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William Wulf

William Allan Wulf (December 8, 1939 – March 10, 2023) was an American computer scientist notable for his work in programming languages and compilers.

Early life and education
Born in Chicago, Wulf attended the University of Illinois Urbana–Champaign, receiving a Bachelor of Science (B.S.) in engineering physics in 1961 and an Master of Science (M.S.) in electrical engineering in 1963. He then achieved the first Doctor of Philosophy (Ph.D.) in computer science from the University of Virginia in 1968.

Career
In 1970, while at Carnegie Mellon University (CMU), he designed the BLISS programming language and developed a groundbreaking optimizing compiler for it.

From 1971 to 1975, as part of CMUs C.mmp project, he worked on an operating system (OS) microkernel named Hydra which is capability-based, object-oriented, and designed to support a wide range of possible OSs to run on it.

With his wife Anita K. Jones, Wulf was a founder and vice president of Tartan Laboratories, a compiler technology company, in 1981.

Wulf served as president of the National Academy of Engineering from 1996 to 2007. He chaired the Computer Science and Telecommunications Board of the National Research Council from 1992 to 1996. Prior to that, he served as Assistant Director of the US National Science Foundation's Computer and Information Science and Engineering (CISE) directorate from 1988-1990. During this time, he played a major role in making the NSFnet computer network (as it was known at that time) available to the public as the Internet, for which he received the ACM Policy Award in 2017. He served on the Council of the ACM, on the board of directors of CRDF Global, and was a reviewing editor of Science. In 1994 he was inducted as a Fellow of the ACM. In 2007 Wulf was awarded the honor of delivering the prestigious Charles P. Steinmetz Lecture at Union College. He was elected to the American Philosophical Society that same year.

Wulf's research also included computer architecture, computer security, and hardware-software codesign.

Wulf ended his career at the University of Virginia by resigning on Tuesday, June 19, 2012, in protest of the forced resignation of former President Teresa A. Sullivan, in what he called, "the worst example of corporate governance I have ever seen.   After widespread challenges from the faculty, student body, alumni, and the national academic community; and in the face of a direct threat from the Governor of Virginia that he would replace the entire board if they did not resolve the conflict, Sullivan was unanimously rehired some two weeks later.

Personal life and death
Wulf was married to Anita K. Jones, an Emeritus Professor of Computer Science at the University of Virginia.

William Wulf died in Charlottesville, Virginia, on March 10, 2023, at the age of 83.

Publications

 * Wulf, W. A., "Programming Without the GOTO", Proceedings of the Internationale Federation of Information Processing, Ljubljana, Yugoslavia, August 1971.
 * Wulf, W. A., et al., "Reflections on a Systems Programming Language", Proceedings of the SIGPLAN Symposium on System Implementation Languages, Purdue University, October 1971.
 * McCredie, J., Wulf, W. A., "The Selection of a Computing Alternative", Proceedings of the IEEE Computer Conference, IEEE, Boston, September 1971.
 * Wulf, W. A., "A Case Against the GOTO", Proceedings of the ACM National Conference, ACM, Boston, August 1972.
 * Wulf, W. A., and Shaw, M., "Global Variables Considered Harmful", SIGPLAN Notices 8(2), February 1973.
 * Wulf, W. A., Shaw, M., Hilfinger, P. N., and Flon, L., Fundamental Structures of Computer Science Addison-Wesley, 1980.
 * Wulf, W. A., Johnson, R., Weinstock, C., Hobbs, S., and Geschke, C., The Design of an Optimizing Compiler American Elsevier Publishing Company, Inc., New York, 1975.
 * Shaw, M. and Wulf, W., "Tyrannical Languages Still Preempt System Design", Proceedings of the International Conference on Computer Languages, April 1992.

title: William Wulf


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Frederick VIII, Duke of Schleswig-Holstein

Frederick VIII, Duke of Schleswig-Holstein and of Schleswig-Holstein-Sonderburg-Augustenburg (Frederik Christian August af Slesvig-Holsten-Sønderborg-Augustenborg; Friedrich Christian August Herzog von Schleswig-Holstein-Sonderburg-Augustenburg; 6 July 1829 – 14 January 1880) was the German pretender to the throne of second duke of Schleswig-Holstein from 1863, although in reality Prussia took overlordship and real administrative power.

Life
He was the eldest son of Christian August II, Duke of Schleswig-Holstein-Sonderburg-Augustenburg and Countess Louise Sophie of Danneskiold-Samsøe. He was ethnically perhaps the most Danish Prince of the Danish Royal dynasty in his generation (at the time of Denmark's most recent succession crisis).

His family belonged to the House of Oldenburg, the royal house that included all the medieval Scandinavian royal dynasties among its distant forebears - which it shared with his rivals and relatives, other claimants to the Danish throne. Both lines claim descent from the medieval Danish House of Estridsen via Christian I of Denmark's ancestress Richeza of Denmark, Lady of Werle, the daughter of Eric V of Denmark, but Frederick also descended from Eric V's son Christopher II of Denmark whom no heir or monarch of Denmark had been descended from since Christopher III of Denmark. Frederik's paternal grandfather happened to have both grandfathers who were "Royal" dukes from the Oldenburg dynasty.

Frederick also differed from his rivals in his specific ancestry among the contemporary Danish high nobility. His mother was from an ancient Danish family (Danneskiold-Samsøe), and his paternal grandmother Louise Auguste of Denmark was its royal princess. His paternal grandfather Frederik Christian II, Duke of Augustenborg numbered two ladies of Danish high nobility as his grandmothers (Danneskiold-Samsøe and Reventlow), and one Danish Countess as paternal great-grandmother (Ahlefeldt-Langeland). Frederick's family had high hopes that in the then-rising era of nationalism, this ancestry would be viewed with favour when the legal question over whose claim was strongest would be decided. The family groomed Frederick to become a King of Denmark.

Unfortunately, Frederick, despite his more ethnically Danish ancestry was to become a symbol of German nationalism. Insider circles of Danish Royal government, for various reasons, were not favourable to the Augustenburgs. Instead, the Princess of Hesse and Prince of Glucksburg, closer relatives of the then royal family's core, were preferred. Prince Frederick's father became a protagonist in the 1848-1851 First Schleswig War, to the hostility of Danish nationalists.

Prince Frederick's inherited claims were strongest to the almost wholly German-speaking Duchy of Holstein, while his rights as the heir-male of the House of Oldenburg proved too difficult to pursue, and Holstein, an originally Holy Roman Empire fief, had the Salic Law as a leading principle in its fundamental succession law. Schleswig and Denmark, much more Scandinavian in legal history, had legal precedents for elective and female succession. Frederick and his father, however Danish they actually were, realised this and leant towards German interests.

Young Frederick's father found himself in an untenable position after the collapse of Prussian support and defeat of his own government at the end of the First Schleswig War in 1851. He renounced his claims as first in line to inherit the twin duchies in favour of the king of Denmark and his successors on 31 March 1852 in return for a financial compensation. The ducal family was banished. Frederick now became the symbol of the nationalist German independence movement in Schleswig-Holstein. The renunciation was a hurdle which was explained away by the Augustenburg dynasty and the German nationalists as not having any effect on Frederick, who had not personally renounced anything and on whose behalf no one, including the father, was empowered to make renunciations. Frederick's marriage in 1856 was part of an appeal to German nationalism (however, his younger brother married a daughter of Queen Victoria).

In November 1863 Frederick claimed the twin-duchies in succession after the death without a male heir of King Frederick VII of Denmark, who was also the Duke of Schleswig and Holstein. As Holstein was inherited after the salic law among descendants of Hedwig of Holstein, the independence movement had long nourished hopes that the king's death would lead to their goal. The Kingdom of Denmark was also under so-called Semi-Salic Law, but its male line ended with Frederick VII and Danish law contained a Semi-Salic provision which resulted in the election of Christian of Glücksburg as new monarch. German nationalists claimed that Schleswig was also inherited according to the unmodified Salic Law, but this claim was refused by the Danish government, arguing that this province was subject to Danish law.

Otto von Bismarck used the turbulence to invade the duchies in a Second War of Schleswig. The rule of Denmark in the duchies was terminated, and Frederick triumphantly entered Kiel, where he was eagerly welcomed. However, numerous political complications arose which prevented the formal reinstatement of the dynasty. By the terms of the Treaty of Vienna (October, 1864), the duchies were relinquished to Prussia and Austria, to be disposed of by them. Prussia, however, imposed conditions upon Frederick which made it impossible for him to assume the government. After the Peace of Prague, which terminated the Austro-Prussian War of 1866, the lands were finally absorbed into the Kingdom of Prussia.

Frederick subsequently served on the staff of the Crown Prince, Frederick William of Prussia, during the Franco-Prussian War of 1870-71. Frederick and his heirs continued to use their title, which after the next generation passed to the Glucksburg branch, to heirs of an elder brother of Christian IX of Denmark.

Marriage and children
On September 11, 1856 Frederick married Princess Adelheid of Hohenlohe-Langenburg, a German. She was the second daughter of Ernst Christian Carl IV, Duke of Hohenlohe-Langenburg and Princess Feodora of Leiningen, elder half-sister of Queen Victoria. They were parents to seven children:

 * 1) Prince Friedrich Wilhelm Victor Karl Ernst Christian August (August 3, 1857 – October 29, 1858).
 * 2) Princess Auguste Viktoria Friederike Luise Feodora Jenny (October 22, 1858 – April 11, 1921). Married Wilhelm II, German Emperor.
 * 3) Princess Victoria Friederike Augusta Maria Karoline Mathilde (January 25, 1860 – February 20, 1932). Married Friedrich Ferdinand, Duke of Schleswig-Holstein-Sonderburg-Glücksburg
 * 4) Prince Friedrich Viktor Leopold Christian Gerhard (January 20, 1862 – April 11, 1862).
 * 5) Ernst Günther II, Duke of Schleswig-Holstein-Sonderburg-Augustenburg, Duke of Schleswig-Holstein (August 11, 1863 – February 21, 1921).
 * 6) Princess Feodora Louise Sophie Adelheid Henriette Amalie (April 8, 1866 – April 28, 1952). Married Prince Friedrich Leopold of Prussia. He was a male-line great-grandson of Frederick William III of Prussia.
 * 7) Princess Feodora Adelheid Helene Luise Karoline Gustave Pauline Alice Jenny (July 3, 1874 – June 21, 1910).

