Red Edges Research Articles

High Sensitivity of Stark-Shift Voltage-Sensing Dyes by One- or Two-Photon Excitation Near the Red Spectral Edge

Sensitivity spectra of Stark-shift voltage sensitive dyes, such as ANNINE-6, suggest the use of the extreme red edges of the excitation spectrum to achieve large fractional fluorescence changes with membrane voltage. This was tested in cultured HEK293 cells. Cells were illuminated with light at the very red edge of the dye's excitation spectrum, where the absorption cross section is as much as 100 times smaller than at its peak. The small-signal fractional fluorescence changes were −0.17%/mV, −0.28%/mV, and −0.35%/mV for one-photon excitation at 458 nm, 488 nm, and 514 nm, respectively, and −0.29%/mV, −0.43%/mV, and −0.52%/mV for two-photon excitation at 960 nm, 1000 nm, and 1040 nm, respectively. For large voltage swings the fluorescence changes became nonlinear, reaching 50% and −28% for 100 mV hyper- and depolarization, respectively, at 514 nm and 70% and −40% at 1040 nm. Such fractional sensitivities are ∼5 times larger than what is commonly found with other voltage-sensing dyes and approach the theoretical limit given by the spectral Boltzmann tail.

Physical Characteristics of the RR Lyrae Stars in the Very Metal Poor Globular Cluster NGC 5053

The physical characteristics of the 10 RR Lyrae stars in the very metal-poor globular cluster NGC 5053 are derived from photometry of ∼1000 B and V CCD frames acquired from 1994 to 2002 with the Dominion Astrophysical Observatory 1.8 m Plaskett Telescope. Revised pulsation periods and light curves, mean magnitudes, colors, amplitudes, and Fourier parameters are presented. Periods accurate to ≲10-5 days are now known for all 10 RR Lyrae stars. Using times of maximum light dating back to Baade's original 1923–1927 observations, period change rates, dP/dt, accurate to ≲0.07 days Myr-1, have been derived for the 10 stars. Seven stars have increasing periods, and three have decreasing periods, with the estimated period change rates for V1, V2, V9, and V10 being very close to zero. The mean dP/dt is equal to 0.04 ± 0.04 days Myr-1 and is consistent with Lee's evolutionary model predictions for a cluster with horizontal-branch type ∼0.5. Mean B - V colors range from 0.20 to 0.40 and are more consistent with near-zero reddening than alternative higher estimates. A reddening EB-V = 0.018 ± 0.003 is derived from the 1998 SFD maps. Mean effective temperatures vary from 6040 K (V10) to 7290 K (V6), with 2.6 ≤ log g ≤ 3.1. Visual and bolometric absolute magnitudes, bolometric corrections, and luminosities are derived using Fourier methods and using intensity- and magnitude-averaged mean magnitudes. Mean locations of the stars in the H-R diagram tend to progress from hotter, lower L stars to cooler, higher L stars and are consistent with theoretical blue and red edges of the instability strip. Masses estimated assuming zero reddening and Dorman's oxygen-enhanced models range from 0.68 ⊙ (V6) to 0.78 ⊙ (V10) for the 10 stars. The mean metal abundance for NGC 5053 derived using the Jurcsik-Kovács method lies significantly higher than the range -2.3 to -2.6 dex determined using other, more well established methods. This finding supports recent suggestions that metallicities derived from Fourier-based [Fe/H] calibrations need to be revised downward by at least 0.3 dex for RR Lyrae stars with very low metal abundances.

A Comparative Femtosecond Coherence Study of the Unligated Monomeric Hemeproteins Myoglobin and Leghemoglobin

Impulsive optical excitation has been performed on wild type, unligated leghemoglobin for the first time to compare the induced vibrational coherence with that observed in myoglobin. Both proteins were excited at the Soret maxima and probed at red and blue edges of the Soret band. The resulting kinetic traces were modulated by low-frequency vibrations. Leghemoglobin shows a decrease in vibrational amplitude compared with myoglobin. The possible cause for the amplitude differences is discussed in terms of contributions from both ground- and excited-state vibrational coherences and ground-state heterogeneity.

