Hyers–Ulam stability of functional equations with a square-symmetric operation

The stability of the functional equation f(x ○ y) = H(f(x), f(y)) (x, y ∈ S) is investigated, where H is a homogeneous function and ○ is a square-symmetric operation on the set S. The results presented include and generalize the classical theorem of Hyers obtained in 1941 on the stability of the Cauchy functional equation.

A modified gambler's ruin model of polyethylene chains in the amorphous region.

Polyethylene chains in the amorphous region between two crystalline lamellae M unit apart are modeled as random walks with one-step memory on a cubic lattice between two absorbing boundaries. These walks avoid the two preceding steps, though they are not true self-avoiding walks. Systems of difference equations are introduced to calculate the statistics of the restricted random walks. They yield that the fraction of loops is (2M - 2)/(2M + 1), the fraction of ties 3/(2M + 1), the average length of loops 2M - 0.5, the average length of ties 2/3M2 + 2/3M - 4/3, the average length of walks equals 3M - 3, the variance of the loop length 16/15M3 + O(M2), the variance of the tie length 28/45M4 + O(M3), and the variance of the walk length 2M3 + O(M2).

Regulation of Telomere Length by Checkpoint Genes in Schizosaccharomyces pombe

We have studied telomere length in Schizosaccharomyces pombe strains carrying mutations affecting cell cycle checkpoints, DNA repair, and regulation of the Cdc2 protein kinase. Telomere shortening was found in rad1, rad3, rad17, and rad26 mutants. Telomere lengths in previously characterized rad1 mutants paralleled the replication checkpoint proficiency of those mutants. In contrast, rad9, chk1, hus1, and cds1 mutants had intact telomeres. No difference in telomere length was seen in mutants affected in the regulation of Cdc2, whereas some of the DNA repair mutants examined had slightly longer telomeres than did the wild type. Overexpression of the rad1+ gene caused telomeres to elongate slightly. The kinetics of telomere shortening was monitored by following telomere length after disruption of the rad1+ gene; the rate was ∼1 nucleotide per generation. Wild-type telomere length could be restored by reintroduction of the wild-type rad1+ gene. Expression of the Saccharomyces cerevisiae RCK1 protein kinase gene, which suppresses the radiation and hydroxyurea sensitivity of Sz. pombe checkpoint mutants, was able to attenuate telomere shortening in rad1 mutant cells and to increase telomere length in a wild-type background. The functional effects of telomere shortening in rad1 mutants were assayed by measuring loss of a linear and a circular minichromosome. A minor increase in loss rate was seen with the linear minichromosome, and an even smaller difference compared with wild-type was detected with the circular plasmid.

A numerical strategy for efficient modeling of the equatorial wave guide

Convection in the tropics is observed to involve a wide-ranging hierarchy of scales from a few kilometers to the planetary scales and also has a profound impact on short-term climate. The mechanisms responsible for this behavior present a major unsolved problem. A promising emerging approach to address these issues is cloud-resolving modeling. Here a family of numerical models is introduced specifically to model the feedback of small-scale deep convection on tropical planetary waves and tropical circulation in a highly efficient manner compatible with the approach through cloud-resolving modeling. Such a procedure is also useful for theoretical purposes. The basic idea in the approach is to use low-order truncation in the meriodonal direction through Gauss–Hermite quadrature projected onto a simple discrete radiation condition. In this fashion, the cloud-resolving modeling of equatorially trapped planetary waves reduces to the solution of a small number of purely zonal two-dimensional wave systems along a few judiciously chosen meriodonal layers that are coupled only by some additional source terms. The approach is analyzed in detail with full mathematical rigor for linearized equatorial primitive equations with source terms.