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/


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Mikhl Gelbart

Mikhl Gelbart (August 21, 1889 – December 20, 1962) was an American composer of Yiddish songs. He was born in Ozorków, Poland. His music reflected a very American Yiddish motif, and was integral to the curricula of the Arbeter Ring (Workmen's Circle) schools and camps.

He died in New York of bone cancer.

title: Mikhl Gelbart


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Wrongdoing

A wrong or wrength (from Old English wrang – 'crooked') is an act that is illegal or immoral. Legal wrongs are usually quite clearly defined in the law of a state or jurisdiction. They can be divided into civil wrongs and crimes (or criminal offenses) in common law countries, while civil law countries tend to have some additional categories, such as contraventions.

Moral wrong is an underlying concept for legal wrong. Some moral wrongs are punishable by law, for example, rape or murder. Other moral wrongs have nothing to do with law but are related to unethical behaviours. On the other hand, some legal wrongs, such as many types of parking offences, could hardly be classified as moral wrongs.

Legal wrong
A violation of law is any act (or, less commonly, failure to act) that fails to abide by existing law. Violations generally include both crimes and civil wrongs. Some acts, such as fraud, can violate civil and criminal laws. In law, a wrong can be a legal injury, which is any damage resulting from a violation of a legal right. A legal wrong can also imply being contrary to the principles of justice or law. It means that something is contrary to conscience or morality and results in treating others unjustly. If the loss caused by a wrong is minor enough, there is no compensation, which principle is known as de minimis non curat lex. Otherwise, damages apply.

The law of England recognised the concept of a "wrong" before it recognised the distinction between civil wrongs (governed by civil law) and crimes (defined by criminal law), which distinction was developed during the thirteenth century.

Civil law violations usually lead to civil penalties like fines, criminal offenses to more severe punishments.

The severity of the punishment should reflect the severity of the violation (retributive justice). In realistic situations and for minor violations, however, altruistic punishment was shown not 'to fit the crime'. This subdivision is similar to the distinction between misdemeanours, and felonies.

Other examples of violations of the law include:

 * Infraction, in United States law, minor or petty offenses that do not require jury trial. In common usage, "violations" are treated as synonymous with infractions
 * Willful violation, in U.S. law, an act with intentional disregard for a regulation, statute, and policy
 * Infringement, various violations of laws or rights, usually used in the context of intellectual property
 * e.g. copyright violation
 * Breach of contract
 * Probation violation
 * against traffic rules
 * Moving violation, any violation of law committed by a driver while the vehicle is in motion
 * Parking violation, parking a motor vehicle in a restricted place or an unauthorized manner

title: Wrongdoing


text:
Lappi cheese

Lappi is a cheese made from partially skimmed cow's milk, very similar to Emmental except that it is pasteurized, and so is a little less flavorful, with smaller holes and a slightly firmer texture. It is so named because its recipe was developed in the Lapland region of Finland.

title: Lappi cheese


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Naval Communication Station Harold E. Holt

Naval Communication Station Harold E. Holt is a joint Australian and United States naval communication station located on the north-west coast of Australia, 6 km north of the town of Exmouth, Western Australia. The station is operated and maintained by the Australian Department of Defence on behalf of Australia and the United States and provides very low frequency (VLF) radio transmission to United States Navy, Royal Australian Navy and allied ships and submarines in the western Pacific Ocean and eastern Indian Ocean. The frequency is 19.8 kHz. With a transmission power of 1 megawatt, it is claimed to be the most powerful transmission station in the Southern Hemisphere.

The town of Exmouth was built at the same time as the communications station to provide support to the base and to house dependent families of US Navy personnel.

VLF transmitter masts
The station features thirteen tall radio towers. The tallest tower is called Tower Zero and is 387.4 m tall, and was for many years the tallest man-made structure in the Southern Hemisphere. Six odd numbered outer towers T1-T11, located on an outer ring, each 358 m tall, are placed in a hexagon around Tower Zero. The other six even numbered inner towers T2-T12, which are each 303.6 m tall, are placed in a smaller hexagon around Tower Zero.

On 3 March 2009, the Defence Materiel Organisation advertised on the AusTender website a tender to construct two new roads at the station. The tender stated the 357 guy wires which support the 13 towers had exceeded their life expectancy and the roads will support the installation of the VLF guy wires. It states: "Naval Communication Station Harold E Holt (NCSHEH) is sited on the northernmost tip of the peninsula known as North West Cape. The Very Low Frequency (VLF) antennas are large spider webs of wire supported in a top hat arrangement. The centre tower 'Tower Zero', rises to a height of 387.4 metres. The other towers are spread out in two concentric rings around Tower Zero; the towers of the inner ring are 303.5 metres high while those of the outer ring are 358. Buried in the ground beneath the antenna array is 386 kilometres of bare copper ground mat."

- Defence Materiel Organisation

History
Sir Garfield Barwick, Australian Minister for External Affairs, negotiated the lease on the US Base at North West Cape in 1963 with US Ambassador William Battle. The station was commissioned as U.S. Naval Communication Station North West Cape on 16 September 1967 at a ceremony with the US Ambassador to Australia Edward A. Clark and the Prime Minister of Australia Harold Holt, at which peppercorn rent for the base for the first year was paid.

On 20 September 1968, the station was officially renamed to US Naval Communication Station Harold E. Holt in memory of the late Prime Minister of Australia, who disappeared whilst swimming and was declared dead, presumed drowned, three months after the station was commissioned.

With the election of the Labor Government to power in 1972, Defence Minister Lance Barnard started negotiations on the condition of operation of the US military bases in Australia. On 9 January 1974 a joint statement by Lance Barnard and James Schlesinger, the US Secretary of Defense, assigned the Deputy Commander of the base to a Royal Australian Navy officer and gave Australian personnel roles in base technical and maintenance functions. The cipher room was closed to Australian scrutiny. The joint statement stressed the importance of consultations in crises. There was no undertaking given by the US to relay fire orders to their submarines bearing nuclear missiles.

In May 1974 several hundred people travelled to North West Cape from around Australia to protest and occupy the base and "symbolically reclaiming it for the Australian people". During the occupation the Eureka Flag was flown over the base with fifty-five people arrested during the protest. Songs composed in the campaign against North West Cape and other US bases in Australia include We don't want no Yankee Bases and Omega Doodle which have become part of the Australian folkloric tradition. From 1967 until October 1992 a USN Naval Security Group Detachment was stationed at the facility.

In Western Australian domestic politics, the presence of foreign military installations in the state has occasionally been questioned over the decades. The "U.S." was dropped from the station's official title with the advent of joint United States and Royal Australian Navy operation in 1974. In 1991, an agreement was reached between the governments of Australia and the United States that would make the facility an Australian Naval Communication Station by 1999, a transition that began with a Royal Australian Navy officer taking command of the facility in 1992. The majority of US Naval presence ended in 1993 with the withdrawal of all US Naval personnel.

In July 2002, the Royal Australian Navy handed over operation of the station to the Defence Materiel Organisation. The base is currently operated under contract by Raytheon Australia. On 15 July 2008, Australia and the US signed a bilateral treaty governing the future joint use of the facility for the next 25 years.

Harold E. Holt was identified as a potential Air Force Space Surveillance System (or Space Fence) site in 2011. On 6 December 2013 it was announced that the Space Surveillance Telescope (SST), part of the United States Space Surveillance Network, will be relocated to the Harold E. Holt Naval Communication Station from its initial deployment at the White Sands Missile Range in New Mexico. The SST is expected to be fully operational in 2022.

A C-Band Space Surveillance Radar is also being installed and once completed will be operated remotely by Royal Australian Air Force personnel from No. 1 Remote Sensor Unit at RAAF Base Edinburgh. It will provide a Space Situational Awareness capability, allowing the tracking of space assets and debris.

Aircraft interference controversy
On 7 October 2008, Qantas Flight 72 made an emergency landing at Learmonth airport near the town of Exmouth, Western Australia following an inflight accident featuring a pair of sudden uncommanded pitch-down manoeuvres that resulted in serious injuries to many of the occupants. The Australian Transport Safety Bureau (ATSB) identified in a preliminary report that a fault occurred within the Number 1 Air Data Inertial Reference Unit (ADIRU) and is the "likely origin of the event". The ADIRU – one of three such devices on the aircraft – began to supply incorrect data to the other aircraft systems. The ATSB assessment of speculation that possible interference from Naval Communication Station Harold E. Holt or passenger personal electronic devices could have been involved was "extremely unlikely".

On 27 December 2008, another aircraft, Qantas Flight 71, also had a malfunction in its ADIRU. The incident again fuelled media speculation regarding the significance of the Harold E. Holt facility, with the Australian and International Pilots Association calling for commercial aircraft to be barred from the area as a precaution until the events are better understood, while the manager of the facility has claimed that it is "highly, highly unlikely" that any interference has been caused.


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Brendan Smyth

Brendan Smyth O.Praem (8 June 1927 – 22 August 1997) was a Catholic priest and convicted sex offender from Belfast, Northern Ireland, who became notorious as a child molester, using his position in the Catholic Church to obtain access to his victims. During a period of over 40 years, Smyth sexually abused and indecently assaulted at least 143 children in parishes in Belfast, Dublin and the United States. His actions were frequently hidden from police and the public by Roman Catholic officials. Controversy surrounding his case contributed to the downfall of the government of Republic of Ireland in December 1994.

Early life and ordination
Born John Gerard Smyth, in Belfast, Northern Ireland, Smyth, upon joining the Norbertine Roman Catholic religious order in 1945, changed his name to Brendan. The Norbertines, also known as the "Premonstratensians," were aware of Smyth's crimes as early as the late 1970s, yet they did not report him to either the Garda Síochána or the Royal Ulster Constabulary. Smyth was moved from parish to parish and between dioceses and countries whenever allegations were made. In some cases, the order did not inform the diocesan bishop that Smyth had a history of sexual abuse and should be kept away from children. He abused children in parishes in Rhode Island and North Dakota and at one time worked in Boston, and was suspected of similar actions while on pastoral work in Wales and Italy. Norbertine Father Bruno Mulvihill made several attempts to alert church authorities about the abuse committed by Smyth.

