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Ari Brynjolfsson: Time Dilation and Supernovas Ia
Plasma Redshift, Time Dilation, and Supernovas Ia
Ari Brynjolfsson ∗
Applied Radiation Industries, 7 Bridle Path, Wayland, MA 01778, USA
The measurements of the absolute magnitudes and redshifts of supernovas Ia show that con-
ventional physics, which includes plasma redshift, fully explains the observed magnitude-redshiftrelation of the supernovas. The only parameter that is required is the Hubble constant, whichin principle can be measured independently. The contemporary theory of the expansion of theuniverse (Big Bang) requires in addition to the Hubble constant several adjustable parameters,such as an initial explosion, the dark matter parameter, and a time adjustable dark energyparameter for explaining the supernova Ia data. The contemporary Big Bang theory also re-quires time dilation of distant events as an inherent premise. The contention is usually that thelight curves of distant supernovas show or even prove the time dilation. In the present article,we challenge this assertion. We document and show that the previously reported data in factindicate that there is no time dilation. The data reported by Riess et al. in the AstrophysicalJournal in June 2004 confirm the plasma redshift, the absence of time dilation, dark matter,and dark energy.

Keywords: Cosmology, cosmological redshift, plasma redshift, Hubble constantPACS: 52.25.Os, 52.40.-w, 98.80.Es
The remarkable measurements of the supernovas' absolute magnitudes and redshifts by the manywell-equipped groups of experienced researchers help us define some important cosmological param-eters. The good quality of this work gives us opportunity to test the different cosmological models.

Analyses of the light curves of low redshift supernovas Ia show that the width of the light curves
(the increase and subsequent reduction in the light intensity with time) varies with the maximumabsolute magnitudes of the supernovas. The increased width of the light curves with the increasingbrightness of the supernovas is reasonable, as we usually expect a larger explosion to result in biggerdimensions of the explosion, and therefore longer time for explosion to expand, and longer time forthe larger amount of energy to decay after maximum. The increased width, however, can be par-tially obscured by the usually assumed time-dilation effect. The observed width of the light curvesof the high-redshift supernovas is reduced by dividing the width by the assumed time-dilation factor,(1 + z), before it is compared with the template curves for the nearby supernovas, where the timedilation is insignificant. This reduced width of the light curve for a distant supernova then resultsin a reduced brightness estimate.

When applying the plasma-redshift theory [1] (see in particular Eqs. (54)-(56) and Table 4 of that
source), there is no time dilation. Therefore, had we applied the plasma redshift when interpretingthe observations, the supernovas would be estimated to be brighter, ∆M = −2.5 log (1 + z), than theestimate obtained assuming time dilations. However, the concurrent dimming, ∆M = 5 log (1 + z),caused by the Doppler shift on the intergalactic plasma electrons, in accordance with the plasma-redshift theory, causes a dimming that is twice the dimming caused by the time dilation. Thisadditional dimming is however reduced, because the distance modulus is also different in the twotheories. In fact the dimming with increasing z of the supernovas in the plasma-redshift theory is
∗ Corresponding author: aribrynjolfsson@comcast.net
Ari Brynjolfsson: Time Dilation and Supernovas Ia
almost equal to the dimming with increasing z of the supernovas in the contemporary Big Bangtheory. Occasionally, the researchers felt incorrectly that they had proven the time-dilation effect,because they were unaware of the plasma-redshift theory.

In Section 2, we will first explore what the observations of the supernovas indicate about the time
dilation. As we will see, the data, contrary to common beliefs, strongly indicate that there is, infact, no time-dilation effect. The observed lack of time-dilation effect contradicts the contemporaryexpansion or Big Bang theory and indicates thus that we should explore other theories for explainingthe cosmological perspectives. In section 3, we find that the supernova observations nicely confirmthe redshift magnitude relation predicted by the plasma-redshift theory, which has no time dilation.

What do the supernova observations indicate about thetime dilation?
The research teams investigating the absolute magnitudes, Mmax, of the nearby supernovas oftenuse the rate of decrease in brightness or rate of increase in absolute magnitude, ∆M15, during thefirst 15 days after the maximum brightness, as a measure of the width of the light curve. The greaterthe value of ∆M15, the steeper is the decay of the light intensity, or the smaller is the width, w, ofthe light curve. The increase in maximum magnitude (corresponding to a decrease in the maximumbrightness), is then also found to increase roughly proportional to the change in magnitude ∆M15.

For the low-redshift supernovas, this relation appears consistent and reliable.

