous and that the comparison principle is valid for them.     

Reactions of small negative ions with O2(a Δg) and O2(X Σg)

The rate constants and product ion branching ratios were measured for the reactions of various small negative ions with O₂(X ³Σ_g⁻) and O₂(a ¹Δ_g) in a selected ion flow tube (SIFT). Only NH₂⁻ and CH₃O⁻ were found to react with O₂(X) and both reactions were slow. CH₃O⁻ reacted by hydride transfer, both with and without electron detachment. NH₂⁻ formed both OH⁻, as observed previously, and O₂⁻, the latter via endothermic charge transfer. A temperature study revealed a negative temperature dependence for the former channel and Arrhenius behavior for the endothermic channel, resulting in an overall rate constant with a minimum at 500 K. SF₆⁻, SF₄⁻, SO₃⁻ and CO₃⁻ were found to react with O₂(a ¹Δ_g) with rate constants less than 10⁻¹¹ cm³ s⁻¹. NH₂⁻ reacted rapidly with O₂(a ¹Δ_g) by charge transfer. The reactions of HO₂⁻ and SO₂⁻ proceeded moderately with competition between Penning detachment and charge transfer. SO₂⁻ produced a SO₄⁻ cluster product in 2% of reactions and HO₂⁻ produced O₃⁻ in 13% of the reactions. CH₃O⁻ proceeded essentially at the collision rate by hydride transfer, again both with and without electron detachment. These results show that charge transfer to O₂(a ¹Δ_g) occurs readily if the there are no restrictions on the ion beyond the reaction thermodynamics. The SO₂⁻ and HO₂⁻ reactions with O₂(a) are the only known reactions involving Penning detachment besides the reaction with O₂⁻ studied previously [R.S. Berry, Phys. Chem. Chem. Phys., 7 (2005) 289–290].     

Graphene/activated carbon supercapacitors with sulfonated-polyetheretherketone as solid-state electrolyte and multifunctional binder

Sulfonated polyetheretherketone (SPEEK) has been synthesised by sulphonation process and used as the solid-state electrolyte, binder and surfactant for supercapacitors. Reduced graphene dispersed by SPEEK is used as a high-efficiency conducting additive in solid-state supercapacitors. It is found that SPEEK can improve the stability of the reduced graphene dispersion significantly, and therefore, the solid-state supercapacitors show a large decrease in IR drop and charge-transfer resistance (R_ct), resulting in a higher rate capability. The solid-state supercapacitors with the activated carbon/reduced graphene/SPEEK/electrode can be operated from 1 to 8 A/g and exhibit capacity retention of 93%. The noteworthy is more than twice higher value for capacity retention by comparison with the solid-state supercapacitors using activated carbon/reduced graphene/PVDF electrode (capacity retention is 36%). The cell of reduced graphene with SPEEK can be cycled over 5000 times at 5 A/g with no capacitance fading.     

茉莉花中7种金属元素含量及其浸出率研究

茉莉花是我国的健康饮品,由于茉莉花具有药食两用功效,本实验对茉莉花中7种金属元素含量进行了研究,结果表明,茉莉花中含有丰富的人体所必需的金属矿质元素,K、Ca、Mg的含量较多,具有较高的开发利用价值,但不同金属元素含量存在差异。同时对茉莉花进行了全量浸提,不同元素的浸提率存在一定的差异,其中K的浸出率最高。研究结果对人们日常正确选择饮用花茶提供了一定的理论依据,具有一定的实际意义和推广价值。     

Interval-valued probability density estimation based on quasi-continuous histograms: Proof of the conjecture

The sensitivity of histogram computation to the choice of a reference interval and number of bins can be attenuated by replacing the crisp partition on which the histogram is built by a fuzzy partition. This involves replacing the crisp counting process by a distributed (weighted) voting process. The counterpart to this low sensitivity is some confusion in the count values: a value of 10 in the accumulator associated with a bin can mean 10 observations in the bin or 40 observations near the bin. This confusion can bias the statistical decision process based on such a histogram. In a recent paper, we proposed a method that links the probability measure associated with any subset of the reference interval with the accumulator values of a fuzzy partition-based histogram. The method consists of transferring counts associated with each bin proportionally to its interaction with the considered subset. Two methods have been proposed which are called precise and imprecise pignistic transfer. Imprecise pignistic transfer accounts for the interactivity of two consecutive cells in order to propagate, in the estimated probability measure, counting confusion due to fuzzy granulation. Imprecise pignistic transfer has been conjectured to include precise pignistic transfer. The present article proposes a proof of this conjecture.     

Arbitrage valuation and bounds for sinking-fund bonds with multiple sinking-fund dates

The paper tackles the problem of pricing, under interest-rate risk, a default-free sinking-fund bond which allows its issuer to recurrently retire part of the issue by (a) a lottery call at par, or (b) an open market repurchase. By directly modelling zero-coupon bonds as diffusions driven by a single-dimensional Brownian motion, a pricing formula is supplied for the sinking-fund bond based on a backward induction procedure which exploits, at each step, the martingale approach to the valuation of contingent-claims. With more than one sinking-fund date, however, the pricing formula is not in closed form, not even for simple parametrizations of the process for zerocoupon bonds, so that a numerical approach is needed. Since the computational complexity increases exponentially with the number of sinking-fund dates, arbitrage-based lower and upper bounds are provided for the sinking-fund bond price. The computation of these bounds is almost effortless when zero-coupon bonds are as described by Cox, Ingersoll and Ross. Numerical comparisons between the price of the sinking-fund bond obtained via Monte Carlo simulation and these lower and upper bounds are illustrated for different choices of parameters.     

A family of minimax rates for density estimators in continuous time

In continuous time, rates of convergence of density estimators fluctuate with the nature of observed sample paths. In this paper, we give a family of rates reached by the kernel estimator and we show that these rates are minimax. Finally, we study applications of these results for specific classes of processes including the Gaussian ones     

Analysis of industry equilibria in models with sustaining and disruptive technology

This paper analyzes a special type of technology evolution, referred to in the literature as disruptive technology vs. sustaining technology. In general, “old” products based on sustaining technology are perceived to be superior to the “new” ones based on disruptive technology. However, the latter have distinctive features that allow them to attract an exclusive set of customers. Examples include notebooks vs. netbooks, hard-disk drives vs. solid-state drives, laser printers vs. inkjet printers, etc. We consider a model with an established firm and an entrant firm that have heterogeneous product-offering capabilities: the established firm can offer either or both types of products, while the entrant firm can only offer new products. Firms make capacity, pricing, and quantity decisions that maximize their ex-ante profit. Within this framework, we analyze deterministic games with perfect information and stochastic games with uncertain valuation of the disruptive technology. Equilibrium decisions are discussed under various market conditions, as well as under dedicated vs. flexible capacity assumptions.