1994 arrest
Smyth's first conviction followed the reporting to police of his abuse of four siblings in Belfast's Falls Road. After his arrest in 1991, he fled to the Republic of Ireland, where he spent the next three years on the run, staying mostly at Kilnacrott Abbey. This led to the collapse of the Fianna Fáil–Labour Party coalition government in December 1994 when the poor handling of an extradition request from the RUC by the Irish Attorney General's office led to a further delay of Smyth's trial. An award-winning UTV Counterpoint programme on the scandal by journalist Chris Moore, followed by a book, accused the head of the Norbertines and the Archbishop of Armagh of mishandling the case, and the Norbertines of negligence and a failure to tell others of Smyth's crimes, enabling Smyth to sexually abuse large numbers of children for 40 years.

Death
Smyth died at 70 in prison of a heart attack in 1997 after collapsing in the exercise yard, one month into a 12-year prison sentence. The Norbertines held his funeral before dawn and covered his grave with concrete to deter vandalism. Smyth was buried in Kilnacrott Abbey, which was later put up for sale with 44 acres of land, including the grave.

On 27 October 2005 the title "Reverend" was removed from his gravestone following a campaign by one of Smyth's victims.

Later investigations
Reviewers of the case differ as to whether there was a deliberate plot to conceal Smyth's behaviour, incompetence by his superiors at Kilnacrott Abbey, or some combination of factors. Cahal Daly, both as Bishop of Down and Connor, a diocese where some of the abuse took place, and later as Cardinal Archbishop of Armagh, is recorded as having been privately furious at the Norbertine "incompetence". Smyth's activities were investigated by the Northern Ireland Historical Institutional Abuse Inquiry, finding that: "..despite knowing his history of abusing children, the Norbertine religious order moved Smyth to different dioceses where he abused more children.."

In 2010, Daly's successor as Roman Catholic Archbishop of Armagh, Cardinal Seán Brady, faced "huge pressure to resign" after he admitted that in 1975 he witnessed two teenage boys sign oaths of silence after testifying in a Church inquiry against Smyth. Survivors groups saw this as evidence of collusion, but Brady said he "did not have the authority" to turn Smyth in. On 17 March 2010, the Deputy First Minister for Northern Ireland, Martin McGuinness, called for Brady to resign.

In 2013, some of Smyth's alleged Rhode Island victims between 1965 and 1968, both male and female, called for the Diocese of Providence to investigate Smyth. As of 2019, Smyth is among those listed by the Diocese of Providence as being "credibly accused" of committing sex abuse.

Module 6 of the 2014-2016 Northern Ireland Historical Institutional Abuse Inquiry is dedicated to Smyth's crimes in Northern Ireland.

Dramatisation
A two-part dramatisation of the Smyth case, Brendan Smyth: Betrayal of Trust, was broadcast by the BBC on 13 March 2011 with Ian Beattie in the title role and Richard Dormer as Chris Moore.

title: Brendan Smyth


text:
Time-scale calculus

In mathematics, time-scale calculus is a unification of the theory of difference equations with that of differential equations, unifying integral and differential calculus with the calculus of finite differences, offering a formalism for studying hybrid systems. It has applications in any field that requires simultaneous modelling of discrete and continuous data. It gives a new definition of a derivative such that if one differentiates a function defined on the real numbers then the definition is equivalent to standard differentiation, but if one uses a function defined on the integers then it is equivalent to the forward difference operator.

History
Time-scale calculus was introduced in 1988 by the German mathematician Stefan Hilger. However, similar ideas have been used before and go back at least to the introduction of the Riemann–Stieltjes integral, which unifies sums and integrals.

Dynamic equations
Many results concerning differential equations carry over quite easily to corresponding results for difference equations, while other results seem to be completely different from their continuous counterparts. The study of dynamic equations on time scales reveals such discrepancies, and helps avoid proving results twice—once for differential equations and once again for difference equations. The general idea is to prove a result for a dynamic equation where the domain of the unknown function is a so-called time scale (also known as a time-set), which may be an arbitrary closed subset of the reals. In this way, results apply not only to the set of real numbers or set of integers but to more general time scales such as a Cantor set.

The three most popular examples of calculus on time scales are differential calculus, difference calculus, and quantum calculus. Dynamic equations on a time scale have a potential for applications such as in population dynamics. For example, they can model insect populations that evolve continuously while in season, die out in winter while their eggs are incubating or dormant, and then hatch in a new season, giving rise to a non-overlapping population.

Formal definitions
A time scale (or measure chain) is a closed subset of the real line $$\mathbb{R}$$. The common notation for a general time scale is $$\mathbb{T}$$.

The two most commonly encountered examples of time scales are the real numbers $$\mathbb{R}$$ and the discrete time scale $$h\mathbb{Z}$$.

A single point in a time scale is defined as:
 * $$t:t\in\mathbb{T}$$

Operations on time scales
The forward jump and backward jump operators represent the closest point in the time scale on the right and left of a given point $$t$$, respectively. Formally:

 * $$\sigma(t) = \inf\{s \in \mathbb{T} : s>t\}$$ (forward shift/jump operator)
 * $$\rho(t) = \sup\{s \in \mathbb{T} : s t$$
 * dense if both left dense and right dense
 * isolated if both left scattered and right scattered

As illustrated by the figure at right:
 * Point $$t_1$$ is dense
 * Point $$t_2$$ is left dense and right scattered
 * Point $$t_3$$ is isolated
 * Point $$t_4$$ is left scattered and right dense

Continuity
Continuity of a time scale is redefined as equivalent to density. A time scale is said to be right-continuous at point $$t$$ if it is right dense at point $$t$$. Similarly, a time scale is said to be left-continuous at point $$t$$ if it is left dense at point $$t$$.

Derivative
Take a function:
 * $$f: \mathbb{T} \to \R,$$

(where R could be any Banach space, but is set to the real line for simplicity).

Definition: The delta derivative (also Hilger derivative) $$f^{\Delta}(t)$$ exists if and only if:

For every $$\varepsilon > 0$$ there exists a neighborhood $$U$$ of $$t$$ such that:
 * $$\left|f(\sigma(t))-f(s)- f^{\Delta}(t)(\sigma(t)-s)\right| \le \varepsilon\left|\sigma(t)-s\right|$$

for all $$s$$ in $$U$$.

Take $$\mathbb{T} =\mathbb{R}.$$ Then $$\sigma(t) = t$$, $$\mu(t) = 0$$, $$f^{\Delta} = f'$$; is the derivative used in standard calculus. If $$\mathbb{T} = \mathbb{Z}$$ (the integers), $$\sigma(t) = t + 1$$, $$\mu(t)=1$$, $$f^{\Delta} = \Delta f$$ is the forward difference operator used in difference equations.

Integration
The delta integral is defined as the antiderivative with respect to the delta derivative. If $$F(t)$$ has a continuous derivative $$f(t)=F^\Delta(t)$$ one sets

 * $$\int_r^s f(t) \Delta(t) = F(s) - F(r).$$

Laplace transform and z-transform
A Laplace transform can be defined for functions on time scales, which uses the same table of transforms for any arbitrary time scale. This transform can be used to solve dynamic equations on time scales. If the time scale is the non-negative integers then the transform is equal to a modified Z-transform: $$\mathcal{Z}'\{x[z]\} = \frac{\mathcal{Z}\{x[z+1]\}}{z+1}$$

Partial differentiation
Partial differential equations and partial difference equations are unified as partial dynamic equations on time scales.

Multiple integration
Multiple integration on time scales is treated in Bohner (2005).

Stochastic dynamic equations on time scales
Stochastic differential equations and stochastic difference equations can be generalized to stochastic dynamic equations on time scales.

Measure theory on time scales
Associated with every time scale is a natural measure defined via

 * $$\mu^\Delta(A) = \lambda(\rho^{-1}(A)),$$

where $$\lambda$$ denotes Lebesgue measure and $$\rho$$ is the backward shift operator defined on $$\mathbb{R}$$. The delta integral turns out to be the usual Lebesgue–Stieltjes integral with respect to this measure

 * $$\int_r^s f(t) \Delta t = \int_{[r,s)} f(t) d\mu^\Delta(t)$$

and the delta derivative turns out to be the Radon–Nikodym derivative with respect to this measure

 * $$f^\Delta(t) = \frac{df}{d\mu^\Delta}(t).$$

Distributions on time scales
The Dirac delta and Kronecker delta are unified on time scales as the Hilger delta:

 * $$\delta_{a}^{\mathbb{H}}(t) = \begin{cases}

\dfrac{1}{\mu(a)}, & t = a \\ 0, & t \neq a \end{cases}$$

Fractional calculus on time scales
Fractional calculus on time scales is treated in Bastos, Mozyrska, and Torres.

title: Time-scale calculus


text:
Talk:Bernard Francis Law

Tricking the Massachusetts Legislature
Nowhere does this article mention one of Law's dirtiest moves: tricking the Massachusetts House of Delegates into passing a law which shielded him from prosecution. [] In the 1990's, Law pushed a law which would shield confessors from being prosecuted for keeping secret the content of confessions. The Mass. legislature, which was dominated by Roman Catholics, went along compliantly with this law. There was some discussion at the time as to whether it was right for a priest not to tell anyone about a confession of murder, but by Catholic Logic™ it seemed better to leave open the chance to save souls than worry about the needs of the fuzz. However, the key point is that at the same time the legislature was passing laws that made it illegal for teachers not to report signs of child abuse to the authorities. Law saw this and knew he had to cover himself because he was well aware at this time of the pedophile priests and had chosen to pay hush money to families and shielded them from civil authorities. If things continued the way they had been going this would soon become a crime! So, as a "confessor", Law gets immunity from these laws. In 2002 when everything came out, the Mass. Delegates expressed rage at their betrayal by the archbishop and the RCC influence on that body dropped precipitously. (See any number of contemporary Boston Globe articles.) Despite shrill condemnations from the RCC authorities, the Mass. House of Delegates not only upheld the legalization of same-sex marriage in 2005 but scuttled early attempts at plebiscites to ban it, judging correctly that given enough time, popular opinion would swing to its favor.

