Parameter identification and optimization algorithm in microbial continuous culture

In this study, a novelty mathematical model is established to formulate the continuous culture of glycerol to 1,3-Propanediol (1,3-PD) by Klebsiella pneumoniae, in which the inhibition of 3-hydroxypropionaldehyde (3-HPA) to cells growth and activity of some enzymes (such as glycerol dehydratase (GDHt) and 1,3-PD oxidoreductase (PDOR)), and the passive diffusion and active transport of glycerol and 1,3-PD across cell membrane are all taken into consideration. Taking the mean relative error between the experimental data and calculated values as the performance index, a parameter identification model involving multiple nonlinear dynamic systems is presented. The identifiability of the parameter identification model is also proved. Finally, an improved particle swarm optimization (PSO) algorithm is constructed to find the optimal parameters for the systems under substrate limitation and excess conditions, respectively. Numerical results not only show that the established model can be used to describe the continuous fermentation reasonably, but also the improved PSO algorithm is valid.     

Topology and topological sequence entropy

Let X be a compact metric space and T:X-→X be continuous.Let h*(T)be the supremum of topological sequence entropies of T over all the subsequences of Z+and S(X)be the set of the values h*(T)for all the continuous maps T on X.It is known that{0}■S(X)■{0,log 2,log 3,...}∪{∞}.Only three possibilities for S(X)have been observed so far,namely S(X)={0},S(X)={0,log 2,∞}and S(X)={0,log 2,log 3,...}∪{∞}.In this paper we completely solve the problem of finding all possibilities for S(X)by showing that in fact for every set{0}?A?{0,log 2,log 3,...}∪{∞}there exists a one-dimensional continuum XAwith S(XA)=A.In the construction of XAwe use Cook continua.This is apparently the first application of these very rigid continua in dynamics.We further show that the same result is true if one considers only homeomorphisms rather than continuous maps.The problem for group actions is also addressed.For some class of group actions(by homeomorphisms)we provide an analogous result,but in full generality this problem remains open.     

Level 17 Ramanujan–Sato series

The Ramanujan Journal - Two level 17 modular functions $$\begin{aligned} r = q^2 \prod _{n=1}^{\infty } (1-q^{n})^{\left( \frac{n}{17} \right) },\qquad s = q^{2} \prod _{n=1}^{\infty } \frac{(1 -...     

Almost periodic solutions for neutral‐type neural networks with the delays in the leakage term on time scales

In this paper, a class of neutral‐type neural networks with delays in the leakage term on time scales are considered. By using the Banach fixed point theorem and the theory of calculus on time scales, some sufficient conditions are obtained for the existence and exponential stability of almost periodic solutions for this class of neural networks. The results of this paper are new and complementary to the previously known results. Finally, an example is presented to illustrate the effectiveness of our results. Copyright © 2016 John Wiley & Sons, Ltd.     

The extension of a quantized Borcherds superalgebra by a Hopf algebra

A two-parameter quantum group is obtained from the usual enveloping algebra by adding two commutative grouplike elements. In this paper, we generalize this procession further by adding commutative grouplike elements b_(ik), c_(ik), g_(ik), h_(ik)(i ∈I, k = 1,..., mi) of a Hopf algebra H to the quantized enveloping algebra U_q(G) of a Borcherds superalgebra G defined by a symmetrizable integral Borcherds–Cartan matrix A =(aij)i,j∈I. Therefore, we define an extended Hopf superalgebra HU_q(G). We also discuss the basis and the grouplike elements of HU_q(G).     

雷公藤内酯醇和缬沙坦对高糖诱导小鼠足细胞活性的影响

目的观察不同浓度高糖对小鼠足细胞活性的抑制作用,以及不同浓度雷公藤内酯醇（TP）和缬沙坦（Val）对高糖抑制后小鼠足细胞活性的影响,探讨高糖对足细胞的损伤作用,以及有效的药物干预浓度范围。方法将培养成熟的小鼠足细胞随机分为对照组（11.1mmol/L葡萄糖）和不同浓度高糖组（16.1、21.1、26.1、31.1、36.1mmol/L）,以上述浓度培养48h后采用CCK-8检测足细胞活性的变化。取活性变化最大的浓度为高糖诱导浓度,在此基础上随机分为不同浓度的TP组（4、8、16、32、64ng/ml）和Val组（2×10-8、2×10-7、2×10-6、2×10-5、2×10-4mol/L）,以上述浓度干预48h后,采用CCK-8检测足细胞活性的变化。结果（1）与对照组相比,除16.1mmol/L高糖组外,其余各高糖组的足细胞活性显著减少,其中以26.1mmol/L葡萄糖组减少最为明显（P＜0.01）。（2）与26.1mmol/L葡萄糖组相比,TP组（除4ng/ml组外）和Val组（除2×10-8mol/L组外）足细胞活性部分恢复,其中以16ng/mlTP组和2×10-5mol/LVal组足细胞活性恢复最为明显（P＜0.01）。结论一定浓度范围的TP和Val可部分恢复受高糖抑制的小鼠足细胞活性。     

