Comparison of the Minimum Bounding Rectangle and Minimum Circumscribed Ellipse of Rain Cells from TRMM

Based on the TRMM dataset, this paper compares the applicability of the improved MCE(minimum circumscribed ellipse), MBR(minimum bounding rectangle), and DIA(direct indexing area) methods for rain cell fitting. These three methods can reflect the geometric characteristics of clouds and apply geometric parameters to estimate the real dimensions of rain cells. The MCE method shows a major advantage in identifying the circumference of rain cells. The circumference of rain cells identified by MCE in most samples is smaller than that identified by DIA and MBR, and more similar to the observed rain cells. The area of rain cells identified by MBR is relatively robust. For rain cells composed of many pixels(N> 20), the overall performance is better than that of MCE, but the contribution of MBR to the best identification results,which have the shortest circumference and the smallest area, is less than that of MCE. The DIA method is best suited to small rain cells with a circumference of less than 100 km and an area of less than 120 km^(2), but the overall performance is mediocre. The MCE method tends to achieve the highest success at any angle, whereas there are fewer “best identification”results from DIA or MBR and more of the worst ones in the along-track direction and cross-track direction. Through this comprehensive comparison, we conclude that MCE can obtain the best fitting results with the shortest circumference and the smallest area on behalf of the high filling effect for all sizes of rain cells.

An Inequality Concerning the Center of Simplex's Circumscribed Sphere

Let A={A_1, A_2,…, A_(n+1)} be a simplex in E^n which its center O of circumscribed sphere is in inside of A. If R and R_i are radiuses of A_i respectively (A_i={A_1, A_2,…, A_(i-1), O, A_(i+1),…,A_(n+1)} ,i=1,2,…,n+1),then we have The equality holds if and only if A is a regular simplex.

Subtotal gastrectomy combined with chemotherapy: An effective therapy for patients with circumscribed Borrmann type Ⅳ gastric cancer

BACKGROUND Although Borrmann type Ⅳ(B-4) gastric cancer has a higher mortality rate and presents distant metastasis easily, especially peritoneal metastasis, when diagnosed, some B-4 patients were found to have no distant metastasis by preoperative detection and underwent curative surgery, which was defined as circumscribed B-4 in our study. In this study, we focused on the circumscribed B-4 patients without distant metastasis during surgery to identify factors related to prognosis and postoperative peritoneal cavity metastasis(PPCM), which is important for selecting an appropriate therapeutic strategy.AIM To identify factors related to the prognosis and PPCM of B-4 patients.METHODS A total of 117 B-4 patients who underwent gastrectomy between January 2005 and December 2012 were included in this study. Survival analysis was performed using Kaplan–Meier analysis and Cox multivariate models. Pearson correlation analyses were performed to identify the factors related to PPCM. All statistical analyses were performed using SPSS 20.0.RESULTS Lymph node status, gastrectomy type, and postoperative chemotherapy were independent prognostic factors in 117 circumscribed B-4 patients. Subtotal gastrectomy combined with chemotherapy could significantly improve the longterm survival time. Six patients who were diagnosed with pN0 and received the combination therapy had a 3-year survival rate of 100% and a median survival of 77.7 mo. Even for patients with metastatic lymph nodes(n = 13), the combination therapy also increased the 3-year overall survival rate to 57.1%. In addition, positive lymph node status was the only factor(P = 0.005) correlated with PPCM in certain B-4 patients, and chemotherapy was useful for suppressing PPCM in patients with subtotal gastrectomy but not in those with total gastrectomy.CONCLUSION Lymph node status is an independent prognostic factor for circumscribed B-4 patients. In addition, subtotal gastrectomy and postoperative chemotherapy could effectively improve prognosis and even suppress PPCM.

On a Fixed Value Theorem for Directed Areas in Conic Circumscribed Polygons and Applications

Using polar equations for conic sections, we research conic circumscribed n-sided polygons（n ≥ 4） deeply on the basis of papers[1-3]. We obtain a general fixed value theorem for directed areas of some triangles in conic circumscribed n-sided polygons and derive as many as n（n - 3） concurrent points of three lines and some other collinear, equiareal results in conic circumscribed n-sided polygons（n ≥ 4）. So the results of papers[1-3] are unified.

A case of circumscribed choroidal hemangioma in Sturge-Weber syndrome in China

We present a case of circumscribed choroidal hemangioma (CCH) in Sturge-Weber syndrome in a 30-year-old woman with congenital port-wine stains on the left side of face involving the upper eyelid, cheek and the nose, and she had undergone facial hemangioma surgery 3 years ago suggestive of Sturge-Weber syndrome. She presented with a 1-month history of rapidly decreased visual acuity (VA) to counting fingers in the left eye which had no prior history of visual problem. And there was no evidence of glaucoma. At 3 months after the treatment of the standard photodynannic therapy (PDT) the VA was 20/200. For some reasons, we have no idea about the changes of tumor thickness and subretinal fluid. We confirmed the curative effect of PDT treatment for CCH because of the significantly improved VA in the bad eye.