Whatever Law did to hide priests, this single action exposes the degree of his KNOWING CULPABILITY IN CRIMES AGAINST CHILDREN. Furthermore, it is at a late date (not "it was the 60's, we didn't know any better"). Please do not let this sink into the memory hole. 98.180.8.57 (talk) 18:39, 27 April 2010 (UTC)

USAF in 1931?
The Air Force didn't exist until 1947. I suppose the author meant US Army Air Corps. If that's true, it should be changed.

There was a Torrejon Air Force Base in Spain not Mexico from the 1950s till about 1990. But it was impossible for him to be born there in 1931. There has never been a US Air Force Base in Mexico. —Preceding unsigned comment added by 144.183.31.2 (talk) 14:50, 6 August 2010 (UTC)

Protests during Pope's funeral masses
"Joseph Cardinal Ratzinger gave Cardinal Law the honor of celebrating one of nine official Vatican masses during the nine official days of mourning."

I think it should be noted in the article that there were protests over having Law oversee the mass because of his association w/ the church sex abuse scandals. This was percieved by victims of abuse by priests, and their families, as a demonstration of insensitivity towards the victims. It may have been only a few people demonstrating, but I think it's notable that the Vatican chose this guy honor the pope after shaming the church (kinda makes you wonder if the Vatican really faulted him for his practice of relocating molestors and not notifying authorities or if the Vatican thought he'd done the right thing and this was a 'reward' for his service) and not everyone was happy with that.

 * The statement is somewhat inaccurate. As the archpriest of whatever major basilica, Cardinal Law would traditionally be one of the people to preside at one of the formal funeral Masses for a pope. The issue isn't that then Cardinal Ratzinger gave Law the honor of presiding at Mass, but that his ceremonial function wasn't taken away. Lets remember that he was appointed archpriest to remove him from any actual position of authority in the Church, as it is a mostly ceremonial function with not much more responsibility than a local parish pastor. However, when the time comes for ceremonies at the major basilicas (like papal funerals), the little position suddenly is thrust into the spotlight. Gentgeen 20:38, 16 February 2006 (UTC)

 * So he was given a cushy sinecure in Rome, which "kinda makes you wonder if the Vatican really faulted him for his practice of relocating molestors and not notifying authorities or if the Vatican thought he'd done the right thing and this was a 'reward' for his service". Jhobson1 18:51, 20 September 2007 (UTC)

Name Issues
His full name may be Bernard Cardinal Law but he is much better known simply as Cardinal Law. --mav 03:53 24 Jul 2003 (UTC)
 * Our policy is to use the format [{first name if known} Cardinal {surname}]. See Naming conventions (names and titles) - Efghij 03:57 24 Jul 2003 (UTC)
 * Brain fart - I stand corrected. I'll fix. --mav

Vanadlism
Some one has deleted the entire section on the abuse scandal, can we get this back?

Law in Rome
It is incorrect to say Cardinal Law is a member of the Curia. He is not. Further, it is in accurate to say that the curia governs the Church -- neither it nor its members do. Rather the curia is a pastoral tool of the Pope.217.221.184.119 21:03, 6 June 2006 (UTC)

 * A pastoral tool that is used to govern the Church. Jhobson1 18:49, 20 September 2007 (UTC)

 * I don't know that "govern" properly conveys what it does. What, exactly, is involved in governing the Church?  Perhaps a better word can be found?   —Preceding unsigned comment added by MikeNM (talk) 01:36, 8 April 2010 (UTC)

Vandalism undetected since Oct 19, 2005
On that day User: Pitchka, now known as User: Dwain. inserted an illustration of the coat of arms of the College of Law of Adamson University (Manila), with the caption "Bernard Cardinal Law". How childish! How outrageous that this vandalism has not been corrected for more than 11 months! I shall delete this crap immediately. Too Old 04:54, 25 September 2006 (UTC)
 * An extreme reaction...Dunfermline Scholar (talk) 01:06, 3 January 2008 (UTC)

Article Overly Favorable
The article refers to Mr. Law as being "hounded" by the scandal. This casts his opponents into an unnecessarily unfavorable light. Mr. Law is a disgrace.

130.13.2.104 12:29, 15 November 2007 (UTC)John Paul Parks130.13.2.104 12:29, 15 November 2007 (UTC)

 * Does it really help the neutrality of the Article to edit it to make Cardinal Law sound like a disgrace? He might be one, but wiki readers should decide that for themselves.  —Preceding unsigned comment added by MikeNM (talk • contribs) 01:37, 8 April 2010 (UTC)

Law is a paedophile or not?
It is not clear from the article if Bernard Law is an active paedophile or not. Moreover, as a protector of paedophiles, did he protected other paedophile priests, except those mentioned in the Boston sex abuse scandal? Does the Catholic Church still promote paedophile comportaments among his priests or this practice is currently on hold? Definitely, this article needs more detail informations and disambiguations. —Preceding unsigned comment added by Transsylvanian (talk • contribs) 07:13, 12 January 2008 (UTC)

Bernard Law was never accused of being a paedophile himself. He secretly moved paedophile priests around to unsuspecting Churches, and thereby exposing defenceless children to the dangers of these men.--Splashen (talk) 20:41, 18 June 2016 (UTC)

bad wording
"His father, a career Air Force officer, was stationed at the Torreón United States Air Force base, making Bernard a so-called 'military brat'." His father's being stationed at the Torreon USAF base did not make Law a military brat. Also, the scare-quotes and the phrase "so-called" should not both be used; to do so is redundant. —Preceding unsigned comment added by 139.68.134.1 (talk) 19:44, 20 August 2008 (UTC)
 * I believe that when you move around a lot in childhood because your father is in the military, as Law (apparently?) did, that does, in fact, make you a "military brat". That's what that term means. It's not a value judgment. The article, I notice, currently makes no effort to explain anything about Law's family background or why he moved around so much as a child. Surely we can find and source something to make this clear? john k (talk) 22:04, 29 December 2015 (UTC)

Scandal in Boston
Part of this article might deserve to be split in an different article on the Boston chapter of the sex abuse affairs, in a subset to the article Catholic sex abuse cases. Similar forking could also be done for the Los Angeles diocese, with relevant content being on the Roger Mahony article. The reason that I am proposing a fork is that I always felt that it was inappropriate to blame all the sex abuse cases on just a few bishops, since individual priests are theoretically responsible for their actions, and that there is a general and institutional American sex culture that is unlike anywhere else on Earth. I also feel that it is un-Christian for the laity to refuse to acknowledge its part in the affairs, given that reconciliation and sin are major aspects of Church teaching. ADM (talk) 00:49, 26 March 2009 (UTC)

From above: "...there is a general and institutional American sex culture that is unlike anywhere else on Earth." HUH? I think we need a citation on that! Not sure where that opinion comes from, but much of Western Europe and Canada have a 'sex culture' much like the US (except - IN MY OPINION - they are somewhat less puritanical and hypocritical about sex than the US). William Malmstrom 24.92.217.175 (talk) 19:28, 27 March 2010 (UTC)

In the Sex Abuse Scandal section it says "...a situation furthered by Law's intransigence in not naming priests that he aided with their molestation." I'm changing this. However horribly one might believe Cardinal Law dealt with the sex abuse cases, saying he "aided [them] with their molestation" is taking things too far. "intransigence" itself is a loaded word. MikeNM (talk) 01:46, 8 April 2010 (UTC)

Biography
Early Life

Please be kind - this is my first real entry on Wikipedia. I don't have the experience to edit the page, but I noticed what may be an error.

The article states that Cardinal Law was born in 1931, in Torreón, Mexico, and that his father was "a career Air Force officer was stationed at the Torreón United States Air Force base, making Bernard a so-called "military brat". I have seen this referenced even on the Vatican website.

Two things: First, the United States Air Force was created in 1947; its predecessors were the US Army Air Corps (1926-1941) and then the US Army Air Forces (1941-1947). This does not negate the possibility that Cardinal Law's father was "a career Air Force Officer", as the father may have completed his career after the transition to the United States Air Force (post-'47); but at the time of his birth, his father would have been a "career US Army officer assigned to the US Army Air Corps".

Second, I have doubts that the birth place is incorrect - to the best of my knowledge, the Torreón referenced in the article should not be the city in Mexico but the air base in Madrid, Spain, collocated with what is today Madrid-Torreón Airport. The web references to Cardinal Law's bio appear to be circular, given the same wording used over and over. I have yet to find supporting references to his birth being in Spain vice Mexico, but because of the airbase in Madrid-Torreón, the far most likely birthplace is Spain. If someone can provide a reliable citation, that would help. NewHampshireMatt (talk) 09:35, 11 April 2009 (UTC)

Restoration of text on sexual abuse cases
It has come to my attention that User:ADM has eviscerated the articles on Bernard Law and Roger Mahony, moving out practically all the text regarding the sexual abuse cases. I grant that some of the material may need to be trimmed out but I believe that the reduction has been too drastic and does not provide adequate treatment of the single reason why these men are notable outside the Catholic Church. It is unfortunate that a single incident which is not entirely their fault should overshadow their careers but that's what happened and that's what Wikipedia should report, our own personal feelings notwithstanding. I have reverted to the revision prior to ADM's edits. I'm open to trimming the section on sexual abuse cases; however, moving most of the text out of this article is, IMO, inappropriate. --Richard (talk) 15:42, 2 July 2009 (UTC)

 * Regarding Roger Mahony and Bernard Law, the reason some information was removed was because I decided to put it in sexual abuse scandal in Boston archdiocese and sexual abuse scandal in Los Angeles archdiocese. I guess the reason I did that was because I'm not sure Law or Mahony were in full control of their respective dioceses when the scandals occured, and that it was more of a diocesan scandal than an episcopal scandal, even though it arguably involved both. Also, I feel that the articles about the affairs should be broader in scope than the mere biographical material on certain bishops, and that vice-versa the articles about the bishops should not only talk about the scandals. ADM (talk) 11:59, 5 July 2009 (UTC)

 * I still disagree with ADM. I believe the topic deserves more coverage here than the little stub that ADM left behind. However, there was a bunch of unnecessary detail that was creating an imbalance in the article so I deleted it.  The deleted text is still in the article on sexual abuse scandal in Boston archdiocese. --Richard (talk) 15:12, 5 July 2009 (UTC)

 * I lived in Boston during the entire time of Law's cardinalship. It was both an episcopal AND and a diocesan scandal. It was well known that sex abuse went back to the time of the 1950's or earlier, including abuse of seminarians under Cardinal Cushing. Law inherited the situation; what is relevant is how he dealt with it. And he dealt with it by covering it up. He went around in public proclaiming the most orthodox position considered acceptable at the time (and the Vatican repaid him for that, indeed), banned female altar servers (even though other American congregations had them) banned female laity in services at his own cathedral and demanded shows of fealty from politicians and humility from those who would approach him. Most of the priests in the archdiocese were afraid of him. They literally would avoid certain topics of conversation--even in the confessional!--for fear that one of the Cardinal's spies would report an unorthodox utterance.