以胶原蛋白为基质的肠内营养制剂应用效果多中心临床研究

目的通过多中心随机对照的临床试验研究,比较以胶原蛋白为基质的新型肠内营养制剂与标准型肠内营养制剂对患者营养状况的影响,以了解新型肠内营养制剂的临床应用效果。方法本研究共6家医疗单位共同参与,共收集91例,分为对照组（标准肠内营养）及干预组（以胶原蛋白为基质的肠内营养）,管饲补充104.6~125.5kJ（25~30kcal）/（kg·d）,共7d,检测研究开始前后患者体格指标、营养相关指标、安全性指标等。结果组内比较显示两组患者在管饲两种不同的肠内营养制剂后营养风险筛查评分（NRS2002）较管饲前均有所降低（均P＜0.025）;组间差值比较显示患者营养状况、营养风险筛查（NRS2002）评分、胃肠道不良反应在两组间均无统计学差异（均P＞0.025）。结论以胶原蛋白为基础经氨基酸模式优化后的肠内营养制剂与标准型肠内营养制剂均可以有效改善患者的营养状况,有助于促进患者的疾病预后。     

急性脑梗死患者脑微出血的发病情况及其危险因素分析

目的探讨急性脑梗死患者脑微出血的发病情况及其危险因素。方法选择急性脑梗死患者75例,男51例,女24例,年龄42～83（64.9±10.8）岁。行头颅CT、磁敏感成像（SWI）检查,依据脑微出血检出的结果分成阳性组（23例）与阴性组（52例）,比较两组的一般资料,探讨脑微出血发病的危险因素。结果SWI检查的检出率比CT检出率高（χ2=27.17,P＜0.05）。阳性组年龄、高血压病、糖尿病患病率均较阴性组高,差异均有统计学意义（均P＜0.05）;两组性别、血脂异常、心房颤动、冠心病、吸烟、饮酒情况比较,差异均无统计学意义（均P＞0.05）。logistic回归分析显示年龄增长、高血压病是脑微出血的独立危险因素（P＜0.05）。结论急性脑梗死患者合并存在脑微出血的比例高,SWI检查是检测脑微出血的敏感方法,年龄大、高血压病与脑微出血的发生密切相关。     

一类多维指数分布的参数估计

考虑生存函数为(F)(x1,x2,…,xn)=P{X1＞x1,…,Xn＞xn}=exp{-[n∑i=1(xi/θi)1/δ]δ}(0＜xi＜∞,0＜δ≤ 1,0＜θi＜∞,i=(1,n))的一类多维指数分布,给出了它的密度函数的表示式,并讨论了它的性质.提出了相关参数δ的估计(^δ),证明了(^δ)有相合性和渐近正态性,得到了(^δ)的渐近方差σ2δ.最后还给出了若干随机模拟的结果.     

Subconvexity bounds for Rankin–Selberg L-functions for congruence subgroups

Estimation of shifted sums of Fourier coefficients of cusp forms plays crucial roles in analytic number theory. Its known region of holomorphy and bounds, however, depend on bounds toward the general Ramanujan conjecture. In this article, we extended such a shifted sum meromorphically to a larger half plane Res>1/2 and proved a better bound. As an application, we then proved a subconvexity bound for Rankin–Selberg L-functions which does not rely on bounds toward the Ramanujan conjecture: Let f be either a holomorphic cusp form of weight k, or a Maass cusp form with Laplace eigenvalue 1/4+k², for . Let g be a fixed holomorphic or Maass cusp form. What we obtained is the following bound for the L-function L(s,fg) in the k aspect:

L(1/2+it,fg)k^{1−1/(8+4θ)+ε},