An estimate for meromorphic functions with finite spherical surface area satisfying a minimum modulus condition

1975 ◽  
Vol 80 (2) ◽  
pp. 81-84
Author(s):  
Douglas Michael Campbell
Keyword(s):  
Surface Area ◽  
Meromorphic Functions ◽  
Spherical Surface ◽  
Minimum Modulus ◽  
Modulus Condition

The Maximum Modulus of Normal Meromorphic Functions and Applications to Value Distribution

1970 ◽  
Vol 22 (4) ◽  
pp. 803-814 ◽  
Author(s):  
Paul Gauthier
Keyword(s):  
Holomorphic Function ◽  
Unit Disc ◽  
Meromorphic Functions ◽  
Normal Family ◽  
Holomorphic Functions ◽  
Maximum Modulus ◽  
Value Distribution ◽  
Minimum Modulus ◽  
Image Position

Let f(z) be a function meromorphic in the unit disc D = (|z| < 1). We consider the maximum modulusand the minimum modulusWhen no confusion is likely, we shall write M(r) and m(r) in place of M(r,f) and m(r,f).Since every normal holomorphic function belongs to an invariant normal family, a theorem of Hayman [6, Theorem 6.8] yields the following result.THEOREM 1. If f(z) is a normal holomorphic function in the unit disc D, then(1)This means that for normal holomorphic functions, M(r) cannot grow too rapidly. The main result of this paper (Theorem 5, also due to Hayman, but unpublished) is that a similar situation holds for normal meromorphic functions.

scholarly journals Eremenko’s Conjecture for Functions with Real Zeros: The Role of the Minimum Modulus

2020 ◽  
Author(s):  
D A Nicks ◽  
P J Rippon ◽  
G M Stallard
Keyword(s):  
Finite Order ◽  
Entire Functions ◽  
Minimum Modulus ◽  
Real Zeros ◽  
Modulus Condition ◽  
Transcendental Entire Functions

Abstract We consider the class of real transcendental entire functions $f$ of finite order with only real zeros and show that if the iterated minimum modulus tends to $\infty $, then the escaping set $I(\,f)$ of $f$ has the structure of a spider’s web, in which case Eremenko’s conjecture holds. This minimum modulus condition is much weaker than that used in previous work on Eremenko’s conjecture. For functions in this class, we analyse the possible behaviours of the iterated minimum modulus in relation to the order of the function $f$.

Preparation and characterisation of vanadium pentoxide supported rhodium catalyst

1988 ◽  
Vol 46 ◽  
pp. 946-947
Author(s):  
A. Legrouri
Keyword(s):  
Aqueous Solution ◽  
Thermal Decomposition ◽  
Physicochemical Properties ◽  
Surface Area ◽  
Vanadium Pentoxide ◽  
High Purity ◽  
Gas Adsorption ◽  
Rhodium Catalyst ◽  
Optical Methods ◽  
Reducible Oxides

The industrial importance of metal catalysts supported on reducible oxides has stimulated considerable interest during the last few years. This presentation reports on the study of the physicochemical properties of metallic rhodium supported on vanadium pentoxide (Rh/V2O5). Electron optical methods, in conjunction with other techniques, were used to characterise the catalyst before its use in the hydrogenolysis of butane; a reaction for which Rh metal is known to be among the most active catalysts.V2O5 powder was prepared by thermal decomposition of high purity ammonium metavanadate in air at 400 °C for 2 hours. Previous studies of the microstructure of this compound, by HREM, SEM and gas adsorption, showed it to be non— porous with a very low surface area of 6m2/g3. The metal loading of the catalyst used was lwt%Rh on V2Q5. It was prepared by wet impregnating the support with an aqueous solution of RhCI3.3H2O.

Cell morphology, volume, and surface area determinations from multilevel contouring within HVEM micrographs of serial sections and whole-cell mounts

1987 ◽  
Vol 45 ◽  
pp. 588-589
Author(s):  
M. Marko ◽  
A. Leith ◽  
D. Parsons
Keyword(s):  
Surface Area ◽  
Electron Micrographs ◽  
Cell Morphology ◽  
Individual Variation ◽  
Serial Section ◽  
Stereo Pair ◽  
Complex Structures ◽  
Serial Sections ◽  
Surface Areas ◽  
Computer Based

The use of serial sections and computer-based 3-D reconstruction techniques affords an opportunity not only to visualize the shape and distribution of the structures being studied, but also to determine their volumes and surface areas. Up until now, this has been done using serial ultrathin sections.The serial-section approach differs from the stereo logical methods of Weibel in that it is based on the Information from a set of single, complete cells (or organelles) rather than on a random 2-dimensional sampling of a population of cells. Because of this, it can more easily provide absolute values of volume and surface area, especially for highly-complex structures. It also allows study of individual variation among the cells, and study of structures which occur only infrequently.We have developed a system for 3-D reconstruction of objects from stereo-pair electron micrographs of thick specimens.