Matchings in colored bipartite networks

In K( n, n) with edges colored either red or blue, we show that the problem of finding a solution matching, a perfect matching consisting of exactly r red edges, and ( n− r) blue edges for specified 0⩽ r⩽ n, is a nontrivial integer program. We present an alternative, logically simpler proof of a theorem in (Kibernetika 1 (1987) 7–11) which establishes necessary and sufficient conditions for the existance of a solution matching, and a new O( n 2.5) algorithm. This shows that the problem of finding an assignment of specified cost r in an assignment problem on the complete bipartite graph with a 0−1 cost matrix is efficiently solvable.

Two-edge colorings of graphs with bounded degree in both colors

Let F be the family of all graphs of maximum degree k+ℓ which can be red–blue edge colored with each of its vertices incident to at most k red edges and at most ℓ blue edges. Let m( k,ℓ) be the maximum number such that every graph with at most m( k,ℓ) vertices of maximum degree k+ℓ is in F. This paper determines m( k,ℓ) except when one of k and ℓ is odd and the other even, in which case best known bounds are given. These values of m( k,ℓ) are used to determine the size Ramsey number r ̂ (F 1,F 2) for many pairs ( F 1, F 2) of star forests, which gives a partial solution to a conjecture of Burr et al. (Proceedings of the Koninklijke Nederlandse Academie van Wetenschappen, Series A, Vol. 81(2), 1978, p. 187.) made in 1978.

Analysis of in situ hyperspectral data for nutrient estimation of giant sequoia

In this paper, we report some correlation analysis results between in situ hyperspectral data in the spectral range of approximately 350-900 nm and three foliage nutrient constituents. Two hundred and forty hyperspectral measurements were taken using a PSD1000 spectrometer at a giant sequoia plantation site in 1997. Foliage nutrient constituents (expressed in concentration, percentage of dry weight)-total nitrogen (TN), total phosphorus (TP) and total potassium (TK)-were measured from the same site. The potential of hyperspectral data for estimating foliage nutrient status was evaluated using univariate correlation and multivariate regression analysis methods with different types of predictors: original and the first-order derivative spectra, vegetation index (VI)-based, spectral position-based, area-based and principal component analysis (PCA)-based predictors. The eight VIs were constructed from the blue, green, red and near-infrared spectra bands; spectral position-based predictors consisted of parameters extracted from the blue, yellow and red edges, the green peak and the red well; area-based variables were calculated as the sum of the first derivative values at each of the three edges; and the PCA-based predictors were obtained from principal component transformation applied to the first derivative spectra of the three edges. Results showed that the best foliage nutrient prediction was obtained with the PCA-based predictors in four-term prediction models for all three nutrient constituents. In univariate correlation analysis, it seems that only two VIs RB ( R 760-850 / R 350-400 ) and NRB (( R 760-850 - R 350-400 )/( R 760-850 + R 350-400 )) may be employed to predict all three nutrient constituents ( p =0.01), and better R 2 values were obtained from the maximum first derivative spectra of blue edge and yellow edge and the spectral reflectance difference between green peak and red well for TN, TP and TK. The results obtained from the univariate analysis, however, indicate that the level of correlation between foliage nutrient concentrations and hyperspectral data is low. In fact for TN there existed rather low correlations with different types of variables. In general, the best univariate correlation results were obtained for TK, then TP, with TN the worst. For multiple regression with PCA-based predictors, the best results came from TN, then TK, while the worst was associated with TP.

A Proposed Pulsation Driving Mechanism for γ Doradus Variable Stars

AbstractWe propose a pulsation driving mechanism for γ Doradus variable stars. This mechanism requires that the local convective timescale at the base of the envelope convection zone be comparable to or longer than the pulsation period. This mechanism explains both the red and blue edges of the γ Dor instability strip. We predict that some candidate γ Dor stars summarized by Handler (1999) may actually be too hot or too cool to be γ Dor variables.

A note on a triangle-free — complete graph induced Ramsey number

The induced Ramsey number, IR( G, H), is equal to p if there exists a graph F on p vertices such that any 2-colouring of its edges with red and blue leads to either an induced copy G in the subgraph of F spanned by the red edges or an induced blue H, and, furthermore, no graphs on p−1 vertices have the above property. There will be shown that the lower bound of the induced Ramsey number for a triangle-free graph on t vertices and a complete graph K n is roughly n 2 t/4. In one case, when the triangle-free graph is a star, a simple proof of the exact value (about n 2 t/2) will be given.