 * Law induced the legislature to pass a law (under false pretenses, of course) which granted him immunity from prosecution for his actions to shield pedophile priests from prosecution. These efforts (to protect the reputation of the Church) ultimately failed, but the law he had passed covered him long enough to flee to the safety of the Vatican when things got too hot for him in Boston.

 * Law loved the adulation of the people and the great loyalty the Irish Catholics had for the RCC. He abused this trust to the utmost. He spent his Cardinalship being quite harsh with the people and in the end, showed that he considered himself to be a special creation, not subject to their laws. When people call him despicable, they do not simply refer to the fact that he happened to be the sitting archbishop when the scandal broke. There seems to be an attempt here to protect the person of Law and shove his role down the memory hole. This is attempt to erase his role as an active participant. There is no evidence that he is a pedophile--although there is ample evidence of his misogyny. Yet he thought that protecting the reputation of the church, as well as protecting himself, was more important, by far, than protecting innocent children. For that reason his name will always be an evil one. 98.180.8.57 (talk) 18:39, 27 April 2010 (UTC)

Masonic conspiracies
From what I can tell, Cardinal Law did believe in Masonic conspiracy theories and certainly felt that Masons were a threat to Christianity and the civil State (cf Letter to U.S. Bishops Concerning Masonry). It would be interesting if anyone could find out if he has ever received any kind of negative backlash from the Masons because of his condemnation of their associations. I know it's a stretch to say this, but there is a good chance that many Masonic groups in the U.S. were happy that he was forced to resign, and they may even have encouraged this through their secretive influence in the wider culture. ADM (talk) 14:57, 21 July 2009 (UTC)
 * You're nuts. The Masons are so broke they had to give up their buildings. And AFAIC they aren't registered as a religious organization to the IRS, so not only are they not a religion, they don't play one on TV either. 98.180.8.57 (talk) 18:39, 27 April 2010 (UTC)

Civil Rights activism
So far, the only evidence that Law was involved with Civil rights comes from the Church itself. It seems like an awfully self-serving attempt at whitewashing its own role during the civil rights movement. The sources from the Boston Globe and the Church's own newsletters are all the same. Absent third-party evidence, this seems like awfully thin evidence - especially given the more obvious proof that occurs later in Law's career, that the Church was willing to lie about the past in order to cover up its own abuses. Those who know Law or knew those he victimized know he never marched for civil rights nor did he perform any significant part in the movement. The Church cannot be the only soruce that provides evidence that he did. —Preceding unsigned comment added by DeanArrest (talk • contribs) 05:09, 6 March 2010 (UTC)
 * Please, reconsider what you have written. Just because it has the word "Catholic" in its title, do you really distrust everything that appears in a magazine (not a newsletter) such as the National Catholic Reporter?  Are you really saying that Gill Donovan may have been lying when quoting Charles Evers's praise of his fellow-activist Law?  Indeed, are you perhaps thereby diffaming that journalist?  Do you think that the Boston Globe made a crass error in stating that as a young priest Law "takes an activist role in support of civil rights, joining the Mississippi Leadership Conference and the Mississippi Human Relations Council. His views on civil rights expressed as editor of the Natchez-Jackson diocesan newspaper lead to threats on his life"?  There seems to be no valid reason for wiping all this off the record.  The accounts of Law's civil rights activities go back long before the abuse scandal that engulfed him; so there was no reason whatever for you to speak of "an awfully self-serving attempt at whitewashing".  Esoglou (talk) 10:32, 6 March 2010 (UTC)
 * The Boston Globe is considered a hostile source by many Catholics, so, if anything, they would have a bias against Law. Remember, the Globe broke the pedophile priest scandal. They are the paper of the wealthy 'burbs which are more Protestant than Catholic. 98.180.8.57 (talk) 18:39, 27 April 2010 (UTC)
 * 1. The claim that "the only evidence that Law was involved with Civil rights comes from the Church itself" is not only completely false but is emblematic of the rampant anti-Catholic bigotry on Wikipedia. Charles Evers, brother of Medgar Evers: "We feel that Father Law is not just a priest; he's a great humanitarian. If it had not been for Father Law, our problems wouldn't be as far along in being solved as they are. He has done it not for the Negro, but for justice and what is right" 2. The Boston Globe did not break the pedophile priest scandal. The issue had been reported for years before 2002! Steakpeak (talk) 16:28, 18 September 2016 (UTC)

Bad faith editing on this page
Articles on Wikipedia should be edited by those with actual knowledge of the subject, not hijacked by those with an ugly agenda. The second paragraph contains the false and sinister claim that "church documents showed [Law] had covered up sexual abuse." In truth, the documents showed no such thing. The documents only show that Law had knowledge of the abuse.

The line that "Law orchestrated secret settlements for abuse claims made against at least seventy of his priests" is utterly false, as it was the victims and their tort lawyers who demanded the secrecy. Even the Boston Globe has acknowledged this. Don't believe it? Read this: http://archive.boston.com/globe/spotlight/abuse/stories2/060302_lawyers.htm.

The line that "One priest alone was revealed to have raped or molested 130 children for decades while Law and other local officials moved him among churches rather than going to the authorities" is false on many level. While it is true that the Church paid out settlements for 130 individuals, there were no extensive investigations into the vast majority of the accusations, and it is certain to those with close knowledge of the Geoghan case - not those with an agenda to advance - that many, many of those cases are false.

If Wikipedia has anything to do with truth and honesty, my changes will be honored.

Enough with the anti-Catholic bigotry, agenda-driven editing, and the passive aggressive attacks, please!! Steakpeak (talk) 16:28, 18 September 2016 (UTC)

 * I will also add that Wikipedia articles are supposed to represent impartial fact, not personal ideologies and agendas. See [Help:Introduction]. Steakpeak (talk) 16:44, 18 September 2016 (UTC)

"Law orchestrated secret settlements"
The Boston Globe article cited above mentions the church's reluctance to settle cases without confidentiality clauses. It mentions that in some cases it was the victims who insisted on accepting confidentiality deals required by the church. It quotes a plaintiff lawyer as saying that, By requiring confidentiality, he said, "the church overwhelms lawyers and survivors into silence and secrecy". This obviously does not contradict the other sources which say that it was the church that required the confidentiality deals, and the plaintiff lawyers merely agreed to those demands in some cases, rightly or wrongly. MPS1992 (talk) 18:08, 18 September 2016 (UTC)

 * There is no basis in fact for Jeff Anderson's remark. He even makes my case by admitting he's never settled an agreement with secrecy! And I could go on for days how Jeff Anderson is not even close to being a reliable source when speaking about the abuse story. []

 * It is clear that tort lawyers have an agenda and a desire to change history about the secrecy they demanded in the past. So let's turn to a more impartial source and the experience of Patrick J. Schiltz, the U.S. District Court judge who says he has had experience dealing with over 500 cases involving abuse in the Catholic Church and other Christian denominations.

 * Here is Judge Schiltz on so-called "secret settlements":

 * "'Finally, a few words about 'secret settlements.' Here is the story that we have all heard many times: When churches would pay settlements to victims, we are told, churches would insist on secrecy agreements, prohibiting victims from disclosing any details of their abuse, saving churches from embarrassing publicity and, in some cases, allowing pastors to go on abusing. Many media outlets have run such stories, often carrying quotations from plaintiffs' attorneys condemning this practice, and sometimes featuring victims who, after being paid to keep quiet, broke their word and essentially dared the church to try to take back its money."
 * "'In the fifteen years I have been advising churches, I have always considered these secrecy agreements to be worse than useless. As far as I can remember, I never asked for one (although my clients were on a few occasions parties to secrecy agreements that had been requested by others). That said, let me make three points about secrecy agreements."
 * "'First, in many cases - perhaps a majority of cases - it was the victim who asked for the secrecy agreement. There is a reason why victims often sue as 'Jane Doe' or 'John Doe' and often seek protective orders from courts. Victims are understandably concerned to protect their privacy. That concern does not go away when the case is settled."
 * "'Second, even when it was the church that asked for a secrecy agreement, in the vast majority of cases that agreement extended only to the amount of the settlement. I have been involved in hundreds of settlements, and I literally cannot recall one that required the victim not to talk about his or her abuse. Such clauses are uncommon."
 * "'Finally, even with respect to these uncommon clauses - that is, clauses insisted upon by churches that required victims to remain silent about their abuse - what happened to the other half of the story? If it was wrong for defense attorneys to buy secrecy, why was it not wrong for plaintiffs' attorneys to sell it?"
 * "'After all, it was plaintiffs' lawyers who would sometimes call church attorneys and say that, unless they were paid an outrageous amount, they would file a complaint against the church and call a press conference to publicize it. It was plaintiffs' lawyers who would sometimes make two settlement demands - a lower demand that did not include a secrecy agreement and a higher demand that did. It was plaintiffs' lawyers who would happily sell secrecy and happily take their 40-percent cut of the price of that secrecy. And yet some of these same plaintiffs' lawyers now tell reporters how very, very wrong it was for churches to buy what they were selling. With just one or two exceptions, I do not know of a reporter who has paused to contemplate the obvious hypocrisy of these lawyers.'"
 * "From []"

 * And back to the Globe article: "[Lawyer Mitchell] Garabedian said he harbors no regrets about the settlements he negotiated in secrecy, often at his clients' insistence. 'They were embarrassed, and many victims thought they were the only ones,' he said."