Comparison of outcomes between overlapping-spot and single-spot photodynamic therapy for circumscribed choroidal hemangioma

AIM: To compare the efficacy and safety of photodynamic therapy(PDT) with overlapping multiple spots and single spot for treating circumscribed choroidal hemangioma. · METHODS: Twenty-two patients(22 eyes) with symptomatic circumscribed choroidal hemangioma received PDT treatment. Fourteen patients received overlapping spots(two to three spots) PDT,whereas eight patients received single-spot PDT. Laser was used at 50J/cm2for 83s in the overlapping-spot group and 50J/cm2for 166s in the single-spot group. Clinical examination,funduscopy,fluorescein angiography,and ultrasonography were performed at baseline and after treatment. ·RESULTS: The mean follow-up time was 28.5 ±8.0 months in the overlapping-spot group and 27.0 ±5.0 months in the single-spot group. Nine patients(64.2%) had their vision improved over two lines on the Snellen chart,and five patients showed stable visual acuity in the overlapping-spot group. The mean thickness of tumor decreased from 2.7 ±0.8mm to 1.2±0.9mm,and the mean greatest tumor linear dimension decreased from 7.4 ± 1.5mm to 4.5 ±3.5mm after treatment. In the single-spot group,two patients(25%) had their vision improved over two lines on the Snellen chart,and six patients had unchanged stable vision. The mean tumor thickness in this group decreased from 2.5±0.7mm to 1.4±1.0mm,and the mean greatest tumor linear dimension decreased from 7.2±1.3mm to 4.7±3.6mm. No significant differences in visual improvement and tumor regression were found between the two groups. ·CONCLUSION:Overlapping-spotPDTunderappropriate treatment parameters and strategies is as effective andsafe as single-spot PDT for treating symptomatic circumscribed choroidal hemangioma. Improved or stabilized visual acuity was achieved as a result of tumor regression.

Treatment review of sight threatening circumscribed choroidal haemangioma

AIMTo describe our clinical experience in treating circumscribed choroidal haemangioma (CCH) in a tertiary referral centre over a fifteen year period prior to photodynamic therapy.

High-dose ruthenium-106 plaque therapy for circumscribed choroidal hemangioma: a retrospective study of 25 Chinese patients

AIM:To evaluate the efficacy and safety of ruthenium-106(106Ru)plaque radiotherapy at a dose(>50 Gy)higher than recommended(29-50 Gy)for treatment of circumscribed choroidal hemangioma(CCH)in Chinese patients.METHODS:This retrospective study included 25symptomatic CCH patients undergoing 106Ru plaque brachytherapy involving 25 eyes between January 2005and August 2016.Ophthalmic examination was performed at the baseline and at each post-treatment follow-up visit,using best-corrected visual acuity(BCVA),dilated fundus examination,and B-scan ultrasonography.The primary efficacy outcome measures included the changes in BCVA and hemangioma dimensions at the last followup visit from the baseline.RESULTS:The mean follow-up duration was 28.0±26.6(range,12-110)mo.All the hemangiomas were located in the posterior pole except for two involving the fovea.The mean apex dose of 106Ru plaque radiotherapy was84.4±19.7 Gy.The mean BCVA improved from 41.4±29.3(0-97)at the baseline to 53.0±33.8(0-97)ETDRS letters at the last visit(P=0.01).The mean hemangioma height declined from 3.98±0.88(2.40-5.50)mm to 0.84±1.63(0-6.47)mm(P≤0.001),and the greatest linear diameter(GLD)reduced from 9.36±2.23(6.80-15.00)to 7.40±2.45(0-13.00)mm(P≤0.001).Hemangioma size increased in one(4%)eye with a worsened vision,and subretinal fluid completely resolved in all but one patient(4%).Radiationrelated retinopathy was observed in two patients at posttreatment 9 and 11mo,respectively.CONCLUSION:106Ru plaque brachytherapy at a dose(>50 Gy)higher than recommended(29-50 Gy)is an effective treatment regimen for symptomatic CCH associated with significantly improved visual acuity and a favorable safety profile in Chinese patients.

Minimal circumscribed Hermitian ellipsoid of Hartogs domains and an application to an extremal problem

In this paper we construct circumscribed Hermitian ellipsoids of Hartogs domains of least volume and as an application, we obtain the Carathéodory extremal mappings between the Hartogs domains and the unit ball, and also give an explicit formula for calculating the extremal values.