On the excited-state energy transfer between tryptophan residues in proteins: the case of penicillin acylase

The problem, whether excited-state energy transfer occurs between Trp residues in a multi-tryptophan proteins and if it does, what kind of changes it induces in different parameters of protein fluorescence, is currently under active investigation. In our previous paper [Biophys. Chem. 72 (1998) 265], the energy transfer was found and studied in detail for Na,K-ATPase. It was shown that this transfer influences all parameters of fluorescence emission, which is detected at site-selective conditions (red-edge of excitation, blue and red edges of emission). Present experiments were performed on unusually tryptophan-rich protein, bacterial penicillin acylase (28 Trp per dimer of 82 kDa) and were aimed to extend these observations. They demonstrate substantial heterogeneity in the environments of tryptophan residues within the protein structure. This suggests, that in the present case, if the energy transfer exists, it should be directed from short-wavelength-emitting to long-wavelength-emitting tryptophan residues and thus could be easily observed by a number of time-resolved and steady-state fluorescence techniques. Unexpectedly, no signature of inter-tryptophan energy transfer was found.

Some medications of Ramsey numbers

Abstract The planar Ramsey number PR (G, H) is defined as the smallest integer n for which any 2-colouring of edges of Kn with red and blue where red edges induce a planar graph leads to either are red copy of G, or a blue H. In this note we study the value of the planar Ramsey numbers as well as their weak induced versions IPRw(G, H), for some classes of graphs Inparticular we calculate almost all values of PR (G, Kn) and IPRw(G, Kn) where G is connected.

The Clusters AgeS Experiment (CASE): RR Lyrae variables in the globular cluster NGC 6362

We present V- and B-band charge-coupled device (CCD) photometry of 35 RR Lyr stars in the Southern hemisphere globular cluster NGC 6362. Fourier decomposition of the light curves was used to estimate the basic properties of these variables. From the analysis of the RRc stars we obtain a mean mass M=0.531±0.014 M⊙, luminosity log L/L⊙=1.656±0.006, effective temperature Teff=7429±20 and helium abundance Y=0.292±0.002. The mean values of the absolute magnitude, metallicity (on Jurcsik's scale) and effective temperature for 14 RRab stars with ‘regular’ light curves are: MV=0.86±0.01,[Fe/H]=−0.93±0.04 and Teff=6555±25, respectively. From the B–V colours, periods and metallicities of the RRab stars we estimate the colour excess for NGC 6362 to be equal to E(B–V)=0.08±0.01. Using this value we derive the colours of the blue and red edges of the instability strip in NGC 6362 to be (B–V)BE0=0.17 and (B–V)RE0=0.43. From the relations between the Fourier coefficients of RRab and RRc stars and their absolute magnitudes we estimate the apparent distance modulus to NGC 6362 to be (m—M)V=14.46±0.10. From the mean value of log L/L⊙ of the RRc stars we obtain 14.59±0.03. The V-band light curves of three of the RRc stars exhibit changes in amplitude of over 0.1 mag on the time-scale of around one week. Near the radial first overtone frequency we find one or two peaks, which strongly suggests that these variables belong to the newly identified group of non-radial pulsating RR Lyr stars.

RR Lyrae: Theory versus Observation

The luminosities, effective temperatures, and metallicities that are derived empirically by Kovacs & Jurcsik from the light curves of a large number of globular cluster and field RRab and RRc stars are compared to theoretical RR Lyrae models. The strong luminosity dependence of the empirical blue and red edges (log L vs. log Teff diagram) is in disagreement with that of both radiative and convective models. A reexamination of the theoretical uncertainties in the modeling leads us to conclude that the disagreement appears irreconcilable.

