Pseudo Approximation Algorithms with Applications to Optimal Motion Planning

We introduce a technique for computing approximate solutions to optimization problems. If $X$ is the set of feasible solutions, the standard goal of approximation algorithms is to compute $x\in X$ that is an $\varepsilon$-approximate solution in the following sense: $$d(x) \leq (1+\varepsilon)\, d(x^*),$$ where $x^* \in X$ is an optimal solution, $d\colon\ X\rightarrow {\Bbb R}_{\geq 0}$ is the optimization function to be minimized, and $\varepsilon>0$ is an input parameter. Our approach is first to devise algorithms that compute pseudo $\varepsilon$-approximate solutions satisfying the bound $$d(x) \leq d(x_R^*) + \varepsilon R,$$ where $R>0$ is a new input parameter. Here $x^*_R$ denotes an optimal solution in the space $X_R$ of $R$-constrained feasible solutions. The parameter $R$ provides a stratification of $X$ in the sense that (1) $X_R \subseteq X_{R}$ for $R < R$ and (2) $X_R = X$ for $R$ sufficiently large. We first describe a highly efficient scheme for converting a pseudo $\varepsilon$-approximation algorithm into a true $\varepsilon$-approximation algorithm. This scheme is useful because pseudo approximation algorithms seem to be easier to construct than $\varepsilon$-approximation algorithms. Another benefit is that our algorithm is automatically precision-sensitive. We apply our technique to two problems in robotics: (A) Euclidean Shortest Path (3ESP), namely the shortest path for a point robot amidst polyhedral obstacles in three dimensions, and (B) $d_1$-optimal motion for a rod moving amidst planar obstacles (1ORM). Previously, no polynomial time $\varepsilon$-approximation algorithm for (B) was known. For (A), our new solution is simpler than previous solutions and has an exponentially smaller complexity in terms of the input precision.     

Observation of radiative B-->phi K gamma decays

The radiative decay B-->phi K gamma is observed for the first time. The branching fraction for the charged B--->phi K- gamma decay mode is measured to be B(B--->phi K- gamma)=(3.4+/-0.9+/-0.4)x10(-6). The photon energy distribution for the B--->phi K- gamma decay is presented. The signal for the neutral B(0)-->phi K(0)gamma decay mode is not statistically significant and an upper limit, B(B(0)-->phi K(0)gamma)<8.3x10(-6) at 90% C.L., is set. The analysis is based on a data set of 90 fb(-1) collected by the Belle experiment at the e(+)e(-) asymmetric collider KEKB.     

Measurement of branching fractions for B-->eta(c)K(*) decays

We report measurements of branching fractions for charged and neutral B-->eta(c)K decays where the eta(c) meson is reconstructed in the K(0)(S)K+/-pi(-/+), K+K-pi(0), K(*0)K-pi(+), and pp; decay channels. The neutral B0 channel is a CP eigenstate and can be used to measure the CP violation parameter sin(2phi(1). We also report the first observation of the B0-->eta(c)K(*0) mode. The results are based on an analysis of 29.1 fb(-1) of data collected by the Belle detector at KEKB.     

Beam-polarization asymmetries for the p(gamma-->, K+)Lambda and p(gamma-->, K+)Sigma(0) reactions for E(gamma)=1.5-2.4 GeV

Beam polarization asymmetries for the p(gamma-->,K+)Lambda and p(gamma-->,K+)Sigma(0) reactions are measured for the first time for E(gamma)=1.5-2.4 GeV and 0.6相似文献   

ESR investigation on the breather mode and the spinon-breather dynamical crossover in Cu benzoate

A "breather excitation" is observed directly by electron spin resonance in the quantum spin chain Cu benzoate, in which an unexpected field-induced gap has recently been found. The nonlinear field dependence of the resonance field agrees well with the formula based on a quantum sine-Gordon model. The power-law temperature dependence of the linewidth is observed in the gapless spinon regime while the width decreases exponentially for the gapped breather regime. In the intermediate range, a distinct anomaly is found, which is the manifestation of "the spinon-breather dynamical crossover."     

Aromaticity and π-bond covalency: prominent intermolecular covalent bonding interaction of a Kekulé hydrocarbon with very significant singlet biradical character

An anthracene-linked bisphenalenyl Kekulé molecule with very significant singlet biradical character has shown a prominent covalent bonding interaction between molecules in a molecular aggregate. High aromatic stabilization energy in the anthracene linker is responsible for the significant singlet biradical character.     

Behaviors of sodium glycochenodeoxycholate and sodium glycoursodeoxycholate in binary mixed micelles of bile salt and nonionic surfactant

The behavior of sodium glycochenodeoxycholate (NaGCDC) and sodium glycoursodeoxycholate (NaGUDC) in binary mixed micelles consisting of bile salt and octaoxyethylene glycol mono n-decyl ether (C₁₀E₈) has been studied on the basis of micellar compositions, polarities of the interior of intramicelles, mean aggregation numbers and ¹H NMR measurements. Micellar compositions for both NaGCDC---C₁₀E₈ and NaGUDC---C₁₀E₈ systems showed a tendency to change from C₁₀E₈-rich micelles to bile-salt-rich micelles with an increase on the mole fraction of bile salts from the results of both theoretical calculations using the critical micelle concentration and the micellar polarity. The microenvironment of intramicelles for the NaGCDC---C₁₀E₈ system was found to be more hydrophobic than that for the NaGUDC---C₁₀E₈ system. Mean aggregation numbers of mixed micelles for both systems decreased abruptly with an increase in the mole fraction of bile salts in the range of low mole fraction, but those for NaGCDC were larger than those for NaGUDC. Furthermore, from the results of ¹H NMR measurements, the motions of the methyl group protons in the 18 position of the molecular structure of NaGCDC were slightly restricted with an increase in the mole fraction of NaGCDC. In contrast, the methyl group protons in the 18 and 19 positions of the molecular structure of NaGUDC became freer with an increase in the mole fraction of NaGUDC.     

Total synthesis of the antiviral marine natural product (-)-hennoxazole A

[structure:see text] The marine natural product hennoxazole A was synthesized by a convergent approach. The diastereoselective Mukaiyama aldol reaction with beta-alkoxy aldehyde was used to construct the tetrahydropyran segment, and the preparation of the nonconjugated triene moiety was accomplished via S(N)2 displacement of allylic bromide with vinyllithium and Takai's iodoolefination followed by palladium-catalyzed cross coupling with MeMgBr. The final steps involve an amide coupling using DEPC and oxazole synthesis via a oxidation/cyclodehydration process.     

Organotrichlorogermane synthesis by the reaction of elemental germanium, tetrachlorogermane and organic chloride via dichlorogermylene intermediate

Organotrichlorogermanes were synthesized by the reaction of elemental germanium, tetrachlorogermane and organic chlorides, methyl, propyl, isopropyl and allyl chlorides. Dichlorogermylene formed by the reaction of elemental germanium with tetrachlorogermane was the reaction intermediate, which was inserted into the carbon-chlorine bond of the organic chloride to give organotrichlorogermane. When isopropyl or allyl chloride was used as an organic chloride, organotrichlorogermane was formed also in the absence of tetrachlorogermane. These chlorides were converted to hydrogen chloride, which subsequently reacted with elemental germanium to give the dichlorogermylene intermediate. The reaction of elemental germanium, tetrachlorogermane and organic chlorides provides a simple and easy method for synthesizing organotrichlorogermanes, and all the raw materials are easily available.