SOME INEQUALITIES ABOUT DUAL MIXED VOLUMES OF STAR BODIES

The authors establish some inequalities about the dual mixed volumes of star bodies in Rn. These inequalities are the analogue in the Brunn-Minkowski theory of the inequalities of Marcus-Lopes and Bergstrom about symmetric functions of positive reals.

On the L_p-Dual Mixed Volumes

We establish the cyclic inequality for i-th L p-dual mixed volume and Lp-dual Urysohn inequality between p-mean width and Lp-dual quermassintegral. Moreover, the dual isoperimetric inequality for Lp-dual mixed volume is proved, which is an extension of the classical dual isoperimetric inequality.

EVOLUTION FILTRATION PROBLEMS WITH SEAWATER INTRUSION: TWO-PHASE FLOW DUAL MIXED VARIATIONAL ANALYSIS

Tow-phase flow mixed variational formulations of evolution filtration problems with seawater intrusion are analyzed. A dual mixed fractional flow velocity-pressure model is considered with an air-fresh water and a fresh water-seawater characterization. For analysis and computational purposes, spatial decompositions based on nonoverlapping multidomains, above and below the sea level, are variationally introduced with internal boundary fluxes dualized as weak transmission constraints. Further, parallel augmented and exactly penalized duality algorithms, and proximation semi-implicit time marching schemes, are established and analyzed.

Experimental Investigation of Environmental Hydraulic Parameters for Dual Mixed Media Biofilter for Greywater Treatment

Laboratory scale model of DMMBF （dual mixed media biofilter） were designed and installed in AI-Mustansiriya University Environmental Hydraulic Lab. Experiments were conducted using two mixed layers through PVR column--2.2 m height and 300 mm diameter. The first mixed media filter of depth 640mm mixed of sand, rice husk and granular activated carbon. The percentage volume mix is 1：1：1. While the other mixed media of depth 740 mm, consisting of coal, crash porcelinaite, rock and granite with equally percentage volume. Fifty samples were collected during the experiments, which was spread over a period of forty two weeks. The obtained results indicate that when the flow loading raised from 0.15 L/min to 2.7 L/rain, the removal efficiency of BOD decreased 8%-11%, and the removal efficiency of COD deceased 3%-4%, while the removal efficiency of turbidity increased with the decreasing of hydraulic loading. The results showed that the removal efficiency of turbidity is more than 95% at the lower discharge （0.15 L/min）. Therefore, infiltration should be conservatively designed using low loading rates.

Design and analysis of dual mixed refrigerant processes for high-ethane content natural gas liquefaction

Recovery and purification of ethane has a significant impact on economic benefit improvement of the high-ethane content natural gas.However,current LNG-NGL integrated processes mainly focus on conventional natural gas,which are not applicable to natural gas with high ethane content.To fill this gap,three dual mixed refrigerant processes are proposed for simulation study of high-ethane content natural gas liquefaction.The proposed processes are optimized by a combination method of sequence optimization and genetic algorithm.Comparatively analysis is conducted to evaluate the three processes from the energetic and exergetic points of view.The results show that the power consumption of Process 3 which compressing natural gas after distillation is the lowest.For safety or other considerations,some common compositions of the mixed refrigerant may need to be removed under certain circumstances.Considering this,case studies of mixed refrigerant involving six composition combinations are carried out to investigate the effects of refrigerant selection on the process performance.

Inequalities for Dual Orlicz Mixed Quermassintegrals

In this paper, we establish the dual Orlicz-Minkowski inequality and the dual Orlicz-Brunn-Minkowski inequality for dual Orlicz mixed quermassintegrals.

SOME DUAL KINEMATIC FORMULAS

In this article, some kinematic formulas for dual quermassintegral of star bodies and for chord power integrals of convex bodies are established by using dual mixed volumes. These formulas are the extensions of the fundamental kinematic formula involving quermassintegral to the case of dual quermassintegral and chord power integrals.

On the Dual Orlicz Mixed Volumes

In this paper,the authors define a harmonic Orlicz combination and a dual Orlicz mixed volume of star bodies,and then establish the dual Orlicz-Minkowski mixedvolume inequality and the dual Orlicz-Brunn-Minkowksi inequality.

Some Inequalities for the General Radial Bo dies

Lutwak showed the radial bodies combining with the radial Minkowski linear combinations of star bodies. In this paper, the general radial bodies are introduced and its some properties and inequalities are established.

THE DUAL MIXED METHOD FOR AN UNILATERAL PROBLEM

In this paper, the dual mixed method for an unilateral problem, which is the simplified modelling of scalar function for the friction-free contact problem, is considered. The dual mixed problem is introduced, the existence and uniqeness of the solution of the problem are presented, and error bounds O(h3/4) and O(h3/2) are obtained for the dual mixed finite element approximations of Raviart-Thomas elements for k = 0 and k = 1 respectively.

Some Inequalities for L_p-Dual Mixed Quermassintegrals

Wang and Zhang defined a type of Lp-dual mixed quermassintegrals based on the Lp-radial combinations and dual quermassintegrals of star bodies. In the article, the product inequalities for this Lp-dual mixed quermassintegrals are established. As the applications, we obtain the lower bounds of dual quermassintegrals product. Further, the Brunn-Minkowski type inequality and the cycle inequality for the Lp-dual mixed quermassintegrals are given.

INEQUALITIES FOR MIXED INTERSECTION BODIES

In this paper, some properties of mixed intersection bodies are given, and inequalities from the dual Brunn-Minkowski theory (such as the dual Minkowski inequality, the dual Aleksandrov-Fenchel inequalities and the. dual Brunn-Minkowski inequalities) are established for mixed intersection bodies.

Dual Orlicz Affine Surface Area

According to the notion of Orlicz mixed volume, in this paper, we extend L_p-dual affine surface area to the Orlicz version. Further, we obtain the affine isoperimetric inequality and the Blachke-Santaló inequality for the dual Orlicz affine surface area. Besides, we also get the monotonicity inequality for Orlicz dual affine surface area.

On the generalized Busemann-Petty problem

The generalized Busemann-Petty problem asks whether the origin-symmetric convex bodies in ? n with a larger volume of all i-dimensional sections necessarily have a larger volume. As proved by Bourgain and Zhang, the answer to this question is negative if i > 3. The problem is still open for i = 2, 3. In this article we prove two specific affirmative answers to the generalized Busemann-Petty problem if the body with a smaller i-dimensional volume belongs to given classes. Our results generalize Zhang’s specific affirmative answer to the generalized Busemann-Petty problem.

Generalized Intersection Bodies with Parameter

In 2005, the classical intersection bodies and L_p intersection bodies were extended. Afterwards, the concept of gen-eral L_p intersection bodies and the generalized intersection bodies was introduced. In this paper, we define the generalized bodies with parameter. Besides, we establish the extremal values for volume, Brunn-Minkowski type inequality for radial combination and L_p harmonic Blaschke combination of this notion.

A Quasi-Funk's Section Theorem in n-Complex Space

The Funk＇s section theorem in the n-complex space Cn is investigated. It turns out that this theorem does not admit an extension for the class of general origin-symmetric star bodies in Cn but for a class of star bodies called generalized complex intersection bodies. A quasi-version of Funk＇s section theorem in Cn is established then.