It is concerned with the Anderson localization for the discrete one-dimensional quasi-periodic Schr & ouml;dinger operator with some particular Denjoy-Carleman potentials. First, it is proved that when the disorder parameter is sufficiently large and the frequency belongs to the strong Diophantine class (with a measure-zero set excluded), the operator satisfies Anderson localization. This demonstrates the exponential localization of eigenstates under these conditions, a hallmark of Anderson localization in disordered systems. Second, for all energy values , both the Lyapunov exponent and the integrated density of states (IDS) of the Schr & ouml;dinger operator are shown to be positive. Additionally, these quantities satisfy a specific modulus of continuity, which provides important insights into the regularity and spectral properties of the operator.

In this paper, we investigate the eigenvalue properties of a nonlocal Sturm–Liouville equation involving fractional integrals and fractional derivatives under different boundary conditions. Based on these properties, we obtained the geometric multiplicity of eigenvalues for the nonlocal Sturm–Liouville problem with a non-Dirichlet boundary condition. Furthermore, we discussed the continuous dependence of the eigenvalues on the potential function for a nonlocal Sturm–Liouville equation under a Dirichlet boundary condition.

Background Venous malformations (VMs) are the most common vascular malformations, which can be classified as focal, multifocal, or diffuse types. But the risk of focal venous malformations with muscle involvement is not well defined. Methods This is a single-center, retrospective review of patients treated for focal VMs between February 2021 and February 2022. Results We assessed 26 patients focal VMs with 47 lesions; 18 (69%) were unifocal, 3 (12%) were dual-focal, and 5 (19%) were multifocal type VMs, and 29 (62%) were intramuscular VMs. The lower limbs intramuscular VMs had a significantly elevated risk of focal VMs (relative risk [RR],1.7; 95% confidence interval [CI], 1.148–2.394). Conclusion Intramuscular involvement of the body should be considered in focal VMs. The lower limbs intramuscular VMs had a significantly elevated risk of focal VMs.

In this paper, we consider the optimal recovery of potentials for a Sturm-Liouville problem $$-y''+qy= \lambda y, y(0)=0=y(1)-hy'(1), 0<h<1, q\in L^1[0,1]$$ with only one given eigenvalue. Denote by $$\lambda _n(q)$$ the $$n-$$ th eigenvalue of this problem. For $$\lambda \in \mathbb {R}$$ , denote by $$\Omega _{n}(\lambda )=\left\{ q: q \in L^{1}[0,1], \lambda _{n}(q)=\right. $$ $$\left. \lambda \right\} $$ , $$n \ge 1$$ and $$E_{n}(\lambda )=\inf \left\{ \Vert q\Vert : q \in \Omega _{n}(\lambda )\right\} .$$ The optimal recovery of potential function in this paper refers to finding the infimum of the $$L^1$$ -norm for potential function in the set $$\Omega _{n}(\lambda ).$$ We will obtain a formula for $$E_{n}(\lambda )$$ and specify where the infimum can be attained. Our results are closely related to the discontinuity of the eigenvalues with respect to the boundary conditions. Since the optimal recovery problem with only one fixed eigenvalue is just the duality problem to the extremum problem of eigenvalues, we also give the extremum of the n-th eigenvalue of a problem for potentials on a sphere in $$L^1[0, 1]$$ .

Assume the mapping $$A:\left\{ \begin{array}{ll} x_{1}=x+\omega+y+f(x,y), y_{1}=y+g(x,y), \end{array} \right. (x, y)\in \mathbb{T}^{d}\times B(r_{0}) $$ is reversible with respect to $G: (x, y)\mapsto (-x, y),$ and $| f | _{C^{\ell}(\mathbb{T}^{d}\times B(r_{0}))}\leq \varepsilon_{0}, | g |_{C^{\ell+d}(\mathbb{T}^{d}\times B(r_{0}))}\leq \varepsilon_{0},$ where $B(r_{0}):=\{|y|\le r_0:\; y\in\mathbb R^d\},$ $\ell=2d+1+\mu$ with $0<\mu\ll 1.$ Then when $\varepsilon_{0}=\varepsilon_{0}(d)>0$ is small enough and $\omega$ is Diophantine, the map $A$ possesses an invariantS torus with rotational frequency $\omega.$ As an application of the obtained theorem, the Lagrange stability is proved for a class of reversible Duffing equation with finite smooth perturbation.

