In mathematics and computational science, the Euler method (also called the forward Euler method) is a first-order numerical procedure for solving ordinary differential equations (ODEs) with a given initial value. It is the most basic explicit method for numerical integration of ordinary differential equations and is the simplest Runge–Kutta method. The Euler method is named after Leonhard Euler, who first proposed it in his book Institutionum calculi integralis (published 1768–1770).

The Euler method is a first-order method, which means that the local error (error per step) is proportional to the square of the step size, and the global error (error at a given time) is proportional to the step size.
The Euler method often serves as the basis to construct more complex methods, e.g., predictor–corrector method.

Geometrical description

Purpose and why it works
Consider the problem of calculating the shape of an unknown curve which starts at a given point and satisfies a given differential equation. Here, a differential equation can be thought of as a formula by which the slope of the tangent line to the curve can be computed at any point on the curve, once the position of that point has been calculated.

The idea is that while the curve is initially unknown, its starting point, which we denote by  is known (see Figure 1). Then, from the differential equation, the slope to the curve at  can be computed, and so, the tangent line.

Take a small step along that tangent line  up to a point  Along this small step, the slope does not change too much, so  will be close to the curve. If we pretend that   is still on the curve, the same reasoning as for the point  above can be used. After several steps, a polygonal curve () is computed. In general, this curve does not diverge too far from the original unknown curve, and the error between the two curves can be made small if the step size is small enough and the interval of computation is finite.

First-order process
When given the values for  and , and the derivative of  is a given function of  and  denoted as . Begin the process by setting . Next, choose a value  for the size of every step along t-axis, and set  (or equivalently ). Now, the Euler method is used to find  from  and :

The value of  is an approximation of the solution at time , i.e., . The Euler method is explicit, i.e. the solution  is an explicit function of  for .

Higher-order process
While the Euler method integrates a first-order ODE, any ODE of order  can be represented as a system of first-order ODEs. When given the ODE of order  defined as

as well as , , and , we implement the following formula until we reach the approximation of the solution to the ODE at the desired time:

These first-order systems can be handled by Euler's method or, in fact, by any other scheme for first-order systems.

First-order example
Given the initial value problem

we would like to use the Euler method to approximate .

Using step size equal to 1 ()

The Euler method is

so first we must compute .  In this simple differential equation, the function  is defined by . We have

By doing the above step, we have found the slope of the line that is tangent to the solution curve at the point .  Recall that the slope is defined as the change in  divided by the change in , or .

The next step is to multiply the above value by the step size , which we take equal to one here:

Since the step size is the change in , when we multiply the step size and the slope of the tangent, we get a change in  value.  This value is then added to the initial  value to obtain the next value to be used for computations.

The above steps should be repeated to find ,  and .

Due to the repetitive nature of this algorithm, it can be helpful to organize computations in a chart form, as seen below, to avoid making errors.

{| class="wikitable"
|-
!  !!  !!  !! !!  !!  !!
|-
| 0 || 1 || 0 || 1 || 1 || 1 || 2
|-
| 1 || 2 || 1 || 2 || 1 || 2 || 4
|-
| 2 || 4 || 2 || 4 || 1 || 4 || 8
|-
| 3 || 8 || 3 || 8 || 1 || 8 || 16
|}

The conclusion of this computation is that . The exact solution of the differential equation is , so . Although the approximation of the Euler method was not very precise in this specific case, particularly due to a large value step size , its behaviour is qualitatively correct as the figure shows.

Using other step sizes

As suggested in the introduction, the Euler method is more accurate if the step size  is smaller. The table below shows the result with different step sizes. The top row corresponds to the example in the previous section, and the second row is illustrated in the figure.

{| class="wikitable"
|-
! step size !! result of Euler's method !! error
|-
| 1 || 16.00 || 38.60
|-
| 0.25 || 35.53 || 19.07
|-
| 0.1 || 45.26 || 9.34
|-
| 0.05 || 49.56 || 5.04
|-
| 0.025 || 51.98 || 2.62
|-
| 0.0125 || 53.26 || 1.34
|}

The error recorded in the last column of the table is the difference between the exact solution at  and the Euler approximation. In the bottom of the table, the step size is half the step size in the previous row, and the error is also approximately half the error in the previous row. This suggests that the error is roughly proportional to the step size, at least for fairly small values of the step size. This is true in general, also for other equations; see the section Global truncation error for more details.

Other methods, such as the midpoint method also illustrated in the figures, behave more favourably: the global error of the midpoint method is roughly proportional to the square of the step size. For this reason, the Euler method is said to be a first-order method, while the midpoint method is second order.

We can extrapolate from the above table that the step size needed to get an answer that is correct to three decimal places is approximately 0.00001, meaning that we need 400,000 steps. This large number of steps entails a high computational cost. For this reason, higher-order methods are employed such as Runge–Kutta methods or linear multistep methods, especially if a high accuracy is desired.

Higher-order example
For this third-order example, assume that the following information is given:

From this we can isolate y''' to get the equation:

Using that we can get the solution for :And using the solution for , we can get the solution for :We can continue this process using the same formula as long as necessary to find whichever  desired.

Derivation

The Euler method can be derived in a number of ways.

(1) Firstly, there is the geometrical description above.

(2) Another possibility is to consider the Taylor expansion of the function  around :

The differential equation states that . If this is substituted in the Taylor expansion and the quadratic and higher-order terms are ignored, the Euler method arises.

The Taylor expansion is used below to analyze the error committed by the Euler method, and it can be extended to produce Runge–Kutta methods.

(3) A closely related derivation is to substitute the forward finite difference formula for the derivative,

in the differential equation . Again, this yields the Euler method.

A similar computation leads to the midpoint method and the backward Euler method.

(4) Finally, one can integrate the differential equation from  to  and apply the fundamental theorem of calculus to get:

Now approximate the integral by the left-hand rectangle method (with only one rectangle):

Combining both equations, one finds again the Euler method.

This line of thought can be continued to arrive at various linear multistep methods.

Local truncation error
The local truncation error of the Euler method is the error made in a single step. It is the difference between the numerical solution after one step, , and the exact solution at time . The numerical solution is given by

For the exact solution, we use the Taylor expansion mentioned in the section Derivation above:

The local truncation error (LTE) introduced by the Euler method is given by the difference between these equations:

This result is valid if  has a bounded third derivative.

This shows that for small , the local truncation error is approximately proportional to . This makes the Euler method less accurate than higher-order techniques such as Runge-Kutta methods and linear multistep methods, for which the local truncation error is proportional to a higher power of the step size.

A slightly different formulation for the local truncation error can be obtained by using the Lagrange form for the remainder term in Taylor's theorem. If  has a continuous second derivative, then there exists a  such that

In the above expressions for the error, the second derivative of the unknown exact solution  can be replaced by an expression involving the right-hand side of the differential equation. Indeed, it follows from the equation  that

Global truncation error
The global truncation error is the error at a fixed time , after however many steps the method needs to take to reach that time from the initial time. The global truncation error is the cumulative effect of the local truncation errors committed in each step. The number of steps is easily determined to be , which is proportional to , and the error committed in each step is proportional to  (see the previous section). Thus, it is to be expected that the global truncation error will be proportional to .

This intuitive reasoning can be made precise. If the solution  has a bounded second derivative and  is Lipschitz continuous in its second argument, then the global truncation error (denoted as ) is bounded by

where  is an upper bound on the second derivative of  on the given interval and  is the Lipschitz constant of . Or more simply, when , the value  (such that  is treated as a constant). In contrast,  where function  is the exact solution which only contains the  variable.

The precise form of this bound is of little practical importance, as in most cases the bound vastly overestimates the actual error committed by the Euler method. What is important is that it shows that the global truncation error is (approximately) proportional to . For this reason, the Euler method is said to be first order.

Example

If we have the differential equation , and the exact solution , and we what to find  and  for when . Thus we can find the error bound at t=2.5 and h=0.5:

Notice that t0 is equal to 2 because it is the lower bound for t in .

Numerical stability

The Euler method can also be numerically unstable, especially for stiff equations, meaning that the numerical solution grows very large for equations where the exact solution does not. This can be illustrated using the linear equation

The exact solution is , which decays to zero as . However, if the Euler method is applied to this equation with step size , then the numerical solution is qualitatively wrong: It oscillates and grows (see the figure). This is what it means to be unstable. If a smaller step size is used, for instance , then the numerical solution does decay to zero.

If the Euler method is applied to the linear equation , then the numerical solution is unstable if the product  is outside the region

illustrated on the right. This region is called the (linear) stability region. In the example, , so if  then  which is outside the stability region, and thus the numerical solution is unstable.

This limitation — along with its slow convergence of error with  — means that the Euler method is not often used, except as a simple example of numerical integration.

Rounding errors
In step  of the Euler method, the rounding error is roughly of the magnitude  where  is the machine epsilon. Assuming that the rounding errors are independent random variables, the expected total rounding error is proportional to . Thus, for extremely small values of the step size the truncation error will be small but the effect of rounding error may be big. Most of the effect of rounding error can be easily avoided if compensated summation is used in the formula for the Euler method.

Modifications and extensions
A simple modification of the Euler method which eliminates the stability problems noted above is the backward Euler method:

This differs from the (standard, or forward) Euler method in that the function  is evaluated at the end point of the step, instead of the starting point. The backward Euler method is an implicit method, meaning that the formula for the backward Euler method has  on both sides, so when applying the backward Euler method we have to solve an equation. This makes the implementation more costly.

Other modifications of the Euler method that help with stability yield the exponential Euler method or the semi-implicit Euler method.

More complicated methods can achieve a higher order (and more accuracy). One possibility is to use more function evaluations. This is illustrated by the midpoint method which is already mentioned in this article:
.
This leads to the family of Runge–Kutta methods.

The other possibility is to use more past values, as illustrated by the two-step Adams–Bashforth method:

This leads to the family of linear multistep methods. There are other modifications which uses techniques from compressive sensing to minimize memory usage

In popular culture
In the film Hidden Figures, Katherine Goble resorts to the Euler method in calculating the re-entry of astronaut John Glenn from Earth orbit.

