New Ultimate Boundedness and Periodicity Results for Certain Third-order Nonlinear Vector Differential Equations

The principle aim of this paper is to present some new results related to the ultimate boundedness and existence of periodic of solutions a certain non-linear ordinary vector differential equation of third order. Our results improve some well-known results in the literature.</p

On the oscillatory behavior of even order neutral delay dynamic equations on time-scales

We establish some new criteria for the oscillation of the even order neutral dynamic equation \begin{equation*} \left( a(t)\left( \left( x(t)-p(t)x(\tau (t))\right) ^{\Delta^{n-1}}\right) ^{\alpha }\right) ^{\Delta }+q(t)\left( x^{\sigma}(g(t))\right) ^{\lambda }=0 \end{equation*} on a time scale $\mathbb{T}$, where $n \geq 2$ is even, $\alpha$ and $\lambda$ are ratios of odd positive integers, $a$, $p$ and $q$ are real valued positive rd-continuous functions defined on $\mathbb{T}$, and $g$ and $\tau$ are real valued rd-continuous functions on $\mathbb{T}$. Examples illustrating the results are included

Oscillatory behavior of a third-order neutral dynamic equation with distributed delays

The authors present some new oscillation criteria for the third-order neutral dynamic equation with distributed delays \begin{equation*} \left[ r(t)\left( \left[ x(t)+\int\limits_{a}^{b}p(t,\eta )x\left[ \tau (t,\eta )\right] \Delta \eta \right] ^{\Delta \Delta }\right) ^{\alpha }% \right] ^{\Delta }+\int\limits_{c}^{d}q(t,\xi )f\left( x\left[ \phi (t,\xi )% \right] \right) \Delta \xi =0 \end{equation*} on a time scale $\mathbb{T}$, where $\alpha$ is the quotient of odd positive integers. Using a Riccati type transformation and a comparison technique, they establish some new sufficient conditions to ensure that a solution $x$ of this equation either oscillates or satisfies $\lim_{t\rightarrow\infty}x(t)=0$

Asymptotic behavior of solutions of forced fractional differential equations

The authors study the boundedness of nonoscillatory solutions of forced fractional differential equations of the form \begin{equation*} ^{C}D_{c}^{\alpha }y(t)=e(t)+f(t,x(t)),\qquad c>1, \quad\alpha \in (0,1), \end{equation*} where $y(t)=\left( a(t)x^{\prime }(t)\right) ^{\prime }$, $c_{0}=\frac{y(c)}{\Gamma (1)}=y(c)$, and $c_{0}$ is a real constant. The technique used in obtaining their results will apply to related fractional differential equations with Caputo derivatives of any order. Examples illustrate the results obtained in this paper

Remote cerebellar hemorrhage following resection of a supratentorial tumor: a case report

Remote cerebellar hemorrhage after supratentorial surgery is rare, ranging between 0.08% and 0.29% in adults and children. However, it is extremely rare in children. This phenomenon underlying mechanisms remain obscure. A 14-year-old male child patient had a history of right focal seizures and underwent craniotomy for a left frontal mass (Dysembryoplastic Neuroepithelial Tumor). First hours post recovery period, the patient was somnolent and had right hemiparesis. Postoperative Computer Tomography and magnetic resonance imaging findings revealed that the patient had developed remote cerebellar hemorrhage. He was treated conservatively, and was free of neurological deficits

Analysis of the common genetic component of large-vessel vasculitides through a meta- Immunochip strategy

Giant cell arteritis (GCA) and Takayasu's arteritis (TAK) are major forms of large-vessel vasculitis (LVV) that share clinical features. To evaluate their genetic similarities, we analysed Immunochip genotyping data from 1,434 LVV patients and 3,814 unaffected controls. Genetic pleiotropy was also estimated. The HLA region harboured the main disease-specific associations. GCA was mostly associated with class II genes (HLA-DRB1/HLA-DQA1) whereas TAK was mostly associated with class I genes (HLA-B/MICA). Both the statistical significance and effect size of the HLA signals were considerably reduced in the cross-disease meta-analysis in comparison with the analysis of GCA and TAK separately. Consequently, no significant genetic correlation between these two diseases was observed when HLA variants were tested. Outside the HLA region, only one polymorphism located nearby the IL12B gene surpassed the study-wide significance threshold in the meta-analysis of the discovery datasets (rs755374, P?=?7.54E-07; ORGCA?=?1.19, ORTAK?=?1.50). This marker was confirmed as novel GCA risk factor using four additional cohorts (PGCA?=?5.52E-04, ORGCA?=?1.16). Taken together, our results provide evidence of strong genetic differences between GCA and TAK in the HLA. Outside this region, common susceptibility factors were suggested, especially within the IL12B locus