The Night Owl was a passenger train operated by Amtrak on the Northeast Corridor between Washington, D.C., and Boston, Massachusetts, via New York City. It operated from 1972 to 1995 on an overnight schedule with sleeper service; it was the only such train on the Northeast Corridor. In 1995 Amtrak dropped most individual train names from its Northeast Corridor services and the Night Owl became another NortheastDirect service, but still on an overnight schedule. Amtrak replaced it with the Twilight Shoreliner in 1997.

History

At first Amtrak did not feature overnight service on the Northeast Corridor. The last such train was the Federal, operated by Penn Central. Amtrak did not retain the Federal and it made its last run on April 30, 1971. Amtrak restored overnight service on June 6, 1972. The new train was named the Night Owl (numbered 168/169) and carried coaches, sleeping cars, and a buffet-lounge-sleeper. The southbound Night Owl departed Boston's South Station at 10 PM and arrived in Washington's Union Station at 8:30 AM. The northbound train departed Washington at 10:30 PM and arrived in Boston at 8:25 AM.

In early 1977 Amtrak upgraded the Night Owl with Amfleet coaches and an Amfleet dinette. Beginning on January 8, 1978, the Night Owl was combined with the Hilltopper, creating through service from Boston to Catlettsburg, Kentucky. The Hilltopper was discontinued on September 30, 1979, and the Night Owl reverted to Boston-Washington service.

Between April–October in 1992 Amtrak operated a section of the eastbound Night Owl via the so-called "Inland Route". At New Haven, cars separated and operated via Hartford, Connecticut, and Springfield, Massachusetts, into Boston. At the time Amtrak contemplated replacing the overnight Washington–Montreal Montrealer with a Boston–Montreal day train. If this had come to pass the Inland Route section would have connected with this train in Worcester, Massachusetts. Nothing came of the proposed change to the Montrealer and ridership on the section was low. Amtrak permitted smoking aboard the Night Owl until 1994.

One regular traveler on the Night Owl was then-senator Joe Biden, who recalled falling asleep (on more than one occasion) on the train north out of Washington and waking up in Philadelphia's 30th Street Station, well past his usual stop at Wilmington, Delaware. Biden jokingly blamed the incidents on fellow senator Arlen Specter, who, Biden claimed, "told [the conductors] not to wake me up in Wilmington."

Executive Sleeper
In October 1984 Amtrak revived the concept of the "set-out sleeper", last seen on the Northeast Corridor in 1970. Amtrak parked a sleeping car at Pennsylvania Station in New York City. Ticketed southbound passengers were permitted to board beginning at 9:30 PM. The car was attached to the southbound Night Owl, which had a scheduled departure time from New York of 3:50 AM. Conversely, the northbound Night Owl dropped a sleeping car in New York at a similarly early hour, but passengers could remain aboard until 8:00 AM. This service made the Night Owl a real option for business travelers between New York and Washington. Amtrak termed this service Executive Sleeper, although New York Executive and Washington Executive were also employed. Amtrak ended the service on August 19, 1994, because of equipment shortages.

MBTA crash

On December 12, 1990, the Night Owl was involved in what was then the most serious accident in the history of the Massachusetts Bay Transportation Authority (MBTA). While under the direction of an apprentice engineer, the Night Owl entered a curve near Back Bay station in Boston at excessive speed. The train derailed and struck an MBTA Stoughton Line commuter train on a different track. 453 people were injured, although no fatalities resulted. The crash wrecked the two EMD F40PH diesel locomotives which were hauling the train, a material-handling car (carrying express freight), a baggage car, and two Amfleet coaches.

Replacement
In 1995 Amtrak applied the NortheastDirect branding to all intercity services on the Northeast Corridor, save long-distance trains, the New York-Philadelphia Clockers, and the premium Metroliners. The schedule remained the same and timetables still showed the Night Owl name underneath the "Northeast Direct" brand.

The Night Owl made its last run on July 10, 1997. Losses were high and its equipment was outdated. Amtrak relaunched the service as the Twilight Shoreliner. The train carried Viewliner sleeping cars, replacing Heritage Fleet equipment, and a first class-only lounge called the "Twilight Lounge". The train's southern terminus was extended from Washington to Newport News, Virginia. Dave Nogar, then Amtrak's general manager for NortheastDirect services, reflected that "Anyone who rode the Night Owl knows it was a rather unique experience. Now we have a deluxe overnight train."

References

External links
 1977 brochure

Former Amtrak routes
Night trains of the United States
Passenger rail transportation in Connecticut
Passenger rail transportation in Delaware
Passenger rail transportation in Maryland
Passenger rail transportation in Massachusetts
Passenger rail transportation in New Jersey
Passenger rail transportation in New York (state)
Passenger rail transportation in Pennsylvania
Passenger rail transportation in Rhode Island
Railway services introduced in 1972
Railway services discontinued in 1997

Night Owl (train)


The Nigeria Advance Party was a progressive political party during the Second Nigerian Republic, registered for the 1983 elections. Headed by lawyer Tunji Braithwaite, known for his opposition and as a lawyer, the party was the only new political organization allowed to field candidates for the 1983 elections. The party was composed of southern Nigerian intellectuals favoring a reformist government.

History

The party was launched on 13 October 1978 in Ibadan. Party leaders initially took a cautious attitude towards the idea of free education, but later advocated free university education and mandatory primary education. It positioned itself as an alternative to the old politicians of the first republic.

In its first two decades, Nigeria witnessed extensive military rule. Gen. Olusegun Obasanjo was the last military head of state prior to the 1983 elections. Tunji Braithwaite was a prominent Lagosian who claimed that Nigeria's potential could be achieved by reform—especially through the eradication of deep-rooted corruption.
Notable associates of Tunji Braithwaite include Wole Soyinka, Nobel Peace Prize Winner, and musician Fela Anikulapo Kuti, whose mother was murdered by soldiers in a raid on Fela's Kalakuta Republic under Obasanjo's Military Regime.

Campaign
In December 1978, three political pressure groups joined the party. They were the Nigeria Tenants and Labour Congress, headed by I.H. Igali, the Nigeria Social Democratic Congress, led by Balali Dauda, and the Youth Force Alliance, led by Olayinka Olabiwonu. However, its registration was rejected two months later based on insufficient grassroots support.

1983 Elections
The party, led by Tunji Braithwaite, was one of six to contest in the Nigerian Presidential Elections of 1983. Shehu Shagari of the National Party of Nigeria was elected President, with a plurality of 45% percent of votes.

On 7 December 2012, The party was one of 28 to be de-registered by INEC, ahead of 2015 election campaign.

References

Defunct political parties in Nigeria
1978 establishments in Nigeria
Fela Kuti

Nigeria Advance Party


Günnigfeld is a district of Bochum, a city in the Ruhr area of
North Rhine-Westphalia, western Germany. Günnigfeld belongs to the Stadtbezirk (district of a town) of Wattenscheid, Germany, which was a town until 1974 and is now part of Bochum. Günnigfeld is the northernmost part of Wattenscheid.

The population used to speak Westphalian, but now High German is the norm.

