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

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

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 $\lim_{t\rightarrow\infty}x(t)=0$

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

Serum levels of TNF-α and osteoprotegerin and bone mineral density in patients with Behçet’s Disease

Objectives: Osteoporosis is commonly developed due tonatural course of Behçet’s disease (BD) and therapeuticagents. It was aimed to investigate levels of osteoprotegerinand TNF-α (tumor necrosis factor), and bone mineral density(BMD) and correlation between them in BD.Materials and methods: The study included two groupsas the study and the control group. Serum levels of TNF-α,osteoprotegerin, osteocalcine, erythrocyte sedimentation rate(ESR), C-reactive protein (CRP), and urinary creatinine anddeoxypyridinoline along with BMD level were evaluated andcompared. Correlation between TNF-α and osteoprotegerinlevel was investigated.Results: The study enrolled 41 BD patients and 36 agedmatchedcontrol subjects. Mean age was 42.26±11.64 and41.66±70.99, in the study and control groups, respectively.There was no significant difference in body mass index(BMI) of subjects between groups (p>0.05). Level of TNF-α(p<0.001), deoxypyridinoline (p<0.001) and osteocalcine(p=0.041) was significantly higher in the study group comparedto the control group. Osteoprotegerin was lower inBD patients, but the difference was not significant (p>0.05).Urinary deoxypyridinoline/ urinary creatinine ratio in patientswith BD was significantly higher than those in control group(p=0.030). Patients had significantly lower BMD comparfedto the control group, except L2-L4 vertebral area (p<0.001,p<0.001, p=0.035, p<0.001, p=0.012, p<0.001, p<0.001 andp=0.111, respectively). No correlation was found betweenTNF-α and osteoprotegerin.Conclusions: The present study indicated that TNF-α andBMD was negatively correlated with each other and TNF-αhad an effect on osteoporotic process in patients with BD.Osteoprotegerin level was not decreased, and not correlatedwith TNF-α.Key words: Behçet’s disease, osteoprotegerin, TNF-α, osteocalcin

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