 * I have a lot more, but that is enough for now. Thank you. Steakpeak (talk) 01:05, 20 September 2016 (UTC)

130 children
The source cited for this (again the Boston Globe) says more than 130 people have come forward with horrific childhood tales about how former priest John J. Geoghan allegedly fondled or raped them. On this basis it is fine to go with "alleged" here, which I think is better wording than "accused". The same source says Cardinal Bernard F. Law knew about Geoghan’s problems in 1984, Law’s first year in Boston, yet approved his transfer to St. Julia’s parish in Weston. This means it does not make sense to mention Geoghan without mentioning his relevance to Law. "those with close knowledge of the Geoghan case" is not a source we can use. MPS1992 (talk) 18:25, 18 September 2016 (UTC)
 * I think "alleged" is a more loaded word than "accused," but "alleged" is certainly acceptable compared to the factually inaccurate word "revealed," which was there before. Thanks. Steakpeak (talk) 01:12, 20 September 2016 (UTC)

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Death, and date of death
According to a journalist on Twitter, the death was "at Midnight Wednesday". Should the death date thus be Wednesday the 20th, or Tuesday the 19th? Presumably in the coming hours an official release from the Vatican will make this clear. power~enwiki ( π, ν ) 03:06, 20 December 2017 (UTC)

title: Talk:Bernard Francis Law


text:
Elastography

Elastography is any of a class of medical imaging modalities that map the elastic properties and stiffness of soft tissue. The main idea is that whether the tissue is hard or soft will give diagnostic information about the presence or status of disease. For example, cancerous tumours will often be harder than the surrounding tissue, and diseased livers are stiffer than healthy ones.

The most prominent techniques use ultrasound or magnetic resonance imaging (MRI) to make both the stiffness map and an anatomical image for comparison.

Historical background
Palpation is the practice of feeling the stiffness of a person's or animal's tissues with the health practitioner's hands. Manual palpation dates back at least to 1500 BC, with the Egyptian Ebers Papyrus and Edwin Smith Papyrus both giving instructions on diagnosis with palpation. In ancient Greece, Hippocrates gave instructions on many forms of diagnosis using palpation, including palpation of the breasts, wounds, bowels, ulcers, uterus, skin, and tumours. In the modern Western world, palpation became considered a respectable method of diagnosis in the 1930s. Since then, the practice of palpation has become widespread, and it is considered an effective method of detecting tumours and other pathologies.

Manual palpation has several important limitations: it is limited to tissues accessible to the physician's hand, it is distorted by any intervening tissue, and it is qualitative but not quantitative. Elastography, the measurement of tissue stiffness, seeks to address these challenges.

How it works
There are numerous elastographic techniques, in development stages from early research to extensive clinical application. Each of these techniques works in a different way. What all methods have in common is that they create a distortion in the tissue, observe and process the tissue response to infer the mechanical properties of the tissue, and then display the results to the operator, usually as an image. Each elastographic method is characterized by the way it does each of these things.

Inducing a distortion
To image the mechanical properties of tissue, we need to see how it behaves when deformed. There are three main ways of inducing a distortion to observe. These are:
 * Pushing/deforming or vibrating the surface of the body (skin) or organ (prostate) with a probe or a tool,
 * Using acoustic radiation force impulse imaging using ultrasound to remotely create a 'push' inside the tissue, and
 * Using distortions created by normal physiological processes, e.g. pulse or heartbeat.

Observing the response
The primary way elastographic techniques are categorized is by what imaging modality (type) they use to observe the response. Elastographic techniques use ultrasound, magnetic resonance imaging (MRI) and pressure/stress sensors in tactile imaging (TI) using tactile sensor(s). There are a handful of other methods that exist as well.

The observation of the tissue response can take many forms. In terms of the image obtained, it can be 1-D (i.e. a line), 2-D (a plane), 3-D (a volume), or 0-D (a single value), and it can be a video or a single image. In most cases, the result is displayed to the operator along with a conventional image of the tissue, which shows where in the tissue the different stiffness values occur.

Processing and presentation
Once the response has been observed, the stiffness can be calculated from it. Most elastography techniques find the stiffness of tissue based on one of two main principles: Some techniques will simply display the distortion and/or response, or the wave speed to the operator, while others will compute the stiffness (specifically the Young's modulus or similar shear modulus) and display that instead. Some techniques present results quantitatively, while others only present qualitative (relative) results.
 * For a given applied force (stress), stiffer tissue deforms (strains) less than does softer tissue.
 * Mechanical waves (specifically shear waves) travel faster through stiffer tissue than through softer tissue.

Ultrasound elastography
There are a great many ultrasound elastographic techniques. The most prominent are highlighted below.

Quasistatic elastography / strain imaging
Quasistatic elastography (sometimes called simply 'elastography' for historical reasons) is one of the earliest elastography techniques. In this technique, an external compression is applied to tissue, and the ultrasound images before and after the compression are compared. The areas of the image that are least deformed are the ones that are the stiffest, while the most deformed areas are the least stiff. Generally, what is displayed to the operator is an image of the relative distortions (strains), which is often of clinical utility.

From the relative distortion image, however, making a quantitative stiffness map is often desired. To do this requires that assumptions be made about the nature of the soft tissue being imaged and about tissue outside of the image. Additionally, under compression, objects can move into or out of the image or around in the image, causing problems with interpretation. Another limit of this technique is that like manual palpation, it has difficulty with organs or tissues that are not close to the surface or easily compressed.

Acoustic radiation force impulse imaging (ARFI)
Acoustic radiation force impulse imaging (ARFI) uses ultrasound to create a qualitative 2-D map of tissue stiffness. It does so by creating a 'push' inside the tissue using the acoustic radiation force from a focused ultrasound beam. The amount the tissue along the axis of the beam is pushed down is reflective of tissue stiffness; softer tissue is more easily pushed than stiffer tissue. ARFI shows a qualitative stiffness value along the axis of the pushing beam. By pushing in many different places, a map of the tissue stiffness is built up. Virtual Touch imaging quantification (VTIQ) has been successfully used to identify malignant cervical lymph nodes.

Shear-wave elasticity imaging (SWEI)
In shear-wave elasticity imaging (SWEI), similar to ARFI, a 'push' is induced deep in the tissue by acoustic radiation force. The disturbance created by this push travels sideways through the tissue as a shear wave. By using an image modality like ultrasound or MRI to see how fast the wave gets to different lateral positions, the stiffness of the intervening tissue is inferred. Since the terms "elasticity imaging" and "elastography" are synonyms, the original term SWEI denoting the technology for elasticity mapping using shear waves is often replaced by SWE. The principal difference between SWEI and ARFI is that SWEI is based on the use of shear waves propagating laterally from the beam axis and creating elasticity map by measuring shear wave propagation parameters whereas ARFI gets elasticity information from the axis of the pushing beam and uses multiple pushes to create a 2-D stiffness map. No shear waves are involved in ARFI and no axial elasticity assessment is involved in SWEI. SWEI is implemented in supersonic shear imaging (SSI).

Supersonic shear imaging (SSI)
Supersonic shear imaging (SSI) gives a quantitative, real-time two-dimensional map of tissue stiffness. SSI is based on SWEI: it uses acoustic radiation force to induce a 'push' inside the tissue of interest generating shear waves and the tissue's stiffness is computed from how fast the resulting shear wave travels through the tissue. Local tissue velocity maps are obtained with a conventional speckle tracking technique and provide a full movie of the shear wave propagation through the tissue. There are two principal innovations implemented in SSI. First, by using many near-simultaneous pushes, SSI creates a source of shear waves which is moved through the medium at a supersonic speed. Second, the generated shear wave is visualized by using ultrafast imaging technique. Using inversion algorithms, the shear elasticity of medium is mapped quantitatively from the wave propagation movie. SSI is the first ultrasonic imaging technology able to reach more than 10,000 frames per second of deep-seated organs. SSI provides a set of quantitative and in vivo parameters describing the tissue mechanical properties: Young's modulus, viscosity, anisotropy.

This approach demonstrated clinical benefit in breast, thyroid, liver, prostate, and musculoskeletal imaging. SSI is used for breast examination with a number of high-resolution linear transducers. A large multi-center breast imaging study has demonstrated both reproducibility and significant improvement in the classification of breast lesions when shear wave elastography images are added to the interpretation of standard B-mode and Color mode ultrasound images.

Transient elastography
In the food industry, low-intensity ultrasonics has already been used since the 1980s to provide information about the concentration, structure, and physical state of components in foods such as vegetables, meats, and dairy products and also for quality control, for example to evaluate the rheological qualities of cheese.

Transient elastography was initially called time-resolved pulse elastography when it was introduced in the late 1990s. The technique relies on a transient mechanical vibration which is used to induce a shear wave into the tissue. The propagation of the shear wave is tracked using ultrasound in order to assess the shear wave speed from which the Young's modulus is deduced under hypothesis of homogeneity, isotropy and pure elasticity (E=3ρV²). An important advantage of transient elastography compared to harmonic elastography techniques is the separation of shear waves and compression waves. The technique can be implemented in 1D and 2D which required the development of an ultrafast ultrasound scanner.

Transient elastography gives a quantitative one-dimensional (i.e. a line) image of "tissue" stiffness. It functions by vibrating the skin with a motor to create a passing distortion in the tissue (a shear wave), and imaging the motion of that distortion as it passes deeper into the body using a 1D ultrasound beam. It then displays a quantitative line of tissue stiffness data (the Young's modulus). This technique is used mainly by the Fibroscan system, which is used for liver assessment, for example, to diagnose cirrhosis. A specific implementation of 1D transient elastography called VCTE has been developed to assess average liver stiffness which correlates to liver fibrosis assessed by liver biopsy. This technique is implemented in a device which can also assess the controlled attenuation parameter (CAP) which is good surrogate marker of liver steatosis.

Magnetic resonance elastography (MRE)

Magnetic resonance elastography (MRE) was introduced in the mid-1990s, and multiple clinical applications have been investigated. In MRE, a mechanical vibrator is used on the surface of the patient's body; this creates shear waves that travel into the patient's deeper tissues. An imaging acquisition sequence that measures the velocity of the waves is used, and this is used to infer the tissue's stiffness (the shear modulus). The result of an MRE scan is a quantitative 3-D map of the tissue stiffness, as well as a conventional 3-D MRI image.