The researchers also use the width, w = s(1 + z), of the supernova's light curve, where s is called
a stretch factor, and (1 + z) is the time-dilation factor. For the nearby supernovas, we have that thewidth is roughly proportional to 1/∆M15. When we observe low-redshift supernovas, the width, w,of the light curve is found to increase with the brightness. For low-redshift supernovas (z ≤ 0.1) , thechange in the factor of (1+z) is small, so it is principally the stretch factor, s, that increases when thewidth increases and the brightness increases (or the absolute magnitude decreases). When observinga distant supernova at a redshift of z > 0.1, the supernova researchers will divide that measuredlight-curve width, w, by a time-dilation factor, (1 + z), to obtain an estimate of the stretch factor,s, representing the width of a corresponding supernova at close range. From this reduced width,they estimate the maximum intensity of the distant supernova, based on the maximum brightnessor magnitude for corresponding width of the nearby supernovas.

When evaluating distant objects, there is always a tendency for a Malmquist bias. Amongst the
distant supernovas, we are likely to observe the brightest members of that group of supernovas. Thequestion then arises, how big is the Malmquist bias? It is noteworthy, that in sample of 10 distantsupernovas reported in table 6 of the article by Riess et al. [2] the two supernovas with the highestredshift have the greatest widths of their light curves, while the five supernovas with the smallestredshift have the smallest widths, even after the division by the time-dilation factor (1 + z). Thisindicates a slight Malmquist bias.

For nearby (z ≤ 0.1) supernovas, which are practically independent of the time-dilation effect,
Phillips [3] (see in particular Table 2 of that source) finds that if we write peak brightness magnitudeas:
Mmax = a + b ∆M15
then the experiments for nine low-redshift sample of supernovas, with z ≤ 0.01, indicate that for thespectral bands B, V, and I, the values of a and b are respectively as shown in the following array ofequations:
−21.726 (0.498) + 2.698 (0.359) ∆M15,
V. : VMmax = −20.883 (0.417) + 1.949 (0.292) ∆M15,
σ(V Mmax) = 0.28
−19.591 (0.415) + 1.076 (0.273) ∆M15,
σ(I Mmax) = 0.38
The effect of possible time dilation on the magnitude estimates of these low redshift supernovas isless than 0.0017 redshift units, and therefore insignificant.

Ari Brynjolfsson: Time Dilation and Supernovas Ia
Phillips [3] (see last sentence of the abstract of that source) makes the following comment:
"Considerable care must be exercised in employing Type Ia supernovae as cosmological standardcandles, particularly at large redshifts where Malmquist bias could be an important effect".

Subsequently, Phillips et al. [4] slightly modified the approach by using second order polynomials
in (∆m15(B) − 1.1) instead of the linear equations above, and by taking into account the absorptionin our Galaxy and the host galaxy, and by considering a larger number of supernovas (62 instead of9). Phillips et al. [4] comment (see the introduction of that source) that: ". there is now abundantevidence for the existence of a significant dispersion in the peak luminosities of these events at opticalwavelengths, the absolute magnitudes fortuitously appear to be closely correlated with the decaytime of the light curve."
Goldhaber et al. [5] adjust the R-band photometric data to one maximum intensity Imax and
scale the time axis by the light-curve width, w. This width factor has the form w ≡ s (1 + z), wheres is the stretch factor, and (1 + z) is the time-dilation factor. For a sample of 35 supernovas outof total of 42 their Table 1 shows that the stretch factor s varies from between 0.71 and 1.55, orabout a factor of 2.18, while the (1 + z)-values vary from 1.172 to 1.657, or a factor of 1.41. The 7supernovas that were excluded would, if included, not have changed their conclusions
Goldhaber et al. [5] analyzed similarly 18 of the 29 SNe of the Calan/Tololo set. Their Table 2
shows that the stretch factor s varies from 0.53 to 1.12, or about a factor of 2.11, while the (1 + z)-values varied from 1.014 to 1.088, or a factor of 1.073. The variations in the width are thus mostlydue to variations in s. Their Fig. 1-(f) shows clearly that the width factor, w, results in a ratheruniform light curve width as is to be expected. This curve then also fits well to the template curvefor Parab-18 as demonstrated in their Fig. 2-(a).

Goldhaber et al. [5] show in their Fig. 3-(a) for a sample of 42 high-redshift supernovas that the
light curve width, w is proportional to (1 + z). However, this is self-evident, because according totheir definition w ≡ s (1 + z). They could similarly have shown that the width, w, is proportional tos. However, the relation between s and (1 + z) ≤ 1.83 as shown in Fig. 3-(b), which includes all 42high-redshift supernovas, is meaningful and most important. It indicates clearly that the variationin the average of s with time-dilation factor (1 + z) is insignificant. The variations in s are thusindependent of the time dilation, (1 + z). This is surprising, because according to the contemporaryexpansion theory, we expect the Malmquist bias to result in an increase in the brightness and anincrease in s with increasing z. It appears that the actual increase in the width, s, and the brightnessof the supernova is suppressed by the time dilation, which the supernova researchers use to reducethe width of the light curve, and thereby the brightness.

