This work is motivated by Nathanson’s recent paper on relatively prime sets and a phi function for subsets of {1, 2, 3, . . . , n}. We establish enumeration formulas for the number of relatively prime subsets and the number of relatively prime subsets of cardinality k of {1, 2, 3, . . . , n} under various constraints. Further, we show how this work links up with the study of multicompositions. ...

The Hardy space on the unit ball in C provides examples of a quasi-free, finite rank Hilbert module which contains a pure submodule isometrically isomorphic to the module itself. For n = 1 the submodule has finite codimension. In this note we show that this phenomenon can only occur for modules over domains in C and for finitely-connected domains only for Hardy-like spaces, the bundle shifts. M...

OBJECTIVE To answer the questions: (a) What is the effect of hypertrophy on the intracellular pH (pHi) and buffering power of cardiac muscle, and (b) How does hypertrophy affect the ability of cardiac muscle to recover from intracellular acidosis induced by hypoxia. METHODS In nominally HCO3(-)-free, HEPES-buffered Tyrode solution (35 degrees C), pHi and the intrinsic buffering power (beta i,...

The range of incidence angle, 0 < phi < phi(e), over which p-polarized light is reflected at interfaces between transparent and absorbing media with reflectance below that at normal incidence is determined. Contours of constant phi(e) in the complex plane of the relative dielectric constant epsilon are presented. A method for determining the real and imaginary parts of the complex refractive in...

Growth is one of the key processes in the dynamic of exploited resources, since it provides part of the information required for structured population models. Growth of mangrove cockle, Anadara tuberculosa was estimated through length-based methods (ELEFAN I y NSLCA) and using diverse shell length intervals (SLI). The variability of L(infinity), k and phi prime (phi') estimates and the effect o...

In the present paper, by considering the notion of MV-modules which is the structure that naturally correspond to lu-modules over lu-rings, we prove some results on prime A-ideals and state some conditions to obtain a prime A-ideal in MV-modules. Also, we state some conditions that an A-ideal is not prime and investigate conditions that $Ksubseteq bigcup _{i=1}^{n}K_{i}$ implies $Ksubseteq K_{j...

Cytosolic pH (pHi) was measured in presynaptic nerve terminals isolated from rat brain (synaptosomes) using a fluorescent pH indicator, 2',7'-bis(carboxyethyl)-5,6-carboxyfluorescein (BCECF). The synaptosomes were loaded with BCECF by incubation with the membrane-permanent acetoxy-methyl ester derivative of BCECF, which is hydrolyzed by intracellular esterases to the parent compound. pHi was es...

The ratio rho(t) = T(p)/T(s) of the complex amplitude transmission coefficients for the p and s polarizations of a transparent unbacked or embedded thin film is examined as a function of the film thickness-to-wavelength ratio d/lambda and the angle of incidence Phi for a given film refractive index N. The maximum value of the differential transmission phase shift (or retardance), Delta(t) = arg...

We have used Thomas-type recessed-tip pH-sensitive microelectrodes to measure the intracellular pH (pHi) in Xenopus eggs during both fertilization and ionophore activation. The average pHi in unfertilized eggs is 7.33 +/- 0.11 (SD; n = 21) with a resting membrane potential of -10.1 +/- 3.5 (SD; n = 38) mV. Within 2 min after the onset of the fertilization potential, there is a slight, transient...

We discuss the conditions under which static, finite-energy, configurations of a complex scalar field $\ensuremath{\phi}$ with constant phase and spherically-symmetric norm exist in potential form $V({\ensuremath{\phi}}^{*}\ensuremath{\phi},{\ensuremath{\phi}}^{N}+{\ensuremath{\phi}}^{*N})$ $N\ensuremath{\in}\mathbb{N}$ $N\ensuremath{\ge}2$, i.e., ${Z}_{N}$-symmetry. Such are called ${Z}_{N}$-b...