scholarly journals Nonnegative forms with sublevel sets of minimal volume

2020 ◽  
Author(s):  
Khazhgali Kozhasov ◽  
Jean Bernard Lasserre
Keyword(s):  
Sum Of Squares ◽  
Gram Matrix ◽  
Euclidean Ball ◽  
Probabilistic Interpretation ◽  
Geometric Properties ◽  
Minimal Volume ◽  
Sublevel Sets ◽  
Sublevel Set

Abstract We show that the Euclidean ball has the smallest volume among sublevel sets of nonnegative forms of bounded Bombieri norm as well as among sublevel sets of sum of squares forms whose Gram matrix has bounded Frobenius or nuclear (or, more generally, p-Schatten) norm. These volume-minimizing properties of the Euclidean ball with respect to its representation (as a sublevel set of a form of fixed even degree) complement its numerous intrinsic geometric properties. We also provide a probabilistic interpretation of the results.

On parallelepipeds of minimal volume containing a convex symmetric body in ℝn

1991 ◽  
Vol 109 (1) ◽  
pp. 125-148 ◽  
Author(s):  
A. Pelczynski ◽  
S. J. Szarek
Keyword(s):  
Local Minimum ◽  
The Body ◽  
Symmetric Body ◽  
Alternative Proof ◽  
Euclidean Ball ◽  
Maximal Volume ◽  
Minimal Volume ◽  
Convex Symmetric Body ◽  
Unit Euclidean Ball ◽  
Image Position

AbstractGiven a convex symmetric body C ⊂ ℝn we put a(C) = |C| sup |P|−1 where the supremum extends over all parallelepipeds containing C and |A| denotes the volume of a set A ⊂ ℝn. Let an = inf {a(C): C ⊂ ℝn}. We show thatwhich slightly improves the estimate due to Dvoretzky and Rogers [6]. In every dimension n we construct a convex symmetric polytope Wn such that the unit Euclidean ball is the ellipsoid of maximal volume inscribed into Wn and the volume of every parallelepiped containing Wn is greater thanfor large n which shows ‘the limit’ to the Dvoretzky Rogers method for bounding an below. We present an alternative proof of the result of I. K. Babenko [l] that . We show that , and that a local minimum of the function C→a(C) for C ⊂ ℝn is attained only at an equiframed convex body (that is, a body such that every point of its boundary belongs to a parallelepiped of minimal volume containing the body).

PEMODELAN MATEMATIS ADSORPSI CO2 DENGAN STRONG BASE ANION EXCHANGE RESIN SEBAGAI ADSORBEN UNTUK PURIFIKASI BIOGAS

2015 ◽  
Vol 5 (1) ◽  
pp. 11
Author(s):  
Anies Mutiari ◽  
Wiratni Wiratni ◽  
Aswati Mindaryani
Keyword(s):  
Anion Exchange ◽  
Pilot Plant ◽  
Exchange Resin ◽  
Anion Exchange Resin ◽  
Scale Up ◽  
Sum Of Squares ◽  
Strong Base ◽  
Model Transfer ◽  
Plant Parameter

Pemurnian biogas telah banyak dilakukan untuk menghilangkan kadar CO2  dan meningkatkan kandungan CH4  yang terkandung di dalamnya. Kandungan CH4 yang tinggi akan memberikan unjuk kerja yang lebih baik. Model  matematis proses adsorpsi CO2 disusun berdasarkan teori lapisan film antar fasa, dimana pada proses yang ditinjau terdapat tiga fase yaitu gas, cair dan padat. Model matematis dari data eksperimental   kecepatan dan kesetimbangan proses adsorpsi CO2 melalui mekanisme pertukaran ion di suatu kolom adsorpsi telah dibuat. Model ini dibuat untuk mencari konstanta yang dapat dipergunakan pada proses scale up data laboratorium ke skala pilot plant. Parameter proses kecepatan yang dicari nilainya adalah koefisien transfer massa massa volumetris CO2 pada fase cair (kLa), koefisien transfer massa volumetris CO2 pada fasegas (kGa) dan tetapan laju reaksi (k1 dan k2). Pada hasil penelitian ini ditunjukkan bahwa nilai parameter yang diperoleh sesuai hasil fitting data dengan model matematis yang digunakan, yaitu model transfer massa pada lapisan film antar fase secara seri: adalah kGa, kla, k1 dan k2  dengan nilai Sum of Squares Error (SSE) rata-rata 0,0431. Perbandingan nilai kGa hasil simulasi dan teoritisnya memberikan kesalahan rata-rata 18,79%. Perbandingan nilai kLa hasil simulasi dan teoritis memberikan kesalahan rata-rata 7,92%.Kata kunci: model matematis, adsorpsi CO2, pemurnian biogas

Using Bayesian network models to incorporate uncertainty in the economic analysis of pollution abatement measures under the water framework directive

