Operator stable laws: Series representations and domains of normal attraction

LetX,X ₁,X ₂,... be i.i.d. random vectors in ^d. The limit laws that can arise by suitable affine normalizations of the partial sums,S _n=X ₁+...+X _n, are calledoperator-stable laws. These laws are a natural extension to ^d of the stable laws on. Thegeneralized domain of attraction of [GDOA()] is comprised of all random vectorsX whose partial sums can be affinely normalized to converge to . If the linear part of the affine transformation is restricted to take the formn ^–B for some exponent operatorB naturally associated to thenX is in thegeneralized domain of normal attraction of [GDONA()]. This paper extends the theory of operator-stable laws and their domains of attraction and normal attraction.     

The upper and lower second order directional derivatives of a sup-type function

The purpose of this paper is to give a formula for expressing the second order directional derivatives of the sup-type functionS(x) = sup{f(x, t); t T} in terms of the first and second derivatives off(x, t), whereT is a compact set in a metric space and we assume thatf, f/x and ² f/x ² are continuous on ⁿ × T. We will give a geometrical meaning of the formula. We will moreover give a sufficient condition forS(x) to be directionally twice differentiable.     

Minimum concave cost production system: A further generalization of multi-echelon model

We will consider a concave minimization problem associated with a series production system in which raw material is processed inm consecutive facilities. The products at some facility are either sent to the next facility or stocked in the warehouse. The amount of demand for the final products during periodi, i = 1,,n, are known in advance. Our problem is to minimize the sum of processing, holding and backlogging cost, all of which are assumed to be concave.The origin of this model is the classical economic lot size problem of Wagner and Whitin and was extensively studied by Zangwill. This model is very important from the theoretical as well as practical point of view and this is one of the very rare instances in which polynomial time algorithm has been constructed for concave minimization problems.The purpose of this paper is to extend the model further to the situation in which time lag is associated with processing at each facility. We will propose an efficient O(n ⁴ m) algorithm for this class of problems.     

比光谱-导数吸光光度法及其应用与进展

综述了比光谱－导数吸光光度法的基本原理、主要试验条件的选择及其在多组分混合物同时测定中的应用与进展。全文共引用了参考文献50篇。     

取代硫脲化合物对作物的生长调节作用

取代脲类化合物已广泛用作除草剂、杀虫剂、杀鼠剂。根据结构活性关系,亦对烯丙基、甲基、二芳基取代硫脲衍生物的植物生长调节活性进行了研究。本文合成了3类取代硫脲化合物:R_1NHCSNHR_2,其中:R_1=苯基,α-萘基,叔丁基,R_2=α-苯基乙     

核磁共振法测定高聚物的结构—核磁共振二维谱

介绍了核磁共振(NMR)波谱,尤其是核磁共振二维谱(2D NMR)在最近几年内的进展。内容包括怎样用NMR测定高聚物的序列分布、共聚物结构、聚合物的混溶性、聚合物液晶的取向度、分子量、短链度和长链支化度、凝聚态高聚物的多相结构等。     

壳聚糖衍生物的制备及其吸附性能

壳聚糖衍生物的制备及其吸附性能曲荣君，马千里，郑秀丽，孙言志（烟台师范学院化学系烟台２６４０２５）关键词壳聚精衍生物，制备，吸附壳聚糖（ＣＴＳ）是重金瞩离子的吸附剂￣［１，２］，由于壳聚精分子中的－ＮＨ＿２在ｐＨ较低的水溶液易形成而使ＣＴＳ溶于水，造...     

Networks and chain coverings in partial orders and their products

For an arbitrary poset P, subposets {P _i : 1ik} form a transitive basis of P if P is the transitive closure of their union. Let u be the minimum size of a covering of P by chains within posets of the basis, s the maximum size of a family of elements with no pair comparable in any basis poset, and a the maximum size of an antichain in P. Define a dense covering to be a collection D of chains within basis posets such that each element belongs to a chain in D within each basis poset and is the top of at least k-1 chains and the bottom of at least k-1 chains in D. Dense coverings generalize ordinary chain coverings of poset. Let d=min {|D|–(k–1)|P|}. For an arbitrary poset and transitive basis, a convenient network model for dense coverings yields the following: Theorem 1: da, with equality iff P has a minimum chain decomposition in which every pair of consecutive elements on each chain are comparable in some basis poset. Theorem 2: usda. Theorem 3: s=d iff s=a. The most interesting special case is where the transitive basis expresses P as the product of two posets, in which case u and s measure the minimum and maximum sizes of unichain coverings and semiantichains.     

Photopolymerization induced by a benzophenone derivative photoinitiator

A benzophenone derivative photoinitiator, HBP-TDI-HQ-TDI-HBP （HTCTH）, was synthesized based on 4-hydroxy benzophenone （HBP）, toluene-2,4-diisocyanate （TDI） and hydroquinone （HQ）. HTCTH was a more effective photoinitiator which had longer wavelength absorption in the UV-vis absorption spectra than the low molecular counterpart benzophenone （BP）. It showed that both rate of polymerization （Rp） and final conversion （P） increased with increase of amine and HTCTH concentration in photopolymerization.     

Highly Stereoselective Synthesis of trans-3-Aryl-4-carbethoxy-2,3-dihydro-2-fur-2＇-oyl-5-methylfurans

Multi-substituted dihydrofurans are valuable intermediates for the synthesis of natural products and pharmaceuticals. Considerable attention has been focused on the development of efficient and regioselective methods for their preparation. Using K2CO3 as a base, with the reaction of fur-2-oylmethyltriphenylarsonium bromide 1 and ethyl 2-acetyl-3-arylacrylate 2 in tetrahydrofuran at room temperature, we found an efficient protocol was achieved to synthesize trans-3-aryl-4-carbethoxy-2,3-dihydro-2-fur-2＇-oyl-5-methylfurans 3 in good yield with high stereoselectivity. The structure of compound 3 was confirmed by IR, ^1H NMR, MS and HRMS. The mechanism for the formation of 3 was proposed.