Decomposability in the space of HKP‐integrable functions

In this paper we introduce the notion of decomposability in the space of Henstock‐Kurzweil‐Pettis integrable (for short HKP‐integrable) functions. We show representations theorems for decomposable sets of HKP‐integrable or Henstock integrable functions, in terms of the family of selections of suitable multifunctions.     

A generalized hypergreedy algorithm for weighted perfect matching

We give a generalization of the hypergreedy algorithm for minimum weight perfect matching on a complete edge weighted graph whose weights satisfy the triangle inequality. With a modified version of this algorithm we obtain a logn-approximate perfect matching heuristic for points in the Euclidean plane, inO(n log² n) time.This research was supported in part by the DIMACS Grant No. NSF-STC88-09648.This research was supported in part by the NSF under Grant No. CCR 88-07518.     

SO_4~(2-)_ZrO_2-TiO_2催化剂的制备及性能

本文用三种不同的方法制备了SO_4~(2-)/ZrO_(2-)TiO_2催化剂,并用Caro Eala自动吸附仪、PE683型红外光谱仪及LCT-2型高温差热天平仪分别有选择地测定了催化剂比表面及催化剂表面硫酸根的红外吸收光谱、脱附量、脱附温度,还测定了对酯化反应的催化性能。同时,讨论了制备条件和方式对催化剂性能的影响。     

The fixed point property in -triples and preduals of -triples

We prove that for every member X in the class of real or complex JB^*-triples or preduals of JBW^*-triples, the following assertions are equivalent:

(1) X has the fixed point property.

(2) X has the super fixed point property.

(3) X has normal structure.

(4) X has uniform normal structure.

(5) The Banach space of X is reflexive.

As a consequence, a real or complex C^*-algebra or the predual of a real or complex W^*-algebra having the fixed point property must be finite-dimensional.

An integro-differential equation model for alignment and orientational aggregation

We study an integro-differential equation modeling angular alignment of interacting bundles of cells or filaments. A bifurcation analysis of the related stationary problem was done by Geigant and Stoll in [E. Geigant, M. Stoll, Bifurcation analysis of an orientational aggregation model, J. Math. Biol. 46 (6) (2003) 537-563]. Here we analyze the time-dependent problem and prove that the type of alignment (one- or multi-directional) depends on the initial distribution, the interaction potential, and the preferred optimal orientation of the bundles of cells or filaments. Our main technical tool is the analysis of the evolution of suitable functionals for the cell density, which allows to also specify the direction(s) where the final alignment takes place.     

碱性电解液中K3[Fe(CN)6]在锌阳极上的自发还原和吸附延长锌镍电池的循环寿命

In view of the continuously worsening environmental problems, fossil fuels will not be able to support the development of human life in the future. Hence, it is of great importance to work on the efficient utilization of cleaner energy resources. In this case, cheap, reliable, and eco-friendly grid-scale energy storage systems can play a key role in optimizing our energy usage. When compared with lithium-ion and lead-acid batteries, the excellent safety, environmental benignity, and low toxicity of aqueous Zn-based batteries make them competitive in the context of large-scale energy storage. Among the various Zn-based batteries, due to a high open-circuit voltage and excellent rate performance, Zn-Ni batteries have great potential in practical applications. Nevertheless, the intrinsic obstacles associated with the use of Zn anodes in alkaline electrolytes, such as dendrite, shape change, passivation, and corrosion, limit their commercial application. Hence, we have focused our current efforts on inhibiting the corrosion and dissolution of Zn species. Based on a previous study from our research group, the failure of the Zn-Ni battery was caused by the shape change of the Zn anode, which stemmed from the dissolution of Zn and uneven current distribution on the anode. Therefore, for the current study, we selected K₃[Fe(CN)₆] as an electrolyte additive that would help minimize the corrosion and dissolution of the Zn anode. In the alkaline electrolyte, [Fe(CN)₆]^3– was reduced to [Fe(CN)₆]^4– by the metallic Zn present in the Zn-Ni battery. Owing to its low solubility in the electrolyte, K₄[Fe(CN)₆] adhered to the active Zn anode, thereby inhibiting the aggregation and corrosion of Zn. Ultimately, the shape change of the anode was effectively eliminated, which improved the cycling life of the Zn-Ni battery by more than three times (i.e., from 124 cycles to more than 423 cycles). As for capacity retention, the Zn-Ni battery with the pristine electrolyte only exhibited 40% capacity retention after 85 cycles, while the Zn-Ni battery with the modified electrolyte (i.e., containing K₃[Fe(CN)₆]) showed 72% capacity retention. Moreover, unlike conventional organic additives that increase electrode polarization, the addition of K₃[Fe(CN)₆] not only significantly reduced the charge-transfer resistance in a simplified three-electrode system, but also improved the discharge capacity and rate performance of the Zn-Ni battery. Importantly, considering that this strategy was easy to achieve and minimized additional costs, K₃[Fe(CN)₆], as an electrolyte additive with almost no negative effect, has tremendous potential in commercial Zn-Ni batteries.     