Circadian-Regulated Transcription of the psbD Light-Responsive Promoter in Wheat Chloroplasts1

The level of mRNAs derived from the plastid-encoded psbD light-responsive promoter (LRP) is controlled by a circadian clock(s) in wheat (Triticum aestivum). The circadian oscillations in the psbD LRP mRNA level persisted for at least three cycles in continuous light and for one cycle in continuous dark, with maxima in subjective morning and minima in subjective early night. In vitro transcription in chloroplast extracts revealed that the circadian cycles in the psbD LRP mRNA level were dominantly attributed to the circadian-regulated transcription of the psbD LRP. The effects of various mutations introduced into the promoter region on the psbD LRP activity in vitro suggest the existence of two positive elements located between −54 and −36, which generally enhance the transcription activity, and an anomalous core promoter structure lacking the functional “−35” element, which plays a crucial role in the circadian fluctuation and light dependency of psbD LRP transcription activity.

Accumulation of a Clock-Regulated Transcript during Flower-Inductive Darkness in Pharbitis nil1

To clarify the molecular basis of the photoperiodic induction of flowering in the short-day plant Pharbitis nil cv Violet, we examined changes in the level of mRNA in cotyledons during the flower-inductive photoperiod using the technique of differential display by the polymerase chain reaction. A transcript that accumulated during the inductive dark period was identified and a cDNA corresponding to the transcript, designated PnC401 (P. nil C401), was isolated. RNA-blot hybridization verified that levels of PnC401 mRNA fluctuated with a circadian rhythm, with maxima between 12 and 16 h after the beginning of the dark period) and minima of approximately 0. This oscillation continued even during an extended dark period but was damped under continuous light. Accumulation of PnC401 mRNA was reduced by a brief exposure to red light at the 8th h of the dark period (night-break treatment) or by exposure to far-red light at the end of the light period (end-of-day far-red treatment). These results suggest that fluctuations in levels of PnC401 mRNA are regulated by phytochrome(s) and a circadian clock and that they are associated with photoperiodic events that include induction of flowering.

Benzoic acid 2-hydroxylase, a soluble oxygenase from tobacco, catalyzes salicylic acid biosynthesis.

Benzoic acid 2-hydroxylase (BA2H) catalyzes the biosynthesis of salicylic acid from benzoic acid. The enzyme has been partially purified and characterized as a soluble protein of 160 kDa. High-efficiency in vivo labeling of salicylic acid with 18O2 suggested that BA2H is an oxygenase that specifically hydroxylates the ortho position of benzoic acid. The enzyme was strongly induced by either tobacco mosaic virus inoculation or benzoic acid infiltration of tobacco leaves and it was inhibited by CO and other inhibitors of cytochrome P450 hydroxylases. The BA2H activity was immunodepleted by antibodies raised against SU2, a soluble cytochrome P450 from Streptomyces griseolus. The anti-SU2 antibodies immunoprecipitated a radiolabeled polypeptide of around 160 kDa from the soluble protein extracts of L-[35S]-methionine-fed tobacco leaves. Purified BA2H showed CO-difference spectra with a maximum at 457 nm. These data suggest that BA2H belongs to a novel class of soluble, high molecular weight cytochrome P450 enzymes.

A rat genetic map constructed by representational difference analysis markers with suitability for large-scale typing.

Representational difference analysis (RDA) was applied to isolate chromosomal markers in the rat. Four series of RDA [restriction enzymes, BamHI and HindIII; subtraction of ACI/N (ACI) amplicon from BUF/Nac (BUF) amplicon and vice versa] yielded 131 polymorphic markers; 125 of these markers were mapped to all chromosomes except for chromosome X. This was done by using a mapping panel of 105 ACI x BUF F2 rats. To complement the relative paucity of chromosomal markers in the rat, genetically directed RDA, which allows isolation of polymorphic markers in the specific chromosomal region, was performed. By changing the F2 driver-DNA allele frequency around the region, four markers were isolated from the D1Ncc1 locus. Twenty-five of 27 RDA markers were informative regarding the dot blot analysis of amplicons, hybridizing only with tester amplicons. Dot blot analysis at a high density per unit of area made it possible to process a large number of samples. Quantitative trait loci can now be mapped in the rat genome by processing a large number of samples with RDA markers and then by isolating markers close to the loci of interest by genetically directed RDA.