It used to be the site of the regional association of the National Democratic Party of Germany, a party of the extreme right and formerly the site of the national headquarters of the NPD's youth organization.

The football team (a fusion between DJK Westfalia and Union 1911) of Günnigfeld, the VfB Günnigfeld, plays in the Bezirksliga. Willi Schulz, Niko Bungert and Mike Terranova started their career in Günnigfeld.

Boroughs of Bochum

Günnigfeld


The Battle of Locus Castorum took place during the Year of the Four Emperors between the armies of the rival Roman Emperors Otho and Vitellius. Locus Castorum was a village that existed in the 1st century Roman Empire roughly 15 kilometers from Cremona. It was also referred to as "the Castors" and "at Castor's." The village may have been the location of a temple to the Gemini twins, Castor and Pollux.

The forces of Otho met the forces of Vitellius there. It was one of three early victories for Otho (the first being in the Alps and the second being near Placentia), but Vitellius was eventually the victor at Betriacum.

Locus Castorum is mentioned in Suetonius The Lives of Twelve Caesars Life of Otho, 9 and Tacitus Histories II.24

References

Locus Castorum
Locus Castorum
69
Year of the Four Emperors
Locus Castorum

Battle of Locus Castorum


Wilhelm Freiherr von Engerth (26 May 1814 – 4 September 1884) was an Austrian architect and engineer, known for being the designer of the first practical mountain locomotive. For his services he was elevated in 1875 to the baronetcy.

Life and work
Wilhelm Engerth was born on 26 May 1814 at Pleß in Prussian Silesia (present-day Pszczyna, Silesian Voivodeship, Poland). From 1834 Engerth studied at Vienna - firstly architecture and then mechanical engineering - and then went to Galicia as an architect, where he was soon entrusted with a lot of work. He returned to Vienna in order to devote himself to engineering, became a teacher of mechanics at the Polytechnikum, then  professor of descriptive geometry and, in 1844, professor of mechanics and engineering principles at the Joanneum in Graz.

He designed a tender locomotive for the Semmering railway (Semmeringbahn) which met the requirements so well that, since then, his Engerth system has found many uses.

In 1850 Engerth was nominated as the technical director (Rat) on the executive board for railways, and later took over the Department of Engineering in the Austrian Ministry of Trade. In 1855 he took over as Zentraldirektor of the Austrian railways and later became its managing director (Generaldirektor).

In 1859 he was a member of the Zollenquetekommission and in 1860 he left government service. He worked with great circumspection (Umsicht) on the organisation of technical studies in Austria and was one of the most enthusiastic proponents of regulating the Danube river. He invented the Schwimmtor, a barrier for preventing floating ice from entering the Danube canal. At the Vienna World Exposition in 1873 he acted as the head of engineering and led the construction of the exhibition halls as the chief engineer. He instigated the tunnels through the Arlberg. In 1874 he was called to the upper house (Herrenhaus) of the Austrian parliament, the Reichsrat and, in 1875 awarded a baronetcy.
He died on 4 September 1884 in Leesdorf, part of Baden bei Wien, Lower Austria. His brother was the artist, Eduard von Engerth.

See also
 List of railway pioneers

Sources
 Wilhelm Engerth: Die Lokomotive der Staats-Eisenbahn über den Semmering: Resultate d. Erprobung d. Kettenkuppelung an d. Preis-Lokomotive Bavaria, Erörterung d. Konstruktionen d. Wilhelm Engerth: Bildliche Darstellungen der einfachen Maschinen in isometrischer Projection/entworfen von Wilhelm Engerth. Wien 1845.
 Wilhelm Engerth: Konkurs-Lokomotive u. Beschreibung mehrerer projektirten Gebirgs-Lokomotive; mit einem Atlas von 13 Kupfertaf. u. einem lithogr. Längenprofile d. Semmeringbahn. Aus: Zeitschrift des Österreichischen Ingenieur-Vereins. 1853 u. 1854. (Umschlagt.: Semmering Locomotive).
 Wilhelm Engerth: Personen- und Lastwagen, Tender-Ausrüstung, Werkstätten-Einrichtung und Werkzeuge. Zeichnungen aus der K. K. Österreichischen Staatseisenbahn-Gesellschaft. Wien 1857.
 Wilhelm von Engerth: Das Schwimmthor zur Absperrung des Wiener Donaucanales. Wien 1884.
 Eduard Frhr. von Engerth: Wilhelm Freiherr von Engerth: Ein Gedenkblatt zu seinem 100. Geburtstag (26. Mai 1814). Wien 1914.

External links

1814 births
1884 deaths
People from Pszczyna
People from the Province of Silesia
Barons of Austria
Austrian people of German descent
Members of the House of Lords (Austria)
Austrian railway mechanical engineers
Austrian railway pioneers
Wilhelm

Wilhelm Engerth


Hawthorn Football Club, known as the "Hawks", is a team in the Australian Football League. They won four premierships in 2008, 2013, 2014 and 2015. Their home ground is the Melbourne Cricket Ground. The coach Alastair Clarkson, is a former student at Ballarat and Clarendon College.

Club song
We're a happy team at Hawthorn
We're the Mighty Fighting Hawks.
We love our club and we play to win,
Riding the bumps with a grin at Hawthorn.
Come what may, you'll find us striving
Team work is the thing that talks,
One for all and all for one
Is the way we play at Hawthorn.
We are the Mighty Fighting Hawks.

Australian Football League
Australian rules football clubs

Hawthorn Football Club


"On Denoting" is an essay by Bertrand Russell from 1905. The essay was published in the philosophy journal Mind in 1905. It was reprinted, in both a special 2005 anniversary issue of the same journal and in Russell's Logic and Knowledge, 1956. The essay is one of the most significant and influential philosophical essays of the 20th century. In it, Russell introduces definite and indefinite descriptions, formulates descriptivism with regard to proper names, and characterises proper names as "disguised" or "abbreviated" definite descriptions.

In the 1920s, Frank P. Ramsey referred to the essay as "that paradigm of philosophy". In the Stanford Encyclopedia of Philosophy entry Descriptions, Peter Ludlow singled the essay out as "the paradigm of philosophy", and called it a work of "tremendous insight"; provoking discussion and debate among philosophers of language and linguists for over a century.

References

Works of philosophy
British essays
1905 works

On Denoting


In mathematics, gradient descent (also often called steepest descent) is a first-order iterative optimization algorithm for finding a local minimum of a differentiable function. The idea is to take repeated steps in the opposite direction of the gradient (or approximate gradient) of the function at the current point, because this is the direction of steepest descent. Conversely, stepping in the direction of the gradient will lead to a local maximum of that function; the procedure is then known as gradient ascent.
It is particularly useful in machine learning for minimizing the cost or loss function. Gradient descent should not be confused with local search algorithms, although both are iterative methods for optimization.

Gradient descent is generally attributed to Augustin-Louis Cauchy, who first suggested it in 1847. Jacques Hadamard independently proposed a similar method in 1907. Its convergence properties for non-linear optimization problems were first studied by Haskell Curry in 1944, with the method becoming increasingly well-studied and used in the following decades.