See also
Crank–Nicolson method
Gradient descent similarly uses finite steps, here to find minima of functions
List of Runge-Kutta methods
Linear multistep method
Numerical integration (for calculating definite integrals)
Numerical methods for ordinary differential equations

Notes

References

External links

 Euler method implementations in different languages by Rosetta Code

Numerical differential equations
Runge–Kutta methods
First order methods
Leonhard Euler
Articles with example R code
Articles with example MATLAB/Octave code

Euler method


Natasha Khan (born 25 October 1979) is a British singer-songwriter better known as Bat For Lashes. She is the daughter of Pakistani squash player Rehmat Khan. Her first album, Fur and Gold, was released by The Echo Label on 11 September 2006 in the United Kingdom. It got good reviews. It was nominated for the 2007 Mercury Prize. In 2008 Khan performed at some of the shows in Radiohead's tour. She did a cover of The Cure's song "A Forest". It was put on Perfect as Cats: A Tribute to the Cure. On 3 April 2009 her second album Two Suns was released. It went straight to No.5 in the UK Albums Chart. Like Fur and Gold it was nominated for the Mercury Prize but didn't win. The first single from the album, "Daniel", is her best-selling single so far. It has sold over 46,000 copies around the world. It won Best Contemporary Song at the 2010 Ivor Novello Awards. Khan sang a song with Beck called "Let's Get Lost" for the soundtrack to the 2010 movie The Twilight Saga: Eclipse. Bat For Lashes' third album, The Haunted Man, was released on 11 October 2012. Pitchfork gave it 8.4 out of 10.

In July 2013 Bat For Lashes released a single with Toy called "The Bride".

In 2013 Khan wrote and sung a song with Jon Hopkins called "Garden's Heart". It was released as a single. It is on the soundtrack to the film How I Live Now. Khan directed the music video.

References

Other websites
Official website

1979 births
English guitarists
Living people
Singers from London
Synth-pop singers

Bat For Lashes


A brown dwarf is an object which is made of the same things as stars, but does not have enough mass for hydrogen fusion (the combining of hydrogen atoms into helium atoms). Nuclear fusion is what makes stars glow. Brown dwarfs are not massive enough to do this, so they are not regular stars. On the other hand, they are not regular giant planets, because they do glow. They are thought to be many but few have been found because their absolute magnitude is small.

Their mass is between the heaviest gas giants and the lightest stars, with an upper limit around 75 to 80 times the mass of Jupiter (MJ). Brown dwarfs more massive than 13 MJ are thought to fuse deuterium and those above ~65 MJ, fuse lithium as well.

Despite their name, most brown dwarfs would appear magenta to the human eye.
The nearest known brown dwarf is WISE 1049-5319 about 6.5 light years away, a binary system of brown dwarves discovered in 2013.

Discovery

What became known as brown dwarfs were talked about in the 1960s.  Alternative names for brown dwarfs were proposed, including planetar and substar. They remained hypothetical for decades.

Early theories suggested that an object less than 0.09 solar masses would never go through normal stellar evolution. The discovery of deuterium-burning down to 0.012 solar masses and the impact of dust formation in the cool outer atmospheres of brown dwarfs in the late 1980s brought these theories into question. However, such objects were hard to find because they emit almost no visible light. Their strongest emissions are in the infrared (IR) spectrum, and ground-based IR detectors were too imprecise at that time to readily identify any brown dwarfs.

For many years, efforts to discover brown dwarves were fruitless. In 1988, however, GD 165B was discovered, showing none of the features expected of a low-mass red dwarf star. Today, GD 165B is recognized as the prototype of a class of objects now called "L dwarfs". Although the discovery of the coolest dwarf was highly significant at the time, it was debated whether GD 165B would be classified as a brown dwarf or simply a very-low-mass star, because observationally it is very difficult to distinguish between the two.

Soon after the discovery of GD 165B, other brown-dwarf candidates were reported. Most failed to live up to their candidacy, however, because the absence of lithium showed them to be stellar objects. True stars will burn their lithium within a little over 100 million years (my), whereas brown dwarfs  will not. Confusingly, brown dwarves have temperatures and luminosities similar to some true stars. In other words, the detection of lithium in the atmosphere of an object means that, if it is older than 100 my, it is a brown dwarf.

In 1994/5 the study of brown dwarfs changed with the discovery of two definite substellar objects (Teide 1 and Gliese 229B).

The first confirmed brown dwarf was discovered in 1994. They called this object Teide 1 and it was found in the Pleiades open cluster. Nature highlighted "Brown dwarfs discovered, official" in the front page of that issue. The distance, chemical composition, and age of Teide 1 was established because it is in the young Pleiades star cluster. Teide 1's  mass is 55 times that of Jupiter, and clearly below the stellar-mass limit.

More notable was Gliese 229B, which was found to have a temperature and luminosity well below the stellar range. Remarkably, its near-infrared spectrum clearly exhibited a methane absorption band at 2 micrometres, a feature that had previously only been observed in the atmospheres of giant planets and that of Saturn's moon Titan. This discovery helped to establish yet another spectral class even cooler than L dwarfs, known as "T dwarfs", for which Gliese 229B is the prototype.

A brown dwarf below 65 Jupiter masses is unable to burn lithium by thermonuclear fusion at any time during its evolution. High-quality spectral data showed that Teide 1 had kept the initial lithium amount of the original molecular cloud from which Pleiades stars formed. This proved the lack of thermonuclear fusion in its core.

Teide 1 was considered for some time the smallest object out of the Solar System that had been identified by direct observation. Since then over 1800 brown dwarfs have been identified. Some are very close to Earth such as Epsilon Indi Ba and Bb, a pair of brown dwarfs gravitationally bound to a sunlike star around 12 light-years from the Sun, and WISE 1049-5319 a binary system of brown dwarfs about 6.5 light-years away.

Issues
For some years now there has been debate concerning what criterion to use for defining the separation between a very-low-mass brown dwarf and a giant planet (~13 Jupiter masses). One school of thought is based on formation, and another on interior physics.

References

Types of stars

Brown dwarf


The Heroides (The Heroines), or Epistulae Heroidum (Letters of Heroines), is a collection of fifteen epistolary poems composed by Ovid in Latin elegiac couplets and presented as though written by a selection of aggrieved heroines of Greek and Roman mythology in address to their heroic lovers who have in some way mistreated, neglected, or abandoned them. A further set of six poems, widely known as the Double Heroides and numbered 16 to 21 in modern scholarly editions, follows these individual letters and presents three separate exchanges of paired epistles: one each from a heroic lover to his absent beloved and from the heroine in return.

The Heroides were long held in low esteem by literary scholars but, like other works by Ovid, were re-evaluated more positively in the late 20th century. Arguably some of Ovid's most influential works (see below), one point that has greatly contributed to their mystique—and to the reverberations they have produced within the writings of later generations—is directly attributable to Ovid himself. In the third book of his Ars Amatoria, Ovid argues that in writing these fictional epistolary poems in the personae of famous heroines, rather than from a first-person perspective, he created an entirely new literary genre. Recommending parts of his poetic output as suitable reading material to his assumed audience of Roman women, Ovid wrote of his Heroides: "vel tibi composita cantetur Epistola voce: | ignotum hoc aliis ille novavit opus" (Ars Amatoria 3.345–6: "Or let an Epistle be sung out by you in practiced voice: unknown to others, he [sc. Ovid] originated this sort of composition"). The full extent of Ovid's originality in this matter has been a point of scholarly contention: E. J. Kenney, for instance, notes that "novavit is ambiguous: either 'invented' or 'renewed', cunningly obscuring without explicitly disclaiming O[vid]'s debt to Propertius' Arethusa (4.3) for the original idea." In spite of various interpretations of Propertius 4.3, consensus nevertheless concedes to Ovid much of the credit in the thorough exploration of what was then a highly innovative poetic form.

Dating and authenticity
The exact dating of the Heroides, as with the overall chronology of the Ovidian corpus, remains a matter of debate. As Peter E. Knox notes, "[t]here is no consensus about the relative chronology of this [sc. early] phase of O[vid]'s career," a position which has not advanced significantly since that comment was made. Exact dating is hindered not only by a lack of evidence, but by the fact that much of what is known at all comes from Ovid's own poetry. One passage in the second book of Ovid's Amores (Am.) has been adduced especially often in this context:

Knox notes that "[t]his passage ... provides the only external evidence for the date of composition of the Heroides listed here. The only collection of Heroides attested by O[vid] therefore antedates at least the second edition of the Amores (c. 2 BC), and probably the first (c. 16 BC) ..." On this view, the most probable date of composition for at least the majority of the collection of single Heroides ranges between c. 25 and 16 BC, if indeed their eventual publication predated that of the assumed first edition of the Amores in that latter year. Regardless of absolute dating, the evidence nonetheless suggests that the single Heroides represent some of Ovid's earliest poetic efforts.

Questions of authenticity, however, have often inhibited the literary appreciation of these poems. Joseph Farrell identifies three distinct issues of importance to the collection in this regard: (1) individual interpolations within single poems, (2) the authorship of entire poems by a possible Ovidian impersonator, and (3) the relation of the Double Heroides to the singles, coupled with the authenticity of that secondary collection. Discussion of these issues has been a focus, even if tangentially, of many treatments of the Heroides in recent memory.

As an example following these lines, for some time scholars debated over whether this passage from the Amores—corroborating, as it does, only the existence of Her. 1–2, 4–7, 10–11, and very possibly of 12, 13, and 15—could be cited fairly as evidence for the inauthenticity of at least the letters of Briseis (3), Hermione (8), Deianira (9), and Hypermnestra (14), if not also those of Medea (12), Laodamia (13), and Sappho (15). Stephen Hinds argues, however, that this list constitutes only a poetic catalogue, in which there was no need for Ovid to have enumerated every individual epistle. This assertion has been widely persuasive, and the tendency amongst scholarly readings of the later 1990s and following has been towards careful and insightful literary explication of individual letters, either proceeding under the assumption of, or with an eye towards proving, Ovidian authorship. Other studies, eschewing direct engagement with this issue in favour of highlighting the more ingenious elements—and thereby demonstrating the high value—of individual poems in the collection, have essentially subsumed the authenticity debate, implicating it through a tacit equation of high literary quality with Ovidian authorship. This trend is visible especially in the most recent monographs on the Heroides. On the other hand, some scholars have taken a completely different route, ascribing the whole collection to one or two Ovidian imitators (the catalogue in Am. 2.18, as well as Ars am. 3.345–6 and Epistulae ex Ponto 4.16.13–14, would then be interpolations introduced to establish the imitations as authentic Ovid).