By definition, the maximum light intensity is proportional to 10−0.4Mmax. When we use the
contemporary expansion theory, the light intensity increases roughly proportional to the light curvewidth, w ≡ s (1 + z). According to Fig. 3-(b) of [5], the width, w, appears to increase roughlyproportional to (1+z) with a large noise s. We can then write −0.4 ∆Mw ≈ log w = log (1+z)+log s,or
∆Mw ≈ −2.5 log w = −2.5 log (1 + z) − 2.5 log s.

The analysis by Goldhaber et al. [5] shows thus that the average value of s is independent of z.

Their analysis therefore indicates that the increase in light intensity in units magnitude is actuallygiven by
∆Mz = −2.5 log (1 + z).

The supernova researchers, in accordance with the contemporary Big Bang theory, reduce the ab-solute magnitudes M, when they use the time-dilation effect to reduce the width. Had the theynot corrected the magnitude by using the time dilation in their equations, the corresponding widthfactor would be w = s′. We would then get a reasonable increase in the brightness with z. Theanalysis by Goldhaber et al. [5] (see in particular their Fig. 3-b of that source) thus indicates thatthere is no time dilation. The observations, therefore, appear to contradict the contemporary BigBang theory, which has time dilation as a basic premise.

The following equation describes the major changes when we omit the time dilation:
Ari Brynjolfsson: Time Dilation and Supernovas Ia
M = Mexp − 2.5 log (1 + z) = M1 + ∆M1 − 2.5 log (1 + z) = M0 + ∆M0
∆M0 = ∆M1 − 2.5 log (1 + z)
In Eq. (5), the value of M is the absolute magnitude of the supernova without time dilation, whileMexp = M1 + ∆M1 is the experimentally determined magnitude by the supernova researchers ad-hering to the Big Bang theory. M1 is their estimated reference magnitude without the correctionfor light curve width, while ∆M1 accounts for the correction for the light curve width. The M0 and∆M0 are, respectively, the corresponding magnitude and magnitude correction, which the supernovaresearchers would have measured had they omitted the time dilation and used the plasma redshiftto guide them.

When the researchers correct the observed values by omitting the time dilation, they would have
to take into account the concurrent Doppler effect term +5 log(1 + z). In addition, the researcherswould have to take into account the difference in the distance modulus in the plasma-redshift theoryand in the contemporary Big Bang theory.

Brynjolfsson [1] has shown, (see in particular Eq. (56) and Table 4 of that source) that the mag-
nitude redshift relation in the plasma-redshift theory is very similar to the corresponding relation inthe contemporary Big Bang theory if we omit the acceleration and deceleration terms. The omissionsof acceleration and deceleration in the contemporary Big Bang theory are often not reasonable. Butat small redshifts, the similarity between the values derived from the two theories helps us under-stand why it is difficult for small z-values to see the difference between the plasma redshift theoryand the contemporay expansion theory.

It is often misleading to refer to the plasma-redshift theory as a "tired light theory", because
the plasma redshift leads to the dimming by the Doppler effect and to a different distance modulusfrom that in most "tired light theories".

Omitting the time dilation when correcting the absolute magnitude, increases the brightness cor-
rection of the supernova by the absolute-magnitude correction-term −2.5 log(1 + z). The concurrentdimming caused by the Doppler effect on the electrons and the modification by the difference in theform of the distance modulus made it very difficult for the supernova researchers to discern thesechanges. When applying the contemporary Big Bang theory, the reduction of the width of the lightcurve by the time dilation artificially reduces the Malmquist bias. We will therefore back correctthe magnitudes for the time-dilation effect, which in accordance with Eq. (5) changes the absolutemagnitude from Mexp to M. This change results in a small brightening of the observed supernovaswith increasing z, as is to be expected from the Malmquist bias. This change is also in accordancewith Fig. 3-(b) of reference [5], which shows that the light-curve width-parameter s is independentof the time dilation.

In their Fig. 4, Richardson et al. [6] show the distribution of the absolute magnitudes, MB, at
maximum intensity for 111 normal SNe Ia with a distance modulus µ ≤ 40. The Malmquist bias forthe brightest supernovas is not obvious, but if we omit the time-dilation effect it would be obvious.

