The paper recalls the McNaughton theorem of fuzzy logic and the algorithms underlying its constructive proofs. It then shows how those algorithms can be combined with the algorithm underlying recent extension of the theorem to piecewise-linear functions with rational coefficients, and points out potential importance of the resulting combined algorithm for data mining. That result is immediately weakened through a complexity analysis of the algorithm that reveals that its worst-case complexity is doubly-exponential.
The McShane integral of functions f : I → ! defined on an m-dimensional interval I is considered in the paper. This integral is known to be equivalent to the Lebesgue integral for which the Vitali convergence theorem holds. For McShane integrable sequences of functions a convergence theorem based on the concept of equi-integrability is proved and it is shown that this theorem is equivalent to the Vitali convergence theorem.
We evaluate the mRNA expression of monocarboxylate transporters 1 and 4 (MCT1 and MCT4) in skeletal muscle (soleus, red and white gastrocnemius), heart and liver tissues in mice submitted to a single bout of swimming exercise at the maximal lactate steady state workload (MLSSw). After 72 h of MLSS test, the animals were submitted to a swimming exercise session for 25 min at individual MLSSw. Tissues and muscle samples were obtained at rest (control, n=5 ), immediately (n=5 ), 5 h (n=5 ) and 10 h (n=5 ) after exercise for determination of the MCT1 and MCT4 mRNA expression (RT-PCR). The MCT1 mRNA expression in liver increased after 10 h in relation to the control, immediate and 5 h groups, but the MCT4 remained unchanged. The MCT1 mRNA expression in heart increased by 31 % after 10 h when compared to immediate, but no differences were observed in relation to the control group. No significant differences were observed for red gastrocnemius in MCT1 and MCT4 mRNA expression. However, white gastrocnemius increased MCT1 mRNA expression immediately when compared to rest, 5 and 10 h test groups. In soleus muscle, the MCT1 mRNA expression increased immediately, 5 and 10 h after exercise when compared to the control. In relation to MCT4 mRNA expression, the soleus increased immediately and 10 h after acute exercise when compared to the control group. The soleus, liver and heart were the main tissues that showed improved the MCT1 mRNA expression, indicating its important role in controlling MLSS concentration in mice., G. G. de Araujo, C. A. Gobatto, F. de Barros Manchado-Gobatto, L. F. M. Teixeira, I. G. M. dos Reis, L. C. Caperuto, M. Papoti, S. Bordin, C. R: Cavaglieri, R. Verlengia., and Obsahuje bibliografii
By using the semi-discrete method of differential equations, a new version of discrete analogue of stochastic shunting inhibitory cellular neural networks (SICNNs) is formulated, which gives a more accurate characterization for continuous-time stochastic SICNNs than that by Euler scheme. Firstly, the existence of the 2pth mean almost periodic sequence solution of the discrete-time stochastic SICNNs is investigated with the help of Minkowski inequality, Hölder inequality and Krasnoselskii's fixed point theorem. Secondly, the moment global exponential stability of the discrete-time stochastic SICNNs is also studied by using some analytical skills and the proof of contradiction. Finally, two examples are given to demonstrate that our results are feasible. By numerical simulations, we discuss the effect of stochastic perturbation on the almost periodicity and global exponential stability of the discrete-time stochastic SICNNs.
Let u be a δ-subharmonic function with associated measure µ, and let v be a superharmonic function with associated measure ν, on an open set E. For any closed ball B(x,r), of centre x and radius r, contained in E, let M(u, x, r) denote the mean value of u over the surface of the ball. We prove that the upper and lower limits as s, t → 0 with 0 <s<t of the quotient (M(u, x,s)−M(u, x,t))/(M(v,x,s)−M(v,x,t)), lie between the upper and lower limits as r → 0+ of the quotient µ(B(x,r))/ν(B(x,r)). This enables us to use some well-known measure-theoretic results to prove new variants and generalizations of several theorems about δ-subharmonic functions.
For a differentiable function f : I → ℝ k , where I is a real interval and k ∈ ℕ, a counterpart of the Lagrange mean-value theorem is presented. Necessary and sufficient conditions for the existence of a mean M : I 2 → I such that f (x) − f (y) = (x − y)f ′ (M(x,y)), x,y ∈ I, are given. Similar considerations for a theorem accompanying the Lagrange mean-value theorem are presented.