On the Sensitivity of the Cepheid Period‐Luminosity Relation to Variations of Metallicity

Predictions are made of the effect of variations in the [Fe/H] metallicity on the zero point of the Cepheid period-luminosity relation in bolometric, B, V, and I magnitudes. Theoretical evolutionary tracks in the H-R diagram, computed by three independent groups at Geneva, Padua, and Basel, are combined with the positions of the blue and red edges of the instability strip in the relevant H-R diagrams to give the predicted P-L relations for [Fe/H] metallicities of 0.0, -0.4, -0.7, -1.3, and -1.7. The predictions are based on the pulsation equation, P(,L,Te,Z,Y), calculated at the points where the tracks of a given mass for each metallicity intersect the instability strip in the H-R diagrams. New model atmospheres and synthetic spectra are computed giving sets of grids of the bolometric corrections and B - V, V - R, R - I, and V - I colors for temperatures between 7500 and 5000 K, gravities between log g = 3.0 and log g = 0.75, and metallicities between [Fe/H] = 0.0 and [Fe/H] = -1.7. Interpolation in the grids at the relevant temperatures, gravities, and metallicities of the Cepheid instability strip give theoretical P-L relations on the Cape Cousins BVI photometric system at the blue and red edges of the strip. The metallicity dependence of the P-L relations, read at P = 10 days, are dM/d[Fe/H] = 0.00 mag dex-1 in M(bol), +0.03 mag dex-1 in B, -0.08 mag dex-1 in V, and -0.10 mag dex-1 in I in the sense that lower metallicities mean brighter magnitudes in B and fainter ones in V and I. Similar dependencies are found at P = 31.6 days. Confirmation that the zero points of the Cepheid P-L relations are not steeper functions of [Fe/H] than the theoretical values derived here is found by comparing the distance moduli of the LMC, the SMC, and IC 1613 based on the P-L relation for Galactic Cepheids (〈[Fe/H]〉 = 0) with the distance moduli determined for these galaxies using RR Lyrae variables with the steep absolute magnitude-metallicity calibration of MV(RR) = 0.30[Fe/H] + 0.94. Applying this bright calibration, based on the Oosterhoff-Arp-Preston (OAP) metallicity effect, to the RR Lyrae variables in the LMC, the SMC, and IC 1613 gives individual distance moduli that agree to within 0.10 mag with the Cepheid distance moduli for [Fe/H] =0 for each galaxy, confirming that no metallicity dependence of the Cepheid P-L relation can be detected at this level with the present observational data if the bright RR Lyrae MV ([Fe/H]) calibration is used. Using the stated calibrations with the Cepheid data from the literature gives the distance modulus of the LMC to be (m - M)0 = 18.57. The modulus for the SMC, corrected for the mild metallicity effect derived here, reconciles the deviant individual B, V, and I moduli to within ±0.01 mag, giving (m - M)0 = 18.94 for the SMC.

RR Lyrae Variables in the Globular Cluster M55. The First Evidence for Nonradial Pulsations in RR Lyrae Stars

We present the results of a photometric study of RR Lyrae variables in the field of the globular cluster M55. We have discovered nine new RR Lyrae stars, increasing the number of known RR Lyrae variables in this cluster to 15 stars. Five of the newly discovered variables are Bailey type RRc, and two are type RRab. Two background RRab stars are probable members of the Sagittarius dwarf galaxy. Fourier decomposition of the light curves was used to derive basic properties of the present sample of RR Lyrae variables. From an analysis of the RRc variables we obtain a mean mass of M = 0.53 ± 0.03 M⊙, luminosity log L = 1.75 ± 0.01, effective temperature Teff = 7193 ± 27 K, and helium abundance Y = 0.27 ± 0.01. Based on the B-V colors, periods, and metallicities of the RRab stars, we estimate the value of the color excess for M55 to be equal to E(B - V) = 0.11 ± 0.03. Using this value we derive the colors of the blue and red edges of the instability strip in M55. The blue edge lies at (B - V)0 = 0.20 mag, and the red edge lies at (B - V)0 = 0.38 mag. We estimate the values of the visual apparent distance moduli to be 13.65 ± 0.11 from RRab stars and 13.91 ± 0.08 from RRc stars. The light curves of three of the RRc variables exhibit changes in amplitude of over 0.1 mag on the timescale of less than a week, rather short for the Blazhko effect, but with no evidence for another radial pulsational frequency. However, we do detect other periodicities for these three stars that are clearly visible in the light curve after removing variations with the first overtone radial frequency. This is strong evidence for the presence of nonradial pulsations, a behavior common for δ Scuti stars but not yet observed among RR Lyrae variables.