A simple extension of gradient descent, stochastic gradient descent, serves as the most basic algorithm used for training most deep networks today.

Description

Gradient descent is based on the observation that if the multi-variable function  is defined and differentiable in a neighborhood of a point , then  decreases fastest if one goes from  in the direction of the negative gradient of  at . It follows that, if

for a small enough step size or learning rate , then  . In other words, the term  is subtracted from  because we want to move against the gradient, toward the local minimum. With this observation in mind, one starts with a guess  for a local minimum of , and considers the sequence  such that

We have a monotonic sequence

so, hopefully, the sequence  converges to the desired local minimum. Note that the value of the step size  is allowed to change at every iteration.

It is possible to guarantee the convergence to a local minimum under certain assumptions on the function  (for example,  convex and  Lipschitz) and particular choices of . Those include the sequence

as in the Barzilai-Borwein method, or a sequence  satisfying the Wolfe conditions (which can be found by using line search). When the function  is convex, all local minima are also global minima, so in this case gradient descent can converge to the global solution.

This process is illustrated in the adjacent picture. Here,  is assumed to be defined on the plane, and that its graph has a bowl shape.  The blue curves are the contour lines, that is, the regions on which the value of  is constant. A red arrow originating at a point shows the direction of the negative gradient at that point. Note that the (negative) gradient at a point is orthogonal to the contour line going through that point. We see that gradient descent leads us to the bottom of the bowl, that is, to the point where the value of the function  is minimal.

An analogy for understanding gradient descent

The basic intuition behind gradient descent can be illustrated by a hypothetical scenario. A person is stuck in the mountains and is trying to get down (i.e., trying to find the global minimum). There is heavy fog such that visibility is extremely low. Therefore, the path down the mountain is not visible, so they must use local information to find the minimum. They can use the method of gradient descent, which involves looking at the steepness of the hill at their current position, then proceeding in the direction with the steepest descent (i.e., downhill). If they were trying to find the top of the mountain (i.e., the maximum), then they would proceed in the direction of steepest ascent (i.e., uphill). Using this method, they would eventually find their way down the mountain or possibly get stuck in some hole (i.e., local minimum or saddle point), like a mountain lake. However, assume also that the steepness of the hill is not immediately obvious with simple observation, but rather it requires a sophisticated instrument to measure, which the person happens to have at the moment. It takes quite some time to measure the steepness of the hill with the instrument, thus they should minimize their use of the instrument if they wanted to get down the mountain before sunset. The difficulty then is choosing the frequency at which they should measure the steepness of the hill so not to go off track.

In this analogy, the person represents the algorithm, and the path taken down the mountain represents the sequence of parameter settings that the algorithm will explore. The steepness of the hill represents the slope of the function at that point. The instrument used to measure steepness is differentiation. The direction they choose to travel in aligns with the gradient of the function at that point. The amount of time they travel before taking another measurement is the step size.

Choosing the step size and descent direction
Since using a step size  that is too small would slow convergence, and a  too large would lead to overshoot and divergence, finding a good setting of  is an important practical problem. Philip Wolfe also advocated using "clever choices of the [descent] direction" in practice. Whilst using a direction that deviates from the steepest descent direction may seem counter-intuitive, the idea is that the smaller slope may be compensated for by being sustained over a much longer distance.

To reason about this mathematically, consider a direction  and step size  and consider the more general update:
.
Finding good settings of  and  requires some thought. First of all, we would like the update direction to point downhill. Mathematically, letting  denote the angle between  and , this requires that  To say more, we need more information about the objective function that we are optimising. Under the fairly weak assumption that  is continuously differentiable, we may prove that:

This inequality implies that the amount by which we can be sure the function  is decreased depends on a trade off between the two terms in square brackets. The first term in square brackets measures the angle between the descent direction and the negative gradient. The second term measures how quickly the gradient changes along the descent direction.

In principle inequality () could be optimized over  and  to choose an optimal step size and direction. The problem is that evaluating the second term in square brackets requires evaluating , and extra gradient evaluations are generally expensive and undesirable. Some ways around this problem are:

 Forgo the benefits of a clever descent direction by setting , and use line search to find a suitable step-size , such as one that satisfies the Wolfe conditions. A more economic way of choosing learning rates is backtracking line search, a method that has both good theoretical guarantees and experimental results. Note that one does not need to choose   to be the gradient; any direction that has positive intersection product with the gradient will result in a reduction of the function value (for a sufficiently small value of ).
 Assuming that  is twice-differentiable, use its Hessian  to estimate Then choose  and  by optimising inequality ().
 Assuming that  is Lipschitz, use its Lipschitz constant  to bound  Then choose  and  by optimising inequality ().
 Build a custom model of  for . Then choose  and  by optimising inequality ().
 Under stronger assumptions on the function  such as convexity, more advanced techniques may be possible.

Usually by following one of the recipes above, convergence to a local minimum can be guaranteed. When the function  is convex, all local minima are also global minima, so in this case gradient descent can converge to the global solution.

Solution of a linear system

Gradient descent can be used to solve a system of linear equations

reformulated as a quadratic minimization problem.
If the system matrix  is real symmetric and positive-definite, an objective function is defined as the quadratic function, with minimization of

so that

For a general real matrix , linear least squares define

In traditional linear least squares for real  and  the Euclidean norm is used, in which case

The line search minimization, finding the locally optimal step size  on every iteration, can be performed analytically for quadratic functions, and explicit formulas for the locally optimal  are known.

For example, for real symmetric and positive-definite matrix , a simple algorithm can be as follows,

To avoid multiplying by  twice per iteration,
we note that  implies , which gives the traditional algorithm,

The method is rarely used for solving linear equations, with the conjugate gradient method being one of the most popular alternatives. The number of gradient descent iterations is commonly proportional to the spectral condition number  of the system matrix  (the ratio of the maximum to minimum eigenvalues of , while the convergence of conjugate gradient method is typically determined by a square root of the condition number, i.e., is much faster. Both methods can benefit from preconditioning, where gradient descent may require less assumptions on the preconditioner.

Solution of a non-linear system

Gradient descent can also be used to solve a system of nonlinear equations. Below is an example that shows how to use the gradient descent to solve for three unknown variables, x1, x2, and x3. This example shows one iteration of the gradient descent.

Consider the nonlinear system of equations

Let us introduce the associated function

where

One might now define the objective function

which we will attempt to minimize. As an initial guess, let us use

We know that

where the Jacobian matrix  is given by

We calculate:

Thus

and

Now, a suitable  must be found such that

This can be done with any of a variety of line search algorithms. One might also simply guess  which gives

Evaluating the objective function at this value, yields

The decrease from  to the next step's value of

is a sizable decrease in the objective function. Further steps would reduce its value further until an approximate solution to the system was found.

Comments

Gradient descent works in spaces of any number of dimensions, even in infinite-dimensional ones. In the latter case, the search space is typically a function space, and one calculates the Fréchet derivative of the functional to be minimized to determine the descent direction.

That gradient descent works in any number of dimensions (finite number at least) can be seen as a consequence of the Cauchy-Schwarz inequality, i.e. the magnitude of the inner (dot) product of two vectors of any dimension is maximized when they are colinear. In the case of gradient descent, that would be when the vector of independent variable adjustments is proportional to the gradient vector of partial derivatives.

