The document discusses the results of a study on the effects of a new drug on memory and cognitive function in older adults. The double-blind study involved 100 participants aged 65-80 who were given either the drug or a placebo daily for 6 months. Researchers found that those who received the drug performed significantly better on memory and problem-solving tests at the end of the study compared to those who received the placebo.

1. COS 11 - 1
NEAR REAL-TIME VIEWS: GULF
STREAM AND TROPICAL OCEANS
1. As directed by your instructor, complete this activity. Also
print the Weekly Ocean News
or Supplemental files as designated. (Check for additional
News updates during the
week.)
2. Reference: Chapter 11 in the Ocean Studies textbook.
Complete the Investigations in the
Ocean Studies Investigations Manual as directed by your
instructor.
_____________________________________________________
___________________
Introduction:
The AMS Ocean Studies Investigations Manual’s Investigations
11A and 11B explore the
close coupling of the ocean and atmosphere. The first examined
was the Gulf Stream,
followed by El Niño/La Niña. Here, we will visit recent views

2. of the Gulf of Mexico/North
Atlantic and tropical Pacific to update the current sea surface
conditions.
The Gulf Stream:
The Ocean Studies eInvestigation Manual 2015-2016
Investigation 11A introduced the U.S.
Naval Oceanographic Office’s Gulf Stream maps. For a
colorized animation of the Gulf
Stream for the most recent past 12 months, go to
http://www7320.nrlssc.navy.mil/GLBhycom1-
12/navo/glfstrsst_nowcast_anim365d.gif. It
utilizes real-time 1/12° Global HYCOM Nowcast/Forecast
System ocean model products to
show the position and magnitude of sea surface temperatures
(SST) that reveal the Gulf
Stream. The animation displays numerous features over the
period of a year, including broad
expanses of high SST peaking in late summer to early fall to the
east of Florida and other
southeastern states, and the obvious direction of flow of the
Gulf Stream, as well as rotating
swirls of relatively warmer and cooler water marking locations
of eddies.
For a comparison of ocean conditions associated with the Gulf
Stream at different times of
the year, this Current Ocean Studies 11 Figure 1 displays
information for 22 October 2014
(upper map) and 19 March 2016 (lower map). Among recent
changes in the formatting of
the Gulf Stream satellite analysis map by the U.S. Naval
Oceanographic Office, the upper
map shows SST in Celsius degrees while the more recent lower
map shows SST in

3. Fahrenheit degrees. Notice the differences in latitude and
longitude intervals on the two
maps. On both maps the thinly drawn curves mark water-mass
boundaries. [The boundaries
are labeled: GS for Gulf Stream, LC – Loop Current, SG –
Sargasso Sea, SH – Shelf Water,
and SL – Slope Water, and are combined with E, S, W, and N to
identify eastern, southern,
western, and northern boundary positions.]
http://www7320.nrlssc.navy.mil/GLBhycom1-
12/navo/glfstrsst_nowcast_anim365d.gif
COS 11 - 2
Figure 1. Satellite analysis. Upper map – 22 October 2014.
Lower map –
19 March 2016 [U.S. Naval Oceanographic Office]
COS 11 - 3
1. Compare in the two Figure 1 maps the positions of the Gulf
Stream (boundaries labeled
GSN and GSS) east of mid-Florida to the east of Cape Hatteras,
NC. The positions were
generally [(within two or three)(beyond five)] latitude/longitude
degrees of each other.
Note the close alignment of the Gulf Stream’s northern

4. boundary (GSN) on both maps
from east of Florida to east of Cape Hatteras. This is primarily
due to the physical barrier
presented by the shallow continental shelf.
2. According to the SST values (in Celsius degrees) appearing
on the upper map in the Gulf
Stream segment east of mid-Florida, the SST value on 22
October 2014 was 28° C, or
82.4° F. In Fahrenheit degrees, they were generally [(five
degrees higher)
(about the same)(four degrees lower)] compared to those on 19
March 2016.
3. Intense tropical cyclones (e.g., hurricanes, typhoons) require
broad expanses of ocean
with SST of 26.5 °C (80 °F) or higher, among other
requirements, to form. Examine
Gulf of Mexico and Atlantic Ocean SST on the Figure 1 lower
map for 19 March 2016.
Based only on the temperatures shown on the map in those
areas, you would expect that
during early spring there is generally a [(low)(high)] probability
of hurricane formation in
the map area.
4. Examine the Figure 1 (upper) 22 October 2014 map. Based
on the same minimum SST
requirement, you would expect a [(lower)(higher)] probability
of hurricane formation in

