Applications of the Owa-Srivastava Operator to the Class of K-Uniformly Convex Functions

2000 Mathematics Subject Classification: Primary 30C45, 26A33; Secondary 33C15

The C(K, X) spaces for compact metric spaces K and X with a uniformly convex maximal factor

In this paper, we prove that if a Banach space X contains some uniformly convex subspace in certain geometric position, then the C(K, X) spaces of all X-valued continuous functions defined on the compact metric spaces K have exactly the same isomorphism classes that the C(K) spaces. This provides a vector-valued extension of classical results of Bessaga and Pelczynski (1960) [2] and Milutin (1966) [13] on the isomorphic classification of the separable C(K) spaces. As a consequence, we show that if 1 < p < q < infinity then for every infinite countable compact metric spaces K(1), K(2), K(3) and K(4) are equivalent: (a) C(K(1), l(p)) circle plus C(K(2), l(q)) is isomorphic to C(K(3), l(p)) circle plus (K(4), l(q)). (b) C(K(1)) is isomorphic to C(K(3)) and C(K(2)) is isomorphic to C(K(4)). (C) 2011 Elsevier Inc. All rights reserved.

On Uniformly Convex and Uniformly Kadec-Klee Renomings

We give a new construction of uniformly convex norms with a power type modulus on super-reflexive spaces based on the notion of dentability index. Furthermore, we prove that if the Szlenk index of a Banach space is less than or equal to ω (first infinite ordinal) then there is an equivalent weak* lower semicontinuous positively homogeneous functional on X* satisfying the uniform Kadec-Klee Property for the weak*-topology (UKK*). Then we solve the UKK or UKK* renorming problems for Lp(X) spaces and C(K) spaces for K scattered compact space.

NADPH-oxidase and a hydrogen peroxide-sensitive K+ channel may function as an oxygen sensor complex in airway chemoreceptors and small cell lung carcinoma cell lines

Pulmonary neuroepithelial bodies (NEB) are widely distributed throughout the airway mucosa of human and animal lungs. Based on the observation that NEB cells have a candidate oxygen sensor enzyme complex (NADPH oxidase) and an oxygen-sensitive K+ current, it has been suggested that NEB may function as airway chemoreceptors. Here we report that mRNAs for both the hydrogen peroxide sensitive voltage gated potassium channel subunit (KH2O2) KV3.3a and membrane components of NADPH oxidase (gp91phox and p22phox) are coexpressed in the NEB cells of fetal rabbit and neonatal human lungs. Using a microfluorometry and dihydrorhodamine 123 as a probe to assess H2O2 generation, NEB cells exhibited oxidase activity under basal conditions. The oxidase in NEB cells was significantly stimulated by exposure to phorbol esther (0.1 μM) and inhibited by diphenyliodonium (5 μM). Studies using whole-cell voltage clamp showed that the K+ current of cultured fetal rabbit NEB cells exhibited inactivating properties similar to KV3.3a transcripts expressed in Xenopus oocyte model. Exposure of NEB cells to hydrogen peroxide (H2O2, the dismuted by-product of the oxidase) under normoxia resulted in an increase of the outward K+ current indicating that H2O2 could be the transmitter modulating the O2-sensitive K+ channel. Expressed mRNAs or orresponding protein products for the NADPH oxidase membrane cytochrome b as well as mRNA encoding KV3.3a were identified in small cell lung carcinoma cell lines. The studies presented here provide strong evidence for an oxidase-O2 sensitive potassium channel molecular complex operating as an O2 sensor in NEB cells, which function as chemoreceptors in airways and in NEB related tumors. Such a complex may represent an evolutionary conserved biochemical link for a membrane bound O2-signaling mechanism proposed for other cells and life forms.

Alternative Characterization of the Class k-UCV and Related Classes of Univalent Functions

In this paper an alternative characterization of the class of functions called k -uniformly convex is found. Various relations concerning connections with other classes of univalent functions are given. Moreover a new class of univalent functions, analogous to the ’Mocanu class’ of functions, is introduced. Some results concerning this class are derived.

A PVT-Type Algorithm for Minimizing a Nonsmooth Convex Function

2000 Mathematics Subject Classification: 90C25, 68W10, 49M37.

Topological K-equivalence of analytic function-germs

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Cation Transport Coupled to ATP Hydrolysis By the (Na, K)-ATPase AN INTEGRATED, ANIMATED MODEL

An Adobe (R) animation is presented for use in undergraduate Biochemistry courses, illustrating the mechanism of Na(+) and K(+) translocation coupled to ATP hydrolysis by the (Na, K)-ATPase, a P(2c)-type ATPase, or ATP-powered ion pump that actively translocates cations across plasma membranes. The enzyme is also known as an E(1)/E(2)-ATPase as it undergoes conformational changes between the E(1) and E(2) forms during the pumping cycle, altering the affinity and accessibility of the transmembrane ion-binding sites. The animation is based on Horisberger`s scheme that incorporates the most recent significant findings to have improved our understanding of the (Na, K)-ATPase structure function relationship. The movements of the various domains within the (Na, K)-ATPase alpha-subunit illustrate the conformational changes that occur during Na(+) and K(+) translocation across the membrane and emphasize involvement of the actuator, nucleotide, and phosphorylation domains, that is, the ""core engine"" of the pump, with respect to ATP binding, cation transport, and ADP and P(i) release.