The gradient descent can take many iterations to compute a local minimum with a required accuracy, if the curvature in different directions is very different for the given function. For such functions, preconditioning, which changes the geometry of the space to shape the function level sets like concentric circles, cures the slow convergence. Constructing and applying preconditioning can be computationally expensive, however.

The gradient descent can be combined with a line search, finding the locally optimal step size  on every iteration. Performing the line search can be time-consuming. Conversely, using a fixed small  can yield poor convergence, and a great  can lead to divergence. Nevertheless, one may alternate small and large stepsizes to improve the convergence rate.

Methods based on Newton's method and inversion of the Hessian using conjugate gradient techniques can be better alternatives. Generally, such methods converge in fewer iterations, but the cost of each iteration is higher. An example is the BFGS method which consists in calculating on every step a matrix by which the gradient vector is multiplied to go into a "better" direction, combined with a more sophisticated line search algorithm, to find the "best" value of  For extremely large problems, where the computer-memory issues dominate, a limited-memory method such as L-BFGS should be used instead of BFGS or the steepest descent.

While it is sometimes possible to substitute gradient descent for a local search algorithm, gradient descent is not in the same family: although it is an iterative method for local optimization, it relies on an objective function's gradient rather than an explicit exploration of a solution space.

Gradient descent can be viewed as applying Euler's method for solving ordinary differential equations  to a gradient flow.  In turn, this equation may be derived as an optimal controller for the control system  with  given in feedback form .

Modifications
Gradient descent can converge to a local minimum and slow down in a neighborhood of a saddle point. Even for unconstrained quadratic minimization, gradient descent develops a zig-zag pattern of subsequent iterates as iterations progress, resulting in slow convergence. Multiple modifications of gradient descent have been proposed to address these deficiencies.

Fast gradient methods
Yurii Nesterov has proposed a simple modification that enables faster convergence for convex problems and has been since further generalized. For unconstrained smooth problems, the method is called the fast gradient method (FGM) or the accelerated gradient method (AGM). Specifically, if the differentiable function  is convex and  is Lipschitz, and it is not assumed that  is strongly convex, then the error in the objective value generated at each step  by the gradient descent method will be bounded by . Using the Nesterov acceleration technique, the error decreases at . It is known that the rate  for the decrease of the cost function is optimal for first-order optimization methods. Nevertheless, there is the opportunity to improve the algorithm by reducing the constant factor. The optimized gradient method (OGM) reduces that constant by a factor of two and is an optimal first-order method for large-scale problems.

For constrained or non-smooth problems, Nesterov's FGM is called the fast proximal gradient method (FPGM), an acceleration of the proximal gradient method.

Momentum or heavy ball method
Trying to break the zig-zag pattern of gradient descent, the momentum or heavy ball method uses a momentum term in analogy to a heavy ball sliding on the surface of values of the function being minimized, or to mass movement in Newtonian dynamics through a viscous medium in a conservative force field. Gradient descent with momentum remembers the solution update at each iteration, and determines the next update as a linear combination of the gradient and the previous update. For unconstrained quadratic minimization, a theoretical convergence rate bound of the heavy ball method is asymptotically the same as that for the optimal conjugate gradient method.

This technique is used in stochastic gradient descent and as an extension to the backpropagation algorithms used to train artificial neural networks. In the direction of updating, stochastic gradient descent adds a stochastic property. The weights can be used to calculate the derivatives.

Extensions
Gradient descent can be extended to handle constraints by including a projection onto the set of constraints. This method is only feasible when the projection is efficiently computable on a computer. Under suitable assumptions, this method converges.  This method is a specific case of the forward-backward algorithm for monotone inclusions (which includes convex programming and variational inequalities).

Gradient descent is a special case of mirror descent using the squared Euclidean distance as the given Bregman divergence.

See also

 Backtracking line search
 Conjugate gradient method
 Stochastic gradient descent
 Rprop
 Delta rule
 Wolfe conditions
 Preconditioning
 Broyden–Fletcher–Goldfarb–Shanno algorithm
 Davidon–Fletcher–Powell formula
 Nelder–Mead method
 Gauss–Newton algorithm
 Hill climbing
 Quantum annealing
 Continuous Local Search
 Neuroevolution

References

Further reading

External links

 Using gradient descent in C++, Boost, Ublas for linear regression
 Series of Khan Academy videos discusses gradient ascent
 Online book teaching gradient descent in deep neural network context
 Archived at Ghostarchive and the Wayback Machine:
 Handbook of Convergence Theorems for (Stochastic) Gradient Methods

Mathematical optimization
First order methods
Optimization algorithms and methods
Gradient methods

Gradient descent


Jean Louis Barthou (; 25 August 1862 – 9 October 1934) was a French politician of the Third Republic who served as Prime Minister of France for eight months in 1913. In social policy, his time as prime minister saw the introduction (in July 1913) of allowances to families with children.

In 1917 and in 1934, Barthou also served as Minister of Foreign Affairs.

Early life
Louis Barthou was born on 25 August 1862 in Oloron-Sainte-Marie, Pyrénées-Atlantiques, France.

Career
Barthou served as a  deputy from his home constituency and was an authority on trade-union history and law.

He served as prime minister from 22 March 1913 to 9 December 1913. In social policy, Barthou's time as prime minister saw the passage of a law in June 1913 aimed at safeguarding women workers before and after childbirth.

He also held ministerial office on 13 other occasions. He served as Foreign Minister in 1917 and 1934. He was the primary figure behind the Franco-Soviet Treaty of Mutual Assistance of 1935, but it was signed by his successor, Pierre Laval. As a national World War I hero and a recognized author, Barthou was elected to the Académie française at the end of that war.

In 1934 he tried to create an Eastern Pact, which would have included Germany (in some proposals) the Soviet Union, Poland, Czechoslovakia and the Baltic states on the basis of guarantees - of the European borders of the Soviet Union by France, and of the eastern borders of Nazi Germany by the Soviet Union. He succeeded in obtaining the entry of the Soviet Union into the League of Nations in September 1934. In response to the withdrawal of Nazi Germany from the League in 1933, he began a program of rearmament, which focused initially on the  Navy and the Air Force.

Barthou was a lover of the arts, and in power he worked with leaders of the arts to publicize their fields. He felt that world-class leadership in the arts made Paris a mecca for tourists and collectors, and enhanced the nation's stature worldwide as the exemplar of truth and beauty. In turn, the arts community honoured Barthou by dubbing him the "minister of poets".

Death
As Foreign Minister, Barthou met King Alexander I of Yugoslavia during his state visit to Marseille in October 1934. On 9 October, King Alexander was assassinated by Velicko Kerin, a Bulgarian far-right nationalist terrorist wielding a handgun. Another bullet struck Barthou in the arm, passing through and fatally severing an artery. He died of blood-loss less than an hour later. The assassination had been planned in Rome by Ante Pavelić, head of the Croatian Ustaše, in August 1934. Pavelić was assisted by Georg Percevic, a former Austro-Hungarian Armed Forces officer. France unsuccessfully requested the extradition of Percevic and Pavelić. This assassination ended the careers of the  Bouches-du-Rhone prefect, , and of the director of the Surete Nationale, Jean Berthoin.

