A maximum principle for controlled time-symmetric forward-backward doubly stochastic differential equation with initial-terminal sate constraints

In this paper, we study the optimal control problem of a controlled time-symmetric forward-backward doubly stochastic differential equation with initial-terminal sate constraints. Applying the terminal perturbation method and Ekeland's variation principle, a necessary condition of the stochastic optimal control, i.e., stochastic maximum principle is derived. Applications to backward doubly stochastic linear-quadratic control models are investigated.Comment: 22 page

Primary isolated intracranial Rosai–Dorfman disease: Report of a rare case and review of the literature

Background Intracranial involvement is an uncommon manifestation of Rosai–Dorfman disease (RDD) and had been rarely reported. In this study, we explore clinical characteristics, imageology manifestations and pathological features of primary intracranial RDD so as to improve the understanding for this disease. Methods One case (16-years-old boy) with primary intracranial RDD was analyzed and studied retrospectively by MRI features, histopathological observation and immunohistochemical staining, and the related literatures were reviewed. Results The case was single lesion and involved the dura of the left middle cranial fossa base, which was iso-hypo signal intensity on T1WI and hypointense on T2WI and FLAIR image. The lesion was a homogeneous contrast enhancement mass with dural tail sign and had peritumoral brain edema. Pathological analysis showed the lesion consisted of variable numbers of mature lymphocytes, plasma cells and neutrophils. The characteristic histiocytes were emperipolesis and positively expressed for S-100 and CD-68 and negatively expressed for CD-1a by immunohistochemical analysis. Based on clinical presentations and histological findings after surgical excision, a final diagnosis of primary intracranial RDD was made. Conclusion Primary intracranial RDD, especially located in the cranial base, is exceptionally rare, which hard to be distinguished with meningoma by imageology and clinical manifestations, but could be diagnosed by pathological and immunohistochemical examinations. Surgery is of the most importance treatment and prognosis is optimistic for this disease

Nonlinear dynamic response analysis of a cantilever beam with a breathing crack

The nonlinear dynamic characteristics of plane cracked beam subjected to a harmonic load at the tip are researched. A crack opens and closes during vibration that is simulated as a frictionless plane contact problem, and a finite element contact model for a cantilever cracked beam is established. The quarter-point element is used to describe the crack tip singularity. Based on the proposed finite element contact model, the influence of excitation frequency, crack depth and crack position on nonlinear dynamic characteristics are discussed in detail. Relative amplitude of frequency spectrum with respect to different factors is analyzed to realize sub-harmonics or super-harmonics of cracked beam. The research results demonstrate that there is obvious nonlinear dynamic behavior for plane beam with a fatigue crack, and the different feature of frequency spectrum can be used to identify the beam damage in structure. Meanwhile, the strategy of experimental validation to the FEM results is discussed

Long-term surgical outcomes of primary congenital glaucoma in China

OBJECTIVE: To evaluate the long-term outcomes of three surgical procedures for the treatment of primary congenital glaucoma (PCG). INTRODUCTION: PCG is one of the main causes of blindness in children. There is a paucity of contemporary data on PCG in China. METHODS: A retrospective study of 48 patients (81 eyes) with PCG who underwent primary trabeculectomy, trabeculotomy, or combined trabeculotomy and trabeculectomy (CTT). RESULTS: All patients were less than 4 years (yrs) of age, with a mean age of 2.08 ± 1.23 yrs. The mean duration of follow-up was 5.49 ± 3.09 yrs. The difference in success rates among the three surgical procedures at 1, 3, 6 and 9 yrs was not statistically significant (p = 0.492). However, in patients with over 4 yrs of follow-up, Kaplan-Meier survival analysis revealed that the success rates of trabeculectomy and CTT declined more slowly than that of trabeculotomy. Among the patients, 66.22% acquired good vision (VA >; 0.4), 17.57% acquired fair vision (VA = 0.1 - 0.3), and 16.22% acquired poor vision (VA < 0.1). The patients with good vision were mostly in the successful surgery group. Myopia was more prevalent postoperatively (p = 0.009). Reductions in the cup-disc ratio and corneal diameter were only seen in the successful surgery group (p = 0.000). In addition, the successful surgery group contained more patients that complied with a regular follow-up routine (p = 0.002). DISCUSSION: Our cases were all primary surgeries. Primary trabeculectomy was performed in many cases because no treatment was sought until an advanced stage of disease had been reached. CONCLUSIONS: In contrast to most reports, in the present study, trabeculectomy and CTT achieved higher long-term success rates than trabeculotomy. The patients with successful surgical results had better vision. Compliance with a routine of regular follow-up may increase the chances of a successful surgical outcome

Interval linguistic fuzzy decision making in perspective of preference relations

Consistency analysis is a crucial topic for preference relations. This paper studies the consistency of interval linguistic fuzzy preference relations (ILFPRs) using the constrained interval linguistic arithmetic and introduces a new consistency definition. Then, several properties of this definition are researched. Meanwhile, the connection between this concept and a previous one is discussed. Following this concept, programming models for judging the consistency and for deriving consistent ILFPRs are constructed, respectively. Considering the case that incomplete ILFPRs may be obtained, a programming model for obtaining missing judgments following the consistency discussion is built. Afterwards, the consensus for group decision making (GDM) is studied and a model for adjusting individual ILFPRs to reach the consensus threshold is established. Consequently, an interactive procedure for GDM with ILFPRs is presented. A practical problem is provided to illustrate the utilization of the new algorithm and comparative discussion is offered