A NOTE IN APPROXIMATIVE COMPACTNESS AND MIDPOINT LOCALLY K-UNIFORM ROTUNDITY IN BANACH SPACES

In this article, we prove the following results： （1） A Banach space X is weak midpoint locally k-uniformly rotund if and only if every closed ball of X is an approximatively weakly compact k-Chebyshev set; （2） A Banach space X is midpoint locally k-uniformly rotund if and only if every closed ball of X is an approximatively compact k-Chebyshev set.

Rotundity of Orlicz-Bochner Space with Luxemburg Norm

In this paper, by using the generating function Φ and X the criteria of the rotundity for the Orlicz-Bochner function and sequence spaces endowed with the Luxemburg norm were obtained. And the sufficient and necessary conditions were given for the extreme point of Orlicz-Bochner sequence space and the conditions in part for Orlicz-Bochner function space.

Complex locally uniform rotundity of Musielak-Orlicz spaces

The concepts of complex locally uniform rotundity and complex locally uniformly rotund point are introduced. The sufficient and necessary conditions of them are given in complex Musielak-Orlicz spaces.

SOME GEOMETRIC PROPERTIES OF A NEW DIFFERENCE SEQUENCE SPACE INVOLVING LACUNARY SEQUENCES

In this paper, we define a new generalized difference sequence space involving lacunary sequence. Then, we examine k-NUC property and property （β） for this space and also show that it is not rotund where p = （pr） is a bounded sequence of positive real numbers with pr ≥ 1 for all r ∈ N.

RELATIVE PRINCIPLE COMPONENT AND RELATIVE PRINCIPLE COMPONENT ANALYSIS ALGORITHM

In this letter,the new concept of Relative Principle Component (RPC) and method of RPC Analysis (RPCA) are put forward. Meanwhile,the concepts such as Relative Transform (RT),Ro-tundity Scatter (RS) and so on are introduced. This new method can overcome some disadvantages of the classical Principle Component Analysis (PCA) when data are rotundity scatter. The RPC selected by RPCA are more representative,and their significance of geometry is more notable,so that the application of the new algorithm will be very extensive. The performance and effectiveness are simply demonstrated by the geometrical interpretation proposed.

Some Rotundities of Orlicz–Lorentz Spaces

K-UR,K-LUR and K-R are the generalizations of UR,LUR and R respectively,which are of great significance in Banach space theory.While in Orlicz–Lorentz function spaceΛ_(ϕ,ω)^(◦)[0,γ)equipped with the Orlicz norm,the research methods of K-UR,K-LUR and K-R are much more complicated than those of UR,LUR and R.In this paper we obtain some criteria of K-UR,K-LUR and K-R ofΛ_(ϕ,ω)^(◦)[0,γ)by means of the norm of dual space and H_(μ)property ofΛ_(ϕ,ω)^(◦)[0,γ).

UGD PROPERTY OF MUSIELAK-ORLICZ SEQUENCE SPACES

By the properties of the Musielak_Orlicz funciton's sequence, the necessary and sufficient condition for uniform Gateaux differential (UGD) property of Musielak_Orlicz sequence spaces equipped with the Luxemburg norm and a criterion for weakly uniform rotundity of Musielak_Orlicz sequence space with Orlicz norm are given.

Absolute bioavailability,dose proportionality,and tissue distribution of rotundic acid in rats based on validated LC-QqQ-MS/MS method

Rotundic acid(RA),an ursane-type pentacyclic triterpene acid isolated from the dried barks of Ilex rotunda Thunb.(Aquifoliaceae),possesses diverse bioactivities.To further study its pharmacokinetics,a simple and sensitive liquid chromatography with triple quadrupole mass spectrometry(LC-QqQ-MS/MS)method was developed and validated to quantify RA concentration in rat plasma and tissue using etofesalamide as an internal standard(IS).Plasma and tissue samples were subjected to one-step protein precipitation.Chromatographic separation was achieved on a ZORBAX Eclipse XDB-C_(18) column(4.6mm×50mm,5μm)under gradient conditions with eluents of methanol:acetonitrile(1:1,V/V)and 5mM ammonium formate:methanol(9:1,V/V)at 0.5mL/min.Multiple reaction monitoring transitions were performed at m/z 487.30→437.30 for RA and m/z 256.10→227.10 for IS in the negative mode.The developed LC-QqQ-MS/MS method exhibited good linearity(2-500 ng/mL)and was fully validated in accordance with U.S.Food and Drug Administration bioanalytical guidelines.Dose proportionality and bioavailability in rats were determined by comparing pharmacokinetic data after single oral(10,20,and 40mg/kg)and intravenous(10mg/kg)administration of RA.Tissue distribution was studied following oral administration at 20mg/kg.The results showed that the absolute bioavailability of RA after administration at different doses ranged from 16.1%to 19.4%.RA showed good dose proportionality over a dose range of 10-40 mg/kg.RA was rapidly absorbed in a dose-dependent manner and highly distributed in the liver.In conclusion,this study is the first to systematically elucidate the absorption and distribution characteristics of RA in rats,which can provide additional information for further development and evaluation of RA in drug metabolism and pharmacokinetic studies.