Surface fields excited by a vertical electric point source located on a conducting concave spherical surface

1981 ◽  
Vol 64 (9) ◽  
pp. 79-88 ◽  
Author(s):  
Kazuyoshi Inami ◽  
Kunio Sawaya ◽  
Yasuto Mushiake
Keyword(s):  
Point Source ◽  
Spherical Surface ◽  
Surface Fields

Risk Factors for Bleeding during Treatment of Acute Venous Thromboembolism

1996 ◽  
Vol 76 (05) ◽  
pp. 682-688 ◽  
Author(s):  
Jos P J Wester ◽  
Harold W de Valk ◽  
Karel H Nieuwenhuis ◽  
Catherine B Brouwer ◽  
Yolanda van der Graaf ◽  
...  
Keyword(s):  
Risk Factors ◽  
Venous Thromboembolism ◽  
Surface Area ◽  
Body Surface Area ◽  
Body Surface ◽  
Small Body ◽  
Bleeding Risk ◽  
Risk Scores ◽  
Risk Of Bleeding ◽  
Acute Venous Thromboembolism

Summary Objective: Identification of risk factors for bleeding and prospective evaluation of two bleeding risk scores in the treatment of acute venous thromboembolism. Design: Secondary analysis of a prospective, randomized, assessor-blind, multicenter clinical trial. Setting: One university and 2 regional teaching hospitals. Patients: 188 patients treated with heparin or danaparoid for acute venous thromboembolism. Measurements: The presenting clinical features, the doses of the drugs, and the anticoagulant responses were analyzed using univariate and multivariate logistic regression analysis in order to evaluate prognostic factors for bleeding. In addition, the recently developed Utrecht bleeding risk score and Landefeld bleeding risk index were evaluated prospectively. Results: Major bleeding occurred in 4 patients (2.1%) and minor bleeding in 101 patients (53.7%). For all (major and minor combined) bleeding, body surface area ≤2 m2 (odds ratio 2.3, 95% Cl 1.2-4.4; p = 0.01), and malignancy (odds ratio 2.4, 95% Cl 1.1-4.9; p = 0.02) were confirmed to be independent risk factors. An increased treatment-related risk of bleeding was observed in patients treated with high doses of heparin, independent of the concomitant activated partial thromboplastin time ratios. Both bleeding risk scores had low diagnostic value for bleeding in this sample of mainly minor bleeders. Conclusions: A small body surface area and malignancy were associated with a higher frequency of bleeding. The bleeding risk scores merely offer the clinician a general estimation of the risk of bleeding. In patients with a small body surface area or in patients with malignancy, it may be of interest to study whether limited dose reduction of the anticoagulant drug may cause less bleeding without affecting efficacy.

Low-Degree Tibial Slope Angle Prevents Component Overhang by Enlarging the Lateral Plateau Surface Area in Total Knee Arthroplasty

2020 ◽  
Author(s):  
Mehmet Emin Simsek ◽  
Mustafa Akkaya ◽  
Safa Gursoy ◽  
Özgür Kaya ◽  
Murat Bozkurt
Keyword(s):  
Total Knee Arthroplasty ◽  
Surface Area ◽  
Knee Arthroplasty ◽  
Tibial Plateau ◽  
Slope Angle ◽  
Three Dimensional ◽  
Tibial Slope ◽  
Total Knee ◽  
Lateral Plateau ◽  
Gender Groups

AbstractThis study aimed to investigate whether overhang or underhang around the tibial component that occurs during the placement of tibial baseplates was affected by different slope angles of the tibial plateau and determine the changes in the lateral and medial plateau diameters while changing the slope angle in total knee arthroplasty. Three-dimensional tibia models were reconstructed using the computed tomography scans of 120 tibial dry bones. Tibial plateau slope cuts were performed with 9, 7, 5, 3, and 0 degrees of slope angles 2-mm below the subchondral bone in the deepest point of the medial plateau. Total, lateral, and medial tibial plateau areas and overhang/underhang rates were measured at each cut level. Digital implantations of the asymmetric and symmetric tibial baseplates were made on the tibial plateau with each slope angles. Following the implantations, the slope angle that prevents overhang or underhang at the bone border and the slope angle that has more surface area was identified. A significant increase was noted in the total tibial surface area, lateral plateau surface area, and lateral anteroposterior distance, whereas the slope cut angles were changed from 9 to 0 degrees in both gender groups. It was found that the amount of posteromedial underhang and posterolateral overhang increased in both the asymmetric and symmetric tibial baseplates when the slope angle was changed from 0 to 9 degrees. Although the mediolateral diameter did not change after the proximal tibia cuts at different slope angles, the surface area and anteroposterior diameter of the lateral plateau could change, leading to increased lateral plateau area. Although prosthesis designs are highly compatible with the tibial surface area, it should be noted that the component overhangs, especially beyond the posterolateral edge, it can be prevented by changing the slope cut angle in males and females.

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