The magnitudes when uncorrected for extinctions in the parent galaxies were compared with themagnitudes when corrected for the adopted extinctions of the galaxies. When approximated with agaussian distribution curve, the distribution moved slightly to the brighter side (as expected), from-19.16 to -19.46 , and the σ-value decreased from 0.76 to 0.56. The brighter tail end of the measureddistribution was slightly smaller than that of the gaussian distribution. This possibly could indicatean upper limit. In this context, we should take in to consideration, however, that if the time-dilationeffects were removed, it would increase the brightness, especially, of the brighter tail end or at thehigher z-values.

When we increase the redshifts from (z ≈ 0.01) to large redshifts (z ≈ 1), we increase the number
of supernovas per redshift interval by a large factor. The fact that observations are limited by themagnitude means that we can expect a significant Malmquist bias. This is generally realized by thesupernova researchers as exemplified by their frequent reference to the Malmquist bias. However,
Ari Brynjolfsson: Time Dilation and Supernovas Ia
because of their use of time dilation in the their estimates, the Malmquist bias was less obvious thanexpected.

Redshift magnitude relation
In section 2 above, we have shown that the supernova data strongly indicate that there is no timedilation. For a given light emission from a supernova, the omission of the time dilation increasesthe observed light intensity, or decreases the observed magnitude, M, of the supernova by a term∆M = −2.5 log (1 + z). For eliminating the time-dilation effect, we must in accordance with Eq. (5)change the experimentally determined value, Mexp, as determined by the supernova researchers to
M = Mexp + ∆M = Mexp − 2.5 log (1 + z).

This new M is then nearly free of the time-dilation effects.

When comparing the predictions of the plasma-redshift theory with experiments, we will use the
M-values, as determined by Eq. (6). For Mexp, we use the very good magnitude data reported byRiess et al. [7] (see in particular the expanded Table 5 of that source). These M-values, which havebeen corrected for the false time-dilation effect, can then be used for testing the different cosmologicaltheories.

As shown by Brynjolfsson [1], the plasma redshift gives a very simple explanation of the magnitude-
redshift relation for the observed supernovas. This relation is (see Eq. (54) of reference [1])
) − 5 + AB.

where AB is the absorptions of light from the supernova expressed in magnitude units, c is thevelocity of light in km s−1, and H0 is the Hubble constant in km s−1 Mpc−1. This equation has noadjustable parameters except the Hubble constant, which only moves the curve in Fig. 1 up anddown independent of z. The supernova experiments can be used to measure accurately the Hubbleconstant. It is thus a very simple equation that must match the many experimental points. Thisequation contrasts the conventional magnitude redshift relation for the Big Bang cosmology, which inaddition to the Hubble constant requires adjustable parameters for dark matter, and time dependantdark energy or a time dependant cosmological constant.

In the reference [1] (see Fig. 5 of that source), the plasma-redshift theory was compared with
supernova data reported by Riess et al. [2]. Although the fit to the data is very good, it can beseen that the three supernovas with the largest redshift are slightly below the theoretically expectedline in spite of the fact that the high z-data also pulled the theoretical curve down. This is becausethe experimental data reported by Riess et al. [2] were not corrected for the false time-dilationeffect conventionally used by the supernova researchers, who assumed the contemporary Big Bangtheory when reporting their data. The contemporary Big Bang theory has time dilation as aninherent premise. Had we in Fig. 5 of [1] applied the back correction for the time dilation given inEq. (6) above, these three points with the largest redshift would have fallen on the theoretical curvepredicted by the plasma redshift.

With the new data reported by Riess et al. in Table 5 of reference [7], showing several supernovas
in the range 1 ≤ z ≤ 1.755, it became necessary to eliminate the false time-dilation effect inaccordance with Eq. (6) above. With this correction, we can use all the newly reported supernovadata listed in Tables 5, by Riess et al. [7] and check them against Eq. (7). In Fig. 1, we have usedall of their 186 data points, the samples indicated with gold as well as silver.

Three correction methods for the effect of light-curve widths and shapes have been used to
determine the magnitude of some of the supernovas. For 10 of the supernovas the magnitude wasdetermined using the MLCS-method and the ∆M15(B)-method and reported in Tables 5 and 6 ofreference [2], and using the MLCS2k2-method in Table 5 of reference [7]. These three methods fordetermination of Mexp, when compared with the predictions of the plasma-redshift theory appearedto be about equally good. The MLC method scored slightly better than the other two; but because
Ari Brynjolfsson: Time Dilation and Supernovas Ia
Supernova's magnitude versus their redshift
Data with time dilation
Data without time dilation
Plasma-redshift theory
Figure 1: The magnitudes, m-M, of supernovas on the ordinate versus their redshifts, z from 0.0 to2, on the abscissa. The data include all 186 supernovas reported by Riess et al. [7] (see the expandedTables 5 of that source). The lower data points indicated with rectangles (blue) are as reported byRiess et al. [7] and include the time dilation, while the data points indicated with triangles (red)are free of time dilation. The black curve shows the theoretical predictions of the plasma-redshifttheory in accordance with Eq. (7), when the a Hubble constant of H0 = 59.44 km s−1 Mpc−1.

of the small sample, the difference was not significant. We use therefore the data as reported byRiess et al. [7].

