Lutwak proved the Brunn-Minkowski inequality for the quermassintegrals of Fiery Lρ-combination. Wang and Leng gave the Brunn-Minkowski inequality for the dual quermassintegrals of Lρ-harmonic radial combination. In ...Lutwak proved the Brunn-Minkowski inequality for the quermassintegrals of Fiery Lρ-combination. Wang and Leng gave the Brunn-Minkowski inequality for the dual quermassintegrals of Lρ-harmonic radial combination. In the paper, we establish the isolate forms of the Brunn-Minkowski inequality for quermassintegrals and dual quermassintegrals,respectively.展开更多
Within the framework of Orlicz Brunn-Minkowski theory recently introduced by Lutwak, Yang, and Zhang [20, 21], Gardner, Hug, and Weil [5, 6] et al, the dual harmonic quermassintegrals of star bodies are studied, and a...Within the framework of Orlicz Brunn-Minkowski theory recently introduced by Lutwak, Yang, and Zhang [20, 21], Gardner, Hug, and Weil [5, 6] et al, the dual harmonic quermassintegrals of star bodies are studied, and a new Orlicz Brunn-Minkowski type inequality is proved for these geometric quantities.展开更多
In this paper,we first establish the dual Brunn-Minkowski inequality for the star duals for the Lp radial sum.Furthermore,we give some Brunn-Minkowski inequalities for the star duals of intersection bodies for the Lp ...In this paper,we first establish the dual Brunn-Minkowski inequality for the star duals for the Lp radial sum.Furthermore,we give some Brunn-Minkowski inequalities for the star duals of intersection bodies for the Lp radial sum and the Lp harmonic Blaschke sum.展开更多
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 symm...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.展开更多
In [1], the authors established the Brunn-Minkowski inequality for centroid body. In this paper, we give an isolate form and volume difference of it, respectively. Both of these results are strength versions of the or...In [1], the authors established the Brunn-Minkowski inequality for centroid body. In this paper, we give an isolate form and volume difference of it, respectively. Both of these results are strength versions of the original.展开更多
Coronary heart disease is the single largest cause of death in developed countries. Guidelines exist for the management of acute myocardial infarction(AMI),yet despite these,significant inequalities exist in the care ...Coronary heart disease is the single largest cause of death in developed countries. Guidelines exist for the management of acute myocardial infarction(AMI),yet despite these,significant inequalities exist in the care of these patients. The elderly,deprived socioeconomic groups,females and non-caucasians are the patient populations where practice tends to deviate more frequently from the evidence base. Elderly patients often had higher mortality rates after having an AMI compared to younger patients. They also tended to present with symptoms that were not entirely consistent with an AMI,thus partially contributing to the inequalities in care that is seen between younger and older patients. Furthermore the lack of guidelines in the elderly age group presenting with AMI can often make decision making challenging and may account for the discrepancies in care that are prevalent between younger and older patients. Other patients such as those from a lower socioeconomic group,i.e.,low income and less than high school education often had poorer health and reduced life expectancy compared to patients from a higher socioeconomic group after an AMI. Lower socioeconomic status was also seen to be contributing to racial and geographical variation is the care in AMI patients. Females with an AMI were treated less aggressively and had poorer outcomes when compared to males. However even when females were treated in the same way they continued to have higher in hospital mortality which suggests that gender may well account for differences in outcomes. The purpose of this review is to identify the inequalities in care for patients who present with an AMI and explore potential reasons for why these occur. Greater attention to the management and a better understanding of the root causes of these inequalities in care may help to reduce morbidity and mortality rates associated with AMI.展开更多
In this paper, we introduce the concept of dual quermassintegral differences. Further, we give the dual Brunn-Minkowski inequality and dual Minkowski inequality for dual quermassintegral differences for mixed intersec...In this paper, we introduce the concept of dual quermassintegral differences. Further, we give the dual Brunn-Minkowski inequality and dual Minkowski inequality for dual quermassintegral differences for mixed intersection bodies.展开更多
It is shown that a convex body has minimal dual p-surface area among its affine transformations of the same volume if and only if its dual p-surface area measure is isotropic. A double-sided estimate for the （n-1）-d...It is shown that a convex body has minimal dual p-surface area among its affine transformations of the same volume if and only if its dual p-surface area measure is isotropic. A double-sided estimate for the （n-1）-dimensional volume of the intersection of a dual p-surface isotropic convex body in terms of its affine invariant dual p-surface quantity is given. Furthermore, the dual p-isopermetric inequality is obtained.展开更多
In this paper, based on the notion of mixed complex projection and generalized the recent works of other authors, we obtain some volume difference inequalities containing Brunn-Minkowski type inequality, Minkowski typ...In this paper, based on the notion of mixed complex projection and generalized the recent works of other authors, we obtain some volume difference inequalities containing Brunn-Minkowski type inequality, Minkowski type inequality and Aleksandrov-Fenchel inequality for the polars of mixed complex projection bodies.展开更多
基金Supported by the Natural Science Foundation of China(10671117)Supported by the Science Foundation of China Three Gorges University
文摘Lutwak proved the Brunn-Minkowski inequality for the quermassintegrals of Fiery Lρ-combination. Wang and Leng gave the Brunn-Minkowski inequality for the dual quermassintegrals of Lρ-harmonic radial combination. In the paper, we establish the isolate forms of the Brunn-Minkowski inequality for quermassintegrals and dual quermassintegrals,respectively.