The collection
The paired letters of the Double Heroides are not outlined here: see the relevant section of that article for the double epistles (16–21). The single Heroides are written from the viewpoints of the following heroines (and heroes). The quotations highlighted are the opening couplets of each poem, by which each would have been identified in medieval manuscripts of the collection:
I. Penelope writes to her famed husband, Odysseus, a hero of the Trojan War, towards the end of his long absence (the subject of Homer's Odyssey).
{|
|valign=top width="80px"|Epistula I:
|width="380px"|
|This your Penelope sends to you, too-slow Ulysses;  A letter in return does me no good; come yourself!
|}
II. Phyllis, the daughter of Lycurgus, writes to her lover Demophoon, the son of Theseus, king of Athens, after he fails in his promised return from his homeland.
{|
|valign=top width="80px"|Epistula II:
|width="380px"|
|I, your hostess, Demophoon—I, your Phyllis of Rhodope—  Complain: you're gone far longer than you promised!
|}
III. Briseis, the daughter of Briseus, writes to Achilles, the central hero of the Trojan War and focal character of Homer's Iliad, urging him to accept her as part of a package-deal from Agamemnon, leader of the Greek forces at Troy, and to return to battle against the Trojans.
{|
|valign=top width="80px"|Epistula III:
|width="380px"|
|What you're reading—this letter came from your ravished Briseis,  The Greek painstakingly copied out by her uncivilised hand.
|}
IV. Phaedra, wife of Theseus, writes to her stepson, Hippolytus, confessing her semi-incestuous and illicit love for him.
{|
|valign=top width="80px"|Epistula IV:
|width="380px"|
|What well-being she herself will lack unless you give it her  The Cretan maiden sends to the man born of an Amazon.
|}
V. The nymph Oenone, by Hellenistic tradition Paris' first wife, writes to Paris, son of Priam King of Troy, after he abandoned her to go on his famed journey to Sparta, and then returned with the abducted Helen of Sparta as a wife.
{|
|valign=top width="80px"|Epistula V:
|width="380px"|
|The Nymph sends words you ordered her to write,  From Mount Ida, to her Paris, though you refuse her as yours.
|}
 VI. Hypsipyle, queen of Lemnos, to Jason, after he abandoned her for Medea
{|
|valign=top width="80px"|Epistula VI:
|width="380px"|
|Hypsipyle of Lemnos, born of the people of Bacchus,  Speaks to Jason: how much of your heart was truly in your words?
|}
 VII. Dido to Aeneas, on his departure to Italy
{|
|valign=top width="80px"|Epistula VII:
|width="380px"|
|Dardanian, receive this song of dying Elissa:  What you read are the last words written by me.
|}
 VIII. Hermione, daughter of Menelaus, to Orestes, son of Agamemnon and Clytemnestra, urging him to save her from marriage to Achilles' son, Pyrrhus
{|
|valign=top width="80px"|Epistula VIII:
|width="380px"|
|Hermione speaks to one lately her cousin and husband,  Now her cousin. The wife has changed her name.
|}
 IX. Deianira, daughter of Oeneus, king of Aetolia, to her husband Hercules, after he laid down his weapons to be with Iole, the daughter of Eurytus, king of Oechalia
{|
|valign=top width="80px"|Epistula IX:
|width="380px"|
|A letter, that shares her feelings, sent to Alcides  By your wife, if Deianira is your wife.
|}
 X. Ariadne to Theseus after he abandoned her on the island of Naxos on his way back to Athens. He does not marry Phaedra until later (see Epistle IV).
{|
|valign=top width="80px"|Epistula X:
|width="380px"|
|Even now, left to the wild beasts, she might live, cruel Theseus.  Do you expect her to have endured this too, patiently?
|}
 XI. Canace, daughter of Aeolus, to her brother and lover, Macareus, before killing herself following the death of their baby at the hands of their father
{|
|valign=top width="80px"|Epistula XI:
|width="380px"|
|An Aeolid, who has no health herself, sends it to an Aeolid,  And, armed, these words are written by her hand.
|}
 XII. Medea to Jason, after he abandoned her to marry Creusa (also known as Glauce)
{|
|valign=top width="80px"|Epistula XII:
|width="380px"|
|Scorned Medea, the helpless exile, speaks to her recent husband,  surely you can spare some time from your kingship?
|}
 XIII. Laodamia, the daughter of Acastus, to her husband Protesilaus, urging him not to take too many risks in the Greeks' attack on Troy
{|
|valign=top width="80px"|Epistula XIII:
|width="380px"|
|She, who sends this, wishes loving greetings to go to whom it's sent:  From Thessaly to Thessaly's lord, Laodamia to her husband.
|}
 XIV. Hypermnestra to her husband, Lynceus, calling for him to save her from death at the hands of her father, Danaus
{|
|valign=top width="80px"|Epistula XIV:
|width="380px"|
|Hypermestra sends this letter to her one cousin of many,  The rest lie dead because of their brides' crime.
|}
 XV. Sappho to her ex-lover Phaon, after he left her
{|
|valign=top width="80px"|Epistula XV:
|width="380px"|
|When these letters, from my eager hand, are examined  Are any of them known to your eyes, straight away, as mine?
|}

Translations and influence
The Heroides were popularized by the Loire valley poet Baudri of Bourgueil in the late eleventh century, and Héloïse used them as models in her famous letters to Peter Abelard.   A translation, Les Vingt et Une Epistres d'Ovide, was made of this work at the end of the 15th century by the French poet Octavien de Saint-Gelais, who later became Bishop of Angoulême. While Saint-Gelais' translation does not do full justice to the original, it introduced many non-Latin readers to Ovid's fictional letters and inspired many of them to compose their own Heroidean-style epistles. Perhaps the most successful of these were the Quatre Epistres d'Ovide (c. 1500) by , a friend and colleague of Saint-Gelais. Later translations and creative responses to the Heroides include Jean Lemaire de Belges's Premiere Epître de l'Amant vert (1505), Fausto Andrelini's verse epistles (1509–1511; written in the name of Anne de Bretagne),  Contrepistres d'Ovide (1546), and Juan Rodríguez de la Cámara's Bursario, a partial translation of the Heroides.

Classics scholar W. M. Spackman argues the Heroides influenced the development of the European novel: of Helen's reply to Paris, Spackman writes, "its mere 268 lines contain in embryo everything that has, since, developed into the novel of dissected motivations that is one of our glories, from La Princesse de Clèves, Manon Lescaut and Les Liaisons Dangereuses to Stendhal and Proust".

The Loeb Classical Library presents the Heroides with Amores in Ovid I. Penguin Books first published Harold Isbell's translation in 1990. Isbell's translation uses unrhymed couplets that generally alternate between eleven and nine syllables. A translation in rhymed couplets by Daryl Hine appeared in 1991.

It was the inspiration for 15 monologues starring 15 separate actors, by 15 playwrights at the Jermyn Street Theatre in 2020.

Notes
All notes refer to works listed in the Bibliography, below.

Selected bibliography
For references specifically relating to that subject, please see the relevant bibliography of the Double Heroides.

Editions
 Dörrie, H. (ed.) (1971) P. Ovidi Nasonis Epistulae Heroidum (Berlin and New York)
 Showerman, G. (ed. with an English translation) and Goold, G. P. (2nd edition revised) (1986) Ovid, Heroides and Amores (Cambridge, MA and London)

Commentaries
 Kenney, E. J. (ed.) (1996) Ovid Heroides XVI–XXI (Cambridge).
 Knox, P. E. (ed.) (1995) Ovid: Heroides. Select Epistles (Cambridge).
 Roebuck, L. T. (ed.) (1998) Heroides I w/ Notes & Comm. (Classical Association of New England)

Literary overviews and textual criticism
 Anderson, W. S. (1973) "The Heroides", in J. W. Binns (ed.) Ovid (London and Boston): 49–83.
 Arena, A. (1995) "Ovidio e l'ideologia augustea: I motivi delle Heroides ed il loro significato", Latomus 54.4: 822–41.
 Beck, M. (1996) Die Epistulae Heroidum XVIII und XIX des Corpus Ovidianum (Paderborn).
 Courtney, E. (1965) "Ovidian and Non-Ovidian Heroides", Bulletin of the Institute of Classical Studies of the University of London (BICS) 12: 63–6.
 ___. (1998) "Echtheitskritik: Ovidian and Non-Ovidian Heroides Again", CJ 93: 157–66.

 Fulkerson, L. (2005) The Ovidian Heroine as Author: Reading, Writing, and Community in the Heroides (Cambridge).
 Heinze, T. (1991–93) "The Authenticity of Ovid Heroides 12 Reconsidered", Bulletin of the Institute of Classical Studies of the University of London (BICS) 38: 94–8.
 Jacobson, H. (1974) Ovid's Heroides (Princeton).
 Kennedy, D. F. (2002) "Epistolarity: The Heroides", in P. R. Hardie (ed.) The Cambridge Companion to Ovid (Cambridge): 217–32.
 Knox, P. E. (1986) "Ovid's Medea and the Authenticity of Heroides 12", Harvard Studies in Classical Philology (HSCP) 90: 207–23.
 ___. (2002) "The Heroides: Elegiac Voices", in B. W. Boyd (ed.) Brill's Companion to Ovid (Leiden): 117–39.
 Lachmann, K. (1876) Kleinere Schriften zur classischen Philologie, Bd. 2 (Berlin).
 Lindheim, S. (2003) Mail and Female: Epistolary Narrative and Desire in Ovid's Heroides (Madison, WI).
 Lingenberg, W. (2003) Das erste Buch der Heroidenbriefe. Echtheitskritische Untersuchungen (Paderborn).
 Palmer, A. (ed.) [completed by L.C. Purser (ed.)] (1898) P. Ovidi Nasonis Heroides, with the Greek translation of Planudes (Oxford).
 Rahn, H. (1963) "Ovids elegische Epistel", Antike und Abendland (A&A) 7: 105–120.
 Reeve, M. D. (1973) "Notes on Ovid's Heroides", Classical Quarterly (CQ) 23: 324–338.
 Rosenmeyer, P. A. (1997) "Ovid's Heroides and Tristia: Voices from Exile", Ramus 26.1: 29–56. [Reprinted in Knox (ed.) (2006): 217–37.]
 Smith, R. A. (1994) "Fantasy, Myth, and Love Letters: Text and Tale in Ovid's Heroides", Arethusa 27: 247–73.
 Spentzou, E. (2003) Readers and Writers in Ovid's Heroides: Transgressions of Genre and Gender (Oxford).
 Steinmetz, P. (1987) "Die literarische Form der Epistulae Heroidum Ovids", Gymnasium 94: 128–45.
 Stroh, W. (1991) "Heroides Ovidianae cur epistolas scribant", in G. Papponetti (ed.) Ovidio poeta della memoria (Rome): 201–44.
 Tarrant, R. J. (1981) "The Authenticity of the Letter of Sappho to Phaon", Harvard Studies in Classical Philology (HSCP) 85: 133–53.

 Verducci, F. (1985) Ovid's Toyshop of the Heart (Princeton).