In this paper, we discuss the continuous dependence of eigenvalues on the potential function for a nonlocal Sturm–Liouville equation with truncated Marchaud fractional derivative term by two‐parameter method. To this end, we first study the properties of eigenvalues for a two‐parameter nonlocal Sturm–Liouville eigenvalue problem. We obtain the two‐parameter nonlocal Sturm–Liouville eigenvalue problem that has countable number of simple real eigenvalues. Meanwhile, the asymptotic behavior of eigenvalues is studied by aid of the analytic perturbation theory.

Background: Intracystic hemorrhage from lymphangiomas is a common phenomenon in lymphatic malformations (LMs); however, little is known about the associated compositional changes in the lymphatic fluid. Materials and Methods: We prospectively collected lymphatic fluid from children with LMs. Lymphatic fluid was divided depending on the bleeding status into the bleeding and nonbleeding groups. The fluid was subjected to cytological and biochemical analyses to determine protein and cytokine levels. The Mann-Whitney U test was used to compare the two groups. Results: There were significant differences in the levels of interleukin (IL)-6, IL-10, and glucose, and the percentage of white blood cells between the bleeding and nonbleeding groups. There was no significant difference in chlorine and protein content; white blood cell count; and IL-2, IL-4, tumor necrosis factor α, and interferon γ levels between the two groups. Conclusion: Lymphatic fluid is less stable in bleeding LMs than in non-bleeding LMs and is prone to inflammatory reactions. The inflammatory reaction in lymphatic fluid does not stimulate the cytokine storm in blood. The inflammatory reaction due to LMs does not affect the contents of protein and chlorine in lymphatic cyst fluid.

In this paper, a relationship between the spectral zeta series of a class of higher order self-adjoint differential operators on the unit circle and the integral of Green functions is established by Mercer’s Theorem. Furthermore, the explicit expression and the transcendental nature of the spectral series are obtained by the integral representation. Finally, several applications in physics about differential operators’ spectral theory, yellow some further works, and the transcendental nature of some zeta series are listed.

We prove that there is an invariant torus with the given Diophantine frequency vector for a class of Hamiltonian systems defined by an integrable large Hamiltonian function with a large non-autonomous Hamiltonian perturbation. As for application, we prove that a finite network of Duffing oscillators with periodic external forces possesses Lagrange stability for almost all initial data.

目的:探讨微信群管理模式下的延伸护理在慢性心力衰竭患者中的应用效果.方法:选取2020年6月1日～2021年6月1日收治的82例慢性心力衰竭患者为研究对象,按照入院时间的奇偶月份分为对照组40例和观察组42例,对照组给予健康教育,观察组在此基础上给予微信群管理模式下的延伸护理;比较两组家庭监测血压和心率、按时复诊、药物治疗依从性及心功能恢复情况.结果:出院后6个月,观察组家庭自我监测心率、血压、按时复诊、遵医嘱用药、左室射血分数(LVEF)绝对值较基线升高≥20％及护理满意度均优于对照组(P<0.05,P<0.01).结论:微信群管理模式下的延伸护理有助于提高慢性心力衰竭患者自我管理、治疗依从性及护理满意度.

目的 了解经济欠发达地区县-乡-村三级医疗机构工作人员培训需求,为其开展培训工作提供参考价值.方法 对陕西省清涧县人民医院、14个乡镇卫生院、村卫生室共418名工作人员进行问卷调查,采用一般资料调查表、自行设计的县-乡-村三级医疗机构工作人员培训需求调查问卷进行调查.结果 在418名被调查的工作人员中,44.26％的工作人员认为自己掌握的技术不能足够应对现阶段工作;45.69％的工作人员认为最适合的培训方式是参加上级医疗机构的进修学习;44.50％的工作人员最希望的授课老师是三级医院专家;41.87％的工作人员最希望的授课形式是临床跟班式;外出培训最大的担心是培训内容不适用和个人需要承担培训费用;医疗机构目前最需要的是已经接受过全科医学培训的医生.结论 各级卫生主管部门和医疗机构要提高对人才培养重要性和紧迫性的认识,加大人才培养的力度,建立系统化、制度化、常规化的培训及考核体系,切实解决医疗机构人才培养中的困难,建设经费中划定一定比例的经费作为培训的专项经费,并加强对全科医生的培养.