A ballistic report on the bullets found in the car was made in 1935, but its results were not made available to the public until 1974. The report revealed that Barthou had been hit by an 8 mm Modèle 1892 revolver round, commonly used in weapons carried by French police. Thus Barthou was killed during the frantic police response, rather than by the assassin.

Legacy
The deaths of Barthou and the King led to the Convention for the Prevention and Punishment of Terrorism concluded at Geneva by the League of Nations on 16 November 1937. The Convention was signed by 25 nations, ratified only by India. Barthou was granted a state funeral four days after his demise.

Ministries

Barthou's ministry, 22 March 1913 – 9 December 1913
 Louis Barthou – President of the Council and Minister of Public Instruction and Fine Arts
 Stéphen Pichon – Minister of Foreign Affairs
 Eugène Étienne – Minister of War
 Louis Lucien Klotz – Minister of the Interior
 Charles Dumont – Minister of Finance
 Henry Chéron – Minister of Labour and Social Security Provisions
 Antony Ratier – Minister of Justice
 Pierre Baudin – Minister of Marine
 Étienne Clémentel – Minister of Agriculture
 Jean Morel – Minister of Colonies
 Joseph Thierry – Minister of Public Works
 Alfred Massé – Minister of Commerce, Industry, Posts, and Telegraphs

References

Further reading
 Atkin, Nicholas. "Power and Pleasure. Louis Barthou and the Third French Republic." Journal of European Studies 23.91 (1993): 357-359.
 Buffotot, Patrice. "The French high command and the Franco‐Soviet alliance 1933–1939." Journal of Strategic Studies 5.4 (1982): 546-559.
 French, G. "Louis Barthou and the German Question: 1934." Report of the Annual Meeting. Vol. 43. No. 1. 1964. online
 Rife, John Merle. "The political career of Louis Barthou" (PhD. Diss. The Ohio State University, 1964) online.
 Roberts, Allen. The turning point: the assassination of Louis Barthou and King Alexander I of Yugoslavia (1970).
 Schuman, Frederick L. Europe On The Eve 1933-1939 (1939) pp 94–109.online
 Young, Robert J.  Power and Pleasure: Louis Barthou and the Third French Republic (1991)
 Young, Robert J. "Cultural Politics and the Politics of Culture: The Case of Louis Barthou," French Historical Studies (Fall 1991) 17#2 pp. 343–358 online
 Young, Robert J. "A Talent for All Seasons: The Life and Times of Louis Barthou." Queen's Quarterly 98.4 (1991): 846-64; online.

External links

 "The King is Dead, Long Live the Balkans! Watching the Marseilles Murders of 1934" The Watson Institute

1862 births
1934 deaths
People from Oloron-Sainte-Marie
Politicians from Nouvelle-Aquitaine
Democratic Republican Alliance politicians
Prime Ministers of France
French Foreign Ministers
Transport ministers of France
French Ministers of Public Works, Posts and Telegraphs
French interior ministers
French Ministers of War
Members of the 5th Chamber of Deputies of the French Third Republic
Members of the 6th Chamber of Deputies of the French Third Republic
Members of the 7th Chamber of Deputies of the French Third Republic
Members of the 8th Chamber of Deputies of the French Third Republic
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Members of the 10th Chamber of Deputies of the French Third Republic
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Members of the 12th Chamber of Deputies of the French Third Republic
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1934 murders in France
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Louis Barthou


Edward Drinker Cope (July 28, 1840 – April 12, 1897) was an American biologist. He was notable for his work on fossil animals of North America. Cope was born in Philadelphia, Pennsylvania.

Cope was a paleontologist, comparative anatomist, herpetologist and ichthyologist. He wrote many papers. His parents were rich Quakers.

His father wanted him to be a farmer, but he became a scientist. He married his cousin. Later, they owned a museum in Philadelphia.

Mostly, he read books on his own to learn science and found things out himself. He was not a teacher. He did field work, and wrote a lot. In the 1870s and 1880s, went to the American West to report what the land was like to the government. He was often on a mapping team sent by the United States Geological Survey.

For a while he and Othniel Charles Marsh were competing to find dinosaurs. This fight between them is called the Bone Wars. Sometimes being a scientist cost him more money than he could afford. In the 1880s, Cope lost so much money in his silver mines that he had to sell a lot of his fossil collection in 1886. In the 1890s he was no longer poor, but he died when he was only 57.

1,400 of his articles were published in science journals. He found over 1,000 species of extinct animals. He wrote about hundreds of kinds of ancient fish. He found dozens of dinosaurs. He wrote about the evolution of mammalian  molars teeth, and produced two huge works on the amphibia and reptiles of North America.

Cope showed that horses evolved to be larger as they moved from woodland onto grassland. The fact that the fossils show the mammals getting bigger over time is called Cope's rule.

Early life

Cope was the first son of Alfred and Hanna Cope. His father was a serious Quaker and ran the shipping business started by his father, Thomas P. Cope. The business was started in 1821. His parents took him to gardens, museums, and zoos. They taught him to read and write and draw.

He started going to school when he was 9 years old. When he was 12, his parents sent him away to a Quaker boarding school. At 15 years old he studied biology (natural history) and often visited  the Academy of Natural Sciences in Philadelphia. They had a Natural history museum.

His letters home show he felt farm work was not for him.p15 Cope's father made him get a summer job on a farm when he was 14 and 15. When he was 16 he was not sent to the boarding school any more because his father wanted him to be a farmer.p100 His father wanted him to get more exercise, so he bought him a farm. Cope rented out the land to farmers and worked on farms.

When he was 18 years old he, began working at the Academy of Natural Sciences part-time. He took classes. His father paid for them.  Still, his father said he should farm. Until he was 23, his letters to his father kept saying he did not want to be a farmer and that he wanted to be a scientist.p100

He worked at the Academy of Natural Sciences for two years, and became a member.p21 He sometimes had to visit the Smithsonian Institution where he met Spencer Baird, who knew all about fish and birds.p107 He also joined the American Philosophical Society. The Academy and the Society published journals, and they accepted his articles.

In 1861 when he was 21 years old, he wrote about classifying salamanders. A salamander is an amphibian.p835 He then took a comparative anatomy class from a famous teacher at the University of Pennsylvania. Cope then asked his father if he could learn German and French so he could read science books and novels in German and French.p101

European travels
At the beginning of the American Civil War Cope tried to get a job helping in a field hospital. Then, when he was 22, he wanted to somehow help out the freed blacks. That year, 1863, he and his fiancée broke up and he was sad. He went to Ireland, England and Europe. During his trip, he met famous scientists.p26-30

While in Germany, he first met his rival, scientist Othniel Charles Marsh.p11 On February 11, 1864, he wrote to his father, "I shall get home in time to . . . be caught by the new draft. I shall not be sorry for this . . . certain persons . . . would be mean enough to say that I have gone to Europe to avoid the war".p138

Early career
Cope's return home to Philadelphia was before the end of the Civil War. He married a Quaker girl he knew, Annie Pim. She lived on a farm and the wedding was held at her house.