文摘Within the framework of Orlicz Brunn-Minkowski theory recently introduced by Lutwak, Yang, and Zhang [20, 21], Gardner, Hug, and Weil [5, 6] et al, the dual harmonic quermassintegrals of star bodies are studied, and a new Orlicz Brunn-Minkowski type inequality is proved for these geometric quantities.
基金Project supported by the National Natural Science Foundation of China (Grant No.10671119)the Shanghai Leading Academic Discipline Project (Grant No.J50101)the Shanghai University Graduate Innovation Foundation Project (GrantNo.SHUCX092003)
文摘In this paper,we first establish the dual Brunn-Minkowski inequality for the star duals for the Lp radial sum.Furthermore,we give some Brunn-Minkowski inequalities for the star duals of intersection bodies for the Lp radial sum and the Lp harmonic Blaschke sum.
文摘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.
文摘In [1], the authors established the Brunn-Minkowski inequality for centroid body. In this paper, we give an isolate form and volume difference of it, respectively. Both of these results are strength versions of the original.
文摘Coronary heart disease is the single largest cause of death in developed countries. Guidelines exist for the management of acute myocardial infarction(AMI),yet despite these,significant inequalities exist in the care of these patients. The elderly,deprived socioeconomic groups,females and non-caucasians are the patient populations where practice tends to deviate more frequently from the evidence base. Elderly patients often had higher mortality rates after having an AMI compared to younger patients. They also tended to present with symptoms that were not entirely consistent with an AMI,thus partially contributing to the inequalities in care that is seen between younger and older patients. Furthermore the lack of guidelines in the elderly age group presenting with AMI can often make decision making challenging and may account for the discrepancies in care that are prevalent between younger and older patients. Other patients such as those from a lower socioeconomic group,i.e.,low income and less than high school education often had poorer health and reduced life expectancy compared to patients from a higher socioeconomic group after an AMI. Lower socioeconomic status was also seen to be contributing to racial and geographical variation is the care in AMI patients. Females with an AMI were treated less aggressively and had poorer outcomes when compared to males. However even when females were treated in the same way they continued to have higher in hospital mortality which suggests that gender may well account for differences in outcomes. The purpose of this review is to identify the inequalities in care for patients who present with an AMI and explore potential reasons for why these occur. Greater attention to the management and a better understanding of the root causes of these inequalities in care may help to reduce morbidity and mortality rates associated with AMI.
基金Supported by Natural Scientific Research Project of Guizhou Provincial Education Department (2007084)Kaili University (Z1013)the Key Discipline Construction Project of Kaili University (KZD2009001)
文摘In this paper, we introduce the concept of dual quermassintegral differences. Further, we give the dual Brunn-Minkowski inequality and dual Minkowski inequality for dual quermassintegral differences for mixed intersection bodies.
基金Project supported by the National Natural Science Foundation of China (Grant No.10671117)
文摘It is shown that a convex body has minimal dual p-surface area among its affine transformations of the same volume if and only if its dual p-surface area measure is isotropic. A double-sided estimate for the （n-1）-dimensional volume of the intersection of a dual p-surface isotropic convex body in terms of its affine invariant dual p-surface quantity is given. Furthermore, the dual p-isopermetric inequality is obtained.
文摘In this paper, based on the notion of mixed complex projection and generalized the recent works of other authors, we obtain some volume difference inequalities containing Brunn-Minkowski type inequality, Minkowski type inequality and Aleksandrov-Fenchel inequality for the polars of mixed complex projection bodies.