One strength of MRE is the resulting 3-D elasticity map, which can cover an entire organ. Because MRI is not limited by air or bone, it can access some tissues ultrasound cannot, notably the brain. It also has the advantage of being more uniform across operators and less dependent on operator skill than most methods of ultrasound elastography.

MR elastography has made significant advances over the past few years with acquisition times down to a minute or less and has been used in a variety of medical applications including cardiology research on living human hearts. MR elastography's short acquisition time also makes it competitive with other elastography techniques.

Applications
Elastography is used for the investigation of many disease conditions in many organs. It can be used for additional diagnostic information compared to a mere anatomical image, and it can be used to guide biopsies or, increasingly, replace them entirely. Biopsies are invasive and painful, presenting a risk of hemorrhage or infection, whereas elastography is completely noninvasive.

Elastography is used to investigate disease in the liver. Liver stiffness is usually indicative of fibrosis or steatosis (fatty liver disease), which are in turn indicative of numerous disease conditions, including cirrhosis and hepatitis. Elastography is particularly advantageous in this case because when fibrosis is diffuse (spread around in clumps rather than continuous scarring), a biopsy can easily miss sampling the diseased tissue, which results in a false negative misdiagnosis.

Naturally, elastography sees use for organs and diseases where manual palpation was already widespread. Elastography is used for detection and diagnosis of breast, thyroid, and prostate cancers. Certain types of elastography are also suitable for musculoskeletal imaging, and they can determine the mechanical properties and state of muscles and tendons.

Because elastography does not have the same limitations as manual palpation, it is being investigated in some areas for which there is no history of diagnosis with manual palpation. For example, magnetic resonance elastography is capable of assessing the stiffness of the brain, and there is a growing body of scientific literature on elastography in healthy and diseased brains.

In 2015, preliminary reports on elastography used on transplanted kidneys to evaluate cortical fibrosis have been published showing promising results. In Bristol University's study Children of the 90s, 2.5% of 4,000 people born in 1991 and 1992 were found by ultrasound scanning at the age of 18 to have non-alcoholic fatty liver disease; five years later transient elastography found over 20% to have the fatty deposits on the liver of steatosis, indicating non-alcoholic fatty liver disease; half of those were classified as severe. The scans also found that 2.4% had the liver scarring of fibrosis, which can lead to cirrhosis.

Other techniques include elastography with optical coherence tomography (i.e. light).

Tactile imaging involves translating the results of a digital "touch" into an image. Many physical principles have been explored for the realization of tactile sensors: resistive, inductive, capacitive, optoelectric, magnetic, piezoelectric, and electroacoustic principles, in a variety of configurations.

title: Elastography


text: User talk:205.240.11.90

title: User talk:205.240.11.90


text:
Talk:Center of mass

Linear and angular momentum
What's the point of the first equation in this section? It gives no useful information. Because vector addition has the associative property, the equation can be simplified to $$ \mathbf{r}_i = \mathbf{r}_i$$, which is useless. 108.72.4.161 (talk) 04:44, 25 November 2014 (UTC)
 * Good question. Separating the position coordinate ri into the sum of the vector to the reference point R and the relative position vector ri -R is the first step in representing the linear momentum of a body as the sum of the momentum of its reference point and the momentum computed from the relative position vectors which sum to zero when R is the center of mass. I hope this helps. Prof McCarthy (talk) 17:24, 25 November 2014 (UTC)

Datam
"Another way of interpreting the process here is the mechanical balancing of moments about an arbitrary datam." Did you mean datum? Art LaPella (talk) 05:02, 6 March 2015 (UTC)

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== In rock balancing, the stability of a collection of rocks is related to its center of mass in relation to its resting point (contact points) of the rocks. * ==

"In rock balancing, the stability of a collection of rocks is related to its center of mass in relation to its resting point (contact points) of the rocks." is too vague to call it false, but the information content to small to have any effect beyond suggesting the activity is too complicated for the colleague to write or talk usefully about, without waving their hands. Nice picture tho, and i'm giving a shot to writing something at least vaguely related to it. --Jerzy•t 16:38, 4 September 2017 (UTC)

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Postage stamps and postal history of Switzerland

This is a survey of the postage stamps and postal history of Switzerland.

History
The first stamps used in Switzerland were issued by the cantons of Zürich (1843), Geneva (1843) and Basel (1845) for their own use, with the first federal issues coming several years later, on April 7, 1850.

By March 19, 1798, the Helvetic Republic had come into being; although it was not until September 1798 that the entire country was conquered. According to Napoleon, the country was "liberated" to form itself into a new State, which assumed the title of "Republique Helvetique Une et Indivisible." And, the Republic was administratively reorganized into twenty-two (22) Cantons. Later, that number was reduced to nineteen (19) due to mergers and to some changes at the frontiers. In September 1798, all postal mail was ordered to be "a natural and necessary property of the state" or, in modern parlance, nationalization was ordered.

Thus, the cantonal and private mail services were taken over. The country was then divided into five postal districts as follows: Berne, where Fischer Posts were entrusted with the administration of the mails; Basel; Zürich; St. Gallen; and Schaffhausen, where the administration was left in the hands of three mail farmers because of their close association with the Thurn and Taxis mails.

The first Republican Decree of the Helvetic State relating to postal matters was one of suppressing the old and colorful cantonal uniforms worn by the letter carriers, and As a symbol of national service, a new uniform was issued in the Republican colors of green, red and yellow

Swiss stamps are inscribed with the word Helvetia, rather than "Schweiz", "Suisse" "Svizzera", or "Svizra". With four official languages-German, French, Italian, and Romansch. The Swiss would have had to put all four languages on each stamp, quite a problem to overcome with such limited space on a stamp.

Switzerland is officially known by the Latin name "Confoederatio Helvetica" for historical reasons. "Confoederatio" means "confederation" and "Helvetica" is a reference to the Helvetians, a Celtic tribe that lived in Switzerland when the Romans invaded. The English equivalent of the Latin name is "Swiss Confederation." Hence, the use of Helvetia on stamps.

Cantonal Issues, Post Marks, Air Mail, and Extra. -Courier Marks
The first Swiss stamps were those of the Cantons (States) of Zürich, Geneva, and Basel. These early Swiss stamps have another distinction. They were also the 3rd (1843), 4th (1843), and 5th (1845) adhesive postage stamp issuing nations of the World. Unfortunately, the Cantonal postage stamp issues are tremendously rare today.

Basel issued their own stamp, the "Basel Dove" in 1845. This was a 2½-rappen value featuring a white embossed dove carrying a letter in its beak, and inscribed "STADT POST BASEL", a design by the architect Melchior Berry. It is printed in black, crimson, and blue, making it the world's first tri-colored stamp. A first printing in light green instead of the chosen blue was first believed to be a proof, but now acknowledged as first trial printing.
 * BASEL

In 1675, Beat Fischer von Reichenbach was granted permission to operate a private postal service in Bern, Switzerland. The building next to the Berne Minster Gothic Chapel in Berne was used as a post office from 1675 to 1883. The service was named for him "Fischerpost". The service operated until 1832. Beat Fischer von Reichenbach was knighted by Leopold I, Holy Roman Emperor for establishing postal services between Germany and Spain. In 1975 a postage stamp dedicated to Beat Fischer von Reichenbach was issued in Switzerland.
 * BERNE

In June 1799, the Seat of Government was transferred to Berne. A thorough reorganization took place at that time, and the post mark was changed to "Central Post Adminst. (for Central Post Administration).

Therefore, there were two types of postmarks. Berne has a small 20 x 24 mm. mark which reads "Helvt. Republ. at top and "Central Post Bureau" at bottom, and in the center a "E" (for Eingegangen, received) and a "V" ( for Versandt, sent out). In the Lucerne marking, there was a line below the wording, and in the one used in Berne a small "posthorn" appeared. The post horn is synonymous in parts of Europe with the mail, and images of the instrument are still often used as a symbol of the post office. Postmen would often improvise or play well-known melodies on the horn to entertain those along their delivery. This even resulted in some reprimands from their superiors to stop playing “vulgar” opera arias that the post office thought undignified.

The postal clerks were told to put a handwritten manuscript date after the "E" indicating the date the letter was received; yet there are examples of covers (envelopes) where the dates had not been filled in as ordered.

There are of course, recognized misprints called "Freaks" Some Bern covers dated June to December 1799, with the Central Post Bureau wording, and one cover that was dated July 1799, from Lucerne with the postmark applied in red ink; although the use of red ink had been curtailed earlier. The red ink was used in Lucerne from November 1798 to January 1799, when it was replaced with vermillion ink. The next time red ink markings would be found again would be on Berne post markings. This may indicate that when the Seat of the Government was changed, the red ink was taken from Lucerne to Berne for use there; but, perhaps at the last minute, a contingency developed and it was possibly also simultaneously used in Lucerne for a very short period.

On September 30, 1843, Geneva issued their first stamps: the "Double Geneva", which was the world's first postage stamp in green colour. Like the first Zürich issue, it consisted of pairs of stamps; these were each printed in black on yellow-green paper, depicting the city's arms, and inscribed "Poste de Genéve" at the top and "Port local" at the bottom.
 * GENEVA

But, an additional inscription, reading "10 PORT CANTONAL Cent" ran across the top of each pair. The idea was that the user could cut out a single stamp to pay the intra-commune rate, and a pair to make up the inter-commune rate. Only 6,000 of the doubles were ever printed, and, intact used doubles typically go for around US$60,000 at auction. Very rarely, horizontally inverted pairs, and even more rarely, vertical pairs, can be found and are greatly sought after by collectors with values reaching sometimes US$150'000 to US$200'000 at auction.

In 1845, Geneva switched to conventional single 5c stamps. In 1849 it printed a 4c stamp featuring the federal cross, and similar 5c designs in 1850 and 1851. (See for example Spezialkatalog uber die Briefmarken der Schweiz...Zumstein & Cie, Bern 1967.)