Predictors and outcomes of photodynamic therapy on circumscribed choroidal hemangiomas in Chinese patients

Choroidal hemangiomas （CHs） are relatively rare,benign,vascular,hamartomatous tumors.They are categorized to circumscribed choroidal hemangiomas （CCHs） or diffuse choroidal hemangiomas （DCHs） clinically and histologically.Although circumscribed CHs （CCHs） are often asymptomatic,they can affect visual acuity （VA） if they are situated beneath the fovea,where they can cause accumulation of secondary subretinal fluid and/or cystic retinal degeneration.Due to its minimal invasiveness and negligible toxicity to the normal retina,photodynamic therapy （PDT） with verteporfin has been applied widely in the treatment of CCH.1 Treatment strategies for CCHs should take into account tumor size,anatomic location,VA,and presence/absence of complications.The present study was conducted to identify potential predictors of successful PDT treatment other than those previously reported.We also present alternative treatment modalities for larger,more complicated CCHs.Keywords：circumscribed choroidalhemangiomas; photodynamic therapy; tumor height; predictors and outcomes;success rate;fluorescence angiography; indocyanine green angiography

Initial transcatheter thrombolysis for acute superior mesenteric venous thrombosis

AIM: To determine the optimal initial treatment modality for acute superior mesenteric vein thrombosis (ASMVT) in patients with circumscribed peritonitis.

The Extremal Problem on Cartan-egg Domain of the First Type

In this paper,we study the extremal problem on Cartan-egg domain of the first type by using some inequalities.The extremal mapping and extremal value between the first type of Cartan-egg domain and the unit ball when k≤1 and k=2,m=2 are constructed.

Testing method for veer of table tennis ball

Under the premise of fully respecting Technical Leaflet T3developed by the International Table Tennis Federation(I T T F),this paper proposes an effective method for testing the veer degree of the table tennis ball based on airflow suspension and machine vision.By sequentially capturing the images of the ball in the stable state of spinning and suspension,a set of fitting circle centres from different circular sections can be obtained by circle fitting through the least square method.The minimum circumscribed circle(MCC)diameter of these centres is served as a basic parameter to evaluate the veer degree of the ball.Experimental results show that this diameter can effectively reflect the veer degree of the ball.The method proposed in this papercan provide a technical basis for the veer online testing of the table tennis ball.

Palisaded encapsulated neuroma of the upper lip

Palisaded encapsulated neuroma (PEN;solitary circumscribed neuroma) is a benign and hyperplastic lesion consisting of Schwann cells. PEN of the lower lip was reported by Tomich and Moll [1] 35 years ago. However, the accumulation of the information about PEN which occurred in the oral mucosa was not enough. This article describes a case of a PEN on the upper lip of a 41-year-old woman. The lesion with 0.7 cm diameter was performed excisional biopsy. Histologically, the tumor was almost circumscribed by thin fibrous capsule, and consisted of diffusely and dense proliferation of the spindle shape cells arranged in interlacing fascicles. Focal suggestions of nuclear pal-isaded growth were indicated within the tumor. Immunohistochemicallly, the fascicles of tumor cells were positive for S-100 protein, and vimentin and negative for α-actin and GFAP. A few numbers of axons were demonstrated by anti-neurofilament antibody in this lesion. Therefore, the definitive diagnosis was PEN.

Automatic recognition and intelligent analysis of central shrinkage defects of continuous casting billets based on deep learning

The internal quality inspection of the continuous casting billets is very important,and mis-inspection will seriously affect the subsequent production process.The UNet-VGG16 transfer learning model was used for semantic segmentation of the central shrinkage defects of the continuous casting billets.The automatic recognition accuracy of the central shrinkage defects of the continuous casting billets reaches more than 0.9.We use the minimum circumscribed rectangle to quantify the geometric dimensions such as length,width and area of the central shrinkage defects and use the threshold method to rate the central shrinkage defects of the continuous casting billets.The results show that all the testing images are rated correctly,and this method achieves the automatic recognition and intelligent analysis of the central shrinkage defects of the continuous casting billets.

Extremal problems on the Hua domain of the first type

In this paper we study some extremal problems between the Hua domain of the first type and the unit ball.

Some basic inequalities in higher dimensional non-Euclid space

In this paper, the concept of a finite mass-points system ΣN(H(A))(N > n) being in a sphere in an n-dimensional hyperbolic space H n and a finite mass-points system ΣN(S(A))(N > n) being in a hyperplane in an n-dimensional spherical space S n is introduced, then, the rank of the Cayley-Menger matrix-ΛN(H) (or a-ΛN(S)) of the finite mass-points system ΣN(S(A)) (or ΣN(S(A))) in an n-dimensional hyperbolic space H n (or spherical space S n) is no more than n + 2 when ΣN(H(A))(N > n) (or ΣN(S(A))(N > n)) are in a sphere (or hyperplane). On the one hand, the Yang-Zhang’s inequalities, the Neuberg-Pedoe’s inequalities and the inequality of the metric addition in an n-dimensional hyperbolic space H n and in an n-dimensional spherical space S n are established by the method of characteristic roots. These are basic inequalities in hyperbolic geometry and spherical geometry. On the other hand, some relative problems and conjectures are brought.