scholarly journals ISOPERIMETRIC INEQUALITIES FOR Lp GEOMINIMAL SURFACE AREA

2011 ◽  
Vol 53 (3) ◽  
pp. 717-726 ◽  
Author(s):  
BAOCHENG ZHU ◽  
NI LI ◽  
JIAZU ZHOU
Keyword(s):  
Convex Body ◽  
Surface Area ◽  
Type Inequality ◽  
Isoperimetric Inequalities ◽  
Surface Areas ◽  
Cyclic Inequality ◽  
Geominimal Surface Area

AbstractIn this paper, we establish a number of Lp-affine isoperimetric inequalities for Lp-geominimal surface area. In particular, we obtain a Blaschke–Santaló type inequality and a cyclic inequality between different Lp-geominimal surface areas of a convex body.

scholarly journals Some inequalities for the (p,q)-mixed geominimal surface areas and Lp radial Blaschke-Minkowski homomorphisms

Filomat ◽  
2021 ◽  
Vol 35 (4) ◽  
pp. 1393-1403
Author(s):  
Juan Zhang ◽  
Weidong Wang
Keyword(s):  
Surface Area ◽  
Mixed Volume ◽  
Surface Areas ◽  
Cyclic Inequality ◽  
Geominimal Surface Area

Wang et al. introduced Lp radial Blaschke-Minkowski homomorphisms based on Schuster?s radial Blaschke-Minkowski homomorphisms. In 2018, Feng and He gave the concept of (p,q)-mixed geominimal surface area according to the Lutwak, Yang and Zhang?s (p,q)-mixed volume. In this article, associated with the (p,q)-mixed geominimal surface areas and the Lp radial Blaschke-Minkowski homomorphisms, we establish some inequalities including two Brunn-Minkowski type inequalities, a cyclic inequality and two monotonic inequalities.

scholarly journals DualLp-Mixed Geominimal Surface Area and Related Inequalities

2016 ◽  
Vol 2016 ◽  
pp. 1-10
Author(s):  
Tongyi Ma ◽  
Yibin Feng
Keyword(s):  
Surface Area ◽  
Integral Formula ◽  
Isoperimetric Inequalities ◽  
Surface Areas ◽  
Geominimal Surface Area

The integral formula of dualLp-geominimal surface area is given and the concept of dualLp-geominimal surface area is extended to dualLp-mixed geominimal surface area. Properties for the dualLp-mixed geominimal surface areas are established. Some inequalities, such as analogues of Alexandrov-Fenchel inequalities, Blaschke-Santaló inequalities, and affine isoperimetric inequalities for dualLp-mixed geominimal surface areas, are also obtained.

scholarly journals Dual Orlicz mixed geominimal surface areas

Filomat ◽  
2018 ◽  
Vol 32 (14) ◽  
pp. 5053-5061
Author(s):  
Wei Shi ◽  
Weidong Wang ◽  
Tongyi Ma
Keyword(s):  
Surface Area ◽  
Surface Areas ◽  
Geominimal Surface Area

The notion of Lp-geominimal surface area was originally introduced by Lutwak in 1996. Recently, Feng andWang introduced the concept of Lp-dual mixed geominimal surface area based on Lp-dual mixed quermassintegrals. In this paper, based on dual Orlicz mixed quermassintegrals, we define the concept of dual Orlicz mixed geominimal surface area and establish some related inequalities for this new notion.

scholarly journals Lp-dual affine surface areas for the general Lp-intersection bodies

Filomat ◽  
2019 ◽  
Vol 33 (14) ◽  
pp. 4421-4428
Author(s):  
Juan Zhang ◽  
Weidong Wang
Keyword(s):  
Surface Area ◽  
Type Inequality ◽  
Affine Surface ◽  
Affine Surface Area ◽  
Surface Areas ◽  
Intersection Bodies ◽  
Dual Affine

For 0 < p < 1, the notions of symmetric and asymmetric Lp-intersection bodies were introduced by Haberl and Ludwig. Recently, Wang and Li defined the general Lp-intersection bodies. In this paper, associated with the Lp-dual affine surface areas, we give the extremum values of the general Lp-intersection bodies. Moreover, a Brunn-Minkowski type inequality and a monotone inequality for the Lp-dual affine surface area version of general Lp-intersection bodies are established, respectively.

