We motivate and define $$\Phi $$ -energy density, -energy, -harmonic maps stable maps. Whereas harmonic or p-harmonic can be viewed as critical points of the integral first symmetric function $$\sigma _1$$ a pull-back tensor, second _2$$ tensor. By an extrinsic average variational method in calculus variations [cf. Howard Wei (Trans Am Math Soc 294:319–331, 1986), Yau (J Geom Anal 4(2):247–272,...

The interaction between phytochrome photoequilibrium (phi) and photon flux in the photoregulation of anthocyanin production under prolonged irradiation was studied in seedlings of Brassica oleracea L. and Lycopersicon esculentum Mill. In cabbage, anthocyanin production increases with decreasing phi, reaching a maximum at the lowest value (phi = 0.13) used in this study; in tomato, the extent of...

A method was developed in this study to measure the intracellular pH (pHi) of Dictyostelium discoideum cells with a pH-sensitive fluorescence dye, carboxyfluorescein dibutyrate, and the pHi values of cells on the stalk and spore pathways were compared. The pHi of prestalk cells was lower than that of prespore cells by approximately 0.3 pH unit. In monolayer cultures of sporogenous mutants, whic...

During mammalian development the fetal liver plays an important role in hematopoiesis. Studies with the macrophage (M phi)-specific mAb F4/80 have revealed an extensive network of M phi plasma membranes interspersed between developing erythroid cells in fetal liver. To investigate the interactions between erythroid cells and stromal M phi, we isolated hematopoietic cell clusters from embryonic ...

A Dedekind category (locally complete division allegory) D is a category satisfying the following:

In this paper we will study the number-theoretical properties of the expression v1 nkal rcka,, d(p; a I . . . . . an) = ( 1) n/2 ~ cot cot (1) k=l P P and of related finite trigonometric sums. In Eq. (I), p is a positive integer, a~ . . . . . a, are integers prime to p, and n is even (for n odd the sum is clearly equal to zero). There are two reasons for being interested in sums of this type. F...

Let K be a number field and p be a prime number. When we factor (p) = pOK into prime ideals, say (p) = p1 1 · · · p eg g , we refer to the data of the ei’s, the exponents fi in the norms Npi = p fi , and g (the number of pi’s), as the “shape” of the factorization of (p). (What we are leaving out of this is explicit information about generators for the ideals pi.) Similarly, if a monic polynomia...

The regulation of intracellular pH (pHi) is a fundamental aspect of cell physiology that has received little attention in studies of reef-building corals and symbiotic cnidarians. Here, we investigated the hypothesis that dynamic changes in the pHi of coral host cells are controlled by the photosynthetic activity of the coral's dinoflagellate symbionts. Using live cell imaging and the pH-sensit...

Intraperitoneally injected rRNA from Pseudomonas aeruginosa combined with dimethyldioctadecylammonium bromide (DDA) increased nonspecifically the resistance of mice against an intraperitoneal challenge with extracellular (P. aeruginosa, Escherichia coli) and intracellular (Listeria monocytogenes) bacteria. This study concerns the mechanism underlying the nonspecific resistance. RNA with DDA (RN...