2005 ◽  
Vol 5 (6) ◽  
pp. 95-104 ◽  
Author(s):  
D.N. Barton ◽  
T. Saloranta ◽  
T.H. Bakken ◽  
A. Lyche Solheim ◽  
J. Moe ◽  
...  
Keyword(s):  
Water Quality ◽  
At Risk ◽  
Economic Valuation ◽  
Pollution Abatement ◽  
Network Models ◽  
Cost Effective ◽  
Bayesian Belief Networks ◽  
Probabilistic Interpretation ◽  
Belief Networks ◽  
Benefit Cost Analysis

The evaluation of water bodies “at risk” of not achieving the Water Framework Directive's (WFD) goal of “good status” begs the question of how big a risk is acceptable before a programme of measures should be implemented. Documentation of expert judgement and statistical uncertainty in pollution budgets and water quality modelling, combined with Monte Carlo simulation and Bayesian belief networks, make it possible to give a probabilistic interpretation of “at risk”. Combined with information on abatement costs, a cost-effective ranking of measures based on expected costs and effect can be undertaken. Combined with economic valuation of water quality, the definition of “disproportionate cost” of abatement measures compared to benefits of achieving “good status” can also be given a probabilistic interpretation. Explicit modelling of uncertainty helps visualize where research and consulting efforts are most critical for reducing uncertainty. Based on data from the Morsa catchment in South-Eastern Norway, this paper discusses the relative merits of using Bayesian belief networks when integrating biophysical modelling results in the benefit-cost analysis of derogations and cost-effectiveness ranking of abatement measures under the WFD.

Some Properties of Para-Sasakian Manifolds

2017 ◽  
Vol 5 (2) ◽  
pp. 73-78
Author(s):  
Jay Prakash Singh ◽  
Keyword(s):  
Vector Field ◽  
Killing Vector ◽  
Sasakian Manifold ◽  
Subject Classification ◽  
Killing Vector Field ◽  
Sasakian Manifolds ◽  
Geometric Properties ◽  
Paper Author

In this paper author present an investigation of some differential geometric properties of Para-Sasakian manifolds. Condition for a vector field to be Killing vector field in Para-Sasakian manifold is obtained. Mathematics Subject Classification (2010). 53B20, 53C15.

Effect of 12 months of creatine supplementation and whole-body resistance training on measures of bone, muscle and strength in older males

2020 ◽  
pp. 026010602097524
Author(s):  
Darren G Candow ◽  
Philip D Chilibeck ◽  
Julianne Gordon ◽  
Emelie Vogt ◽  
Tim Landeryou ◽  
...  
Keyword(s):  
Bone Mineral Density ◽  
Resistance Training ◽  
Bone Mineral ◽  
Creatine Supplementation ◽  
Whole Body ◽  
Mineral Density ◽  
Geometric Properties ◽  
Section Modulus ◽  
Body Resistance ◽  
Older Males

Background: The combination of creatine supplementation and resistance training (10–12 weeks) has been shown to increase bone mineral content and reduce a urinary indicator of bone resorption in older males compared with placebo. However, the longer-term effects (12 months) of creatine and resistance training on bone mineral density and bone geometric properties in older males is unknown. Aim: To assess the effects of 12 months of creatine supplementation and supervised, whole-body resistance training on bone mineral density, bone geometric properties, muscle accretion, and strength in older males. Methods: Participants were randomized to supplement with creatine ( n = 18, 49–69 years, 0.1 g·kg-1·d-1) or placebo ( n = 20, 49–67 years, 0.1 g·kg-1·d-1) during 12 months of supervised, whole-body resistance training. Results: After 12 months of training, both groups experienced similar changes in bone mineral density and geometry, bone speed of sound, lean tissue and fat mass, muscle thickness, and muscle strength. There was a trend ( p = 0.061) for creatine to increase the section modulus of the narrow part of the femoral neck, an indicator of bone bending strength, compared with placebo. Adverse events did not differ between creatine and placebo. Conclusions: Twelve months of creatine supplementation and supervised, whole-body resistance training had no greater effect on measures of bone, muscle, or strength in older males compared with placebo.

Asymptotic behaviour of sample weighted circuits representing recurrent Markov chains

1990 ◽  
Vol 27 (03) ◽  
pp. 545-556 ◽  
Author(s):  
S. Kalpazidou
Keyword(s):  
Markov Chain ◽  
Markov Chains ◽  
Asymptotic Behaviour ◽  
Probabilistic Interpretation ◽  
Stationary Markov Chain

The asymptotic behaviour of the sequence (𝒞 n (ω), wc,n (ω)/n), is studied where 𝒞 n (ω) is the class of all cycles c occurring along the trajectory ωof a recurrent strictly stationary Markov chain (ξ n ) until time n and wc,n (ω) is the number of occurrences of the cycle c until time n. The previous sequence of sample weighted classes converges almost surely to a class of directed weighted cycles (𝒞∞, ω c ) which represents uniquely the chain (ξ n ) as a circuit chain, and ω c is given a probabilistic interpretation.

Sign in / Sign up

Export Citation Format

Share Document