Bounded solutions of kk-dimensional system of nonlinear difference equations of neutral type

The $k$-dimensional system of neutral type nonlinear difference equations with delays in the following form \begin{equation*} \begin{cases} \Delta \Big(x_i(n)+p_i(n)\,x_i(n-\tau_i)\Big)=a_i(n)\,f_i(x_{i+1}(n-\sigma_i))+g_i(n),\\ \Delta \Big(x_k(n)+p_k(n)\,x_k(n-\tau_k)\Big)=a_k(n)\,f_k(x_1(n-\sigma_k))+g_k(n), \end{cases} \end{equation*} where $i=1,\dots,k-1$, is considered. The aim of this paper is to present sufficient conditions for the existence of nonoscillatory bounded solutions of the above system with various $(p_i(n))$, $i=1,\dots,k$, $k\geq 2$

Sand and sawdust bedding affect populations of coliforms, Klebsiella spp. and Streptococcus spp. on teat ends of dairy cows housed in freestalls

The main objectives of the study were: 1) to compare bacterial populations of mastitis causing organisms on the outside of teats of lactating cows housed on sand and on sawdust bedding and, 2) to examine the relationship between bacterial counts in the two bedding types with those on teat ends. Sixteen cows were housed on either sand or sawdust-bedded freestalls using a crossover design with 3 week per bedding type. Bedding samples were collected on d 0 (prior to cows lying on the bedding), 1, 2 and 6. Teat ends were sampled prior to the morning milking on d 1, 2 and 6. All samples were analyzed to determine coliform, Klebsiella spp., and Streptococcus spp. populations. For teat end samples, there was two times more coliform and six times more Klebsiella spp. on teat ends of cows housed on sawdust compared to those housed on sand. In contrast, there was a 10-fold increase in the number of Streptococcus spp. associated with sand than with sawdust. In both sawdust and sand bedding, coliform, Klebsiella and Streptococcus counts increased over each experimental week, although patterns varied with bedding and bacteria type. Bacterial counts on teat ends were correlated to bacterial counts in sawdust: r = 0.47, r = 0.69 and r = 0.60 for coliforms, Klebsiella spp. and streptococci, respectively. Bacterial counts on teat ends were correlated to bacterial counts in sand: r = 0.35 for coliforms and r = 0.40 for Klebsiella spp. Streptococcal counts on teat ends were not correlated to bacterial counts in sand. In conclusion, coliform and Klebsiella spp. on teat ends were more numerous when using sawdust bedding, but Streptococcus spp. were more numerous on teat ends of cows housed on sand.Land and Food Systems, Faculty ofGraduat