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Notes: The study was conducted to determine the effect of dietary supplementation of vitamin C on anti-acid stress ability in juvenile soft-shelled turtle. The soft-shelled turtles were fed vitamin C supplemented diets at levels of 0, 250, 500, 2500, 5000 and 10 000 mg kg−1 for 4 weeks. The results showed that the phagocytic rate of blood cell in the group fed vitamin C deficient diets, the serum bacteriolytic activity in the two groups fed vitamin C supplemented diet at 0 and 250 mg kg−1 and the serum bactericidal activity in all groups after acid stress significantly decreased compared with those of before stress (P 〈 0.1). The phagocytic rate of blood cells in the two groups fed vitamin C supplemented diet at 2500 and 5000 mg kg−1 were significantly higher than those of the four groups fed at 0, 250, 500 and 10 000 mg kg−1 (P 〈 0.01). The serum bacteriolytic activity in the groups fed vitamin C supplemented diet at 500, 2500, 5000 and 10 000 mg kg−1 were significantly higher than that of the group fed vitamin C deficient diets (P 〈 0.05), and the two groups fed vitamin C at 2500 and 5000 mg kg−1 were significantly higher than those of the groups fed at 250 and 10 000 mg kg−1 (P 〈 0.05). The serum bactericidal activities in the four groups fed vitamin C supplemented diet at 500, 2500, 5000 and 10 000 mg kg−1 were significantly higher than those of the two groups fed at 0 and 250 mg kg−1 diet (P 〈 0.01), and the two groups fed vitamin C at 2500 and 5000 mg kg−1 were significantly higher than those of the two groups fed at 500 and 10 000 mg kg−1 (P 〈 0.1). These results suggest that supplementation of vitamin C higher than 250 mg kg−1 is necessary to reduce the adverse effects of acid stress.

Notes: Abstract In this paper, a weak law of large numbers is obtained for the range of two dimensional reversible random walk in a random environment.

Notes: Abstract The diffusive behavior for a system of directed polymers in a random environment was first rigorously discussed by Imbrie and Spencer, and then by Bolthausen. By means of some basic properties of martingales we extend some results due to Imbrie and Spencer concerning the asymptotic behaviour of the mean square displacement. We also obtain a Wiener process behaviour with probability one for this system. Bolthausen already used some martingale limit theorems to prove a central limit theorem for this system.

Notes: Abstract In this paper, we generalize a theorem due to Telcs concerning random walks on infinite graphs, which describes the relation of random walk dimension, fractal dimension and resistance dimension. Moreover, we obtain a reasonable upper bound and lower bound on the hitting time in terms of resistance for some nice graphs. In fact, the conditions given in this paper are weaker than those obtained by A. Telcs.

Notes: Abstract We address the problem of processing a set of jobs on a single machine under random due dates with a common distribution. The processing times of the jobs are exponentially distributed random variables with means μ i , and the machine is subject to stochastic breakdowns governed by a Poisson process. Each job i is associated with a job-dependent weight w i . The objective is to schedule the jobs so as to minimize the expected sum of the weighted earliness and tardiness costs of all jobs, which are quadratic functions of the deviations of job completion times from the due dates. We show that the problem is NP-complete. Nevertheless, important optimality properties exist, which can be utilized to develop effective algorithms to solve the problem. Specifically, we prove that, in the case where the weights assigned to both the earliness and tardiness are symmetric, an optimal sequence for the problem must be V-shaped with respect to {μ i /w i }, in the sense that the sequence will first process jobs in a nonincreasing order of {μ i /w i } and then in a nondecreasing order of {μ i /w i }. In the case where asymmetric weights are assigned to the earliness and tardiness costs, the optimal sequence must also be V-shaped with respect to {μ i /w i }, if the due dates are exponentially distributed. Dynamic programming algorithms are proposed which can find the best V-shaped sequences.