5. the map area during mid-October than in early spring.
We recommend that you track the Gulf Stream from time to time
to see its changes. The
latest Gulf Stream map similar to those used in this
investigation can be found by going to
the course website and at the bottom of the Physical &
Chemical section, click on
“Additional Physical & Chemical Links.” Then click on “US
Naval Oceanographic Office
products.” Scroll down to the SATELLITE ANALYSIS section
and click on the buttons for
Gulf of Mexico/Lower N. Atlantic Composite - b/w graphic
(gif). You can also acquire
color-coded version of this map at the location to confirm SST
within cold and warm eddies.
El Niño/La Niña:
As described in the AMS Ocean Studies eManual Investigation
11B, the tropical Pacific
Ocean is a coupled ocean-atmosphere system that has global
scale impacts on weather and
climate via the phenomena El Niño and La Niña.
Figure 2 displays monthly average surface wind and temperature
(SST) conditions across the
tropical Pacific as acquired by the TAO/TRITON ocean buoy
network for November 2015.
Winds are reported as arrows with their tails at the observation
location, their orientations
showing direction, and their lengths showing relative speed. On
the upper map, temperature
isotherms are drawn with a 0.5 Celsius degree interval. The
top map shows the warmest

6. mean temperatures were centered at about 175° W, 5° S and the
coolest at about 95° W and
south of the equator.
COS 11 - 4
Figure 2. Mean surface wind and sea surface temperature
conditions and anomalies
from TAO/TRITON buoy array for the month of November
2015.
5. The bottom map in Figure 2 displays mean sea-surface
temperature and wind anomalies
(departures from a long-term average) from about 95° W to
135° E and between about
10° S and 10° N. The temperature anomalies are color-coded
with isotherms drawn at a
0.5 Celsius degree interval. The map shows that the broadest
area of highest positive
temperature anomalies in November 2015 centered on the
equator at about
[(100°W)(130°W)(170°W)(160°E)].
6. During the same November 2015 time period, the lowest SST
anomalies were located in
the [(eastern)(central)(western)] tropical Pacific.

7. The U.S., Canada, and Mexico have agreed to operational
definitions of El Niño and La
Niña. These definitions are based on three-month averages of
SST anomalies (departures
from normal) for a critical region of the equatorial Pacific
Ocean (120° W to 170° W, 5° N to
5° S). Note these boundaries (or make a paper copy on which to
mark the boundaries) on the
Figure 2 bottom map which denotes anomalies (departures) in
SST and winds from the long-
term average. Positive anomaly isotherms are drawn as solid
lines; negative anomaly
isotherms are drawn as dashed lines. A positive SST departure
from normal of 0.5
Celsius degree or greater for three consecutive months defines
El Niño. A negative SST
departure from normal of 0.5 Celsius degree or greater for three
consecutive months
defines La Niña.
7. Assuming that the SST anomalies within the boundaries you
noted or marked on the
Figure 2 bottom map are representative of a three-month
average, the anomalies were
consistent with a [(strong El Niño)(neutral)(strong La Niña)]
episode.
November 2015 was near the peak of the strongest episode
described in Item 7 in recent
years. Figure 3 presents tropical Pacific conditions for March
2016. Compare Figures 2 and

8. COS 11 - 5
3 and note the considerable changes in the several months
between November 2015 and
March 2016.
Figure 3. Mean surface wind and sea surface temperature
conditions and anomalies
from TAO/TRITON buoy array for the month of March 2016.
8. Between November 2015 and March 2016, the tropical
Pacific maximum monthly SST
anomaly [(decreased about 1.0 C degree)(remained
steady)(increased about 1.0 C
degree)].
Summary:
According to the 10 March 2016 EL NIÑO/SOUTHERN
OSCILLATION (ENSO)
DIAGNOSTIC DISCUSSION issued by NOAA’s Climate
Prediction Center, a strong El Niño
was continuing through winter into spring 2016 although SST
and other anomalies were
weakening. The Discussion includes a prediction of a transition
to neutral conditions during
the late Northern Hemisphere spring or early summer 2016, with
a close to 50% chance for
La Niña conditions developing by fall 2016.
There have been several significant El Niño and La Niña
episodes in recent decades. An

9. unusually intense El Niño developed rapidly in early 1997 and
persisted until mid-May 1998.
In late 1998, strong La Niña conditions were observed over the
tropical Pacific and continued
through 1999. The subsequent years experienced alternating
neutral, weak or moderate El
Niño and La Niña episodes. The current 2015-16 El Niño is the
most recent to be classified
as strong and has had significant impacts on weather and
climate on the global scale. To
keep up-to-date on conditions in the tropical Pacific, you can go
to:
http://www.cpc.ncep.noaa.gov/products/analysis_monitoring/ens
o_advisory.
For the latest 5-day and monthly average conditions from the
TAO/TRITON array, go to
http://www.pmel.noaa.gov/tao/jsdisplay/, and then click on one
of the maps to see enlarged
images depicting conditions across the tropical Pacific.
http://www.cpc.ncep.noaa.gov/products/analysis_monitoring/ens
o_advisory
http://www.pmel.noaa.gov/tao/jsdisplay/
COS 11 - 6
_____________________________________________________
___________________
If directed by your instructor, place the answers to
Investigations 11A and 11B on the
Investigations Answer Forms and this Current Ocean Studies on
the Current Ocean
Studies Answer Form linked from the AMS Ocean Studies

