A local criterion for the covering of space by convex bodies

The excess entropy of mixing of mixtures of hard spheres and spherocylinders is determined from an equation of state of hard convex bodies. The obtained dependence of excess entropy on composition was used to find the accuracy of determining ΔSE from relations employed for the correlation and prediction of vapour-liquid equilibrium. Simple rules were proposed for establishing the mean parameter of nonsphericity for mixtures of hard bodies of different shapes allowing to describe the P-V-T behaviour of solutions in terms of the equation of state fo pure substance. The determination of ΔSE by means of these rules is discussed.

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Some Hermite–Hadamard type integral inequalities for convex functions defined on convex bodies in ℝn\mathbb{R}^{n}

Journal of Applied Analysis ◽

10.1515/jaa-2020-2005 ◽

2020 ◽

Vol 26 (1) ◽

pp. 67-77 ◽

Cited By ~ 1

Author(s):

Silvestru Sever Dragomir

Keyword(s):

Euclidean Space ◽

Convex Functions ◽

Convex Bodies ◽

Integral Inequalities ◽

Divergence Theorem ◽

Several Variables ◽

Type Integral ◽

Bounded Convex

AbstractIn this paper, by the use of the divergence theorem, we establish some integral inequalities of Hermite–Hadamard type for convex functions of several variables defined on closed and bounded convex bodies in the Euclidean space {\mathbb{R}^{n}} for any {n\geq 2}.

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A Research on Navigation Star Catalog Selection Algorithm Based on SVM

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.706-708.613 ◽

2013 ◽

Vol 706-708 ◽

pp. 613-617

Author(s):

Fu Cheng Liu ◽

Zhao Hui Liu ◽

Wen Liu ◽

Dong Sheng Liang ◽

Kai Cui ◽

...

Keyword(s):

Support Vector Machine ◽

Field Of View ◽

Support Vector ◽

Selection Algorithm ◽

Boltzmann Entropy ◽

Local Criterion ◽

Star Catalog ◽

Uniform Sampling ◽

Global Criterion ◽

Small Capacity

A navigation star catalog (NSC) selection algorithm via support vector machine (SVM) is proposed in this paper. The sphere spiral method is utilized to generate the sampling boresight directions by virtue of obtaining the uniform sampling data. Then the theory of regression analysis methods is adopted to extract the NSC, and an evenly distributed and small capacity NSC is obtained. Two criterions, namely a global criterion and a local criterion, are defined as the uniformity criteria to test the performance of the NSC generated. Simulations show that, compared with MFM, magnitude weighted method (MWM) and self-organizing algorithm(S-OA), the Boltzmann entropy (B.e) of SVM selection algorithm (SVM-SA) is the minimum, to 0.00207. Simultaneously, under the conditions such as the same field of view (FOV) and elimination of the hole, both the number of guide stars (NGS) and standard deviation (std) of SVM-SA is the least, respectively 7668 and 2.17. Consequently, the SVM-SA is optimal in terms of the NGS and the uniform distribution, and has also a strong adaptability.

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