含间断项的微分方程终值问题的拟上下解方法

在不涉及紧型条件的情形下,利用半序理论和混合单调迭代技术研究了Banach空间中含间断项的一阶微分方程终值问题解的存在唯一性;并给出逼近解迭代序列的误差估计.     

Banach空间一类非线性算子方程的迭代求解及应用

在不假定锥正规、再生和算子连续的条件下,利用锥理论和单调迭代方法证明了一类非线性算子方程x=A(x,x)解的存在性定理,并应用于Banach空间一阶微分方程的终值问题.     

Smooth solutions to portfolio liquidation problems under price-sensitive market impact

We consider the stochastic control problem of a financial trader that needs to unwind a large asset portfolio within a short period of time. The trader can simultaneously submit active orders to a primary market and passive orders to a dark pool. Our framework is flexible enough to allow for price-dependent impact functions describing the trading costs in the primary market and price-dependent adverse selection costs associated with dark pool trading. We prove that the value function can be characterized in terms of the unique smooth solution to a PDE with singular terminal value, establish its explicit asymptotic behavior at the terminal time, and give the optimal trading strategy in feedback form.     

Stochastic models for air cargo terminal manpower supply planning in long‐term operations

In this research, based on two deterministic‐demand planning models, we established two long‐term stochastic‐demand planning models by incorporating the stochastic disturbances of manpower demands that occur in actual operations. The models are formulated as mixed integer linear programs that are solved using a mathematical programming solver. To compare the performance of the two stochastic‐demand and two deterministic‐demand planning models under the stochastic demands that occur in actual operations, we further develop a simulation‐based evaluation method. Finally, we perform numerical tests using real operating data from a Taiwan air cargo terminal. The preliminary results show that the stochastic models could be useful for planning air cargo terminal manpower supply. Copyright © 2008 John Wiley & Sons, Ltd.     

Higher dimensional aposyndetic decompositions

Let be a homogeneous, decomposable continuum that is not aposyndetic. The Aposyndetic Decomposition Theorem yields a cell-like decomposition of into homogeneous continua with quotient space being an aposyndetic, homogeneous continuum.

Assume the dimension of is greater than one. About 20 years ago the author asked the following questions:

Can this aposyndetic decomposition raise dimension? Can it lower dimension? We answer these questions by proving the following theorem.

Theorem. The dimension of the quotient space is one.

     

Synthesis of hydrogels from a polymeric N,N′-diallyl-N,N′-dimethylammonium salt

Feasibility in principle has been demonstrated for obtaining hydrogels with controlled parameters of the three-dimensional network by copolymerization of N,N-methylenebisacrylamine with macromolecules of poly-N,N-diallyl-N,N-dimethylammonium chloride containing terminal double bonds, i.e., with macromonomers of N,N-diallyl-N,N-dimethylammonium chloride. The hydrogels that are obtained have high anion-exchange capacities.A. V. Topchiev Institute of Petrochemical Synthesis, Academy of Sciences of the USSR, Moscow 117912. Translated from Izvestiya Akademii Nauk, Seriya Khimicheskaya, No. 4, pp. 851–854, April, 1992.     

Revisiting the design of experiments for copolymer reactivity ratio estimation

Tidwell and Mortimer used the D-optimal criterion to design terminal model reactivity ratio estimation experiments. In this paper, two problems are investigated which were not addressed by Tidwell and Mortimer. The first problem is the design of reactivity ratio estimation experiments subject to composition constraints. It is shown that all the key information contained in the D-optimal criterion can be summarized in two equations: one which is a function of r?₁, and one which in a function of r?₂. These two equations can be used to design reactivity ratio estimation experiments under composition constraints which are within 3 mol % of the D-optimal feed compositions. The second problem is the design of penultimate reactivity ratio estimation experiments. The D-optimal criterion for the penultimate model was derived and optimized for two existing systems as well as a large number of hypothetical systems. The D-optimal criterion for the penultimate model was found to be much more complicated than the terminal model criterion. For this reason, the optimal penultimate reactivity ratio estimation experiments can not be approximated by simple equations. Anyone interested in designing such experiments must derive and optimize the D-optimal criterion. © 1993 John Wiley & Sons, Inc.     

Thermodynamic properties of the first to fifth generations of carbosilane dendrimers with allyl terminal groups

Temperature dependences of the specific heats, characteristic temperatures, and enthalpies of physical transformations of the first to fifth generations of carbosilane dendrimers with allyl terminal groups were studied using an adiabatic vacuum calorimeter in the temperature range 6—340 K. The error of measurements was, as a rule, about 0.2%. Thermodynamic characteristics of physical transformations of the dendrimers were determined and their thermodynamic functions C _p°(T), H°(T)—H°(0), S°(T)—S°(0), and G°(T)—H°(0) were calculated for the temperature range 0—340 K. The thermodynamic functions of the dendrimers are linearly related to their molecular weights, the number of allyl groups on their outer spheres, and the number of moles of diallylmethylsilane per mole of the dendrimers formed. Additive dependence of the properties of the dendrimers on their chemical composition and structure indicates that the energy of interaction between structural fragments of the dendrimers is independent of the dendrimer generation number. The fractal dimensions, D, of all dendrimers studied in this work are 1.2—1.3 in the temperature range 30—50 K, thus indicating a chain-layered structure of the dendrimer glasses.