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1. A comparison of three recent selection theorems

Creator:
Maniscalco, Caterina
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
variation, oscillation, modulus of variation, and selection theorem
Language:
English
Description:
We compare a recent selection theorem given by Chistyakov using the notion of modulus of variation, with a selection theorem of Schrader based on bounded oscillation and with a selection theorem of Di Piazza-Maniscalco based on bounded A , Λ-oscillation.
Rights:
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2. Bounded oscillation of nonlinear neutral differential equations of arbitrary order

Creator:
Yilmaz, Yeter Şahiner and Zafer, Ağacik
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
oscillation, positive solutions, and neutral equation
Language:
English
Description:
The paper is concerned with oscillation properties of $n$-th order neutral differential equations of the form \[ [x(t)+cx(\tau (t))]^{(n)}+q(t)f\bigl (x(\sigma (t))\bigr )=0,\quad t\ge t_0>0, \] where $c$ is a real number with $|c|\ne 1$, $q\in C([t_0,\infty ),\mathbb R)$, $f\in C(\mathbb R,\mathbb R)$, $\tau ,\sigma \in C([t_0,\infty ),\mathbb R_+)$ with $\tau (t)<t$ and $\lim _{t\rightarrow \infty }\tau (t)=\lim _{t\rightarrow \infty }\sigma (t)=\infty $. Sufficient conditions are established for the existence of positive solutions and for oscillation of bounded solutions of the above equation. Combination of these conditions provides necessary and sufficient conditions for oscillation of bounded solutions of the equation. Furthermore, the results are generalized to equations in which $c$ is a function of $t$ and a certain type of a forcing term is present.
Rights:
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3. Comparison of oscillation of oxygenation in skeletal muscle between early and late phases in prolonged exercise

Creator:
Yano, T., Lian, C.-S., Arimitsu, T., Yamanaka, R., Afroundeh, R., Shirakawa, K., and Yunoki, T.
Type:
article, články, model:article, and TEXT
Subject:
Fyziologie člověka a srovnávací fyziologie, fyziologie člověka, human physiology, deoxygenation, oscillation, power spectra density, prolonged exercise, oxygenation, 14, and 612
Language:
English
Description:
The aim of the present study was to compare the oscillations of oxygenation in skeletal muscle between early and late phases in prolonged exercise. During prolonged exercise at 60 % of peak oxygen uptake ( o2) for 60 min and at rest, oxygenated hemoglobin/myoglobin (Hb/MbO2) and total Hb/Mb (THb/Mb) were determined by near-infrared spectroscopy in the vastus lateralis. Power spectra density (PSD) for the difference between Hb/MbO2 and THb/Mb (−HHb/MbO2: deoxygenation) was obtained by fast Fourier transform at rest, in the early phase (1-6 min) and in the late phase (55-60 min) in exercise. Peak PSD in the early phase was significantly higher than that at rest. There were at least three peaks of PSD in exercise. The highest peak was a band around 0.01 Hz, the next peak was a band around 0.04 Hz, and the lowest peak was a band around 0.06 Hz. PSD in the early phase was not significantly different from that in the late phase in exercise. Heart rate (HR) showed a continuous significant increase from 3 min in exercise until the end of exercise. Skin blood flow (SBF) around the early phase was significantly lower than that around the late phase. It was concluded that oscillation of oxygenation in the muscle oxygen system in the early phase is not different from that in the late phase in prolonged exercise despite cardiovascular drift., T. Yano, ... [et al.]., and Obsahuje seznam literatury
Rights:
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4. Global attractivity of the equilibrium of a nonlinear difference equation

Creator:
Graef, John R. and Qian, C.
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
nonlinear difference equation, global attractivity, and oscillation
Language:
English
Description:
The authors consider the nonlinear difference equation \[ x_{n+1}=\alpha x_n + x_{n-k}f(x_{n-k}), \quad n=0, 1,\dots .1 \text{where} \alpha \in (0, 1),\hspace{5.0pt}k \in \lbrace 0, 1, \dots \rbrace \hspace{5.0pt}\text{and}\hspace{5.0pt}f\in C^1[[0, \infty),[0, \infty )] \qquad \mathrm{(0)}\] with $f^{\prime }(x)<0$. They give sufficient conditions for the unique positive equilibrium of (0.1) to be a global attractor of all positive solutions. The results here are somewhat easier to apply than those of other authors. An application to a model of blood cell production is given.
Rights:
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5. Integral averages and oscillation of second order sublinear differential equations

