Necessary and sufficient conditions for the oscillation of higher-order differential equations involving distributed delays

In this article, we establish necessary and sufficient conditions for the oscillation of both bounded and unbounded solutions of the differential equation \begin{equation} \bigg[x(t)+\int_{0}^{\lambda}p(t,v)x(\tau(t,v))\,\mathrm{d}v\bigg]^{(n)}+\int_{0}^{\lambda}q(t,v)x(\sigma(t,v))\,\mathrm{d}v=\varphi(t)\quad\text{for } t \geq t_{0},\notag \end{equation} where $n\in\mathbb{N}$, $t_{0},\lambda\in\mathbb{R}^{+}$, $p\in C([t_{0},\infty)\times[0,\lambda] \mathbb{R})$, $q\in C([t_{0},\infty)\times[0,\lambda],\mathbb{R}^{+})$, $\tau\in C([t_{0},\infty)\times[0 \lambda],\mathbb{R})$ with $\lim_{t\to\infty}\inf_{v\in[0,\lambda]}\tau(t,v)=\infty$ and $\sup_{v\in[0,\lambda]}\tau(t,v)\leq t$ for all $t\geq t_{0}$, $\sigma\in C([t_{0},\infty)\times[0,\lambda],\mathbb{R})$ with $\lim_{t\to\infty}\inf_{v\in[0,\lambda]}\sigma(t,v)=\infty$, and $\varphi\in C([t_{0},\infty),\mathbb{R})$. We also give illustrating examples to show the applicability of these results

Iterated oscillation criteria for delay dynamic equations of first order

We obtain new sufficient conditions for the oscillation of all solutions of first-order delay dynamic equations on arbitrary time scales, hence combining and extending results for corresponding differential and difference equations. Examples, some of which coincide with well-known results on particular time scales, are provided to illustrate the applicability of our results

Investigation of Double Differential Cross Sections of (γ, p) Reaction for 12 C Nuclei

Photonuclear reaction data, is important for basic and applied research. In additional to this, double differential data is especially vital in the field of nuclear medicine. The increase in the number of patients, admitted for treatment of cancer with heavy ions, poses a serious problem in terms of the risk of secondary cancer, as a result of exposure to particles of different energy and angle values, released after the nuclear reaction. The main point here is the possibility of damaging organs other than the treated one by the radiation generated in the reactions during the heavy ion therapy. Based on this, in order to assess the risk of secondary cancer the investigations of the double differential cross sections of reaction are required. Double differential cross sections of (γ,p) photonuclear reaction for 12 C nuclei were calculated as functions of incoming photon energy and angle. Nuclear reaction simulation program TALYS 1.2 was used in the calculations. The calculated cross sections were compared with both the experimental cross sections and the evaluated cross sections available in literature

A Method to Relate the Affecting Parameters and Estimate Dilution in Coal Mines

This study provides an overview of the various issues influencing Out-of-Seam Dilution (OSD) in longwall mining method. The collected data has been statistically analyzed to examine the effect of the some factors causing OSD in front of the longwall mining face. Multiple parameter regression analysis was conducted on affecting parameters and the OSD. The SPSS (Statistics Package for Social Sciences) for Windows software package was used for the statistics analysis. Finally, a relationship between affecting parameters and the OSD is established by using the multiple parameter regression results. Results of this study have revealed that depth of seam, dip of seam, roof quality and variation in seam thickness are the most important influence factors for OSD. The proposed method may be utilized for the estimation of OSD for similar mines since, it was based on actual collected data from the coal mines

Şerefeddin Health Services Vocational School

Many radioisotopes are used in nuclear medicine diagnostics and therapy. Co-57, In-111 and Tc-99m isotopes are widely used in nuclear medicine and are successfully implemented in renal imaging. In this work, the cross section calculation of the (p, 2n) reaction, which is necessary for production of the nuclei of Co-57, In-111, Tc-99m, were calculated using TALYS 1.6 nuclear reaction code. The calculated cross sections were compared with the experimental data from the EXFOR