Analyses of individual epistles
 Barchiesi, A. (1995) Review of Hintermeier (1993), Journal of Roman Studies (JRS) 85: 325–7.
 ___. (2001) Speaking Volumes: Narrative and Intertext in Ovid and Other Latin Poets, eds. and trans. M. Fox and S. Marchesi (London):
 "Continuities", 9–28. [Translated and reprinted from Materiali e discussioni per l'analisi dei testi classici (MD) 16 (1986).]
 "Narrativity and Convention in the Heroides", 29–48. [Translated and reprinted from Materiali e discussioni per l'analisi dei testi classici (MD) 19 (1987).]
 "Future Reflexive: Two Modes of Allusion and the Heroides", 105–28. [Reprinted from Harvard Studies in Classical Philology (HSCP) 95 (1993).]
 Casali, S. (1992) "Enone, Apollo pastore, e l'amore immedicabile: giochi ovidiani su di un topos elegiaco", Materiali e discussioni per l'analisi dei testi classici (MD) 28: 85–100.
 Fulkerson, L. (2002a) "Writing Yourself to Death: Strategies of (Mis)reading in Heroides 2", Materiali e discussioni per l'analisi dei testi classici (MD) 48: 145–65.
 ___. (2002b) "(Un)Sympathetic Magic: A Study of Heroides 13", American Journal of Philology (AJPh) 123: 61–87.
 ___. (2003) "Chain(ed) Mail: Hypermestra and the Dual Readership of Heroides 14", Transactions of the American Philological Association (TAPA) 133: 123–146.
 Hinds, S. (1993) "Medea in Ovid: Scenes from the Life of an Intertextual Heroine", Materiali e discussioni per l'analisi dei testi classici (MD) 30: 9–47.
 ___. (1999) "First Among Women: Ovid, and the Traditions of 'Exemplary' Catalogue", in amor : roma, S. M. Braund and R. Mayer (eds.), Proceedings of the Cambridge Philological Society (PCPS) Supp. 22: 123–42.
 Hintermeier, C. M. (1993) Die Briefpaare in Ovids Heroides, Palingensia 41 (Stuttgart).
 Jolivet, J.-C. (2001) Allusion et fiction epistolaire dans Les Heroïdes: Recherches sur l'intertextualité ovidienne, Collection de l' École Française de Rome 289 (Rome).
 Kennedy, D. F. (1984) "The Epistolary Mode and the First of Ovid's Heroides", Classical Quarterly (CQ) n.s. 34: 413–22. [Reprinted in Knox (ed.) (2006): 69–85.]
 Lindheim, S. (2000) "Omnia Vincit Amor: Or, Why Oenone Should Have Known It Would Never Work Out (Eclogue 10 and Heroides 5)", Materiali e discussioni per l'analisi dei testi classici (MD) 44: 83–101.
 Rosati, G. (1991) "Protesilao, Paride, e l'amante elegiaco: un modello omerico in Ovidio", Maia 43.2: 103–14.
 ___. (1992) "L'elegia al femminile: le Heroides di Ovidio (e altre heroides)", Materiali e discussioni per l'analisi dei testi classici (MD) 29: 71–94.
 Vessey, D. W. T. (1976) "Humor and Humanity in Ovid's Heroides", Arethusa 9: 91–110.
 Viarre, S. (1987) "Des poèmes d'Homère aux Heroïdes d'Ovide: Le récit épique et son interpretation élégiaque", Bulletin de l'association Guillaume Budé Ser. 4: 3.

Scholarship of tangential significance
 Armstrong, R. (2005) Ovid and His Love Poetry (London) [esp. chs. 2 and 4]
 Hardie, P. R. (2002) Ovid's Poetics of Illusion (Cambridge).
 Holzberg, N. (1997) "Playing with his Life: Ovid's 'Autobiographical' References", Lampas 30: 4–19. [Reprinted in Knox (ed.) (2006): 51–68.]
 ___. (2002) Ovid: The Poet and His Work, trans. G. M. Goshgarian (Ithaca, NY and London).
 James, S. L. (2003) Learned Girls and Male Persuasion: Gender and Reading in Roman Love Elegy (Berkeley). [esp. ch. 5]
 Kauffman, L. S. (1986) Discourses of Desire: Gender, Genre, and Epistolary Fictions (Ithaca, NY).
 Knox, P. E. (ed.) (2006) Oxford Readings in Ovid (Oxford and New York).
 Zwierlein, O. (1999) Die Ovid- und Vergil-Revision in tiberischer Zeit (Berlin and New York).

External links

Latin text at The Latin Library
English translation, A. S. Kline
Perseus/Tufts: Commentary on the Heroides of Ovid

Poetry by Ovid
1st-century BC Latin books
Cultural depictions of Sappho
Roman mythology
Trojan War literature

Heroides


The Hills of Varna (published in the USA as Shadow of the Hawk) is a children's historical novel by Geoffrey Trease, published in 1948. It is an adventure story based on the revival of classical scholarship in the Renaissance.

Plot

Introduction
The book is set mainly in continental Europe during the first decade of the 16th century.  The central character, a young Englishman, is sent by Erasmus to find the lost manuscript of an ancient Greek play at a monastery in the Balkans.

Summary
In 1509, Alan Drayton, a young Yorkshireman, has to leave his college in Cambridge after a tavern brawl. His tutor Erasmus sends him to the continent to try to retrieve a manuscript of The Gadfly, a lost play by the ancient Greek writer Alexis from the time of Socrates. He believes that it is in the monastery of Varna in the Balkans. Alan intends to deliver the play to the printer Aldus Manutius in Venice, refusing to take employment with the ruthless Duke of Molfetta, who wants the play for his private collection. He is joined on the arduous journey to the monastery by a young Italian woman, Angela d'Asola, who disguises herself as a boy.  They encounter Adriatic pirates, shipwreck, Turkish janissaries and sinister monks, all the while being doggedly pursued by the agents of the Duke. They find the manuscript but lose it again. In the end, their love of learning saves the day.

The author avoids the obvious ending of having the two leading characters marry each other, instead following the custom of the time Angela marries an older wealthy man whom she has had in mind for some time. Alan returns to England, on the verge of its own Renaissance, to continue his education.

Literary significance and reception
The book has been widely praised by critics, as illuminating the historical process and is considered by some to be the author's greatest work.

Allusions to history and geography
Erasmus of Rotterdam, the Dutch scholar and humanist, taught at Cambridge for a time, and was associated with the Venetian publishing house the Aldine Press and its founder Aldus Manutius. The author states: "Whenever possible, I have used actual opinions of Aldus and Erasmus in the dialogue." Marcus Musurus, Aldus's Cretan assistant, was a Greek scholar who taught at the University of Padua and was closely involved with the publication of Greek texts. Alexis the playwright is a fictional character, not to be confused with the real Greek writer of this name who lived somewhat later, but he represents the many ancient authors whose work was lost.

The novel starts in Cambridge and moves to the Republic of Venice, then to Dalmatia and the mountainous central Balkans. The monastery at Varna is a fictional place, not connected with the real town of Varna or Lake Varna in Bulgaria.

The Crown of Violet
In 1952 Trease wrote a prequel to The Hills of Varna, The Crown of Violet. The title is taken from a quote from Pindar (see City of the Violet Crown).  Set in ancient Athens, it is about how Alexis wrote The Gadfly, a comedy defending Socrates, and contains vivid descriptions of the Greek theatre. As in The Hills of Varna and Cue for Treason, the hero befriends a spirited, convention-defying girl who plays a vital role in the adventure (in this case Corinna, a metic).

Its American title Web of Traitors refers to the subplot of a planned coup d'état against the Athenian democracy; a speech in Alexis's play is used to trick the plotters into revealing themselves.

This could be a record, outside of science fiction and fantasy, for how far the events of a prequel have preceded the first novel.

References

1948 British novels
1948 children's books
British children's novels
Children's historical novels by Geoffrey Trease
Novels set in the Renaissance
Novels set in the 1500s
Novels set in University of Cambridge
Macmillan Publishers books
Children's books set in the 1500s
Children's books set in Cambridgeshire
Children's books set in Venice
Children's books set in Croatia

The Hills of Varna


The Toyota Yaris is a small automobile made and sold by Toyota since 1999. It is sold as the Toyota Belta, Toyota Vios, and Toyota Vitz. The Yaris is sold as a 3-door and 5-door hatchback and 4-door sedan. It is currently in its third generation. The first generation Yaris was known as the Toyota Echo in some markets. A distinctive feature of the first generation in many markets was a digital instrument display which glows out of a black hole in the centre of the dashboard. The second generation model arrived in 2005 and the current third generation has been on sale since 2011.

The Yaris IV is presented in October 2019 before the opening of the 2019 Tokyo Motor Show for commercialization in early 2020.

Yaris
1990s automobiles
2000s automobiles

Toyota Yaris


A dogma is something that should not be disputed or doubted. Most often, this means the basic beliefs and doctrines of a religion.  What a majority of followers of an ideology or any kind of organization believe in can also be a dogma.

In the context of religion, the term has a neutral meaning. Outside of religion for most people the term means something negative, because it accepts only a particular point of view. If someone disputes a religious dogma, they can be accused of heresy.

In Christianity, the Resurrection of Jesus is a basic dogma.

References

Other websites
Dogma - Catholic Encyclopedia
Dogma - Strong's N.T. Greek Lexicon

Christian theology

Dogma


Fraternities and sororities are social groups for college students, though sometimes high schools have them too. They exist mostly in the United States and Europe. The words frater and soror are Latin for "brother" and "sister" and used to show closeness between members. They also denote whether the group is for men or women. Sororities are only for women. Fraternities are only for men. But there are some fraternities for women.

Fraternities and sororities often have groups at many different schools. Each fraternity or sorority is given two or three Greek letters to call themselves, for example, ΑΦ (Alpha Phi) or ΑΧΩ (Alpha Chi Omega). To tell the difference between groups at different schools, called chapters, each chapter is given another set of Greek letters. For example, a man in the Kappa Sigma fraternity who goes to the University of Louisiana at Lafayette is part of the fraternity's EX (Epsilon Chi) chapter. Chapters sometimes have houses on or near the campus of the college the members attend that members can live in.

Fraternities and sororities often participate in community service.

Joining

Fraternities and sororities are often exclusive, meaning people who want to join need to be invited to do so. This is done during a process called "rushing". During a rush, people who want to join a chapter will talk to current members. If the member think the person rushing is a good fit for the group, they will get an invitation, called a "bid", to join the chapter. If the person rushing accepts, they become a "pledge".

The pledging period is a time when the pledge is not yet a full member, and may leave or be refused membership at any time. Sometimes, members of the chapter will put the pledge through trials. Sometimes they are tests on the history of the fraternity they are trying to join, wearing a badge with the fraternity's letters on it at all times, or performing public service. Sometimes the trials are cruel, dangerous or humiliating. If the trials are cruel, it is called "hazing". Hazing is illegal in 44 states.

After the pledging period, the pledge becomes a full member of the chapter and fraternity or sorority.

