Yet another way of calculating moments of the Kesten's distribution and its consequences for Catalan numbers and Catalan triangles

We calculate moments of the so-called Kesten distribution by means of the expansion of the denominator of the density of this distribution and then integrate all summands with respect to the semicircle distribution. By comparing this expression with the formulae for the moments of Kesten's distribution obtained by other means, we find identities involving polynomials whose power coefficients are closely related to Catalan numbers, Catalan triangles, binomial coefficients. Finally, as applications of these identities we obtain various interesting relations between the aforementioned numbers, also concerning Lucas, Fibonacci and Fine numbers.     

铁缺乏症对婴幼儿智能发育的影响

为分析铁缺乏症(IDD)对婴幼儿智能发育的影响，随机抽取了6个月至3岁婴幼儿200例，按有否铁缺乏分组，比较了其与智能的关系。结果表明，铁缺乏症检出率为17．5％，铁缺乏组婴幼儿智能发育商(DQ)明显下降，与正常组比较差异有显著性，铁缺乏程度越重，DQ值越低。可见铁缺乏症对婴幼儿大脑发育造成不良影响，对该症无贫血阶段及轻度缺铁性贫血期(IDA)应予重视。     

One-dimensional Ising chain with competing interactions: Exact results and connection with other statistical models

We study the ground state properties of a one-dimensional Ising chain with a nearest-neighbor ferromagnetic interactionJ ₁, and akth neighboranti-ferromagnetic interactionJ _k . WhenJ _k/J₁=–1/k, there exists a highly degenerate ground state with a residual entropy per spin. For the finite chain with free boundary conditions, we calculate the degeneracy of this state exactly, and find that it is proportional to the (N+k–1)th term in a generalized Fibonacci sequence defined by,F _N ^(k) =F _N–1 ^(k) +F _N–k ^(k) . In addition, we show that this one-dimensional model is closely related to the following problems: (a) a fully frustrated two-dimensional Ising system with a periodic arrangement of nearest-neighbor ferro- and antiferromagnetic bonds, (b) close-packing of dimers on a ladder, a 2× strip of the square lattice, and (c) directed self-avoiding walks on finite lattice strips.Work partially supported by grants from AFOSR and ARO.     

Effects of Silk Fibroin Enzyme Hydrolysates on Memory and Learning: A Review

Silk protein products have been used for a wide range of applications. This review focuses on the studies conducted relative to cognitive functions with silk fibroin enzyme hydrolysates (FEH) in humans and animals. All known studies reported in PubMed and Google Scholar have been included. Studies have been conducted on children, high school and college students, adults and seniors, ranging in ages from 7–92 years. Doses of 200–600 mg silk FEH per day for three weeks to 16 weeks have been used. Based on these studies, it can be concluded that silk FEH exhibit beneficial cognitive effects with respect to memory and learning, attention, mental focus, accuracy, memory recall, and overall memory and concentration. These conclusions are supported by studies in rats and mice. Mechanistic studies that have been conducted in animals and cell culture systems are also reviewed. These studies indicate that silk FEH exerts its positive effects on memory and learning by providing neuroprotection via a complex mechanism involving its potent antioxidant and inflammation-inhibiting activities. Acetylcholine (ACh) is secreted by cholinergic neurons, and plays a role in encoding new information. Silk FEH were shown to decrease the levels of the pro-oxidant and pro-inflammatory mediators interlukin-1 (IL-1β), IL-6 and tumor necrosis factor-alpha (TNF-α), protecting the cholinergic system from oxidative stress, thus enhancing ACh levels in the brain, which is known to promote cognitive functions. In addition, the expression of brain-derived neurotrophic factor (BNDF), which is involved in the survival of neurons, is enhanced, and an increase in the expression of the phosphorylated cAMP response element-binding protein (p-CREB) occurs, which is known to play a positive role in cognitive functions. No adverse effects have been reported in association with the use of silk FEH.     