10. RealTime Ocean Portal.
©Copyright 2016, American Meteorological Society
Math 126 Spring 2014
Computer Lab 2
General Information
This lab should be completed using Mathematica. Mathematica
is installed on the ma-
chines in the math computer lab in the Math Center (KAP
265/265) and the lab assistants
there can help you should you need it.
Should you want you to work on this lab on the weekend or in
the evenings, the computers
in Leavey Library, Waite Phillips Hall, and King Hall are
available and have Mathematica.
If you haven’t used Mathematica before, I recommend that you
read through F. J. Lin’s
“Introduction to Mathematica for Math 125 and 126” and R. E.
Bruck’s “Mathematica Crib
Sheet” to have at your side. These can be found on Blackboard
in the Mathematica Folder.
Remember also that there are lab assistants in the math
computing lab to help you.
This lab has two parts. Each part explores an application of
integration. The lab should
be completed using Mathematica. Please turn in this booklet
with the answers written in the
spaces provided, and a printout of each Mathematica notebook

11. you created in the process.
Please be sure to edit your notebook(s) before printing to
exclude any extraneous commands.
Part 1: Average Values of Functions
In this part we use Mathematica to explore the value of limb→a
fave,[a,b], where fave,[a,b]
denotes the average value of f(x) on the interval [a, b].
The average value of f(x) on the interval [a, b] is defined as 1
b−a
∫ b
a
f(x)dx.
First we find its value for a variety of functions, f and values of
a. Looking at the answers
we obtain we make a conjecture about its value for a general
function, f, and general value
of a. We try to understand why this conjecture should be true
and then we push the limits
of the truth of the conjecture and come up with an example of
where it is false.
1. Define the function, fave[a, b], to calculate the average value
of f(x) on the interval
[a, b]. You can do this with the commands:
Clear[f]
fave[a ,b ] = (1/(b-a))*Integrate[f[x], {x, a, b}]
2. Define f(x) to be the function f(x) = x4 and have
Mathematica calculate limb→2 fave,[2,b]

12. as follows:
f[x ] = xˆ4
Limit[fave[2, b], b → 2]
What do you get?
Now have Mathematica calculate limb→−3 fave,[−3,b]. What do
you get?
3. Clear f and redefine it to be the function f(x) = ex
2
. Recall that e in Mathematica is
represented with a capital letter, E. Calculate limb→3
fave,[3,b]. What do you get?
Calculate limb→1.7 fave,[1.7,b]. What do you get?
4. Clear f again and redefine it to be the function f(x) = sin x
x
. What is the value of
limb→4 fave,[4,b]?
5. Consider your answers to questions 2, 3, and 4 above. Make a
conjecture about the
value of limb→a fave,[a,b] for a general f and a.
6. Why do you think that the conjecture in question 5 is true?
To answer this, think
about what fave,[a,b] represents and what its value is when b is
very close to a.

13. 7. Now that you’ve convinced yourself that the conjecture is
true, find a function and a
number a for which the conjecture is false. Explain why it is
false for your choices of
f and a. (Hint: continuity is the key word here.)
Part 2: Arc-length of xn
In this part we explore the arc-length of the curve y = xn, 0 ≤ x
≤ 1 for different values
of n. We make a conjecture about what’s happening to the arc-
lengths as n gets larger and
larger. We then sketch the curves and use the sketches to
explain why our conjecture is true.
1. Define arclen to be the arc-length of the curve y = xn on the
interval 0 ≤ x ≤ 1. You
can do this with the command:
arclen = Integrate[Sqrt[1 + D[xˆn, x]ˆ2], {x, 0, 1}]
Notice that Mathematica returns a rather complicated
expression. This is because the
antiderivative involved in this calculation cannot be expressed
in terms of elementary
functions.
2. Find the value of arclen when n = 1 by simply typing:
arclen/.n → 1
What do you get? .

14. 3. Find the numerical value of arclen when n = 10, 20, 100, 500
and 1000. Remember
to use //N at the end of the command to get Mathematica to
express the answer
numerically rather than in terms of the cryptic
Hypergeometric2Fl function. Fill in
the table below.
Value of n Arclength of y = xn
1
10
20
100
500
1000
4. What appears to be happening to the arclengths as n gets
larger and larger?
5. Plot the graphs of y = xn for the values of n we used above.
You can do this with the
single command:
Plot[{x, xˆ10, xˆ20, xˆ100, xˆ500, xˆ1000}, {x, 0, 1}, PlotRange
→
{0, 1}]
Notice that we set the PlotRange option in order to be able to

15. see the complete
curves from y = 0 to y = 1. Use your graphs to explain why your
answer to question
4 is correct.