A SHORT NOTE ABOUT EXPOSED POINTS IN REAL BANACH SPACES

We express the set of exposed points in terms of rotund points and non-smooth points.As long as we have Banach spaces each time＂bigger＂,we consider sets of non-smooth points each time＂smaller＂.

ON VERY ROTUND BANACH SPACE

Three characteristics of the very rotund space ape proved and the relationships between the very rotund space and the geometrical properties of Banach space are discussed. Also connection between the weakly exposed points and Radon Nikodym-property is established.

fat,fally,podgy等词辨异

英语里表示“胖”的词有:chubby,corpulent,fat,flabby,obese,overweight,plump,podgy,portly,rotund,stout,tubby 等,但它们修饰人时的含义和用法不尽相同,主要区别如下:一、fat,flabby,podgy 含有贬义色彩1.fat 是表示“胖”的最常用最直接的词,它表示含有多余的脂肪。若想委婉,应避免使用。In one part,children starve and in the other,a lot of people get

Approximative compactness and continuity of metric projector in Banach spaces and applications

First we prove that the approximative compactness of a nonempty set C in a normed linear space can be reformulated equivalently in another way.It is known that if C is a semi-Chebyshev closed and approximately compact set in a Banach space X,then the metric projectorπC from X onto C is continuous.Under the assumption that X is midpoint locally uniformly rotund,we prove that the approximative compactness of C is also necessary for the continuity of the projectorπC by the method of geometry of Banach spaces.Using this general result we find some necessary and sufficient conditions for T to have a continuous Moore-Penrose metric generalized inverse T^+,where T is a bounded linear operator from an approximative compact and a rotund Banach space X into a midpoint locally uniformly rotund Banach space Y.

Chemical Constituents of Millettia speciosa

Objective To study the chemical constituents from Millettia speciosa. Methods The compounds were isolated and purified by silica gel, Sephadex LH-20, ODS column chromatography, and recrystallization. The structures were identified using physicochemical and spectral data. Results Thirteen compounds were isolated from M. speciosa and identified as docosanoic acid （1）, tetracosane （2）, octadecane （3）, hexacosanoic acid （4）, β-sitosteroi acetate （5）, β-sitosterol （6）, syringin （7）, maackiain （8）, formononetin （9）, ψ-baptigenin （10）, rotundic acid （11）, pedunculoside （12）, and daucosterol （13）. Conclusion Compounds 5, 7, and 10-12 are obtained from this plant for the first time.

Zinc finger protein rotund deficiency affects development of the thoracic leg in Bombyx mori

The insect limb develops from the imaginal disc or larval leg during metamor- phosis. The molecular mechanisms involved in the development from the larval to the adult leg are poorly understood. Herein, we cloned the full length of a zinc finger gene rotund from Bombyx mori （Bmrn）, which contained a 1419 bp open reading frame, and encoded a 473 amino acid protein. Reverse transcription polymerase chain reaction and Western blot analyses demonstrated that Bmrn was expressed at higher levels in the epidermis than in other tissues tested, and it showed a very high expression level during metamorphosis. Knock-down of Bmrn produced defects in the tarsus and pretarsus, including the fusion and reduction of tarsomeres, and the developmental arrest of pretarsus. Our data showed that Bmrn is involved in the formation of the tarsus and pretarsus, whereas its homologous gene in Drosophila has been shown to affect three tarsal segments （t2-t4）, suggesting that the remodeling of the leg has involved changes in the patterning of gene regulation during evolution.

EQUIVALENT CONDITIONS FOR THE UNIFORM CONTINUITY OF DUALITY MAPPING

For a duality mapping F(x), this paper gives equivalent conditions for F(x)being single-valued and uniformly continuous, or uniformly lower semi-continuous, or forexistence a uniformly continuous support functions.

Renormings concerning exposed points and non-smoothness

Intuitively, non-smooth points might look like exposed points. However, in this paper we show that real Banach spaces having dimension greater than or equal to three can be equivalently renormed to obtain non-smooth points which are also non-exposed.