Cauchy’s surface area formula in the Heisenberg groups

2021 ◽  
Author(s):  
Yen-Chang Huang
Keyword(s):  
Surface Area ◽  
Heisenberg Groups ◽  
Area Formula

IMPACT OF PLASMA SURFACE TREATMENT ON BAMBOO CHARCOAL/SILVER NANOCOMPOSITE

2016 ◽  
Vol 23 (01) ◽  
pp. 1550089 ◽  
Author(s):  
K. VIGNESH ◽  
K. A. VIJAYALAKSHMI ◽  
N. KARTHIKEYAN
Keyword(s):  
Antibacterial Activity ◽  
Plasma Treatment ◽  
Surface Area ◽  
Functional Groups ◽  
Oxygen Plasma ◽  
Bet Surface Area ◽  
Oxygen Plasma Treatment ◽  
Bamboo Charcoal ◽  
Area Formula ◽  
Vis Spectroscopy

Bamboo charcoal (BC) accompanied silver (Ag) nanocomposite is synthesized through sol–gel method. The produced BC/Ag nanocomposite was surface modified by air and oxygen plasma treatments. Silver ions (Ag[Formula: see text]) will serve to improve the antibacterial activity as well as the surface area of BC. Plasma treatment has improved the surface functional groups, crystalline intensity and antibacterial activity of the prepared nanocomposite. Scanning electron microscopy (SEM) and X-ray diffraction (XRD) studies show that Ag nanoparticles have good agreement with BC and the particle size has a mean diameter of 20–40[Formula: see text]nm. We observe the carboxyl functional groups in Fourier transform infrared spectroscopy (FTIR) after the oxygen plasma treatment. Moreover surface area and adsorption were analyzed by using the Brunauer, Emmett and Teller (BET) surface area ([Formula: see text]) and UV–Vis spectroscopy.

scholarly journals ECONOMICAL TORIC SPINES VIA CHEEGER'S INEQUALITY

2009 ◽  
Vol 01 (02) ◽  
pp. 101-111 ◽  
Author(s):  
NOGA ALON ◽  
BO'AZ KLARTAG
Keyword(s):  
Recent Result ◽  
Surface Area ◽  
Isoperimetric Inequality ◽  
Short Proof ◽  
General Idea ◽  
Dimensional Torus ◽  
Area Formula ◽  
Discrete Analogues

Let [Formula: see text] denote the graph whose set of vertices is {0,…,m - 1}d, where two distinct vertices are adjacent if and only if they are either equal or adjacent in the m-cycle Cm in each coordinate. Let [Formula: see text] denote the graph on the same set of vertices in which two vertices are adjacent if and only if they are adjacent in one coordinate in Cm and equal in all others. Both graphs can be viewed as graphs of the d-dimensional torus. We prove that one can delete [Formula: see text] vertices of G1 so that no topologically nontrivial cycles remain. This improves an O(d log 2 (3/2)md - 1) estimate of Bollobás, Kindler, Leader and O'Donnell. We also give a short proof of a result implicit in a recent paper of Raz: one can delete an [Formula: see text] fraction of the edges of G∞ so that no topologically nontrivial cycles remain in this graph. Our technique also yields a short proof of a recent result of Kindler, O'Donnell, Rao and Wigderson; there is a subset of the continuous d-dimensional torus of surface area [Formula: see text] that intersects all nontrivial cycles. All proofs are based on the same general idea: the consideration of random shifts of a body with small boundary and no nontrivial cycles, whose existence is proved by applying the isoperimetric inequality of Cheeger or its vertex or edge discrete analogues.

Brunn-Minkowski Theory and Cauchy’s Surface Area Formula

2017 ◽  
Vol 124 (10) ◽  
pp. 922
Author(s):  
Emmanuel Tsukerman ◽  
Ellen Veomett
Keyword(s):  
Surface Area ◽  
Area Formula

scholarly journals Lomustine Analogous Drug Structures for Intervention of Brain and Spinal Cord Tumors: The Benefit of In Silico Substructure Search and Analysis

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
Ronald Bartzatt
Keyword(s):  
Surface Area ◽  
Anticancer Agents ◽  
In Silico ◽  
Hierarchical Cluster ◽  
Oral Drug ◽  
Polar Surface Area ◽  
Area Formula ◽  
Mean Values ◽  
Polar Surface ◽  
The Central Nervous System

Lomustine is a nitrosourea anticancer agent shown to be effective for treatment of childhood medulloblastoma. In silico substructure searches produced 17 novel nitrosourea agents analogous to lumustine and retaining activity for DNA alkylation and cytotoxic activity. The mean values for Log P, polar surface area, formula weight, number of oxygens & nitrogens, and rotatable bonds were 2.524, 62.89 Anstroms2, 232.8, 5, and 2, respectively. All 17 agents have formula weight less than 450 and Log P less than 5, two criteria preferred for blood-brain barrier penetration. These agents have a polar surface area less than 90 Angstroms2. Each show zero violations of the Rule of five indicating favorable drug likeness and oral drug activity. Hierarchical cluster analysis indicated that 16 of the novel agents were highly similar to lomustine, save for agent 12 which bears a hydroxylated branched carbon substituent. A total of 17 novel anticancer agents were elucidated having molecular properties very effective for penetrating through the BBB and into the central nervous system. This study shows the effectiveness of in silico search and recognition of anticancer agents that are suitable for the clinical treatment of brain tumors.

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