Creator:
Manojlović, Jelena V.
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
oscillation, sublinear differential equation, and integral averages
Language:
English
Description:
New oscillation criteria are given for the second order sublinear differential equation \[ [a(t)\psi (x(t))x^{\prime }(t)]^{\prime }+q(t)f(x(t))=0, \quad t\ge t_0>0, \] where $a\in C^1([t_0,\infty ))$ is a nonnegative function, $\psi , f\in C({\mathbb R})$ with $\psi (x)\ne 0$, $xf(x)/\psi (x)>0$ for $x\ne 0$, $\psi $, $f$ have continuous derivative on ${\mathbb R}\setminus \lbrace 0\rbrace $ with $[f(x)/\psi (x)]^{\prime }\ge 0$ for $x\ne 0$ and $q\in C([t_0,\infty ))$ has no restriction on its sign. This oscillation criteria involve integral averages of the coefficients $q$ and $a$ and extend known oscillation criteria for the equation $x^{\prime \prime }(t)+q(t)x(t)=0$.
Rights:
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6. Iterated oscillation criteria for delay partial difference equations

Creator:
Karpuz, Başak and Öcalan, Özkan
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
partial difference equation, oscillation, and variable coefficient
Language:
English
Description:
In this paper, by using an iterative scheme, we advance the main oscillation result of Zhang and Liu (1997). We not only extend this important result but also drop a superfluous condition even in the noniterated case. Moreover, we present some illustrative examples for which the previous results cannot deliver answers for the oscillation of solutions but with our new efficient test, we can give affirmative answers for the oscillatory behaviour of solutions. For a visual explanation of the examples, we also provide 3D graphics, which are plotted by a mathematical programming language.
Rights:
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7. Kamenev type oscillation criteria for nonlinear difference equations

Creator:
Saker, Samir H. and Cheng, Sui-Sun
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
oscillation, nonlinear difference equation, and Riccati transformation
Language:
English
Description:
By means of Riccati transformation techniques, we establish some new oscillation criteria for second-order nonlinear difference equation which are sharp.
Rights:
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8. Non-oscillation of second order linear self-adjoint nonhomogeneous difference equations

Creator:
Parhi, N.
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
oscillation, non-oscillation, second order difference equation, third order difference equation, and generalized zero
Language:
English
Description:
In the paper, conditions are obtained, in terms of coefficient functions, which are necessary as well as sufficient for non-oscillation/oscillation of all solutions of self-adjoint linear homogeneous equations of the form ∆(pn−1∆yn−1) + qyn = 0, n ≥ 1, where q is a constant. Sufficient conditions, in terms of coefficient functions, are obtained for non-oscillation of all solutions of nonlinear non-homogeneous equations of the type ∆(pn−1∆yn−1) + qng(yn) = fn−1, n ≥ 1, where, unlike earlier works, fn > 0 or 6 0 (but 6≡ 0) for large n. Further, these results are used to obtain sufficient conditions for non-oscillation of all solutions of forced linear third order difference equations of the form yn+2 + anyn+1 + bnyn + cnyn−1 = gn−1, n ≥ 1.
Rights:
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9. On oscillation and asymptotic property of a class of third order differential equations

Creator:
Parhi, N. and Pardi, Seshadev
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
math and oscillation
Language:
English
Description:
In this paper, oscillation and asymptotic behaviour of solutions of \[ y^{\prime \prime \prime} + a(t)y^{\prime \prime}+b(t)y^{\prime} + c(t)y=0 \] have been studied under suitable assumptions on the coefficient functions $a,b,c\in C([\sigma ,\infty),R)$, $ \sigma \in R$, such that $a(t)\ge 0$, $b(t) \le 0$ and $c(t) < 0$.
Rights:
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10. On oscillation of solutions of forced nonlinear neutral differential equations of higher order

Creator:
Parhi, N. and Rath, Radhanath N.
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
oscillation, nonoscillation, neutral equations, and asymptotic behaviour
Language:
English
Description:
In this paper, necessary and sufficient conditions are obtained for every bounded solution of \[ [y (t) - p (t) y (t - \tau )]^{(n)} + Q (t) G \bigl (y (t - \sigma )\bigr ) = f (t), \quad t \ge 0, \qquad \mathrm{(*)}\] to oscillate or tend to zero as $t \rightarrow \infty $ for different ranges of $p (t)$. It is shown, under some stronger conditions, that every solution of $(*)$ oscillates or tends to zero as $t \rightarrow \infty $. Our results hold for linear, a class of superlinear and other nonlinear equations and answer a conjecture by Ladas and Sficas, Austral. Math. Soc. Ser. B 27 (1986), 502–511, and generalize some known results.
Rights:
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