Optimal Planar Interception with Fixed End Conditions: Approximate Solutions

In a previous paper (Ref. 1), an exact solution of the optimal planar interception with fixed end conditions was derived in closed form. The optimal control was expressed as an explicit function of the state variables and two fixed parameters, obtained by solving a set of nonlinear algebraic equations involving elliptic integrals. In order to facilitate the optimal control implementation, the present paper derives a highly accurate simplified solution assuming that the ratio of the pursuer turning radius to the initial range is small. An asymptotic expansion further reduces the computational workload. Construction of a near-optimal open-loop control, based on the approximations, completes the present paper.     

非线性光纤方向耦合器孤子动力特性分析

利用变分方法,导出了双曲正割型光孤子在非线性光纤耦合器中传输时满足的动力学方程组,分析了该方程组的平衡点性态,讨论了光孤子的开关特性.指出参数|β|<2π.是能实现完全的开关操作的必要条件.     

Beryllium coordination chemistry

The coordination chemistry of beryllium with particular emphasis on chelates under physiological or near physiological conditions is surveyed. Hard donors such as oxygen are emphasized; equilibrium data and formation constants are reported as an indication of the strength of the complex.     

Synthesis of lanosterol derivatives with a functional group at C-32, including an antineoplastic sterol, 3 beta-hydroxylanost-7-en-32-oic acid

Lanosterol derivatives with a functional group at C-32 have been synthesized from 3 beta-acetoxylanostan-7 alpha-ol. The key reaction of the synthesis is the hypoiodite reaction of 3 beta-acetoxylanostan-7 alpha-ol. In vitro antitumor activity testing of the lanosterol derivatives revealed that 3 beta-hydroxylanost-7-en-32-oic acid has antineoplastic activity.     

Spontaneous magnetization of the Ising model on a 4–8 lattice

The spontaneous magnetization of the Ising model on a 4–8 lattice with six different coupling constants and two different magnetic moments is studied. A formula for the spontaneous magnetization is proposed. The result agrees with the exact low-temperature series expansions up to the 12th order.     

Amino acids and peptides. XIII. Synthetic studies on N-terminal tripeptide amide analogs of fibrin alpha-chain

N-Terminal tripeptide analogs of fibrin alpha-chain were synthesized and their inhibitory effect on fibrinogen/thrombin clotting was examined. A new water-soluble active ester, 3-pyridinium ester, was used for the synthesis. Among the synthetic peptides, H-Gly-Pro-Arg-hexamethyleneimine exhibited the highest inhibitory effect on fibrinogen-thrombin clotting.     

Mode of complement activation by acidic heteroglycans from the leaves of Artemisia princeps PAMP.

The mode of action of the anti-complementary acidic heteroglycans, AAF-IIb-2 and IIb-3 which consisted of rhamnogalacturonan core and arabinogalactan moieties, purified from the leaves of Artemisia princeps PAMP (Japanese name = Gaiyo) were investigated. The anti-complementary activities of AAF-IIb-2 and IIb-3 were reduced partially in the absence of Ca2+ ions. A marked consumption of C4 was observed to have occurred when serum was incubated with both polysaccharides in the presence of Ca2+ ions. AAF-IIb-2 showed more potent C4 consumption than IIb-3. After the incubation of the serum with AAF-IIb-2 in the absence of Ca2+ ions, a cleavage of C3 in the serum was detected by immunoelectrophoresis. AAF-IIb-2 showed more significant consumption of the complement than IIb-3 when rabbit erythrocytes were used in the assay system in the absence of Ca2+ ions. These results indicate that AAF-IIb-2 activates the complement via both the alternative and classical pathways, whereas IIb-3 mainly activates the complement via the classical pathway. The absorption of serum with Protein A-Sepharose results in a decrease of the activity of AAF-IIb-2 and IIb-3. However, the decrease of the activity was restored by the replacement of the immunoglobulin G (IgG) fraction after its recovery from the Protein A-Sepharose. These results suggest that IgG dependent mechanisms are both involved in the anti-complementary activity of AAF-IIb-2 and IIb-3.     

Hilbert重级数定理的一个改进

The object of this note is to prove the followingTheorem Let{a_n}and{b_n}be sequences of real numbers such that0<∑∑a_n~2<+∞and0<∑b_n~2<+∞.Then we have the inequalitysum from m=1 to∞sum from n=1 to∞a_mb_n/m+n<{sum from n=1 to∞(π-θ/n~(1/2)a_n~2}~1/2{sum from n=1 to∞(π-θ/n~(1/2)b_n~2}~1/2 (1)whereθ=3/2~(1/2)-1=1.121320343.