Lucern was chosen as the headquarters seat for mail. All mail was handled through the Central Post Bureau, which was under the authority of the Minister of Finance All letters were handed into the central bureau for sorting and forwarding. At the bureau they received the first Helvetic Republic postmarks.
 * LUCERNE

Because all Postal Departments were in Lucerne, the volume of official correspondence was extremely heavy there; but purely private letters were quite rare. Such letters from Lucerne bore the title, "Central Post Bureau." These are known to have existed from November 1798 to July 1799.

 * ZÜRICH

On March 1, 1843, Zürich issued their first stamps: Zürich 4 and Zürich 6. The Zürich 4 and 6, making it the second type of stamp in the world, after the UK's Penny Black three years earlier. The issue consisted of two imperforate stamps printed separately, each in five types, in sheets of 100, one with a large numeral "4" and the other with a "6", both inscribed "Zürich" at the top. The 4-rappen stamp was also inscribed "LOCAL-TAXE" at the bottom, since it was intended to pay for letters mailed within a city, while the 6-rappen, inscribed "CANTONAL-TAXE", was for use with letters going anywhere in the canton. The design was lithographed in black by Orell, Fuessli, and Company, with a pattern of fine red lines underneath, to discourage counterfeiting. Initially the red line were vertical, but starting in 1846 they were printed horizontal. These stamps were popular from the start, but were not printed in large numbers and are quite scarce today, with values ranging from US$1,500 to $20,000 depending on type. With the exception of one 6-rappen block of 9 (3x3) later split into a block of 6 (3x2) and a strip of three, all sheets were cut horizontally, so that no vertical pairs or larger are known to exist today.

Canton of Zürich also issued a stamp in 1850, known to collectors as the Winterthur issue, depicting the Swiss federal cross and a posthorn, which served as a transitional issue until the stamps of the Swiss federal government made their appearance later that same year (see under Geneva above).

Local mail and rayon stamps

The adoption of the federal constitution in 1848 made it practical to issue confederation-wide stamps, and the first of these came out in 1850 (the exact date is uncertain). All used the same basic design, a Swiss cross surmounted by a posthorn, but there were a number of variations. The local-rate stamps had a value of 2½ rappen, with some inscribed "ORTS-POST" (German) and "POSTE LOCALE" (French). This was the first of many multi-language issues. For longer-distance mail, the 5-rappen stamp was inscribed "RAYON I" and the 10-rappen (for a greater distance) "RAYON II". Initially the stamps were issued with a black frame separating the white cross from the red background, but as a technically incorrect rendition of the Swiss arms, these were withdrawn.

In 1852 a 15-rappen/centime value inscribed "RAYON III" was issued, using the same design as previously, but printed entirely in vermilion. The "zone" (Rayon) system, in which the letter paid according to the distance travelled was later abolished: a fixed price took the mail to anywhere within Switzerland.

Definitives of 1854–1862
Strubel Type - Part 1 The classical definitive Swiss stamps were issued between 1854 and 1862, and were known as the Strubel Issues. They are the most popular specialization subject for most serious classical Swiss philatelists. Officially, these stamps are called The Imperforate Sitting Helvetia Issues of 1854-1862.

These stamps feature a seated figure of Helvetia wearing a laurel wreath. She holds a spear in her right arm, and her left arm is resting on a shield, emblazoned with the arms of the Helvetic Confederation. The effect given by the shape of the wreath around her embossed head caused many German speaking collectors to jokingly refer to the design as "Strubel", referring to the visual effect of Helvetia having "unkempt" or "frizzy" hair. The nickname for these issues stuck, and just about every collector of Swiss stamps now refers to them as "The Strubels".

This series of stamps have many, different variations including differing inks, paper, and paper thickness. Colored silk threads were used as a security device in the papers used to print the definitive Swiss stamps of 1854-1862.

Helvetias

All of the preceding issues were declared invalid on 1 October 1854, and replaced with the seated allegorical figure "Helvetia", the first of several issues known as "seated Helvetias". The figure was embossed but only the outline was colored, making it rather hard to pick out. This was the first issue to deal with the multiple languages of Switzerland; in addition to the word "FRANCO" at the top, the other three sides listed the denomination in rappen, centimes, and (Italian) centesimi.

The issue was also notable for the use of a colored silk thread running horizontally through the paper, as an anti-counterfeiting measure. (In the illustration to the left, the thread is faintly visible about 1/3 of the distance from the bottom of the stamp, looking almost like a crease.)

A number of values were printed between 1854 and 1862, ranging from 5 rappen to 1 franc, and philatelists distinguish them further by type of paper and color of thread. The commonest type surviving today is the 5-rappen brown on thick paper with a green thread, costing US$20 used; certain other types are rare, and the pale yellow-green shade of the 40-rappen value will go for $7,000 or more.

A new design with more legible seated Helvetia appeared in 1862, now sporting a "watermark" consisting of a cross inside an ellipse (not a true watermark because it was impressed into the paper after printing), and for the first time, perforations. The units of currency disappeared, with "HELVETIA" inscribed at the top and "FRANCO" at the bottom. Initially printed on white wove paper, the stamps switched to granite paper in 1881. (The paper has red and blue silk threads, clearly visible in the larger image of the stamp to the left.) The stamps continued in use until 1883; many of them are common and cheaply available today, although legitimate cancellations on the granite paper varieties are uncommon because of the short period of use.

In 1882, the low value stamps (up to 15c) were numerals, while the higher values featured a "Standing Helvetia". These continued in use, with a number of variations in color, perforation, and paper, until 1907. 1900 saw Switzerland's first commemorative stamps, a set of three values issued for the 25th anniversary of the Universal Postal Union, with an allegorical design featuring various symbols of communication.

20th century
A new definitive series in 1907 showed William Tell's son holding a crossbow and an apple pierced by an arrow for values below 10c, a bust of Helvetia for 10c to 15c values, and another seated Helvetia for higher values. The William Tell's son design (by Albert Welti) went through several redrawings, including a temporary move of the bowstring in front of the crossbow's stock. From 1914 on, a portrait of William Tell himself was used for values between 10c and 30c.

Also in 1914, the first of many scenic stamps were issued. The 5fr depicted the Rütli meadow, while the 3fr and 10fr stamps showed the Mythen and Jungfrau mountains, respectively.

The first semi-postal stamp was issued in 1913, but regular annual issues did not start until 1915. For many years an issue of 3-5 stamps came out on 1 December each year, until 1972.

An set of three stamps in 1919 celebrated peace at the end of World War I. Stamp printing experienced some difficulties during this period, and a variety of surcharges were needed in 1915 and 1921. The UPU was noted on its 50th anniversary in 1924 with two stamps, one depicting its building in Bern and the other the location of the 1874 Congress.

In about 1930 Switzerland began to use "grilled gum", a light grill applied along the gum to counteract the tendency for gummed stamps to curl. The grill is most obvious on mint stamps, but is faintly visible on used stamps as well. This was abandoned around 1944.

The next definitive series was a set of scenic views issued in 1934. The designs were typographed, resulting in a vigorous albeit somewhat crude-looking appearance, and they were superseded by engraved versions of the same basic designs, beginning in 1936.

Several commemorative issues appeared in the 1930s, then in 1941 came new definitives honoring Swiss military heroes. Another definitive set in 1945 marked the end of the war; the higher values of this were issued in small numbers, and are relatively expensive today.

The definitive series of 1949 depicted achievements of Swiss technology. Since that time, Swiss stamps have generally followed a regular pattern; an issue of about four commemoratives on a single date in the spring, and a similar group in the fall, as well as a Europa issue, usually in the spring. Starting in the 1980s, there have been additional themed issues; for instance, in 1993 an issue of four stamps featured works of art by Swiss women.

Postal history

 * Faulstich, Edith M. Central Post and Extra.-Courier Marks of the Helvetic Republic, 1798-1803, (with Catalog of Markings in English), Reprinted from Postal History Journal, December 1964, 16p.
 * Keller, Max. Stempel aus der Stadt Bern zwischen 1803 und 1850. Erlach: Philatelistenverein Bern, 2010, 78p.
 * Schäfer, Richard. Handbuch Postgeschichte von Genf: Anfänge bis 1854 = Histoire postale de Genève. Waldstetten: Just-prephilately, 2006, 276p.
 * Schäfer, Richard. Das Postwesen der alten Eidgenossenschaft: Anfänge bis 1798 = Swiss postal history of the old Confederation = Histoire postale de l'ancienne Confédération. Reinach: Multipress Verlag, 2000, 418p.

Cantonal issues

 * Bach, Jean-Paul and Felix Winterstein. Basler Taube. Reinach: Multipress, 1995 ISBN 3-9520837-2-0, 148p.
 * Gnagi, Jakob. Die Zurcher Kantonalmarken von 1843. Bern: Organisationskomitee der NABA ZURI 84, mit Unterstutzung durch den Fonds zur Forderung der Philatelie, 1984, 113p.
 * Reuterskiold, Axel de, Baron. Les timbres cantonaux de la Suisse et leurs falsifications. Lausanne: Societe Lausannoise de Timbrologie, 1898, 51p.

General issues

 * Hall, Richard T. Philately of Switzerland: an introductory handbook. Asheville, N.C.: American Helvetia Philatelic Society, 2010 ISBN 0984431705, 345p.
 * Hermann, Urs. Sitzende Helvetia Ungezähnt = Les Rappen (1854-1863). Wettingen: Strubel-Literatur, 2006 2 vols.
 * Mirabaud, Paul and Alex de Reuterskiöld. The postage stamps of Switzerland, 1843-1862. Lawrence, MA.: Quarterman Publications, 1975, 266p.
 * Zinsmeister, Marian Carne. Switzerland, 1850-1958: detailed information concerning the stamps of Switzerland, when, why, and how issued. Lemont, Pa.: Society of Philatelic Americans, 1959, 80p.
 * Zumstein. Katalog Schweiz/Liechtenstein, Campione und Vereinte Nationen, Genf = Catalogue Suisse/Liechtenstein, Campione et Nations Unies, Genève. Annual.

International organisations

 * International Labour Office. Postage stamps and the International Labour Organisation. Genèva: International Labour Office, 1965, 15p.
 * Misteli, Charles. Study on the postal stamps and cancellations of the League of Nations, the International Labor Office and their international conferences. Pasadena, CA.: United Nations Philatelists, Inc., 1995, 72p.