The utility of microorganisms for solubilizing the unavailable forms of potassium(K) from soil has led to renewed interest in fabrication of rapid and sensitive plate assays for their isolation and screening. The pres...The utility of microorganisms for solubilizing the unavailable forms of potassium(K) from soil has led to renewed interest in fabrication of rapid and sensitive plate assays for their isolation and screening. The present study developed a modified plate assay and compared it with previously reported methods for the isolation and screening of K-solubilizing bacteria. The newly developed plate assay is based on improved visualization of halo zone formation around the colonies on agar plates, through inclusion of an acid-base indicator dye, bromothymol blue(BTB), to modify the previously reported Aleksandrov medium. The halo zone exhibited a significant correlation(R = 0.939) with K released in liquid medium. The visualization of potential K solubilizers was improved using this method, which would help in detection of weak/non-acid producers based on secretion of organic acids in the medium. Organic acids in plate diffuse radially and form halo zones in response to reaction with the acid-base indicator dye BTB. Furthermore, K solubilization on plates with this method can be observed within 48–72 h, against the incubation time of 4–5 d needed in the earlier method. Therefore, the newly developed protocol for the plate assay was time saving, more sensitive, and beneficial in comparison to the previously reported Aleksandrov plate assay.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
The purpose of this paper is to generalize the notion of intersection bodies to that of quasi Lp-intersection bodies. The Lp-analogs of the Busemann intersection inequality and the Brunn- Minkowski inequality for the ...The purpose of this paper is to generalize the notion of intersection bodies to that of quasi Lp-intersection bodies. The Lp-analogs of the Busemann intersection inequality and the Brunn- Minkowski inequality for the quasi Lp-intersection bodies are obtained. The Aleksandrov Fenchel inequality for the mixed quasi Lp-intersection bodies is also established.展开更多
In this paper, we consider a discrete version of Aleksandrov＇s projection theorem. We prove that an origin-symmetric convex lattice set, whose lattice＇s y-coordinates＇ absolute values are not bigger than 2, can be ...In this paper, we consider a discrete version of Aleksandrov＇s projection theorem. We prove that an origin-symmetric convex lattice set, whose lattice＇s y-coordinates＇ absolute values are not bigger than 2, can be uniquely determined by its lattice projection counts if its cardinality is not 11. This partly answers a question on the discrete version of Aleksandrov＇s projection theorem which was proposed by Gardner, Gronchi and Zong in 2005.展开更多
基金the Department of Biotechnology (DBT), IndiaICAR-Indian Agricultural Research Institute (IARI) for providing financial support
文摘The utility of microorganisms for solubilizing the unavailable forms of potassium(K) from soil has led to renewed interest in fabrication of rapid and sensitive plate assays for their isolation and screening. The present study developed a modified plate assay and compared it with previously reported methods for the isolation and screening of K-solubilizing bacteria. The newly developed plate assay is based on improved visualization of halo zone formation around the colonies on agar plates, through inclusion of an acid-base indicator dye, bromothymol blue(BTB), to modify the previously reported Aleksandrov medium. The halo zone exhibited a significant correlation(R = 0.939) with K released in liquid medium. The visualization of potential K solubilizers was improved using this method, which would help in detection of weak/non-acid producers based on secretion of organic acids in the medium. Organic acids in plate diffuse radially and form halo zones in response to reaction with the acid-base indicator dye BTB. Furthermore, K solubilization on plates with this method can be observed within 48–72 h, against the incubation time of 4–5 d needed in the earlier method. Therefore, the newly developed protocol for the plate assay was time saving, more sensitive, and beneficial in comparison to the previously reported Aleksandrov plate assay.
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.
基金Supported by National Natural Sciences Foundation of China(10671117)
文摘The purpose of this paper is to generalize the notion of intersection bodies to that of quasi Lp-intersection bodies. The Lp-analogs of the Busemann intersection inequality and the Brunn- Minkowski inequality for the quasi Lp-intersection bodies are obtained. The Aleksandrov Fenchel inequality for the mixed quasi Lp-intersection bodies is also established.
基金Supported by National 973 Project (Grant No.2011CB808003)National Natural Science Foundation ofChina (Grant No.11131001)
文摘In this paper, we consider a discrete version of Aleksandrov＇s projection theorem. We prove that an origin-symmetric convex lattice set, whose lattice＇s y-coordinates＇ absolute values are not bigger than 2, can be uniquely determined by its lattice projection counts if its cardinality is not 11. This partly answers a question on the discrete version of Aleksandrov＇s projection theorem which was proposed by Gardner, Gronchi and Zong in 2005.
