Batch Fermentation Model of Propionic Acid Production by Propionibacterium acidipropionici in Different Carbon Sources

Propionic acid (PA) is widely used as additive in animal feed and also in the manufacturing of cellulose-based plastics, herbicides, and perfumes. Salts of propionic acid are used as preservative in food. PA is mainly produced by chemical synthesis. Nowadays, PA production by fermentation of low-cost industrial wastes or renewable sources has been an interesting alternative. In the present investigation, PA production by Propionibacterium acidipropionici ATCC 4965 was studied using a basal medium with sugarcane molasses (BMSM), glycerol or lactate (BML) in small batch fermentation at 30 and 36 degrees C. Bacterial growth was carried out under low dissolved oxygen concentration and without pH control. Results indicated that P. acidipropionici produced more biomass in BMSM than in other media at 30 degrees C (7.55 g l(-1)) as well as at 36 degrees C (3.71 g l(-1)). PA and biomass production were higher at 30 degrees C than at 36 degrees C in all cases studied. The best productivity was obtained by using BML (0.113 g l(-1) h(-1)), although the yielding of this metabolite was higher when using glycerol as carbon source (0.724 g g(-1)) because there was no detection of acetic acid. By the way, when using the other two carbon sources, acetic acid emerged as an undesirable by-product for further PA purification.     

Langmuir monolayers of a photoisomerizable macrocycle surfactant

An amphiphilic photoisomerizable macrocycle has been prepared that forms stable Langmuir monolayers at the air-water interface. The hydrophilic core of the molecule switches between closed and open isomers upon irradiation by the appropriate wavelengths of light. Isotherm measurements, Brewster angle microscope images, and atomic force micrographs (of transferred Langmuir-Blodgett films) suggest a phase transition between a face-on to a tilted edge-on molecular orientation as a function of surface concentration. In the face-on phase, in situ photoisomerization results in a reversible increase in surface pressure due to greater molecular crowding in the open configuration.     

Series expansions for the third incomplete elliptic integral via partial fraction decompositions

We find convergent double series expansions for Legendre's third incomplete elliptic integral valid in overlapping subdomains of the unit square. Truncated expansions provide asymptotic approximations in the neighborhood of the logarithmic singularity (1,1)$(1,1)$ if one of the variables approaches this point faster than the other. Each approximation is accompanied by an error bound.     

Algorithms for graph partitioning on the planted partition model

The NP‐hard graph bisection problem is to partition the nodes of an undirected graph into two equal‐sized groups so as to minimize the number of edges that cross the partition. The more general graph l‐partition problem is to partition the nodes of an undirected graph into l equal‐sized groups so as to minimize the total number of edges that cross between groups. We present a simple, linear‐time algorithm for the graph l‐partition problem and we analyze it on a random “planted l‐partition” model. In this model, the n nodes of a graph are partitioned into l groups, each of size n/l; two nodes in the same group are connected by an edge with some probability p, and two nodes in different groups are connected by an edge with some probability r<p. We show that if p−r≥n^−1/2+ϵ for some constant ϵ, then the algorithm finds the optimal partition with probability 1− exp(−n^Θ(ε)). © 2001 John Wiley & Sons, Inc. Random Struct. Alg., 18: 116–140, 2001     

The rank of sparse random matrices over finite fields

Let M be a random (n×n)-matrix over GF[q] such that for each entry M_ij in M and for each nonzero field element α the probability Pr[M_ij=α] is p/(q−1), where p=(log n−c)/n and c is an arbitrary but fixed positive constant. The probability for a matrix entry to be zero is 1−p. It is shown that the expected rank of M is n−𝒪(1). Furthermore, there is a constant A such that the probability that the rank is less than n−k is less than A/q^k. It is also shown that if c grows depending on n and is unbounded as n goes to infinity, then the expected difference between the rank of M and n is unbounded. © 1997 John Wiley & Sons, Inc. Random Struct. Alg., 10 , 407–419, 1997     

连续波锁模Pr3+:YLF激光器

本文报导了采用氩离子激光器来泵浦Pr³⁺:YLF晶体,应用声光调制器实现了主动锁模;同时应用振动─高反射平面镜也实现了被动锁模,两种锁模均得到了ps光脉冲.据作者了解这是这种晶体材料的第一次锁模运转.     

Solution of sparse quasi-square rectangular systems by Gaussian elimination

We present a general method for the linear least-squares solutionof overdetermined and underdetermined systems. The method isparticularly efficient when the coefficient matrix is quasi-square,that is when the number of rows and number of columns is almostthe same. The numerical methods for linear least-squares problemsand minimum-norm solutions do not generally take account ofthis special characteristic. The proposed method is based onLU factorization of the original quasi-square matrix A, assumingthat A has full rank. In the overdetermined case, the LU factorsare used to compute a basis for the null space of A^T. The right-handside vector b is then projected onto this subspace and the least-squaressolution is obtained from the solution of this reduced problem.In the case of underdetermined systems, the desired solutionis again obtained through the solution of a reduced system.The use of this method may lead to important savings in computationaltime for both dense and sparse matrices. It is also shown inthe paper that, even in cases where the matrices are quite small,sparse solvers perform better than dense solvers. Some practicalexamples that illustrate the use of the method are included.     

Bounded branching process and and/or tree evaluation

We study the tail distribution of supercritical branching processes for which the number of offspring of an element is bounded. Given a supercritical branching process {Z_n} with a bounded offspring distribution, we derive a tight bound, decaying super-exponentially fast as c increases, on the probability Pr[Z_n > cE(Z_n)], and a similar bound on the probability Pr[Z_n ≤ E(Z_n)/c] under the assumption that each element generates at least two offspring. As an application, we observe that the execution of a canonical algorithm for evaluating uniform AND/OR trees in certain probabilistic models can be viewed as a two-type supercritical branching process with bounded offspring, and show that the execution time of this algorithm is likely to concentrate around its expectation, with a standard deviation of the same order as the expectation.