Classical Cepheid Pulsation Models. I. Physical Structure

The pulsation properties and modal stability of Cepheid models are investigated in both linear and nonlinear regimes. The linear survey is based on nonadiabatic, radiative models, whereas the nonlinear one relies on full-amplitude models that include a nonlocal and time-dependent treatment of stellar convection. To account for Cepheid pulsation characteristics over a substantial portion of the region in which they are expected to be pulsationally unstable, a wide range of stellar masses (5?M/M${s}$ -->?11) and effective temperatures (4000?T -->e?7000 K) was adopted. The luminosity of each model was fixed according to the mass-luminosity (ML) relations predicted by evolutionary models that either neglect or take into account a mild convective core overshooting. Moreover, in order to estimate the effects of the helium and metal content on the limiting amplitude behavior of both Magellanic Clouds and Galactic Cepheids we adopted three different chemical compositions, namely, Y=0.25, Z=0.004; Y=0.25, Z=0.008; and Y=0.28, Z=0.02. For each set of input parameters we investigated the modal stability of both fundamental and first-overtone modes. The results of recent linear investigations are confirmed by our finding that linear observables such as periods and blue edges of the instability strip are only marginally affected by the chemical composition and that either an increase in metallicity or an increase in both the helium and metal content causes a mild shift of these edges toward lower effective temperatures. The approach to the nonlinear limit cycle stability, the physical structure, and the mechanisms that govern the pulsation instability are described in detail. The main results of this analysis are as follows: (1) At fixed chemical composition the width of the instability strip changes going from low- to high-mass Cepheids. (2) At fixed mass and luminosity an increase in metallicity shifts the instability strip toward lower effective temperatures. A thorough analysis of the total nonlinear work inside the instability strip points out that this effect is due to a decrease in the pulsation destabilization caused by the H ionization region. Therefore, the current theoretical scenario suggests that, at fixed period, metal-poor pulsators are brighter than metal-rich pulsators. (3) The dynamical structure of full-amplitude, first-overtone models supports the evidence that their nonlinear limit cycle behavior has been properly identified. The variations over a full pulsation cycle of the convective structure of fundamental and first-overtone pulsators located close to the blue and the red edges of the instability strip are discussed by taking into account the changes of the convective quantities across the convectively unstable region. As expected, we find that the main effect of convection on the limit cycle behavior is either to reduce the local radiative driving of the destabilizing regions, thus reducing the final amplitudes, or to damp the oscillations toward lower effective temperatures. We also find that the limiting amplitude behavior of high-mass, high-amplitude fundamental pulsators, and in particular the appearance of secondary features along their light and velocity curves, is tightly connected with the convection/pulsation interaction. By comparing the convective velocity perturbations close to the surface layers with the turbulent velocities obtained by spectroscopic measurements we find that toward lower effective temperatures both the absolute values of the convective velocity and its variation over the cycle agree reasonably well with observational data. However, the time behavior of the convective velocity in blue models and the strong decrease of this velocity predicted at low optical depths out of the maximum compression phases are presently not confirmed by observations. Both theoretical and observational shortcomings that could explain such a discrepancy are briefly discussed. The comparison between the linear periods currently adopted in the literature and the nonlinear periods obtained in this investigation shows a very good agreement in the mass range from 5 to 9 M?, whereas at 11 M? we find that linear, nonadiabatic, convective periods are systematically shorter than the nonlinear ones. Finally, the drawbacks of adopting linear observables for constraining the actual properties of Cepheids are discussed.

The MACHO Project LMC Variable Star Inventory: Classical Cepheids, AGB Variables, and the Nine Million Star Color-Magnitude Diagram

We measure the ratio of ~ 5M⊙ blue and red LMC supergiants (representative of classical Cepheids) using the MACHO Project's 9 million star color-magnitude diagram (9M CMD) of the LMC bar. We find b/r = 0.39, which favors the Z=0.008, 5M⊙ theoretical model of Schaerer et al. (1993) over that of Fagatto et al. (1994). Next, we examine the low mass (old) and low metallicity LMC field population (Pop. II). Features in the 9M CMD and properties of LMC field RRab variables are consistent with a mean iron abundance of [Fe/H] ≈ −1.5 dex for this population. Newly discovered post-HB/early-AGB Pop. II variables are identified in order to delineate the instability strip (IS). Good agreement with the theoretical IS of Bono et al. (1997) is found. We then compare the field RRab with newly identified RRab variables in the LMC clusters NGC 1898 and NGC 1835. We find the mean colors of these cluster RRab lie near the red and blue edges of the IS, respectively, which is similar to their respective (overall) red and blue HB morphologies. Since the field RRab lie on the red side of the IS, we infer the LMC field Pop. II is likely to have a red HB morphology.

