It was hypothesized that an oscillation of tissue oxygen index (TOI) determined by near-infrared spectroscopy during recovery from exercise occurs due to feedback control of adenosine triphosphate and that frequency of the oscillation is affected by blood pH. In order to examine these hypotheses, we aimed 1) to determine whether there is an oscillation of TOI during recovery from exercise and 2) to determine the effect of blood pH on frequency of the oscillation of TOI. Three exercises were performed with exercise intensities of 30 % and 70 % peak oxygen uptake (Vo2peak) for 12 min and with exercise intensity of 70 % Vo2peak for 30 s. TOI during recovery from the exercise was analyzed by fast Fourier transform in order to obtain power spectra density (PSD). There was a significant difference in the frequency at which maximal PSD of TOI appeared (Fmax) between the exercises with 70 % Vo2peak for 12 min (0.0039±0 Hz) and for 30 s (0.0061±0.0028 Hz). However, there was no significant difference in Fmax between the exercises with 30 % (0.0043±0.0013 Hz) and with 70 % Vo2peak for 12 min despite differences in blood pH and blood lactate from the warmed fingertips. It is concluded that there was an oscillation in TOI during recovery from the three exercises. It was not clearly shown that there was an effect of blood pH on Fmax., T. Yano, R. Afroundeh, K. Shirakawa, C.-S. Lian, K. Shibata, Z. Xiao, T. Yunoki., and Obsahuje bibliografii
We obtain sufficient conditions for every solution of the differential equation [y(t) − p(t)y(r(t))](n) + v(t)G(y(g(t))) − u(t)H(y(h(t))) = f(t) to oscillate or to tend to zero as t approaches infinity. In particular, we extend the results of Karpuz, Rath and Padhy (2008) to the case when G has sub-linear growth at infinity. Our results also apply to the neutral equation [y(t) − p(t)y(r(t))](n) + q(t)G(y(g(t))) = f(t) when q(t) has sign changes. Both bounded and unbounded solutions are consideted here; thus some known results are expanded.
In this paper we consider the nonlinear difference equation with several delays (axn+1 + bxn) k − (cxn) k + ∑m i=1 pi(n)x k n−σi = 0 where a, b, c ∈ (0, ∞), k = q/r, q, r are positive odd integers, m, σi are positive integers, {pi(n)}, i = 1, 2, . . . , m, is a real sequence with pi(n) ≥ 0 for all large n, and lim inf n→∞ pi(n) = pi < ∞, i = 1, 2, . . . , m. Some sufficient conditions for the oscillation of all solutions of the above equation are obtained.
Some new criteria for the oscillation of difference equations of the form \[ \Delta ^2 x_n - p_n \Delta x_{n-h} + q_n |x_{g_n}|^c \mathop {\mathrm sgn}x_{g_n} = 0 \] and \[ \Delta ^i x_n + p_n \Delta ^{i-1} x_{n-h} + q_n |x_{g_n}|^c \mathop {\mathrm sgn}x_{g_n} = 0, \ i = 2,3, \] are established.
We study oscillatory properties of solutions of systems \[ \begin{aligned} {[y_1(t)-a(t)y_1(g(t))]}^{\prime }=&p_1(t)y_2(t), y_2^{\prime }(t)=&{-p_2}(t)f(y_1(h(t))), \quad t\ge t_0. \end{aligned} \].
One of the important methods for studying the oscillation of higher order differential equations is to make a comparison with second order differential equations. The method involves using Taylor's Formula. In this paper we show how such a method can be used for a class of even order delay dynamic equations on time scales via comparison with second order dynamic inequalities. In particular, it is shown that nonexistence of an eventually positive solution of a certain second order delay dynamic inequality is sufficient for oscillation of even order dynamic equations on time scales. The arguments are based on Taylor monomials on time scales.
Necessary and sufficient conditions are obtained for every solution of
\[ \Delta (y_{n}+p_{n}y_{n-m})\pm q_{n}G(y_{n-k})=f_{n} \] to oscillate or tend to zero as $n\rightarrow \infty $, where $p_{n}$, $q_{n}$ and $f_{n}$ are sequences of real numbers such that $q_{n}\ge 0$. Different ranges for $p_{n}$ are considered.
We study oscillatory behavior of a class of fourth-order quasilinear differential equations without imposing restrictive conditions on the deviated argument. This allows applications to functional differential equations with delayed and advanced arguments, and not only these. New theorems are based on a thorough analysis of possible behavior of nonoscillatory solutions; they complement and improve a number of results reported in the literature. Three illustrative examples are presented.
In this work we investigate some oscillatory properties of solutions of non-linear differential systems with retarded arguments. We consider the system of the form \[ y^{\prime }_i(t)-p_i(t)y_{i+1}(t)=0, \quad i=1,2,\dots , n-2, y^{\prime }_{n-1}(t)-p_{n-1}(t)|y_n(h_n(t))|^\alpha \mathop {\mathrm sgn}[y_n(h_n(t))]=0, y^{\prime }_n(t) \mathop {\mathrm sgn}[y_1(h_1(t))]+p_n(t)|y_1(h_1(t))|^\beta \, \le 0, \] where $ n\ge 3 $ is odd, $ \alpha >0$, $ \beta >0$.
In this paper the three-dimensional nonlinear difference system ∆xn = anf(yn−l ), ∆yn = bng(zn−m), ∆zn = δcnh(xn−k), is investigated. Sufficient conditions under which the system is oscillatory or almost oscillatory are presented.