References

Fraternities and sororities


Cottage Gallery was an art gallery that was located in Carmel, California.  It was owned and operated by George Goff.  It opened in November 1984, and closed in 2001. The significance of the Gallery is primarily due to the involvement of artist Thomas Kinkade who was a friend of Goffs.  Kinkade suggested the name, Cottage Gallery, because of Carmel's quaint look and because of the actual building that the Gallery was located in had a pseudo-cottage feel. The Gallery was located at the corner of Sixth and Mission. In addition, Kinkade also designed the Gallery's logo which appeared on the main wood sign outdoors, all stationary and secondary collateral material. Cottage Gallery was one of the first galleries in which Kinkade started showing his fine art paintings in. Kinkade also produced paintings under a "brush name" of Robert Girrard. Cottage Gallery was the only gallery that showed the "Robert Girrard" paintings of Kinkade. For decades there were only a handful of people who knew that Robert Girrard and Thomas Kinkade were one and the same. The gallery mostly showed original oil paintings by living artists.

Artists represented by Cottage Gallery

 Tom Browning
 Lindsay Dawson
 Robert Girrard (a.k.a. Thomas Kinkade)
 Thomas Kinkade
 John Terelak
 Barry Thomas
 Edward Ward
 Sha-Kong Wang
 Edward Glafke
 Dave DeMatteo

References

 The faqs page at Girrard.com

Defunct art museums and galleries in California
Buildings and structures in Monterey County, California
History of Monterey County, California
Art galleries established in 1984
Art galleries disestablished in 2001
1984 establishments in California
2001 disestablishments in California
Carmel-by-the-Sea, California

Cottage Gallery


Maximum likelihood estimation (or maximum likelihood) is the name used for a number of ways to guess the parameters of a parametrised statistical model. These methods pick the value of the parameter in such a way that the probability distribution makes the observed values very likely. The method was mainly devleoped by R.A.Fisher in the early 20th century. A likelihood estimation, where probabilities are known beforehand is known as Maximum a posteriori estimation.

Statistics

Maximum likelihood


Decolonization is when a colony of any country becomes independent. Thus, decolonization is the opposite of colonization. Sometimes, a colony may not get full freedom, but may become part of another country or even the part of the country which colonized it. This is also decolonization.

In some cases, decolonization may result after non-violent discussion. In a relatively small number of cases, decolonization happens only after armed struggle and revolt. Decolonization is different from the break-up of traditional empires like the Mongol Empire or the Ottoman Empire. Decolonization generally means independence of non-Europeans from European rule. Thus, the break-up of the Union of Sweden and Norway and the independence of Manchukuo from the Empire of Japan were not decolonization. Major decolonization occurred in the 20th century. It began with the independence of Pakistan and India in 1947 from the British Empire. Soon after, many countries of Africa became independent from the rule of many countries of Europe.

Colonialism

Decolonization


Alois Alzheimer (14 June 1864 – 19 December 1915) was a German psychiatrist. He is credited with the first published case of "presenile dementia", which Emil Kraepelin would later identify as Alzheimer's disease.

On 25th of November 1901, Alzheimer started treating a new patient, called Auguste Deter. Auguste was married, and her husband brought her to the clinic, because within a year she had changed very much. She had started to become jealous, and was unable to perform simple household tasks. Alzheimer found out that the patient had little knowledge of where she was or about the time of day or the week. She also remembered few things about her life. When she was asked a question, the answer often had little to do with the question. Auguste Deter's mood changed rapidly. Alzheimer had seen similar symptoms with other patients he treated, but generally these were over 70 years old; Auguste Deter was only 51. Several times, Auguste Deter stated that she knew that she "had lost herself" and that she "was helpless".  For this reason, Alzheimer originally said that this was the "disease of forgetting".  Deter died in 1906.

Related pages
 Lewy Body Disease
 History of Neuroscience: Alois Alzheimer (1864-1915)
 This is Alzheimer's

German psychiatrists
German neuroscientists
Deaths from heart failure
1864 births
1915 deaths

Alois Alzheimer


Dellingr (Old Norse, possibly "the dayspring" or "shining one") is a god in the Norse mythology. He is a personification of a dawn.

He married Nótt (Night) and she bore him a son named Dagr (Day).

The English family name Dallinger has been theorized as deriving from Dellingr.

Norse gods and goddesses

Dellingr


The Fender Precision Bass (sometimes shortened to P-Bass) is an electric bass guitar that has been made by Fender since 1951. It was the first popular electric bass guitar to be made and has four strings with one split-coil humbucking pickup. It was also the first bass guitar to have a solid body.

History
Acoustic, fretted plucked string instruments have been around for a very long time. One example is the bass lute, which has been around since the 17th century. The berda, which is a Slavic folk instrument, has also been around for hundreds of years. In the 19th century, some bass instruments made like a guitar were created. Gibson made an acoustic "mando bass", which was made like a mandolin.

First electric basses
Many inventors tried to make electric bass guitars because most bassists were using the double bass, which was very big, heavy, and too quiet. Before the Precision Bass was made, many inventors used the double bass and tried to make it electric. Lloyd Loar was one of the first to try to make them louder. He put a pickup on double bass in order to play it through an amplifier. He did this between 1919 and 1924.

In the 1930s, Rickenbacker made an electric double bass. Then American Paul Tutmarc made the first electric bass that could be played like a guitar, called the "Audiovox 736 Bass". This bass also had frets. Even though these were the first of this kind, they never sold very well.

First Fender Precision Bass
Leo Fender, the founder of Fender, had the idea in the 1940s to build a solid-body bass guitar. He wanted it to be easier to play than a double bass. He also wanted it to be smaller so it was easy to move. He got this idea when talking to guitarists who didn't have jobs. They said that they could have gotten jobs being bassists, but found the double bass too hard to play.

The idea of an electric, solid-body bass was new, so Fender had to make it themselves. They spoke to many bassists and guitarists to work out what design would be best. Fender had made the Telecaster guitar before and so used his designs from it to help him make the Precision. The bass was tuned the same as a double bass, EADG, with four strings. The body was a lot like the telecaster, but the top stuck out more towards the headstock so the neck wasn't too heavy to hold when playing the bass with a strap standing.

References

Bass guitars

Fender Precision Bass


A transistor is a semiconductor device uised tae amplify an switch electronic signals an electrical pouer. It is componed o semiconductor material wi at least three terminals for connection tae an freemit circuit. A voltage or current applee'd tae ane pair o the transistor's terminals chynges the current throu anither pair o terminals. Acause the controlled (ootput) pouer can be heicher than the controllin (input) pouer, a transistor can amplify a signal. The day, some transistors are packaged individually, but mony mair are foond embedded in integratit circuits.

The transistor is the fundamental biggin block o modren electronic devices, an is ubiquitous in modren electronic seestems. Follaein its development in 1947 bi John Bardeen, Walter Brattain, an William Shockley, the transistor revolutionized the field o electronics, an paved the wey for smawer an cheaper radios, calculators, an computers, amang ither things.  The transistor is on the leet o IEEE milestones in electronics, an the inventors wur jyntly awairdit the 1956 Nobel Prize in Pheesics for thair achievement.

American inventions
Semiconductor devices
1947 introductions

Transistor


Roger Broders (born Paris, France, 1883, died, Paris, 1953) was a French illustrator and artist. He was best known for his travel posters promoting tourism destinations in France, typically fashionable beaches of the Côte d'Azur and skiing resorts in the French Alps in the early 20th century.

Broders' illustrations were distinctive for their simple lines and bold, flat areas of color, combined with noticeable graphical perspective showing the featured mountains and seascapes in the background.  Broders' illustrations depicting people show active elongated figures wearing elegant, contemporary clothes.  His posters were simply and boldly lettered identifying the destination, and were supplemented with a brief slogan.

The Paris Lyon Mediteranée Company (PLM), a railway, commissioned Broders' poster art, sponsoring his travel so he could visit the subjects of his work.  From 1922 to 1932, Broders fully dedicated himself to poster art, though overall he produced fewer than 100 posters.  Lithographs of Broders' travel posters are still available commercially. See for instance Christie's London Ski Sale on 21 January 2010. Others are shown in the book about Railway Posters, published in Munich in 2011 and listed below.

During the 1940s he illustrated four of the works of the German author Karl May which were published by Éditions Mame at Tours in France in French language.

Literature
 Thierry Favre: Eisenbahnplakate - Railway Posters. Hirmer, München 2011, .
 Roger Broders: Travel Posters. Weill, Alain; Perry, Israel, New York 2002, .

References

20th-century French painters
20th-century French male artists
French male painters
French illustrators
1953 deaths
1883 births

Roger Broders


The Promise is a 2005 Chinese epic fantasy film directed by Chen Kaige, starring Jang Dong-gun, Hiroyuki Sanada, Cecilia Cheung, and Nicholas Tse. It is loosely adapted from The Kunlun Slave, a wuxia romance story written by Pei Xing in the ninth century during the Tang dynasty. Responses to the film were mainly mixed to negative.

Plot
Qingcheng, a starving girl, wanders around the land in search of food. She chances upon a boy, tricks him, steals a mantou from him, and runs away. She encounters the goddess Manshen and accepts an offer to enjoy a wealthy and luxurious life and become the most beautiful woman in the land. However, she has a price to pay: She will never find genuine everlasting love with any man. She becomes the King's concubine when she grows up.

General Guangming defeats a large army of barbarians with only 1,000 soldiers and rushes back to save the King, who is besieged in the palace by the traitorous Duke Wuhuan. He meets Manshen, who tells him someone wearing his Crimson Armour will commit regicide and tarnish his reputation. A while later, Guangming is caught off guard and injured by Snow Wolf, Wuhuan's henchman, but is saved by his slave, Kunlun. He orders Kunlun to wear his crimson armour and save the King. When Kunlun asks his master how he can identify the King, Guangming tells him the King is the one without a weapon. Kunlun arrives at the palace and mistakes Qingcheng for the King because she is unarmed, and instead kills the King, who has just drawn his sword. He flees with Qingcheng, but they end up being cornered at a cliff by Wuhuan and his men. Wuhuan promises to not harm Qingcheng if Kunlun jumps off the cliff.

Kunlun jumps off the cliff but survives the fall. In the meantime, Guangming's subordinates accuse their General of killing the King and turn against him. Kunlun returns, saves his master and gives him back his Crimson Armour. They go to rescue Qingcheng from Wuhuan later. Qingcheng falls in love with Guangming after mistaking him for the person who jumped off the cliff. On the other hand, Kunlun is captured by Wuhuan, who realises he is actually the one who killed the King. While Guangming and Qingcheng lead a happy life in the countryside, Kunlun uses his speed power to see the Veil of Time and learns that Wuhuan is responsible for the destruction of his family and homeland. Snow Wolf is actually from the same land as Kunlun and was forced to become Wuhuan's servant. Snow Wolf also tells Kunlun that no one is capable of crossing over to the other side of the Veil of Time.