Cope wrote papers on fish, whales, and one on a fossil frog with a tail.p835 Cope's father gave money to a small Quaker college called Haverford College. The college gave Cope an honorary master's degree and hired him to teach Zoology.p48

Cope went on scientific trips to the American west and wrote letters to his parents and to his wife and daughter while on those trips. He told his father that teaching took up too much of his time for him to make scientific discoveries.p143/6 He quit his job at the college. He and his wife and daughter then moved to Haddonfield to be closer to the fossil beds in western New Jersey.

In Haddonfield, New Jersey were marlpits, where a dinosaur skeleton was discovered in 1858 by William Foulke and named Hadrosaurus foulkii by Dr. Leidy of Philadelphia's Academy of Natural Sciences.p151/8 Cope found more fossils in the marlpits there. For example, he described Elasmosaurus platyurus and Laelaps in 1868. Edward Cope also went on expeditions to caves; the last cave he visited was the Wyandotte Caves in Indiana in 1871.p151/5

In his 30s the Quaker wrote a lot of scientific papers that were published. Charles Sternberg said that in the fossil fields of Kansas Cope had a "severe attack of nightmare . . . every animal of which we had found trace during the day played with him at night . . . sometimes he would lose half the night in this exhausting slumber".p167

Cope also looked for fossils in the west of the United States. In 1872 he explored Eocene rocks. The rocks were 55 to 38 million years old. That year, he worked too much and had a breakdown.p583 In 1873 he studied the Titanothere beds (strata) of northeastern Colorado. Titanothere was a large extinct herbivore.p183/194

The Wheeler Survey
In 1874 Cope volunteered for the Wheeler Survey. These geological mapping trips were led by George Montague Wheeler. They mapped parts of the United States west of the 100th meridian.p200 The 100th meridian west is the boundary between the dry West and the rainy East of the United States.

In 1874 Cope discovered the Puerco formation in New Mexico during the Wheeler Survey.p200 The Puerco formation was a layer of soft rock 500 feet thick along the upper Puerco River near Cuba, New Mexico. It was green and black marl (that contained chemicals used in making fertilizer). Fossils were later found by someone at a similar formation west of there in a different county. Cope said it was like those fossils came from his Puerco formation, which he discovered. His cliff may have been dug by the river over a long time and it looked like it had been there a long time. It was something the scientists he knew had not seen before him. As part of the Wheeler Survey, he was able to shop at commissaries. He was able to get his finding in the reports the survey published. He brought his wife and daughter along on one trip of the survey, renting a house for them. As a volunteer, he paid his own way.p63

Independence

When Cope was 35, his father died, leaving him a quarter of a million dollars.p837 The next year, 1876, Cope moved his wife and daughter from their house by the apple orchard in Haddonfield, New Jersey back to Philadelphia, Pennsylvania – this time to a row house in the City. He bought two units and used the one next door as a paleo-lab for his fossil collection. He stopped doing field work to catch up on his writing. He hired teams to look for fossils for him. And, he helped the Philadelphia Centennial Exhibition set up their fossil displays.p218 In 1877 he was able to buy half of the American Naturalist.

He published papers so fast his rival, Professor Marsh, had doubts about when Cope's fossils were found. In August 1878 when he was 38, Cope sailed to the British Isles to attend a scientific convention in Dublin Ireland. He then sailed to France to go to a two-day scientific convention there. At one of the conventions he decided to buy some boxes of Argentine fossils, maybe for the museum in Philadelphia.

When Cope came back, two years-worth of collecting by his man Lucas awaited him. This included a Camarasaurus, a sauropod.p42

The bone wars

Cope introduced his (then) friend Marsh to the marl pit owner, Albert Vorhees, when the two visited the site. Later he discovered that Marsh had gone—behind Cope's back and made a private agreement with Vorhees: any fossils that Vorhees's men found were sent back to Marsh at New Haven.p35

In 1868 Professor Marsh said Cope put the skull of dinosaur at the tail end. It was Elasmosaurus, a long-necked plesiosaur. It turned out Marsh was right, and Cope was humiliated.

The feud lasted for the rest of Cope's life. Both became less wealthy trying to keep the other's men from digging for fossils. Each criticized the other's work in the New York Herald. Another time Marsh tried to keep Cope from getting his articles and books published, so Cope hired two fossil-finders away from Marsh.p257

In 1889, U.S. Geological Survey stopped giving grants to Cope. Marsh persuaded John Wesley Powell to ask Cope to give the Survey the specimens Cope found back in 1874.p233/7 249 Cope did not want to give the fossils to the Survey because when he found them he was a volunteer paying his own way. So, he spoke to the New York Herald.p245/9 The first article was on January 12, 1890. Cope said Marsh underpaid his workers, and said some of what Marsh wrote was really written by others. Also, he said Powell was spending tax money wrong and had made mistakes in classifying fossils.p404 Later, another article gave their side of the story.p206 As a result of the articles, the Survey lost its funding for fossil-finding. Marsh got fired from the Survey. And, Cope almost got fired from the University of Pennsylvania.p329/334 Cope wondered if people thought of him as "a liar . . . actuated by jealousy and disappointment." He seemed sorry Marsh had been fired, writing to Paleontologist Henry Osborn, "I think Marsh is impaled on the horns of Monoclonius sphenocerus.p408

Later years

In 1882 Cope wrote a paper about a fossil  pelycosaur Edaphosaurus. It looked like a lizard with a huge fin along its back. In 1886 Professor Cope fired his fossil diggers and started selling some of his large fossil collection to museums. He also wrote forty more scientific reports about their findings that year.p242

In 1889 he reported Coelophysis, a slender dinosaur from the Upper Triassic. This little carnivore is one of the earliest dinosaurs found. The same year, he succeeded Joseph Leidy, who had died the previous year, as professor of zoology at the University of Pennsylvania.

In 1892, Cope (then 52 years old) was granted expense money for field work from the Texas Geological Survey. With his finances improved, he was able to publish a massive work on the Batrachians of North America, which was the most detailed work on the continent's frogs and amphibians ever done,p350 and the 1,115-page The Crocodilians, Lizards and Snakes of North America.

In the 1890s his publication rate increased to an average of 43 articles a year.p350 His final expedition to the West took place in 1894, when he prospected for dinosaurs in South Dakota and visited sights in Texas and Oklahoma.

In 1895 Cope re-hired Sternberg, who knew about the nightmares he had about dinosaurs, to look for fossils for him.p358

Cope sold fossils to museums. For example, in 1895 the American Museum of Natural History in New York City bought his collection of about 10,000  fossil mammals.

Cope sold three other collections for $29,000. Although his collection still contained more than 13,000 specimens, Cope's fossil hoard was much smaller than Marsh's collection, which was valued at over a million dollars.

Cope's death

In 1896 Cope got sick, and he died on April 12, 1897. His friends told of how they remembered him. They then held the reading of his will. The American Journal of Science had an obituary about Cope. The Naturalist had a longer one. And, the National Academy of Sciences' journal had one years later.

