This paper deals with the solvability of initial-value problem and with Lyapunov exponents for linear implicit random difference equations, i.e. the difference equations where the leading term cannot be solved. An index-1 concept for linear implicit random difference equations is introduced and a formula of solutions is given. Paper is also concerned with a version of the multiplicative theorem of Oseledets type.

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Comprehensive insight into the human gut microbiota and the interaction with their environment in communities with a high background of antibiotic use and antibiotic resistance genes is currently largely lacking. In a cohort (Vietnam), individuals within the same household, also individuals within their geographical cluster share more bacterial taxa than individuals from different households or geographical clusters. The microbial diversity among individuals who used antibiotics in the past four months was significantly lower than those who did not. Fecal microbiota of humans was more diverse than non-human samples, shared a small part of its amplicon sequence variants (ASVs) with feces from animals (7.4%), water (2.2%) and food (3.1%). Sharing of ASVs between humans and companion animals was not associated with household. There is a correlation between an Enterobacteriaceae ASV and the presence of blactx-m-2 in feces from humans and animals, hinting towards an exchange of antimicrobial resistant strains between reservoirs.

Abstract:In the article proposed an effective method estimating transfer function model of controlled plant including dead-time delay, based on stochatstic time series of input-output signals. The model structure is modified with parameters optimized until the model error becomes "white-noise" series that with inough smal auto-correlation function. ProposeThe Real signals which occur in the control process always imlpy influences of many random factors, so the Directive Object Identification Problem is often related to random process. Mathematically, the Controlled Object Identification problem is the problem that predicts the trend of Random Process:-regressive function that reflects the trend of non-random process or is the model of the identification problem; ( ) u trandom error. The Theory of Prediction and Identification has been studied and developed with thousands of scientific works made public since last century. We can find the fundamental results of studies of statistics and prediction in [1,2], of kinetics system identification in detail in [3,4].To use linear algebra methods, we often try to change the regressive models into linear combination forms of coefficients: , to increase the model accuracy. With this approach, the object identification problem without dead time delay is considered to be completely solved in theory [1,4]. In fact, however, applying the pure polynomial