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.

scholarly journals Tuning the hierarchical pore structure of graphene oxide through dual thermal activation for high-performance supercapacitor

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Jeongpil Kim ◽  
Jeong-Hyun Eum ◽  
Junhyeok Kang ◽  
Ohchan Kwon ◽  
Hansung Kim ◽  
...  
Keyword(s):  
Graphene Oxide ◽  
Pore Structure ◽  
Specific Capacitance ◽  
Surface Area ◽  
Thermal Annealing ◽  
High Performance ◽  
Annealing Process ◽  
Supercapacitor Electrode ◽  
Simple Method ◽  
Surface Areas

AbstractHerein, we introduce a simple method to prepare hierarchical graphene with a tunable pore structure by activating graphene oxide (GO) with a two-step thermal annealing process. First, GO was treated at 600 °C by rapid thermal annealing in air, followed by subsequent thermal annealing in N2. The prepared graphene powder comprised abundant slit nanopores and micropores, showing a large specific surface area of 653.2 m2/g with a microporous surface area of 367.2 m2/g under optimized conditions. The pore structure was easily tunable by controlling the oxidation degree of GO and by the second annealing process. When the graphene powder was used as the supercapacitor electrode, a specific capacitance of 372.1 F/g was achieved at 0.5 A/g in 1 M H2SO4 electrolyte, which is a significantly enhanced value compared to that obtained using activated carbon and commercial reduced GO. The performance of the supercapacitor was highly stable, showing 103.8% retention of specific capacitance after 10,000 cycles at 10 A/g. The influence of pore structure on the supercapacitor performance was systematically investigated by varying the ratio of micro- and external surface areas of graphene.

Measuring the Surface Area of a Convex Body

1944 ◽  
Vol 45 (4) ◽  
pp. 793 ◽  
Author(s):  
P. A. P. Moran
Keyword(s):  
Convex Body ◽  
Surface Area

scholarly journals Inequalities for the Surface Area of Projections of Convex Bodies

2018 ◽  
Vol 70 (4) ◽  
pp. 804-823 ◽  
Author(s):  
Apostolos Giannopoulos ◽  
Alexander Koldobsky ◽  
Petros Valettas
Keyword(s):  
Convex Body ◽  
Surface Area ◽  
Convex Bodies ◽  
Maximal Surface ◽  
Projection Body ◽  
Projections Of Convex Bodies ◽  
Lower Dimensional

AbstractWe provide general inequalities that compare the surface area S(K) of a convex body K in ℝn to the minimal, average, or maximal surface area of its hyperplane or lower dimensional projections. We discuss the same questions for all the quermassintegrals of K. We examine separately the dependence of the constants on the dimension in the case where K is in some of the classical positions or K is a projection body. Our results are in the spirit of the hyperplane problem, with sections replaced by projections and volume by surface area.

The new face of large dams in the 21st century

2021 ◽  
Author(s):  
Atal Ahmadzai
Keyword(s):  
Surface Area ◽  
Aquatic Ecosystems ◽  
Energy Demand ◽  
Environmental Aspects ◽  
Water Insecurity ◽  
Surface Areas ◽  
Large Dams ◽  
Physical Attributes ◽  
Under Construction ◽  
Ecological Disturbances

Alerted by increasing water insecurity and energy demand, countries, mainly in the Global South, are building dams of unprecedented magnitude. Hundreds of large dams (≥ 100 metres) have been constructed since 2000, with hundreds more under construction. Analyses of the physical attributes of these dams present a concerning image. While they create expansive reservoirs with large surface areas, they have inefficient surface area-to-volume ratios ('S2VR'). Their unprecedented size and the reservoirs’ expansive surface area, indicate severe environmental costs, mainly through ecological disturbances to the (riverine) aquatic ecosystems; and greenhouse gas emissions (GHG). Other ecological costs due to the larger S2VR include a high evaporation rate and compromised biodiversity of a wider area, both up- and downstream. The safety and environmental aspects of these large dams should be robustly scrutinised.

Sign in / Sign up

Export Citation Format

Share Document