Wuhuan lures Guangming back to the palace and captures him. He then places Guangming, Kunlun, and Qingcheng on a show trial for regicide. During the trial, Kunlun confesses that he killed the King, and Qingcheng realises he is actually the one who saved her earlier. Guangming, Kunlun, and Qingcheng are sentenced to death but they break free and fight Wuhuan, who tells Qingcheng he is the boy she stole a mantou from. As a result of Qingcheng betraying his trust, Wuhuan grew up in hatred and became the evil person he is today. Both Wuhuan and Guangming die in the fight while Kunlun is  severely wounded. Kunlun survives after wearing Snow Wolf's immortality robe. Manshen appears when Kunlun and Qingcheng are attempting to pass through the Veil of Time, and tells Qingcheng that the promises made between deities and humans are as fragile as ordinary promises. Qingcheng has finally found her true love and thus given herself an opportunity to choose again. Manshen advises her to choose wisely. The film ends with the opening scene showing Qingcheng, as a little girl, wandering around.

Cast
 Jang Dong-gun as Kunlun
 Hiroyuki Sanada as General Guangming
 Cecilia Cheung as Qingcheng
 Guan Xiaotong as Qingcheng (young)
 Nicholas Tse as Duke Wuhuan
 Shi Lei as Wuhuan (young)
 Liu Ye as Snow Wolf
 Chen Hong as Manshen

Production
The budget for The Promise was estimated to be about 282–340 million yuan (US$35–42 million), which surpassed the cost of Zhang Yimou's Hero (2002).

Release
The Promise was first released on 15 December 2005 in mainland China, Hong Kong, and Singapore.

In North America, The Promise was originally scheduled to be released in December 2005 by The Weinstein Company (TWC) under the title Master of the Crimson Armor. TWC also removed approximately 25 minutes of footage from the original cut. However, TWC eventually cancelled the release and sold the film's distribution rights to Warner Independent Pictures (WIP). WIP retained the changes made by TWC, but reverted the film's title back to The Promise and released it on 5 May 2006 in 213 theatres.

Reception

Critical reception
The Promise received mixed reactions when it was first released in Asian countries. In China, most of the responses were mainly negative even though it grossed about US$9 million in the first week.

Despite the negative reception, The Promise was one of two Chinese films in 2006 to be nominated for Golden Globes Best Foreign Language Film at the 63rd Golden Globe Awards.

Box office
The Promise grossed an estimated US$18 million in mainland China. It did not fare as well in Hong Kong, where it grossed only US$654,435 (HK$5,073,311). It grossed US$272,838 in its opening weekend in North America and collected US$669,625 by the end of its run. The Promise grossed a total of US$33,539,654 worldwide.

Controversies
The film was criticised for the environmental damage it caused while it was shooting in Yunnan. The film's production crew were accused of damaging the vegetation and natural scenery of the area and the surrounding Bigu Lake, and for leaving behind a large amount of undisposed household waste.

Hu Ge's 2005 short film A Murder Case Caused by a Dumpling spoofed The Promise. After it was released on the internet, Chen Kaige threatened legal action for copyright infringement, but the case fizzled out due to widespread support for Hu from Chinese citizens.

References

External links
  The Promise official website  on Sina.com

  Interview with director Chen Kaige
  Interview with actor Hiroyuki Sanada

2005 films
2000s Mandarin-language films
Chinese epic films
2000s fantasy adventure films
Films directed by Chen Kaige
Romantic epic films
Warner Independent Pictures films
Wuxia films
Martial arts fantasy films
Films scored by Klaus Badelt
Chinese romantic fantasy films
Chinese fantasy adventure films
Chinese New Year films
2000s romantic fantasy films

The Promise (2005 film)


A nut is a type of fastener with a threaded hole. Nuts are almost always used with a mating bolt to fasten  parts together. Because of this "nut and bolt" or "nuts and bolts" are a term which recognise their pairing.

Like bolt heads, their shape is usually hexagonal, because this is best for gripping with tools. Nuts are graded with strength ratings like their respective bolts. For example, an ISO property class 10 nut can support the bolt proof strength load of an ISO property class 10.9 bolt without stripping its thread (the inside spiral groove).

Hardware (mechanical)

Nut (hardware)


Hone Peneamine Anatipa Te Pona Tuwhare (21 October 1922 – 16 January 2008) was a noted Māori New Zealand poet. He is closely associated with The Catlins in the Southland region of New Zealand, where he lived for the latter part of his life.

Early years
Tuwhare was born in Kaikohe, Northland, into the Ngāpuhi tribe (hapu Ngati Korokoro, Ngati Tautahi, Te Popoto, Te Uri-o-Hua). Following the death of his mother, his family shifted to Auckland, where Hone attended primary schools in Avondale, Māngere and Ponsonby. He apprenticed as a boilermaker with the New Zealand Railways and took night classes in Mathematics, Trade Drawing and Trade Theory at Seddon Memorial Technical College (1939–41) and Otahuhu College (1941). Tuwhare spoke Māori until he was about 9, and his father, an accomplished orator and storyteller, encouraged his son's interest in the written and spoken word, especially in the rhythms and imagery of the Old Testament.

Poetry career
Starting in 1939, Tuwhare, encouraged by fellow poet R.A.K. Mason, began to write while working as an apprentice at the Otahuhu Railway Workshops.

In 1956, Tuwhare started writing seriously after resigning from a local branch of the Communist party. His first, and arguably best known work, No Ordinary Sun, was published in 1964 to widespread acclaim and subsequently reprinted ten times over the next 30 years, becoming one of the most widely read individual collections of poetry in New Zealand history.

When Tuwhare's poems first began to appear in the late 1950s and early 1960s they were recognised as a new departure in New Zealand poetry, cutting across the debates and divisions between the 1930s and post-war generations. Much of the works' originality was the result of their distinctly Māori perspective. The poems were marked by their tonal variety, the naturalness with which they could move between formal and informal registers, between humour and pathos, intimacy and controlled anger and, especially, in their assumption of easy vernacular familiarity with New Zealand readers.

During the 1970s Tuwhare became involved in Māori cultural and political initiatives. This same era also saw his international reputation grow, with invitations to visit both China and Germany, which, among other opportunities, lead to the publication of Was wirklicher ist als Sterben in 1985.

While his earlier poems were kept in print, new work was constantly produced. Tuwhare's play, "In the Wilderness Without a Hat", was published in 1991. Three further collections of poetry then followed: Short Back and Sideways: Poems & Prose (1992), Deep River Talk (1993), and Shape-Shifter (1997). In 1999 he was named New Zealand's second Te Mata Poet Laureate, the outcome of which was the publication Piggy-Back Moon (2002).

The poet moved to Kaka Point in South Otago in 1992, and many of his later poems reflected the scenery of The Catlins area, and the seafood available. He had a strong working relationship with fellow Otago artist Ralph Hotere, and their work often referenced each other.
Tuwhare's poem "Rain" was in 2007 voted New Zealand's favourite poem by a clear margin.

Poetry by Tuwhare was included in UPU, a curation of Pacific Island writers' work which was first presented at the Silo Theatre as part of the Auckland Arts Festival in March 2020. UPU was remounted as part of the Kia Mau Festival in Wellington in June 2021.

Recognition and awards
Tuwhare was awarded the Robert Burns Fellowship from the University of Otago in 1969 and again in 1974. He was awarded the University of Auckland Literary Fellowship in 1991. In 1999, he was named New Zealand's second Te Mata Poet Laureate. At the end of his two-year term he published Piggy Back Moon (2001), which was shortlisted in the 2002 Montana New Zealand Book Awards.

Tuwhare was among ten of New Zealand's greatest living artists named as Arts Foundation of New Zealand Icon Artists at a ceremony in 2003.

In 2003, Tuwhare was awarded one of the inaugural Prime Minister's Awards for Literary Achievement, for poetry. The other winners were novelist Janet Frame and historian Michael King. Each recipient received a cash prize of $60,000 NZD. The awards are aimed at New Zealand writers who have made an outstanding contribution to the nation's literary and cultural history.

Tuwhare received an honorary Doctor of Literature degree from The University of Auckland in 2005. At the time of his death Tuwhare was described as "New Zealand's most distinguished Maori writer"*.

Hone Tuwhare Charitable Trust
In July 2010 the Hone Tuwhare Charitable trust was formed in honour of Tuwhare. Their goal is: "To inspire people through the preservation, promotion, and celebration of Hone's legacy".

Works

No Ordinary Sun, Auckland, Blackwood and Janet Paul, 1964
Come Rain Hail, Dunedin, University of Otago, 1970
Sapwood and Milk, Dunedin, Caveman Press, 1972
 Something Nothing, Dunedin, Caveman Press, 1973
 Making a Fist of It, Dunedin, Jackstraw Press, 1978
 Selected Poems, Dunedin, McIndoe, 1980
 Year of the Dog. Dunedin, McIndoe, 1982
 Was wirklicher ist als Sterben, Straelen, Straelener-Ms.-Verl, 1985
 Mihi: Collected Poems, Auckland, Penguin, 1987
 Short Back & Sideways, Auckland, Godwit, 1992
 Deep River Talk: Collected Poems, Honolulu, University of Hawaii Press, 1994
 Shape-Shifter, Wellington, Steele Roberts, 1997
 Piggy-back Moon, Auckland, Godwit, 2001
 Oooooo......!!!, Wellington, Steele Roberts, 2005
 '' Friend '',Whangarei, Noah

See also
 New Zealand literature
 Tuwhare - a compilation album of his poems remade by New Zealand artists into songs as a dedication to him.

References

External links

 Hone Tuwhare – full-length documentary available on NZ On Screen
 Biography of Hone Tuwhare as well as links to relevant television appearances and programmes on NZ On Screen
 Tuwhare's biography on Poetry International Web
 Timeline of Hone Tuwhare
 New Zealand Herald - Tributes flow for Poet and Playwright Hone Tuwhare
  from the Dictionary of New Zealand Biography
 Website for Hone Tuwhare Charitable Trust

1922 births
2008 deaths
Ngāpuhi people
Te Uri-o-Hau people
New Zealand Poets Laureate
New Zealand male poets
People from Otago
People from the Catlins
People from Kaikohe
New Zealand Māori writers
People educated at Otahuhu College
20th-century New Zealand poets
20th-century New Zealand male writers

Hone Tūwhare


Wooddrow "Woody "Woodpecker is an animated cartoon character, an anthropomorphic woodpecker who appeared in theatrical short movies produced by Walter Lantz, and distributed by Universal Pictures.

Woody Woodpecker cartoon was created in 1940 by Ben "Bugs" Hardaway. He also created the cartoon characters of Bugs Bunny and Daffy Duck when he worked at the Schlesinger/Warner Bros. studio in the late 1930s.