Notes: Abstract Let {S 1 (n)} n≥0and {S 2 (n)} n≥0be independent simple random walks in Z 4 starting at the origin, and let % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaaiabfc6aqnaaBaaaleaacaqGPbaabeaatCvAUfKttLearyqr1ngB% Prgaiuaakiab-HcaOiaadggacaGGSaGaamOyaiab-LcaPiabg2da9i% ab-Tha7Hqbciab+Hha4jabgIGiolab+PfaAnaaCaaaleqabaGaaGin% aaaakiaacQdaieGacaqFtbWaaSbaaSqaaiaabMgaaeqaaOGae8hkaG% Iaa0xBaiab-LcaPiabg2da9iab+Hha4baa!5761!\[\Pi _{\rm{i}} (a,b) = \{ x \in Z^4 :S_{\rm{i}} (m) = x\]for the some % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaaGqaciaa-1gacqGHiiIZtCvAUfKttLearyqr1ngBPrgaiuaacqGF% OaakcaWGHbGaaiilaiaadkgacqGFPaqkcqGF9bqFaaa!4936!\[m \in (a,b)\} \]. Let two integervalued sequences {a n}n≥0and {b n}n≥0be given, such that the limit limn→∞ a nexists and lim n →∞ b n=+∞. In this paper, it is shown that the probability of % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaaiabfc6aqnaaBaaaleaacaaIXaaabeaatCvAUfKttLearyqr1ngB% Prgaiuaakiab-HcaOiab-bdaWiab-XcaSiabg6HiLkab-LcaPiabgM% Iihlabfc6aqnaaBaaaleaacaaIYaaabeaakiab-HcaOiaadggadaWg% aaWcbaGaamOBaiaacYcaaeqaaOGaamyyamaaBaaaleaacaWGUbaabe% aakiabgUcaRiaadkgadaWgaaWcbaGaamOBaaqabaGccqWFPaqkcqGH% GjsUieaacaGFydaaaa!5904!\[\Pi _1 (0,\infty ) \cap \Pi _2 (a_{n,} a_n + b_n ) \ne \O \] is asymptotic to % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaamaalaaabaGaaGymaaqaaiaaikdaaaGaciiBaiaac+gacaGGNbWe% xLMBb50ujbqeguuDJXwAKbacfaGae8hkaGIae8xmaeJae83kaSIaam% OyamaaBaaaleaacaWGUbaabeaakiaac+cacaWGHbWaaSbaaSqaaiaa% d6gaaeqaaOGae8xkaKIae83la8IaciiBaiaac+gacaGGNbGaamOyam% aaBaaaleaacaWGUbaabeaaaaa!5364!\[\frac{1}{2}\log (1 + b_n /a_n )/\log b_n \] if it tends to zero as n→∞, and the probability of % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaaiabfc6aqnaaBaaaleaacaaIXaaabeaatCvAUfKttLearyqr1ngB% Prgaiuaakiab-HcaOiab-bdaWiab-XcaSiabg6HiLkab-LcaPiabgM% Iihlabfc6aqnaaBaaaleaacaaIYaaabeaakiab-HcaOiaadggadaWg% aaWcbaGaamOBaaqabaGccaGGSaGaamyyamaaBaaaleaacaWGUbaabe% aakiabgUcaRiaadkgadaWgaaWcbaGaamOBaaqabaGccqWFPaqkcqWF% 9aqpieaacaGFydaaaa!583C!\[\Pi _1 (0,\infty ) \cap \Pi _2 (a_n ,a_n + b_n ) = \O \]is asymptotic to % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% abaeqabaaabaGaam4yaiaacUfaciGGSbGaai4BaiaacEgatCvAUfKt% tLearyqr1ngBPrgaiuaacqWFOaakcaWGHbWaaSbaaSqaaiaad6gaae% qaaOGaey4kaSIaamOyamaaBaaaleaacaWGUbaabeaakiab-LcaPiab% -9caViab-XgaSjab-9gaVjab-DgaNjab-HcaOiaadggadaWgaaWcba% GaamOBaaqabaGccqGHRaWkcaaIYaGae8xkaKIae8xxa01aaWbaaSqa% beaacqWFTaqlcqWFXaqmcqWFVaWlcqWFYaGmaaaaaaa!5BAC!\[\begin{array}{l} \Pi _1 (0,\infty ) \cap \Pi _2 (a_n ,a_n + b_n ) = \O \\ c[\log (a_n + b_n )/log(a_n + 2)]^{ - 1/2} \\ \end{array}\], for some constant c, if it tends to a finite constant (≤1) as n→∞. These results extend some results obtained by G. F. Lawler about the intersection properties of simple random walks in Z 4. By using similar arguments, we also get corresponding results for the intersections of Wiener sausages in four dimensions. In particular, a conjecture suggested by M. Aizenman, which describes nonintersection of independent Wiener sausages in R 4, is proven.

Notes: Abstract This paper is concerned with the exact Bahadur efficiencies of spacings statistics. For a general class of statistics based on a fixed number of spacings, the explicit forms of the exact slopes are derived, and it is shown that the sum of the logarithms of spacings is optimal in this class. Some results are extended to the case where the number of spacings increase with the sample size to infinity.

Notes: Al alloy reinforced with SiCp (size: 70-220μm) was fabricated by pressureless-infiltration. Itswear resistant property was investigated under different heat-treatment conditions, and morphology ofworn surface was examined. The results showed that the composite was integrated, uniform and compact,and its wear resistant property was better than that of the unreinforced matrix alloy. It was indicated thatsome rigid SiCp in the abraded surface of the composite could support part of loads and replace matrix towear-tear, which improved the wear resistant property. Compared to annealing, solution agingstrengthens Al alloy matrix and cohesion with SiCp, and the wear resistant property of composites wasbetter. Combining interface is also an important factor which influences on wear resistant property.During the wear test, the smaller SiCp size, the more interfaces, there are more SiCp falling off because ofloosening combining interface, which results in more wear-tearing value. The wear rate of compositeincreases with decreasing SiCp size, thus, the composite with larger SiCp has better wear-resistantproperty than that with smaller SiCp. At last, the wear mechanism of the composite was also studied, andit showed that abrasive wear dominated in the abrasion process