The plasma redshift predicts a small additional redshift due to the corona of the Milky Way
Galaxy and the corona of the host galaxy. For this reason, we have reduced all the redshifts by anamount ∆z = −0.00185. This is nearly an insignificant correction, but in principle a correction onthis order of magnitude should be applied when using the plasma-redshift theory. This correspondsto an average redshift of ∆z = −0.000925 for each galaxy. The corresponding Hubble constant isH0 = 59.44 km s−1 Mpc−1.

Riess et al. [7] characterize 157 out of the 186 SN Ia (in their Table 5) as gold samples, while
the remaining 29 are silver samples. When we compare the corrected observed magnitudes with thepredictions of the plasma-redshift theory, we find that four of the supernovas (SN1997as, Sn1998I,SN200ea, and Sn2001iv) had magnitudes in the range [(m − M) − (m − M)pr] ≤ −0.8, where thesubscript 'pr' referes to the plasma-redshift theory. Of these 3 are gold samples and 1 silver sample.

All of these four samples had negative values for the quantity inside the brackets, which indicatesthat the large and one sided deviations from the predicted values were possibly due to a largerabsorption AB than those assumed for these four supernovas. Analogously, we find that six ofthe supernovas are in the interval −0.8 ≤ [(m − M) − (m − M)pr] ≤ −0.5. Of these 3 are goldsamples and 3 silver samples. Similarly, we find that four of the supernovas are in the interval+0.8 ≥ [(m − M) − (m − M)pr] ≥ +0.5. Of these 2 are gold samples and 2 silver samples. These
Ari Brynjolfsson: Time Dilation and Supernovas Ia
last mentioned, 6 and 4, supernovas, are within the expectation of a gaussian distribution for thislarge number of supernovas.

In spite of the relatively large one sided deviations from the theoretical curve for four of the
samples, the distribution is nearly gaussian with a standard deviation for an individual sampleof about σM = 0.30 of a magnitude. The slightly skewed distribution with heavier negative tailindicates an additional absorption in some of the supernovas. The standard deviation in the averagevalue of the absolute magnitude determining the theoretical curve is only σM
= 0.022 magnitude.

According to Eq. (7), the value of the Hubble constant is then H0 = 59.44 ± 0.6 km s−1 Mpc−1.

This high accuracy in the determination of H0 applies only to the internal consistency between theplasma-redshift theory and the measurements of the supernovas and does not apply to the actualuncertainties, which depend on the uncertainties in determining the absolute magnitudes of thesupernovas at a well determined absolute distances.

In conclusion, the data from the supernovas Ia indicate that there is no time dilation. As
Fig. 1 shows, the data support with very high accuracy the plasma redshift theory, which has notime dilation. The plasma redshift theory rejects the data with time dilation with high degree ofconfidence.

The plasma-redshift cross-section [1] follows directly from well-proven conventional basic physics.

In addition to explaining the magnitude-redshift relation for the supernovas Ia, the plasma redshifthelps explain the heating of the solar corona, the galactic corona, the heating of intergalactic plasma,and the cosmic microwave background [1]. The plasma redshift, when combined with the solarredshift experiments, leads to weightlessness of photons in a local system of reference (and repulsionof photons in a gravitational field when observed by distant observer). This fact invalidates theequivalence principle [1]. All the many experiments that incorrectly have been assumed to prove theequivalence principle are in the domain of classical physics, and therefore do not make it possible todetect quantum mechanical effects, which are essential for observing the weightlessness of photons.

Only the solar redshift experiments are in the domain of quantum mechanics, and these show clearlythe repulsion of photons [1], and therefore that the equivalence principle is false. This in turn canlead to quasi-static universe without Einstein's Λ-coefficient [1]. The plasma-redshift explanationshave no need for dark matter, dark energy, nor black holes.

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[6] Richardson, D., Branch, D., Casebeer, D., Millard, J., Thomas, R. C., & Baron, E. 2002 AJ,
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Source: http://www.mysearch.org.uk/website1/pdf/675.3.pdf

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