Cope's ideas and character

Edward D. Cope was a Quaker. His biographer Henry Osborn wrote, "If Edward... (had) doubts about the... Bible... he did not (tell) them in his letters to his family, but there can be little question... that he shared the intellectual unrest of the period". Cope was conservative about women working or voting.  He felt the husband should be able to take care of his wife and that married women would vote the same as their husbands.p176

He was remembered as not liking the Negro accent, and he believed that if "a race was not white then it was inherently more ape-like".p26, 169, 176

Although his daughter Julia burnt many of his private papers, many of his friends have written about him. Charles R. Knight, a former friend, said that Cope's language was so filthy that "in [Cope's] heyday no woman was safe within five miles of him".p109

People said Cope had great energy and activity and was always interesting, kind and helpful. Others said he had a temper and said he was a "militant paleontologist". Some say he was well-liked by those who lived when he did.p202

Views on evolution
Cope said Charles Darwin's book The Voyage of the Beagle had "too much geology in it".

Over his lifetime Cope's views on evolution shifted.p250 His original view, described in the paper On the Origin of Genera (1868), held that while Darwin's natural selection may affect the preservation of superficial characteristics in organisms, natural selection alone could not explain the formation of genera.

Cope's beliefs became one with an increased emphasis on continual and utilitarian evolution with less involvement of a Creator.p259 He became one of the founders of the Neo-Lamarckism school of thought, which holds that individuals can pass on traits acquired in its lifetime to offspring. Although the view has been shown to be incorrect, it was common among paleontologists in Cope's time.p68 In 1887, Cope published his own Origin of the Fittest: essays in evolution, detailing his views on the subject. He was a strong believer in the law of use and disuse—that an individual will slowly, over time, favor an anatomical part of its body so much that it will become stronger and larger as time progresses down the generations. This theory fails because use and disuse does not affect the genetic code of the gametes, something which became clear in the generations after his death.

References

 Alroy, John 1999. Edward Drinker Cope (1840–1897) National Center for Ecological Analysis and Synthesis. University of California, Santa Barbara URL: http://www.nceas.ucsb.edu/%7Ealroy/lefa/Cope.html  Retrieved, 2008-11-17.
 Bowler, Peter 1977. Edward Drinker Cope and the changing structure of evolutionary theory. Isis, 68, #2, pp. 249–265 University of Chicago URL: https://www.jstor.org/stable/230073 Retrieved, 2009-12-05 doi:10.1086/351770

 Fowler, Henry W. 1963. Special Anniversary Features: Cope in retrospect Copeia, vol. 1963, no. 1, pp. 195–198 URL:  Retrieved, 2009-12-04 American Society of Ichthyologists and Herpetologists doi:10.2307/1441319
 Gill, Theodore 1987. Edward Drinker Cope, Naturalist - a chapter in the history of science. The American Naturalist, 31, 370, pp. 831–886. Chicago, IL :University of Chicago Press. doi:10.1086/276725

 Osborn, Henry Fairfield 1931. Cope: master naturalist: life and letters of Edward Drinker Cope, with a bibliography of his writings. Manchester, New Hampshire: Ayer Company Publishing.  Google Books No preview
 Penick, James. 1971. Professor Cope vs. Professor Marsh. American Heritage, 22, iss. 5. URL: http://www.americanheritage.com/articles/magazine/ah/1971/5/1971_5_4.shtml
 Romer, Alfred S. 1964. Cope versus Marsh. Systematic Zoology, 13, #4, 201–207. Taylor & Francis. URL:   doi:10.2307/2411780

 The Academy of Natural Sciences Bone Wars: the Cope-Marsh rivalry. URL:   Retrieved, 2009-11-08
 Haverford College.  Quaker and Special Collections: Edward Drinker Cope papers  URL: http://www.haverford.edu/library/special/aids/edcope/  Retrieved, 2009-11-10

Other websites

 Dinosaurs named by Cope, at DinoData
 Profile of Edward Drinker Cope  at the Niagara Falls Museum Collection
 Edward Drinker Cope obituary, 1897 archived via JSTOR

1840 births
1897 deaths
American paleontologists
American naturalists
Anatomists
Quakers
Writers from Philadelphia
Scientists from Philadelphia
History of science
Ichthyologists

Edward Drinker Cope


C. Vernon Mason is a former lawyer and civil rights advocate from Tucker, Arkansas.  Best known for his involvement in several high-profile New York City cases in the 1980s, including the Bernhard Goetz, Howard Beach, and Tawana Brawley incidents, Mason has not practiced law since his 1995 disbarment. He then served as the CEO of a non-profit organization. He is also an ordained minister.

Education

Mason graduated from Morehouse College and earned a Master's in Business Administration from Indiana University. He then graduated from Columbia Law School earning a Juris Doctor and, later, earned the Master of Divinity, and the Doctor of Ministry degree from New York Theological Seminary.

Notable cases

In 1983 Mason and William Kunstler represented serial killer Lemuel Smith at his trial for the murder of Donna Payant.

Mason was co-counsel for Darrell Cabey, one of the four men shot by Bernhard Goetz in the famous 1984 "subway vigilante" case.

Mason was one of the lawyers retained by the family of Michael Griffith, manslaughter victim in
the Howard Beach incident.

In 1987 Mason, along with Alton H. Maddox and Al Sharpton, were advisors to Tawana Brawley, an African-American teenager who claimed to have been abducted and sexually assaulted by at least three white men, including at least one police officer and assistant district attorney Steven Pagones.  However, a grand jury investigation into Brawley's allegations determined that she "had not been abducted, assaulted, raped and sodomized as had been claimed" and that "the 'unsworn public allegations against Dutchess County Assistant District Attorney Steven Pagones' were false and had no basis in fact."  Pagones filed a $385 million lawsuit against Brawley and her advisors for 22 purported defamatory statements; Mason was found liable of making one defamatory statement and ordered to pay $185,000.

Disbarment
Mason was disbarred by the New York State Appellate Division, First Department, in 1995.
The court cited 66 instances of professional misconduct with 20 clients over the course of 6 years as its rationale for the action, including "repeated neglect of client matters, many of which concerned criminal cases where a client's liberty was at stake; misrepresentations to clients [and] refusal to refund the unearned portion of fees". Though Mason's involvement in the Brawley case was not specifically cited, Mason would allege that the ruling was intended to punish him for the Brawley case.

References

Year of birth missing (living people)
Living people
Disbarred New York (state) lawyers
20th-century African-American lawyers
20th-century American lawyers
African-American Christian clergy
American Christian clergy
Morehouse College alumni
Indiana University alumni
Columbia Law School alumni
New York Theological Seminary alumni
People from Jefferson County, Arkansas
21st-century African-American people

C. Vernon Mason


Michel Trempont (28 July 1928 – 30 January 2021) was a Belgian operatic baritone whose repertoire extended from the 18th century to the creation of contemporary works. His brother was Pol Trempont (1923–2007), operatic tenor and one time director of the Théâtre de Mons.