Two-color CCD Photometry of Variable Stars in NGC 7006

B and V CCD photometry from 1984 through 1994 is presented for 50 RR Lyrae stars and two red variable stars in the globular cluster NGC 7006. New determinations of pulsation periods and period change rates are given and used to plot B light curves. The new photometry is combined with previously published photometry obtained from photographic plates taken in the 1930s, the 1950s and 1984 and used to derive O - C diagrams and new period change rates. V light curves based on the CCD data are also displayed, and colors derived from mean values of B and V are given. Period-amplitude diagrams and the color-magnitude diagram for the variables are shown. The dereddened blue and red edges to the instability strip in the cluster are found to be at (B-V)0 = 0.14 and 0.38. The period change rates have been revised from those given in an earlier paper and the new median period change rate is found to be +0.03, close to that predicted by the Yale evolutionary models.

Oscillating Blue Stragglers in the Core of 47 Tucanae

Six SX Phe variables detected in a 39 hr time series of Hubble Space Telescope Planetary Camera exposures in the F336W (U) filter are discussed. Two of these stars show both the fundamental and first-overtone modes and are among the first double-mode SX Phe stars reported in globular clusters. One of the double-mode stars shows evidence for a third mode near the expected period for the second overtone. Two of the other SX Phe variables in 47 Tuc are shown to oscillate simultaneously in the fourth and fifth radial overtones. The remaining two variables both have multiple oscillations excited which include nonradial modes. To support interpretation of these variables we provide evolutionary computations using current opacities and physics allowing comparison of the blue straggler stars (BSSs) and several cluster-magnitude diagram features for 47 Tuc. Linear nonadiabatic oscillation analysis is performed for a significant range of envelope and full evolutionary models in order to (1) establish the theoretical characteristics of SX Phe pulsations (e.g., location of primary driving and adiabatic nature), (2) establish the theoretical red and blue edges of the instability strip, and (3) derive the theoretical relations necessary for obtaining evolutionary and pulsational masses. Masses inferred from fundamental period-period ratio relations for the double-mode oscillators are well above the turnoff mass in 47 Tucanae and are consistent with expected masses for these blue stragglers based on position in the color-magnitude diagram (CMD) and comparison with theoretical evolutionary tracks. Combining the evolution and pulsation constraints results in mass estimates for the four double-mode BSSs in 47 Tuc of M = 1.35 ± 0.1 to 1.6 ± 0.2 M☉.

Edge partitions of the countable triangle free homogeneous graph

In this paper we investigate edge partition problems of the countable triangle free homogeneous graph. As consequences of the main result, we obtain the following theorems. For every coloring of the edges of the countable triangle free homogeneous graph U with finitely many colors there exists a copy of U in U whose edges are colored with at most two of the colors. The countable triangle free homogeneous graph U is weakly edge indivisible, that is, for every coloring of the edges of U with two colors, say red and blue, the following holds: If there is a finite triangle free graph G so that every copy of G in U contains a red edge, then there is a copy of U in U which has red edges only.

Hypericin, Hypocrellin, and Model Compounds: Steady-State and Time-Resolved Fluorescence Anisotropies

Steady-state and time-resolved fluorescence anisotropies of hypericin, hypocrellin, and five other analogues have been measured. The steady-state excitation anisotropies for each of these compounds has a broad minimum at ∼400 nm with a negative value. At the blue and red edges of the spectrum the value of the anisotropy is positive. Time-resolved fluorescence anisotropy measurements were performed for both hypericin and hypocrellin at excitation wavelengths of 300 and 570 nm. The limiting anisotropies are in excellent agreement with the corresponding steady-state values. These results are discussed in terms of the directions of the transition dipoles connecting the ground state to various excited states. The role of conformational isomers and tautomers in the ground and excited states is also considered.