His niece and nephew are Knothead and Splinter. His girlfriend is Winnie Woodpecker. In The New Woody Woodpecker Show, Winnie is voiced by B. J. Ward.

Related pages
Knothead and Splinter
Andy Panda
Chilly Willy

Anthromophic characters

Woody Woodpecker


Ocean thermal energy conversion (OTEC) is a way of getting useful energy from the world's oceans. The sun shines on the oceans of the world and in the hot parts near the water at the sea's surface can be quite warm, sometimes as high as 30°C.

Many oceans are very deep and the water at depths of 1,000 meters can be around 5 °C.

If a pipe is put down into the ocean we can bring the cold water to the surface where we also have warm water available.

The difference in temperature between the warm surface water and the cold deep water may only be around 15 °C. But we can build a machine called a heat engine, which can use this  difference to generate power that can be used by people that live in that place. A machine which can do this is called an OTEC machine which stands for ocean thermal energy conversion.

Because the difference in temperature is small we will need to get large quantities of warm and cold water to go through the machine to get a useful amount of work, but large quantities are available in the ocean.

It has been estimated that OTEC could give amounts of energy that are 10 to 100 times greater than the other ocean energy source, wave power.

The first OTEC machine was built in Cuba in 1930 and made 22 kW of electricity. The largest machine built so far generated 250 kW in 1999 and was made by the US. Plans to build even bigger machines of around 10 MW have been made.

OTEC can also supply quantities of cold water as a by-product. This can be used for refrigeration and can help crops and fish grow. OTEC can also produce large amounts of salt-free water, which can be useful on mid-ocean islands as drinking water.

Hydropower

Ocean thermal energy conversion


A manual transmission, kent as a manual gearbox, a standard transmission or colloquially in some countries (e.g. the United States) as a stick shift an aw, is a teep o transmission uised in motor vehicle applications. It uses a driver-operated clutch engaged an disengaged bi a fit pedal (automobile) or haund lever (motorcycle), for regulating torque transfer frae the internal combustion ingine tae the transmission; an a gear selector operated bi haund (automobile) or bi fit (motorcycle).

A conventional 5-speed manual transmission is eften the standard equipment in a base-model vehicle, while mair expensive manual vehicles are uisually equipped wi a 6-speed transmission insteid; ither options include automatic transmissions sic as a traditional automatic (hydraulic planetary) transmission (eften a manumatic), a semi-automatic transmission, or a continuously variable transmission (CVT). The nummer o forrit gear ratios is eften expressed for automatic transmissions as well (e.g., 9-speed automatic).

Automobile transmissions

Manual transmission


The lectisternium was an ancient Roman propitiatory ceremony, consisting of a meal offered to gods and goddesses. The word derives from lectum sternere, "to spread (or "drape") a couch."  The deities were represented by their busts or statues, or by portable figures of wood, with heads of bronze, wax or marble.  It has also been suggested that the divine images were bundles of sacred herbs tied together in the form of a head, covered by a waxen mask so as to resemble a kind of bust, rather like the straw figures called Argei. A couch (lectus) was prepared by draping it with fabric. The figures or sacred objects pertaining to the deity (such as the wreath awarded in a triumph) were laid upon it. Each couch held a pair of deities, sometimes male with female equivalent. If the image was anthropomorphic, the left arms were rested on a cushion (pulvinus) in the attitude of reclining to eat, whence the couch itself was often called pulvinar) The couches were set out in the open street, or a temple forecourt, or in the case of ludi, in the pulvinar or viewing box, and a meal was served on a table before the couch.

History

Livy says that the ceremony took place "for the first time" in Rome in the year 399 BC, after a pestilence had caused the Sibylline Books to be consulted by the duumviri sacris faciundis, the two (later 10, and later 15) priestly officials who maintained the archive. Three couches were prepared for three pairs of gods — Apollo and Latona, Hercules and Diana, Mercury and Neptune. The feast lasted for eight (or seven) days, and was also celebrated by private individuals. The citizens kept open house, quarrels were forgotten, debtors and prisoners were released, and everything done to banish sorrow.

Similar honors were paid to other divinities in subsequent times: Fortuna, Saturnus, Juno Regina of the Aventine, the three Capitoline deities (Jupiter, Juno, Minerva). In 217 BC, after the Roman defeat at Lake Trasimene, a lectisternium was held for three days to six pairs of gods, corresponding to the Twelve Olympians of ancient Greek religion: Jupiter, Juno, Neptune, Minerva, Mars, Venus, Apollo, Diana, Vulcan, Vesta, Mercury, Ceres.

In 205 BC, alarmed by unfavorable prodigies, the Romans were ordered to fetch the Great Mother of the gods from Pessinus in Phrygia; in the following year the image was brought to Rome, and a lectisternium held. In later times, the lectisternium became a constant  or even daily occurrence, celebrated in the different temples. Occasionally the "Draping of Couches" was part of Roman Triumph celebrations. Aulus Hirtius reports that Julius Caesar was greeted with "draped dining couches" following his victory in Gaul, in anticipation of a forthcoming triumph. Such celebrations must be distinguished from those which were ordered, like the earlier lectisternia, by the Sibylline Books in special emergencies.

In the Imperial era, chairs were substituted for couches in the case of goddesses, and the lectisternium in their case became a sellisternium. This was in accordance with Roman custom, since in the earliest times all the members of a family sat at meals, and in later times at least the women and children. This is a point of distinction between the original practice at the lectisternium and the epulum Jovis, the goddesses at the latter being provided with chairs, whereas in the lectisternium they reclined.

In Christian times the word was used for a feast in memory of the dead.

Origins
Offerings of food were made to the gods in very early Roman times on such occasions as the ceremony of confarreatio, and the epulum Jovis (often conflated with the lectisternium). The lectisternia, however, are likely of Greek origin. The Greek theoxenia (Θεοξένια) is similar, except that the gods played the part of host. The gods associated with it were either previously unknown to Roman religion, though often concealed under Roman names, or were provided with a new cult. Thus Hercules was not worshipped as at the Ara Maxima, where, according to Servius and Cornelius Balbus a lectisternium was forbidden. The Sibylline Books, which decided whether a lectisternium was to be held or not, were of Greek origin; the custom of reclining at meals was Greek.

Some, however, assign an Etruscan origin to the ceremony, the Sibylline Books themselves being looked upon as old Italian "black books." It may be that as the lectisternia became an almost everyday occurrence in Rome, people forgot their foreign origin and the circumstances in which they were first introduced, and then the word pulvinar with its associations was transferred to times in which it had no existence.

Sources
Taylor, Lily Ross. "The Sellisternium and the Theatrical Pompa." Classical Philology, vol. 30, no. 2, 1935, pp. 122–30. JSTOR, http://www.jstor.org/stable/263926. Accessed 9 Dec. 2022.
Article by A. Bouché-Leclercq in Daremberg and Saglio, Dictionnaire des antiquités;
Marquardt, Römische Staatsverwaltung, iii. 45, 187 (1885);
G. Wissowa, Religion und Kultus der Römer, p. 355 seq.;
Monograph by Wackermann (Hanau, 1888);
C. Pascal, Studii di antichità e mitologia (1896).

Notes

External links
Lectisternium (article in Smith's Dictionary of Greek and Roman Antiquities)

4th-century BC establishments in the Roman Republic
Ancient Roman religion
Neptune (mythology)
Hercules
Cult of Apollo
Leto
Diana (mythology)
Mercury (mythology)
Ceremonies

Lectisternium


Camp Academia (, ) is a geographical locality in eastern Livingston Island, South Shetland Islands, Antarctica, named for the Bulgarian Academy of Sciences in appreciation of Academy's contribution to the Antarctic exploration.  The site was first occupied in the 2004/05 austral summer, and has been designated since 2004 as the summer post office Tangra 1091, the southernmost branch of the Bulgarian Posts Plc.

Access and survey routes
Camp Academia is strategically situated in upper Huron Glacier, Wörner Gap area, at elevation 541 m in the northwestern foothills of Zograf Peak, central Tangra Mountains.  The site is accessible by 11-12.5 km routes from the Bulgarian base St. Kliment Ohridski and the Spanish base Juan Carlos I respectively.

Camp Academia offers convenient overland access to the main range of Tangra Mountains to the south (with survey and climbing routes leading from Camp Academia to Lyaskovets Peak and Mount Friesland via Catalunyan Saddle, and to Levski Peak, Great Needle Peak and Helmet Peak areas via Lozen Saddle); to Bowles Ridge, Vidin Heights, Kaliakra Glacier and Saedinenie Snowfield areas to the north; to Huron Glacier to the east; and to Pliska Ridge, Burdick Ridge, Perunika Glacier and Huntress Glacier to the west.

Tangra 2004/05 Survey

Camp Academia hosted the base camp of the Bulgarian topographic survey Tangra 2004/05 from 3 December 2004 until 2 January 2005.  The survey was both shipborne from the ships Vanguardia and Akademik Vavilov, and onshore at Livingston Island and Half Moon Island, and was carried out from 25 November 2004 until 11 January 2005 by the two-member team of Lyubomir Ivanov and Doychin Vasilev who covered either on ski or on foot an overall distance of some 200 km, mostly in harsh weather conditions and challenging unfamiliar terrain in Tangra Mountains, Bowles Ridge, Vidin Heights and the glaciers Huron, Kaliakra and Perunika.

First ascents were made of the peaks of Lyaskovets (1473 m), Ongal (1149 m), Zograf (1011 m), Komini (774 m), Melnik (696 m), Miziya (604 m), and several lesser peaks, as well as the third ascent of the summit Mount Friesland (1700 m).  Extensive geodetic and geographic information was gathered, including coordinates and elevation data, actual sea shoreline and ice-free zones configuration, as well as a detailed photographic documentation of previously unexplored and remote areas in the interior of Livingston Island and Greenwich Island.

Based on the survey, some 150 geographical features were mapped for the first time and a new 1:100000 topographic map of the two islands was published in 2005.  Data from the topographic survey Tangra 2004/05 was used also in the 2008 Bulgarian map of Livingston, Greenwich, Robert, Snow, and Smith Islands.

Field work carried out from Camp Academia during the Tangra 2004/05 survey has been noted by Discovery Channel, the Natural History Museum, the Royal Collection and the British Antarctic Survey as a timeline event in Antarctic exploration.

Subsequent occupation
Camp Academia hosted the base camps for the first ascent of Great Needle Peak () by the Bulgarians Doychin Boyanov, Nikolay Petkov and Aleksander Shopov on 8 January 2015, and the first ascent of St. Boris Peak by Boyanov and Petkov on 22 December 2016.