Time-dependent master equation simulation of complex elementary reactions in combustion: Application to the reaction of (CH2)-C-1 with C2H2 from 300-2000 K

Computational simulations of the title reaction are presented, covering a temperature range from 300 to 2000 K. At lower temperatures we find that initial formation of the cyclopropene complex by addition of methylene to acetylene is irreversible, as is the stabilisation process via collisional energy transfer. Product branching between propargyl and the stable isomers is predicted at 300 K as a function of pressure for the first time. At intermediate temperatures (1200 K), complex temporal evolution involving multiple steady states begins to emerge. At high temperatures (2000 K) the timescale for subsequent unimolecular decay of thermalized intermediates begins to impinge on the timescale for reaction of methylene, such that the rate of formation of propargyl product does not admit a simple analysis in terms of a single time-independent rate constant until the methylene supply becomes depleted. Likewise, at the elevated temperatures the thermalized intermediates cannot be regarded as irreversible product channels. Our solution algorithm involves spectral propagation of a symmetrised version of the discretized master equation matrix, and is implemented in a high precision environment which makes hitherto unachievable low-temperature modelling a reality.

Estimation du débit de filtration glomérulaire par la formule DFG = K x T/Pcr [Estimation of glomerular filtration rate by the formula GFR = K x T/Pc].

BACKGROUND: Creatinine clearance is the most common method used to assess glomerular filtration rate (GFR). In children, GFR can also be estimated without urine collection, using the formula GFR (mL/min x 1.73 m2) = K x height [cm]/Pcr [mumol/L]), where Pcr represents the plasma creatinine concentration. K is usually calculated using creatinine clearance (Ccr) as an index of GFR. The aim of the present study was to evaluate the reliability of the formula, using the standard UV/P inulin clearance to calculate K. METHODS: Clearance data obtained in 200 patients (1 month to 23 years) during the years 1988-1994 were used to calculate the factor K as a function of age. Forty-four additional patients were studied prospectively in conditions of either hydropenia or water diuresis in order to evaluate the possible variation of K as a function of urine flow rate. RESULTS: When GFR was estimated by the standard inulin clearance, the calculated values of K was 39 (infants less than 6 months), 44 (1-2 years) and 47 (2-12 years). The correlation between the values of GFR, as estimated by the formula, and the values measured by the standard clearance of inulin was highly significant; the scatter of individual values was however substantial. When K was calculated using Ccr, the formula overestimated Cin at all urine flow rates. When calculated from Ccr, K varied as a function of urine flow rate (K = 50 at urine flow rates of 3.5 and K = 64 at urine flow rates of 8.5 mL/min x 1.73 m2). When calculated from Cin, in the same conditions, K remained constant with a value of 50. CONCLUSIONS: The formula GFR = K x H/Pcr can be used to estimate GFR. The scatter of values precludes however the use of the formula to estimate GFR in pathophysiological studies. The formula should only be used when K is calculated from Cin, and the plasma creatinine concentration is measured in well defined conditions of hydration.

A Note on Shapley's convex measure games

L. S. Shapley, in his paper 'Cores of Convex Games', introduces Convex Measure Games, those that are induced by a convex function on R, acting over a measure on the coalitions. But in a note he states that if this function is a function of several variables, then convexity for the function does not imply convexity of the game or even superadditivity. We prove that if the function is directionally convex, the game is convex, and conversely, any convex game can be induced by a directionally convex function acting over measures on the coalitions, with as many measures as players

A Note on Shapley's convex measure games

L. S. Shapley, in his paper 'Cores of Convex Games', introduces Convex Measure Games, those that are induced by a convex function on R, acting over a measure on the coalitions. But in a note he states that if this function is a function of several variables, then convexity for the function does not imply convexity of the game or even superadditivity. We prove that if the function is directionally convex, the game is convex, and conversely, any convex game can be induced by a directionally convex function acting over measures on the coalitions, with as many measures as players

Cation Transport Coupled to ATP Hydrolysis By the (Na, K)-ATPase : an integrated, animated model

An Adobe (R) animation is presented for use in undergraduate Biochemistry courses, illustrating the mechanism of Na+ and K+ translocation coupled to ATP hydrolysis by the (Na, K)-ATPase, a P-2c-type ATPase, or ATP-powered ion pump that actively translocates cations across plasma membranes. The enzyme is also known as an E-1/E-2-ATPase as it undergoes conformational changes between the E-1 and E-2 forms during the pumping cycle, altering the affinity and accessibility of the transmembrane ion-binding sites. The animation is based on Horisberger's scheme that incorporates the most recent significant findings to have improved our understanding of the (Na, K)-ATPase structure function relationship. The movements of the various domains within the (Na, K)-ATPase alpha-subunit illustrate the conformational changes that occur during Na+ and K+ translocation across the membrane and emphasize involvement of the actuator, nucleotide, and phosphorylation domains, that is, the "core engine" of the pump, with respect to ATP binding, cation transport, and ADP and P-i release.