目的 探讨DSA导引下经皮硬化治疗儿童阴茎区静脉畸形的效果和安全性.方法 回顾性分析2016年1月至2017年6月山东大学齐鲁儿童医院采用经皮穿刺硬化治疗的11例阴茎区静脉畸形患儿临床资料.DSA透视下行局部静脉造影,判断瘤巢形态、范围和引流静脉回流情况.根据造影流速情况选择硬化剂(平阳霉素或聚多卡醇),DSA监视下经皮注射治疗.术后1个月复查MRI,显示仍有残留病灶予重复治疗.每次治疗后记录不良反应,随访评价疗效.结果 11例患儿14处病灶共接受32次硬化治疗,平均(2.5±1.0)次/例.随访24个月,6例治愈,3例症状明显缓解,2例部分缓解,均无复发或进展.所有患儿均未出现溃破、出血、感染及功能障碍等严重并发症.结论 DSA引导经皮硬化治疗儿童阴茎区静脉畸形安全有效,不影响阴茎外观和功能,值得临床推广.

比伐芦定是一种抗凝剂,目前广泛用于择期经皮冠状动脉介入治疗术(PCI)中抗凝.不同于普通肝素,比伐芦定能够明显的减少出血副作用.值得注意的是,部分患者用药后出现低血压、恶心、背痛等不良反应.现报道一例比伐芦定致血小板减少的罕见不良反应.

In this paper, we considered the spectral problem and initial value problem of a nonlocal Sturm-Liouville equation with fractional integrals and fractional derivatives. We proved that the fractional operator associated to the nonlocal Sturm-Liouville equation is self-adjoint in Hilbert space. And then, we derived the corresponding spectral problem consists of countable number of real eigenvalues, and the algebraic multiplicity of each eigenvalue is simple. We also discussed the orthogonal completeness of the corresponding eigenfunction system in the Hilbert spaces. Furthermore, we obtained asymptotic properties of eigenvalues and the number of zeros of eigenfunctions by using the perturbation theory for linear operators. Finally, we studied the uniqueness of solutions for the nonlocal Sturm-Liouville equation under some initial value conditions.

神经鞘瘤起源于周围神经髓鞘的雪旺细胞,又称雪旺细胞瘤,由雪旺细胞和丰富的胶原间质组成.神经鞘瘤是周围神经最常见的良性肿瘤,占上肢肿瘤的5％.丛状神经鞘瘤是神经鞘瘤最罕见的组织学亚型之一,占神经鞘瘤的2％～5％.细胞型丛状神经鞘瘤为丛状神经鞘瘤的亚型,更为罕见.本文报道我院收治的1例先天性细胞型丛状神经鞘瘤患儿的诊治情况,现报告如下.

In this paper, we prove a reducibility result for a relativistic Schrödinger equation on torus with time quasi-periodic unbounded perturbations of order 1/2. As far as we known, this is the first reducibility result for the relativistic Schrödinger equation.

In this paper, the author establishes a reduction theorem for linear Schrödinger equation with finite smooth and time-quasi-periodic potential subject to Dirichlet boundary condition by means of KAM (Kolmogorov-Arnold-Moser) technique. Moreover, it is proved that the corresponding Schrödinger operator possesses the property of pure point spectra and zero Lyapunov exponent.

The present paper obtains the infimum of the densities for vibrating string equations in terms of the gap and ratio of the first two eigenvalues. The main result in this paper can be viewed as a new version of the Lyapunov inequality involving the first two eigenvalues. Some new estimates of the gap and ratio are obtained. Furthermore, the classical Lyapunov inequality can be deduced by the main conclusion.

In the present paper, the reducibility is derived for linear wave equation of finite smooth and time-quasi-periodic potential subject to Dirichlet boundary condition. Moreover, it is proved that the corresponding wave operator possesses the property of pure point spectra and zero Lyapunov exponent.

目的:探讨延续性护理联合多媒体方式的健康教育对高血压患者的影响.方法:选取2019年5月1日～7月31日收治的110例高血压患者为研究对象,采用随机数字表法分为观察组和对照组各55例,对照组给予延续性护理联合传统教育干预措施,观察组给予延续性护理联合多媒体方式的健康教育干预措施,两组均干预4周;比较两组生活方式依从性、服药依从性、血压监测、血压达标情况及满意度.结果:观察组生活方式依从性高于对照组(P<0.05),服药依从性优于对照组(P<0.05),血压自我监测情况好于对照组(P<0.05);干预后,观察组血压低于对照组(P<0.05);观察组护理满意度高于对照组(P<0.05).结论:将延续性护理联合应用多媒体方式的强健康教育应用于高血压患者中,能有效提高患者的管理依从性,改善生活质量,提高满意度.