Tangra 1091 Post Office
The post office Antarctica Tangra 1091 of Bulgarian Posts Plc operated during the entire duration of the expedition Tangra 2004/05 in Antarctica from 25 November 2004 until 11 January 2005, in Camp Academia from 3 December 2004 until 2 January 2005.   The office was given the postcode 1091, and was run by Postmaster Lyubomir Ivanov in compliance with standard Bulgarian postal regulations and procedures.

The mailing address of the office was: Camp Academia; 1091 Tangra; Livingston Island; Antarctica.  The mail (i.e. its postage stamps) was cancelled by a standard circular Bulgarian handstamping cancellation seal (metal issue) with an inscription "POSTE BULGARE ANTARKTIKA TANGRA 1091" on its periphery and date/hour counter in the centre.  Other occasional cachets applied on Tangra 1091 mail often included the triangular cachet of Camp Academia with an inscription  "ANTARCTIC EXPEDITION TANGRA 2004 CAMP ACADEMIA" and/or other personal, station and ship postmarks.

A total of 517 outgoing mail consignments (letters and postcards) were shipped, 364 of them via Sofia, 150 via Punta Arenas, and 3 via the St. Kliment Ohridski post office.  These were distributed geographically between 30 country destinations as follows: Bulgaria – 146, Germany – 144, Belgium – 54, Chile – 50, Britain – 18, U.S.A. – 15, Spain – 13, New Zealand – 11, France – 9, Argentina – 7, Australia – 7, Austria – 7, Switzerland – 7, Falkland Islands – 5, Antarctica (Livingston Island) – 3, Afghanistan – 2, Czech Republic – 2, Italy – 2, Japan – 2, Portugal – 2, Uruguay – 2, Denmark – 1, Greece – 1, Indonesia – 1, Iraq – 1, Montserrat – 1, Slovakia – 1, Slovenia – 1, South Africa – 1, Vanuatu – 1.

Location
Camp Academia is situated at , which is 3.6 km east of Orpheus Gate, 5.25 km east-southeast of Rezen Saddle, 3.2 km south-southeast of Omurtag Pass, 4 km southwest of Pirdop Gate, 1.68 km west of Lozen Saddle, 7.1 km west of Karnobat Pass, and 2.68 km north-northwest of Catalunyan Saddle.

See also
 Tangra Mountains
 St. Kliment Ohridski Base
 Livingston Island
 Antarctic Place-names Commission
 Tangra 2004/05
 List of Antarctic research stations
 List of Antarctic field camps

Gallery

Maps
 L. Ivanov, N. Glavinchev, R. Tosheva and S. Naydenov. Antarctica: Livingston Island and Greenwich Island, South Shetland Islands (from English Strait to Morton Strait, with illustrations and ice-cover distribution). Scale 1:100000 topographic map.  Sofia: Antarctic Place-names Commission of Bulgaria, 2005.
 L.L. Ivanov. Antarctica: Livingston Island and Greenwich, Robert, Snow and Smith Islands. Scale 1:120000 topographic map. Troyan: Manfred Wörner Foundation, 2010.  (First edition 2009. )
 L.L. Ivanov. Antarctica: Livingston Island and Smith Island. Scale 1:100000 topographic map. Manfred Wörner Foundation, 2017.
 Antarctic Digital Database (ADD). Scale 1:250000 topographic map of Antarctica. Scientific Committee on Antarctic Research (SCAR). Since 1993, regularly upgraded and updated.
 A. Kamburov and L. Ivanov. Bowles Ridge and Central Tangra Mountains: Livingston Island, Antarctica. Scale 1:25000 map. Sofia: Manfred Wörner Foundation, 2023.

Notes

Sources
 L.L. Ivanov, Livingston Island: Tangra Mountains, Komini Peak, west slope new rock route; Lyaskovets Peak, first ascent; Zograf Peak, first ascent; Vidin Heights, Melnik Peak, Melnik Ridge, first ascent, The American Alpine Journal, 2005, 312-315.
 Antarctica: Livingston Island, Climb Magazine, Issue 14, Kettering, UK, April 2006, 89-91.
 Ivanov, L.L. Bulgaria in Antarctica. South Shetland Islands. Livingston Island and Greenwich, Robert, Snow and Smith Islands. Sofia: Manfred Wörner Foundation, 2009. 16 pp., with a folded map.
 Ivanov, L. and N. Ivanova. The World of Antarctica. Generis Publishing, 2022. 241 pp.  (2014 Bulgarian edition of the book)
 Ivanov, L. General Geography and History of Livingston Island. In: Bulgarian Antarctic Research: A Synthesis. Eds. C. Pimpirev and N. Chipev. Sofia: St. Kliment Ohridski University Press, 2015. pp. 17–28.

External links
 Tangra 2004/05 Expedition Site
 Tangra - Camp Academia
 Tangra 1091 Post Office
 Das südlichste Postamt Bulgariens - Tangra 1091 (in German)
 Antarctic Place-names Commission of Bulgaria
 Spanish Antarctic Base Juan Carlos I (in Spanish)
 Camp Academia locality. Copernix satellite image

Outposts of the South Shetland Islands
Bulgaria and the Antarctic
Bulgarian Academy of Sciences
Geography of Livingston Island
Postal systems
Outposts of Antarctica
2004 establishments in Antarctica

Camp Academia


Vernam Field (locally spelled Vernamfield) is a former World War II United States Army Air Forces airfield located in Clarendon Parish,  west-southwest of Kingston, Jamaica. The airfield was renamed Vernam Air Force Base by the newly formed United States Air Force in 1948, but was closed in 1949.

History
The base was named in honour of First Lieutenant Remington de Bremont Vernam (March 24, 1896 – December 1, 1918), an American pilot who entered the French air service during World War I. Vernam was shot down behind German lines on October 30, 1918. After the Armistice he was found by American forces in a hospital in Longwey, France, with another wounded aviator, Lt. Arthur C. Dineen. Vernam died of his wounds on December 1. He is buried in the American cemetery at St. Mihiel in Thiaucourt, France, and was posthumously awarded the Distinguished Service Cross (United States).

World War II
The airfield has its origin in the 1940 Destroyers for Bases Agreement between Great Britain and the United States. For material support in the allied war effort, Britain agreed to lease as potential naval and air bases to the United States at several locations in the Americas.

The development of Vernam Field was viewed initially by the Army Air Corps as a staging field for training and for the operations of Borinquen Field, Puerto Rico.  It was given its designation on 14 June 1941, and a force of 200 officers and enlisted men (known as "Force Tuna") embarked from New York and arrived on 17 November as a survey party to establish the airfield.

The design of the airfield was upgraded to that of a bomber airfield, and consisted of three runways: a 6000-foot concrete runway and two shorter asphalt runways to accommodate crosswind landings.  When officially activated on 21 November 1941, the station was assigned to the 24th Composite Wing, Sixth Air Force, which controlled (in addition to this base) Atkinson, Beane, Coolidge, Ramey and Waller Fields in the Antilles Air Command.  Constructions of airfield runways and a support station was ongoing throughout 1942, and the first operational unit did not arrive until September.

With the United States entry into the war in December, the primary mission of Vernam Field was antisubmarine patrols in the Northern Caribbean.  In addition, the Florida-based Army Air Forces School of Applied Tactics would send student groups to Vernam for advanced base operations training in combat tactics, returning to Florida after completion.  By 1944, the airfield had fallen into "backwater" status, as the anti-submarine war in the Caribbean had moved much further south towards South America and Panama.    After the departure of the 35th Bomb Squadron, the remaining units assigned to the field were a detachment of the 10588th Ordnance Company and the 305th Signal Company, along with a medical detachment.   On 30 June 1944, Eleanor Roosevelt visited the station.

In early 1945, Vernam Field became the destination for many B-29 Superfortress aircraft from Second Air Force training flights originating from training bases in Kansas and Nebraska (approximately 2,000 miles distant). The B-29s would fly on cross-country training flights to Vernam and land at the airfield for refuelling and maintenance before returning to the Midwest. It was, unfortunately, the site of several B-29 crashes.

Postwar use
With the end of the war, Vernam Field was reduced in scope to a skeleton staff. By the end of 1946 only two aircraft, a C-45 and a C-47 were assigned to the station with both aircraft being down for parts and minimal maintenance being undertaken. It was placed under the command of the 24th Composite Wing, Headquartered at Borinquen AFB, Puerto Rico. The airfield became a training destination for early jet aircraft cross-country flights, with P-80 Shooting Stars, F-84 Thunderjets and early F-86A Sabres using its long wartime bomber runways.

The airfield was redesignated Vernam Air Force Base on March 26, 1948, by Department of the Air Force General Order Number 10.  The mission of the base was primarily weather reporting, with a detachment of the Military Air Transport Service (MATS) 6th Weather Squadron (Regional) being the primary unit on the base. It also became a destination for long-range Strategic Air Command fighter escort aircraft, with F-82 Twin Mustangs flying to Vernam from Kearney AFB, Nebraska then returning on cross-country training flights. President Harry S. Truman visited Vernam AFB on 30 June 1948 during a tour of the Caribbean.

Vernam AFB closed on 28 May 1949 due to budgetary cutbacks. After closure, the base was essentially abandoned and all structures were removed or torn down. The facility has been derelict for decades. The only use of the former airfield area has been an automobile racetrack known as Vernamfield which uses some of the old runways and taxiways.

Units assigned
 4th Antisubmarine Squadron, Caribbean Sea Frontier (United States Navy) (B-18 Bolo)
 14 September-6 October 1942, 16 October-5 November 1942
 35th Bombardment Squadron, 25th Bombardment Group (B-25 Mitchell)
 7 October 1943-7 February 1944
 417th Bombardment Squadron, 25th Bombardment Group, 24 September 1942 – 29 May 1943 (B-18 Bolo)

Current development plans
During the 2000s (decade), the Government of Jamaica made several proposals to develop Vernam Field as the island's fourth international airport. In September 2008 it was announced that as part of this development Jamaica's military, the Jamaica Defence Force (JDF), was to be moved to Vernam Field from its historic city centre site at Up Park Camp in Kingston. By June 2009 the JDF had secured the site and it was reported that the Vernam Airfield Development Project was to build an initial 10,000-11,000 foot runway and adjoining taxi ways capable of handling the largest contemporary aircraft including the Antonov An-124, Antonov An-225 and the Airbus A380.

References

 Hagendorn, Dan (1997), Alae Supra Canalem : Wings over the Canal: The Sixth Air Force and the Antilles Air Command, Turner Publishing Company, Kentucky
 //////

External links
 Aerial view

Defunct airports
Destroyers for Bases Agreement airfields
Airfields of the United States Army Air Forces
Buildings and structures in Clarendon Parish, Jamaica
Airports in Jamaica
Military of Jamaica

Vernam Field