A novel method for crack detection in beam-like structures by measurements of natural frequencies

A novel method is proposed for calculating the natural frequencies of a multiple cracked beam and detecting unknown number of multiple cracks from the measured natural frequencies. First, an explicit expression of the natural frequencies through crack parameters is derived as a modification of the Rayleigh quotient for the multiple cracked beams that differ from the earlier ones by including nonlinear terms with respect to crack severity. This expression provides a simple tool for calculating the natural frequencies of the beam with arbitrary number of cracks instead of solving the complicated characteristic equation. The obtained nonlinear expression for natural frequencies in combination with the so-called crack scanning method proposed recently by the authors allowed the development of a novel procedure for consistent identification of unknown amount of cracks in the beam with a limited number of measured natural frequencies. The developed theory has been illustrated and validated by both numerical and experimental results.     

A new framework for implicit restarting of the Krylov–Schur algorithm

This paper introduces a new framework for implicit restarting of the Krylov–Schur algorithm. It is shown that restarting with arbitrary polynomial filter is possible by reassigning some of the eigenvalues of the Rayleigh quotient through a rank‐one correction, implemented using only the elementary transformations (translation and similarity) of the Krylov decomposition. This framework includes the implicitly restarted Arnoldi (IRA) algorithm and the Krylov–Schur algorithm with implicit harmonic restart as special cases. Further, it reveals that the IRA algorithm can be turned into an eigenvalue assignment method. Copyright © 2014 John Wiley & Sons, Ltd.     

区域分工水平评价的新方法——区位结构熵法

根据区域产业分工理论,运用区位商测定区域专业化程度.然后,基于复杂系统结构熵理论,从产业在区际和区内聚集分布信息出发,融合行业路径和地区路径分析法于一体,提出并证明了可以用区位结构熵全面衡量产业在空间上的分布状况.在此基础上,构建一维区域分工指数,综合测定区域分工水平.最后,以我国工业空间分布为例,例证了该方法是合理的、可行的,具有一定的推广和应用价值.     

基于Fibonacci序列准周期结构的小角度低通空间滤波器

利用常规材料构造了Fibonacci序列准周期结构,运用传输矩阵法研究了该结构的空间传输特性,并基于该结构优良的空间传输特性设计了小角度低通空间滤波器.数值模拟结果表明,该小角度空间滤波器的角域带宽可通过改变序列的结构类型和序列数来调谐,其调谐规律为:随着Fibonacci序列F(m,1)中m值的增加,对应空间滤波器的角域带宽减小;随着序列数的增大,对应角域带宽也减小.在调谐的基础上,还可通过改变构成准周期结构的介质折射率参量来精确调节其角域带宽.相比于基于超材料的小角度空间滤波器而言,基于Fibonacci序列的小角度空间滤波器制备更简单,且有望应用于新一代的高功率激光系统中.     

The effect of resistant starches on fat oxidation in healthy adults as measured by a 13CO2-breath test

A resistant starch (RS) mixture (MIX) consisting of fibre of potatoes (FP) and wrinkled pea starch (WPS), and high amylose maize starch (HAMS) were supplemented in adults to evaluate their effects on fat oxidation by means of a ¹³CO₂-breath test. Sixteen subjects received a regular diet either without or with the supplementation of MIX and HAMS in randomised order. After administration of a [U-¹³C]algal lipid mixture, exhaled air was collected over 14?h in 0.5- and 1-h intervals. The ¹³C abundances were measured by nondispersive infrared spectroscopy. In comparison to the dry run (DR), supplementation with MIX and with HAMS increased the cumulative percentage dose recovery: (DR: 16.7?%, MIX: 16.9?%, HAMS: 18.0?%), but without statistical significance. The colonic degradation of MIX and HAMS to short-chain fatty acids tends to lower the formation of carbohydrate-derived acetyl-CoA and contributes to a postprandial lipid oxidation increase by using fat-derived acetyl-CoA as a compensatory fuel source.