D-Day

Examples of D-Day in the following topics:

• D-Day and After

  • The Allies developed four plans for the Resistance to execute on D-Day.
  • Nearly 160,000 troops crossed the English Channel on D-Day,with 875,000 men disembarking by the end of June.
  • Caen, a major objective, was still in German hands at the end of D-Day and would not be completely captured until July 21.
  • Civilian casualties on D-Day and D+1 are estimated at 3,000 people.
  • Army's First Division on the morning of June 6, 1944 (D-Day) at Omaha Beach.

• The Invasion of Normandy

  • The Western Allies of World War II launched the largest amphibious invasion in history when they assaulted Normandy, located on the northern coast of France, on 6 June 1944, and were able to establish a beachhead after a successful "D-Day," the first day of the invasion.
  • The invaders were able to establish a beachhead as part of Operation Overlord after a successful "D-Day," the first day of the invasion.
  • Land forces used on D-Day sailed from bases along the south coast of England, the most important of these being Portsmouth.
  • The weather on D-Day was far from ideal, but postponing would have meant a delay of at least two weeks, as the invasion planners had requirements for the phase of the moon, the tides, and the time of day that meant only a few days in each month were deemed suitable.
  • German casualties on D-Day have been estimated at 4,000 to 9,000 men.

• Evaluating goodness of fit for a distribution

  • We will label each day as Up or Down (D) depending on whether the market was up or down that day.
  • If the days really are independent, then the number of days until a positive trading day should follow a geometric distribution.
  • Here each up day (Up) represents a success, and down (D) days represent failures.
  • It took two more days before we observed our next Up trading day, and two more for the third Up day.
  • To find each expected count, we identify the probability of waiting D days based on the geometric model (P(D) = (1 − 0.532)/D−1 (0.532)) and multiply by the total number of streaks, 2948.

• Calculating the Cash Flow Cycle

  • CCC=# days between disbursing cash and collecting cash in connection with undertaking a discrete unit of operations.
  • The Cash Conversion Cycle emerges as interval C→D (i.e., disbursing cash→collecting cash).
  • The operating cycle emerges as interval A→D (i.e., owing cash→collecting cash)
  • The receivables conversion period (or "Days sales outstanding") emerges as interval B→D (i.e., being owed cash→collecting cash)
  • Hence, interval {C → D}=interval {A → B}+interval {B → D}–interval {A → C}

• Osteomalacia and Rickets

  • Women who avoid sun exposure have very low levels of vitamin D.
  • The predominant cause is a vitamin D deficiency.
  • Vitamin D is required for proper calcium absorption from the gut.
  • Endogenous production with full body exposure to sunlight is approximately 250 µg (10,000 IU) per day.
  • According to the American Academy of Pediatrics (AAP), all infants, including those who are exclusively breast-fed, may need vitamin D supplementation until they start drinking at least 17 U.S. fluid ounces (500 ml) of vitamin D-fortified milk or formula a day.

• Discussion questions, exercises, and references

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• The Development of Holidays

  • In 1870, Congress enacted the first four federal holidays: New Year's Day, Independence Day, Thanksgiving Day, and Christmas Day.
  • Federal holidays are only established for certain federally chartered and regulated businesses (such as federal banks) and for Washington, D.C.
  • In 1888 and 1894, respectively, Decoration Day (now Memorial Day) and Labor Day were created.
  • In 1938, Armistice Day (now Veterans Day) was created to mark the end of World War I.
  • For example, New Year's Day and Christmas Day, celebrated in other countries around the world, brought Americans together under a common celebration.

• Interest Rate Parity Theorem

  • An investor invests $1 within the United States for T days and earns the domestic interest rate.
  • At time t, the investor buys a T-day forward contract to exchange the ringgits back into U.S. dollars, once the investment has ended.
  • $F \approx S \left[ 1+\left( i_d - i_f \right) \frac{T}{360} \right]$
  • At time t, we borrow from a foreign bank one unit of a foreign currency for T days.
  • At time t, we buy a T-day forward contract to exchange the domestic currency for foreign currency at F.

• Introduction to Variables

  • For example, if the temperature of the current day, $C$, is 20 degrees higher than the temperature of the previous day, $P$, then the problem can be described algebraically as $\displaystyle C=P+20$.
  • For example, the relationship between the circumference, $C$, and diameter, $d$, of a circle is described by $\displaystyle \pi =C/d$ .
  • Four of them ($a$, $b$, $c$, $d$) represent given numbers, which are referred to as the parameters of the equation.
  • A number on its own (without an unknown variable) is called a constant; in this case, $d$ represents a constant. 
  • In the cubic equation described above, there are four terms: $ax^3$, $bx^2$, $cx$, and $d$.

• Exponential Population Growth

  • After 1 day and 24 of these cycles, the population would have increased from 1000 to more than 16 billion.
  • Therefore, when calculating the growth rate of a population, the death rate (D; the number organisms that die during a particular time interval) is subtracted from the birth rate (B; the number organisms that are born during that interval).
  • where $\Delta N$ = change in number, $\Delta T$ = change in time, $B$ = birth rate, and $D$ = death rate.
  • Thus, B (birth rate) = bN (the per capita birth rate "b" multiplied by the number of individuals "N") and D (death rate) = dN (the per capita death rate "d" multiplied by the number of individuals "N").
  • Notice that the "d" associated with the first term refers to the derivative (as the term is used in calculus) and is different from the death rate, also called "d."