聚(碳酸丁二醇酯-co-三环癸烷二甲醇碳酸酯)的制备与性能

采用熔融酯交换和缩聚两步法,合成了以1,4-丁二醇、4,8-三环[5.2.1.0(2,6)]癸烷二甲醇和碳酸二苯酯为原料的聚(碳酸丁二醇酯-co-三环癸烷二甲醇碳酸酯)(PBTCx, x为进料中TCD占二元醇总量的百分比)。用1H NMR和13C NMR对PBTCs的微观结构和组成进行了表征。采用GPC、 DSC、 XRD、 TG对PBTCs的分子量、玻璃化转变温度(Tg)、热稳定性等进行了研究。结果表明,PBTCs的Mw为10500~124800 g?mol-1, Mn为6300~73000 g?mol-1, PDI为1.59~1.73; PBTCs呈无定形态、Tg为-3.43 ℃~70.90 ℃, PBTCs表现出比PBC更高的热稳定性。薄膜拉伸试验结果表明,PBTC30(拉伸强度为33.54 MPa,断裂伸长率为275.69%)和PBTC40(拉伸强度为32.13 MPa,断裂伸长率为294.63%)具有较高的强度和韧性,在薄膜材料中具有一定的应用潜力。     

Integrated mean square properties of density estimation by orthogonal series methods for dependent variables

Summary The rates at which integrated mean square and mean squre errors of nonparametric density estimation by orthogonal series method for sequences of strictly stationary strong mixing random variables are obtained. These rates are better than those known to hold for the independent case and they are shown to hold for Markov processes. In fact our results when specialized to the independent case are improvements over previously known results of Schwartz (1967,Ann. Math. Statist.,38, 1262–1265). An extension of the results to estimation of the bivariate density is also given. Research supported by a faculty summer research grant MS-STAT-42 from the University of Petroleum and Minerals.     

Two strong limit theorems for processes with independent increments

Two related almost sure limit theorems are obtained in connection with a stochastic process {ξ(t), ?∞ < t < ∞} with independent increments. The first result deals with the existence of a simultaneous stabilizing function H(t) such that $\text{(ξ(t) ? ξ(0))}\text{H(t)}\text{→ 0}$ for almost all sample functions of the process. The second result deals with a wide-sense stationary process whose random spectral distributions is ξ. It addresses the question: Under what conditions does $\text{(2T)}{}^{\mathrm{?1}}\text{∫}{}_{\mathrm{?T}}{}^{\mathrm{T}}\text{X(t)}\text{X(t + τ)}\text{dt}$ converge as T → ∞ for all τ for almost all sample functions?     

On the spectral representation of symmetric stable processes

The so-called spectral representation theorem for stable processes linearly imbeds each symmetric stable process of index p into L^p (0 < p ≤ 2). We use the theory of L^p isometries for 0 < p < 2 to study the uniqueness of this representation for the non-Gaussian stable processes. We also determine the form of this representation for stationary processes and for substable processes. Complex stable processes are defined, and a complex version of the spectral representation theorem is proved. As a corollary to the complex theory we exhibit an imbedding of complex L^q into real or complex L^p for 0 < p < q ≤ 2.