Life and career
After studies with Rogatchewsky, Trempont made his debut in Liège in 1952 as Valentin. He then appeared at La Monnaie in 1956, where he went on to sing, among other roles:
Le mari in Menotti's Amelia Goes to the Ball, Le Mesge in Henri Tomasi's L'atlantide, Ajax Deuxième in Offenbach's La belle Hélène, Marcello in Puccini's La bohème, Moralès in Bizet's Carmen, Silvio in Leoncavallo's Pagliacci, Tourillon in Johann Strauss's Die Fledermaus (as La chauve-souris), Roger de Lansquenet in Reynaldo Hahn's Ciboulette, Jean in Bohuslav Martinů's Comedy on the Bridge (as Comédie sur le pont), Masetto in Mozart's Don Giovanni (as Don Juan), Le frère jardinier in Tomasi's Don Juan de Manara, a vagabond in Carl Orff's Die Kluge (as Echec au roi), Maître Pausanias in Chabrier's Une éducation manquée, Valentin in Gounod's Faust, Louchard in Charles Lecocq's La fille de Madame Angot, Le marquis Bambini in Offenbach's La fille du tambour-major, Vitellius in Massenet's Hérodiade, Jun (one of the gangsters) in Cole Porter's Kiss Me, Kate, Frédéric in Léo Delibes' Lakmé, a rascal in Orff's Der Mond (as La lune), Banquo in Verdi's Macbeth, De Brétigny in Massenet's Manon, Bacarel in Edmond Audran's Miss Helyett, Borello in Henry Février's Monna Vanna, Bantison in André Messager's Monsieur Beaucaire, Bridaine in Louis Varney's Les mousquetaires au couvent, Phorbas in Enescu's Œdipe, Le chien in Albert Wolff's L'oiseau bleu, the Beggar in John Gay's The Beggar's Opera (as L'opéra du gueux), Gustav von Pottenstein in Franz Lehár's The Land of Smiles (as Le pays du sourire), Panatellas in Offenbach's La Périchole, Ceprano in Verdi's Rigoletto, Moussoul in Adolphe Adam's Si j'étais roi, Monsieur Choufleuri in Offenbach's M. Choufleuri restera chez lui le . . ., Gardefeu in Offenbach's La Vie parisienne, and Albert in Massenet's Werther.

Trempont attained an international career with performances at the Opéra-Comique in Paris, where he made his debut in 1966, and sang (French versions) Figaro in the Mozart opera and in Rossini's; Marcello, Sharpless, Gaillardin (Gabriel von Eisenstein) in Die Fledermaus (La Chauve-Souris), Rimbaud in Le comte Ory, Zurga in les pêcheurs de perles and le Marquis de Clainvillela in Sauguet's La Gageure imprévue. He appeared at the Festival d'Aix-en-Provence, the Royal Opera House London, La Scala, Milan, La Fenice, Venice, Teatro San Carlo in Naples and San Francisco Opera. His repertoire has included Figaro (in both Mozart's Le nozze di Figaro and Rossini's Il barbiere di Siviglia), Guglielmo (Così fan tutte), Rimbaud (Le comte Ory), Sulpice (La fille du régiment), Fieramosca (Benvenuto Cellini), Taddeo (L'italiana in Algeri), Sancho (Don Quichotte), and the king in Prokofiev's L'Amour des trois oranges.

At Grand Théâtre de Genève his roles have included: the Sacristan, Pandolphe (Cendrillon), Le Baron de Gondremarck, Crespel, Peter (Hänsel et Gretel), Carpe (La Forêt), V'lan (Le voyage dans la lune, also televised), and Pantalon (L'Amour des trois oranges).

As the Comte de Fritelli he took part in a complete BBC broadcast of Chabrier's Le roi malgré lui recorded in Manchester in 1973, conducted by Manuel Rosenthal.

Discography
List of recordings of complete operas by composer with title, recording label, and role:
 Adolphe Adam: Le toréador (Decca) – Don Belflor
 Daniel Auber: Fra Diavolo (EMI) – Giacomo
 Georges Bizet: Carmen (EMI) – Dancaire
 Gaetano Donizetti: La fille du régiment (EMI) – Sulpice
 André Grétry: Richard Coeur-de-lion (EMI) – Blondel
 Jules Massenet: Manon (DG) - Brétigny
 André Messager: Fortunio (EMI) – Maître André
 Jacques Offenbach:
 Les brigands (EMI) – Pietro
 Mesdames de la Halle (EMI) – Madame Madou
 Monsieur Choufleuri restera… (EMI) – Petermann
 Orphée aux enfers (EMI) – Jupiter
 La Périchole (EMI) – Panatellas
 La Vie parisienne (EMI) – Bobinet
 Gioachino Rossini: La cambiale di matrimonio (Universal) – Mill
 Ambroise Thomas: Hamlet (EMI) – Polonius
 Louis Varney: Les mousquetaires au couvent (EMI) – Brissac

References

This article includes some material adapted from French Wikipedia.

External links

1928 births
2021 deaths
Belgian opera singers
Operatic baritones
People from Boussu

Michel Trempont


An algebraic solution is an algebraic expression which is the solution of an algebraic equation in terms of the coefficients of the variables. It is found only by addition, subtraction, multiplication, division, and the extraction of roots (square roots, cube roots, etc.).

The most well-known example is the solution of the general quadratic equation.

(where a ≠ 0).

There is a more complicated solution for the general cubic equation and quartic equation.  The Abel-Ruffini theorem states that the general quintic equation does not have an algebraic solution. This means that the general polynomial equation of degree n, for n ≥ 5, cannot be solved by using algebra. However, under certain conditions, we can get algebraic solutions; for example, the equation  can be solved as

References

Algebra

Algebraic solution


Founded in 2001 and based in Norwich. Hypertag is a supplier of proprietary proximity marketing technology. It predominantly sells this to brands, allowing them to connect to consumers' mobile phones based on their proximity to a physical location using short-range mobile wireless technologies such as Bluetooth, Infrared, Wi-Fi and NFC.

Hypertag allows digital content such as wallpapers, video clips, games, music clips, vouchers, documents, web links or mobile applications to be downloaded direct to consumers' mobile phones quickly and for free. Hypertag sells its proximity marketing solutions to major brands, their agencies, visitor attractions and through a network of international resellers. Hypertag also integrates its systems with third party infrastructure providers such as in-store advertising display screen providers and has been used by brands such as O2, Vodafone, Peugeot and CNN. And has installed systems at visitor attractions owned by the Royal Institution and English Heritage.

An example campaign in 2005, posters advertising new Gorillaz single, DARE, were established in Sydney and Melbourne, Australia in September 2005. The posters contained Hypertag technology, allowing passers-by to download a 40-second ringtone of the song DARE to their mobile phones.

The technology was also used by the band New Order in advertisements for their album Waiting for the Sirens' Call, and in 2008, Hypertag won a gold award for best location-based advertising technology at the Mobile Advertising and Marketing Awards.

Hypertag was bought by Proxama Ltd on 14 January 2011.

See also
 Proximity marketing
 Mobile marketing

References

Software companies of the United Kingdom
Companies established in 2001
Companies based in Norwich

Hypertag