Uniqueness theorems for meromorphic mappings sharing hyperplanes in general position

The purpose of this article is to study the uniqueness problem for meromorphic mappings from $\mathbb{C}^{n}$ into the complex projective space $\mathbb{P}^{N}(\mathbb{C}).$ By making using of the method of dealing with multiple values due to L. Yang and the technique of Dethloff-Quang-Tan respectively, we obtain two general uniqueness theorems which improve and extend some known results of meromorphic mappings sharing hyperplanes in general position.Comment: 10 page

Oscillation of solutions of some higher order linear differential equations

In this paper, we deal with the order of growth and the hyper order of solutions of higher order linear differential equations $$f^{(k)}+B_{k-1}f^{(k-1)}+\cdots+B_1f'+B_0f=F$$ where $B_j(z) (j=0,1,\ldots,k-1)$ and $F$ are entire functions or polynomials. Some results are obtained which improve and extend previous results given by Z.-X. Chen, J. Wang, T.-B. Cao and C.-H. Li

Oscillation results on meromorphic solutions of second order differential equations in the complex plane

The main purpose of this paper is to consider the oscillation theory on meromorphic solutions of second order linear differential equations of the form $f^{''}+A(z)f=0$ where $A$ is meromorphic in the complex plane. We improve and extend some oscillation results due to Bank and Laine, Kinnunen, Liang and Liu, and others

Bounds for the sums of zeros of solutions of u(m)=P(z)uu^{(m)}=P(z)u where PP is a polynomial

The main purpose of this paper is to consider the differential equation $u^{(m)}=P(z)u$ $(m\geq 2)$ where $P$ is a polynomial with in general complex coefficients. Let $z_{k}(u),$ $k=1,2,\ldots$ be the zeros of a nonzero solution $u$ to that equation. We obtain bounds for the sums $$\sum_{k=1}^{j}\frac{1}{|z_{k}(u)|}\quad (j\in\mathbb{N})$$ which extend some recent results proved by Gil'

Uniqueness and value distribution for q-shifts of meromorphic functions

In this paper, we deal with value distribution for q-shift polynomials of transcendental meromorphic functions with zero order and obtain some results which improve the previous theorems given by Liu and Qi [18]. In addition, we investigate value sharing for q-shift polynomials of transcendental entire functions with zero order and obtain some results which extend the recent theorem given by Liu, Liu and Cao [17]

Orthokeratology lens and conventional frame glasses for ocular parameters of myopia adolescent

AIM: To explore the effects of overnight orthokeratology lens and conventional frame glasses on the myopic diopter, uncorrected visual acuity and ocular parameters of myopia adolescent. METHODS: Totally 102 cases of(204 eyes)of adolescent myopia patients were randomly divided into observation group and control group with 51 cases(102 eyes)in each group during April 2014 to April 2017. Control group was only given conventional frame glasses, and observation group was given overnight orthokeratology lens. The myopic diopter and uncorrected visual acuity(UCVA)before wearing glasses and at 1wk, 1, 3, 6mo and 1a of wearing glasses, and the ocular parameters before wearing glasses and at 1a after wearing glasses were observed in the two groups, and the occurrence of complications was compared between the two groups. RESULTS: After 1wk to 1a of wearing glasses, the myopic diopter in observation group was gradually decreased(PP>0.05), but there was statistically significant difference between-groups at different time points(PPPP>0.05), and the axial length in control group was significantly longer than that before wearing glasses and that in observation group(PP>0.05).CONCLUSION: Overnight orthokeratology lens for adolescent myopia can effectively correct the myopic diopter, and improve the uncorrected visual acuity. It is less harmful to the eyes and less complications, and it is safe and reliable in clinical application

The Abnormality of Topological Asymmetry in Hemispheric Brain Anatomical Networks in Bipolar Disorder

Convergent evidences have demonstrated a variety of regional abnormalities of asymmetry in bipolar disorder (BD). However, little is known about the alterations in hemispheric topological asymmetries. In this study, we used diffusion tensor imaging to construct the hemispheric brain anatomical network of 49 patients with BD and 61 matched normal controls. Graph theory was then applied to quantify topological properties of the hemispheric networks. Although small-world properties were preserved in the hemispheric networks of BD, the degrees of the asymmetry in global efficiency, characteristic path length, and small-world property were significantly decreased. More changes in topological properties of the right hemisphere than those of left hemisphere were found in patients compared with normal controls. Consistent with such changes, the nodal efficiency in patients with BD also showed less rightward asymmetry mainly in the frontal, occipital, parietal, and temporal lobes. In contrast to leftward asymmetry, significant rightward asymmetry was found in supplementary motor area of BD, and attributed to more deficits in nodal efficiency of the left hemisphere. Finally, these asymmetry score of nodal efficiency in the inferior parietal lobule and rolandic operculum were significantly associated with symptom severity of BD. Our results suggested that abnormal hemispheric asymmetries in brain anatomical networks were associated with aberrant neurodevelopment, and providing insights into the potential neural biomarkers of BD by measuring the topological asymmetry in hemispheric brain anatomical networks