Some binomial sums involving absolute values

We consider several families of binomial sum identities whose definition involves the absolute value function. In particular, we consider centered double sums of the form $$S_{\alpha,\beta}(n) := \sum_{k,\;\ell}\binom{2n}{n+k}\binom{2n}{n+\ell} |k^\alpha-\ell^\alpha|^\beta,$$ obtaining new results in the cases $\alpha = 1, 2$. We show that there is a close connection between these double sums in the case $\alpha=1$ and the single centered binomial sums considered by Tuenter.Comment: 15 pages, 19 reference

The reports of questionnaire about the diagnosis and prevention of weak calf syndrome in calves

A questionnaire survey aiming to elucidate the perception among veterinarians on the association between diarrhea in calves and Weak Calf Syndrome (WCS) was conducted in Japan, and 248 veterinarians in 39 prefectures answered the questionnaire. Among the respondents, 85.5% belonged to NOSAI (Farmers’ Mutual Aid Association), 3.2% were independent veterinarians, 5.2% were herd management service veterinarians, and 6.5% answered others. Male were 83.5%, and female 16.5%. Questionnaire covered reasons of WCS, diagnosis and prevention, characteristics of well-managed farms with fewer cases of diarrhea, and collection of information on calf diarrhea. Regarding the contribution of WCS on diarrhea, 77.8% answered that the contribution is large or non-negligible, and 56.3% answered that the proportion of diarrhea with WCS is less than 5%, and 22.1% answered that the proportion is more than 10%. According to the cattle breeds which the veterinarian deals with mainly, the proportion of answering that WCS affects diarrhea greatly or non-negligibly was significantly higher among those who deal with Holstein (Hol, 64/92, 69.5%) breed than Japanese Black (JB, 91/110, 82.7%, x2 = 4.2, df = 1, p = 0.04). The most common two answers for the cause of WCS were pedigree and nutritional status at the late stage of pregnancy, and especially veterinarians of 40s and 50s age raised pedigree. Nutrition status at fetus stage, and history of colostrum feeding were second and third common answers. When the respondents are stratified by main breeds dealing with, both groups dealing with Hol and JB prioritized pedigree and nutritional status at the late stage of pregnancy. However, Hol group tended to raise accidents at delivery and infection in fetus, while JB group pedigree and nutrition at fetus stage, in the second place. Most common criterion of diagnosis with WCS was light body weight, and low vitality, weak suckling of colostrum followed, and as higher age, larger proportion answered light body weight. Most common counter major against WCS was nutrition management around delivery, which accounted more than 50%, and selection of pedigree at insemination and colostrum management followed. Common answers as the second rank were suckling and environmental hygiene management after delivery. Veterinarians chose hygiene, delivery - colostrum management, skill for observation, and feeding management commonly as characteristic of good practice farms with fewer diarrhea; however the proportions varied. For the same question, Hol group tended to answer delivery – colostrum management, while JB group feeding management. As shown above, the perception of WCS among veterinarians differed according to their age and the main cattle breeds dealing with

Apollo asteroids (1566) Icarus and 2007 MK6: Icarus family members?

Although it is more complicated to search for near-Earth object (NEO) families than main belt asteroid (MBA) families, since differential orbital evolution within a NEO family can cause current orbital elements to drastically differ from each other, we have found that Apollo asteroids (1566) Icarus and the newly discovered 2007 MK6 are almost certainly related. Specifically, their orbital evolutions show a similar profile, time shifted by only ~1000 yr, based on our time-lag theory. The dynamical relationship between Icarus and 2007 MK6 along with a possible dust band, the Taurid-Perseid meteor swarm, implies the first detection of an asteroidal NEO family, namely the "Icarus asteroid family".Comment: 11 pages, 1 figure, to appear on Astrophysical Journal Letters (journal info added

Synthesis and characterization of phenylethynylcarbonyl terminated novel thermosetting imide compound

Phenylethynyl terminated novel imide compound based on 1,3-bis(3-aminophenoxy)benzene (APB) and phenylethynyl trimellitic anhydride (PETA) were prepared. The curing behavior of phenylethynyl terminated imide compound was investigated by differential scanning calorimetry and Fourier transform infrared spectrometry. The curing reaction of phenylethynylcarbonyl end group completed at 220°C, and proceeded much faster than that of phenylethynyl end group. Glass transition temperature of the thermosetting resin from phenylethynylcarbonyl terminated novel imide compound determined by dynamic mechanical analysis was almost the same as that of o-cresolnovolac type epoxy resin. In addition, the thermosetting resin from phenylethynylcarbonyl terminated novel imide compound exhibited excellent thermal and dimensional stabilities. These excellent properties of these phenylethynyl terminated imide compound might be due to the incorporation of alkene group or aromatic ring substitutes in the backbones, which might enhance the chain interaction (molecular packing) and reduce the molecular chain mobility