Question: The Royal Medal of Recompense was established by a king that was Duke of Schleswig during what years?

Context paragraphs:
Buchanan Medal: The Buchanan Medal is awarded by the Royal Society "in recognition of distinguished contribution to the medical sciences generally".  The award was created in 1897 from a fund to the memory of London physician Sir George Buchanan (1831–1895).  It was to be awarded once every five years, but since 1990 the medal has been awarded every two years.  Since its creation, it has been awarded 28 times, and unlike other Royal Society medals such as the Royal Medal, it has never been awarded to the same individual multiple times.  As a result of the criteria for the medal, most of the winners have been doctors or other medical professionals; an exception was Frederick Warner, an engineer who won the medal in 1982 "for his important role in reducing pollution of the River Thames and of his significant contributions to risk assessment".

Prince Carl Medal: The Prince Carl Medal (Swedish: "Prins Carl-medaljen" ) is a royal medal of Sweden.  The medal was instituted by Gustaf V of Sweden in 1945 on the retirement of Prince Carl, Duke of Västergötland as chairman of the Red Cross of Sweden.  The medal is awarded for national or international humanitarian activity.

Seraphim Medal: The Seraphim Medal (Swedish: "Serafimermedaljen" ) is a royal medal of Sweden.  Established in 1748, it is awarded by the King of Sweden for service that benefits society or service of a humanitarian nature.

Abel, Lord of Langeland: Abel Abelsøn (1252 – 2 April 1279), Lord of Langeland, was the third son of King Abel of Denmark, Duke of Schleswig and younger brother of Valdemar III, Duke of Schleswig and Eric I, Duke of Schleswig.  As a member of the ducal family, he held several fiefs in Southern Denmark.

Royal Medal: A Royal Medal, known also as The King's Medal or The Queen's Medal, depending on the gender of the monarch at the time of the award, is a silver-gilt medal, of which three are awarded each year by the Royal Society, two for "the most important contributions to the advancement of natural knowledge" and one for "distinguished contributions in the applied sciences", done within the Commonwealth of Nations.  The award was created by George IV and awarded first during 1826.  Initially there were two medals awarded, both for the most important discovery within the year previous, a time period which was lengthened to five years and then shortened to three.  The format was endorsed by William IV and Victoria, who had the conditions changed during 1837 so that mathematics was a subject for which a Royal Medal could be awarded, albeit only every third year.  The conditions were changed again during 1850 so that:

Ulrik of Denmark (1578–1624): Prince Ulrik John of Denmark, (Koldinghus Palace, Kolding, 30 December 1578 – 27 March 1624, Rühn) was a son of King Frederick II of Denmark and his consort, Sophie of Mecklenburg-Güstrow.  As the second-born son he bore the merely titular rank of "Duke of Holstein and Schleswig, Stormarn and Ditmarsh" and had no share in the royal-ducal condominial rule of Holstein and Schleswig, wielded by the heads of the houses of Oldenburg (royal) and its cadet branch Holstein-Gottorp (ducal).  Since 1602 he held the religiously defunct position of "Bishop of Schleswig", enjoying the revenues of the implied estates and manor.  The year after he succeeded his grandfather as "Administrator of the Prince-Bishopric of Schwerin", holding both posts until his death.

Thomas Snow Beck: Thomas Snow Beck FRS FRCS (1814 – 6 January 1877) was a British doctor and surgeon.  He qualified as a doctor in London.  In 1845, he was awarded the Royal Society's Royal Medal for his unpublished paper entitled "On the nerves of the uterus".  The paper was later published, but the award was disputed by the London-resident Scottish surgeon Robert Lee, who had published an earlier paper on the subject and reached different conclusions.  This controversy led to reform of the award process for the Royal Medal, and is thought to have contributed to the resignation of both the President and Secretary of the Royal Society.  Beck also carried out other work on nerves, including work in 1846 on differentiation between white and gray rami.  He was elected a fellow of the Royal Society in 1851.

Royal Medal of Recompense: The Royal Medal of Recompense (Danish: "Den Kongelige Belønningsmedalje" ) is a Danish medal.  Established by King Christian IX the medal is presented at the prerogative of Monarch.  Currently, it is awarded for 40 or 50 years of service to the same private employer.

Leverhulme Medal (Royal Society): The Leverhulme Medal is awarded by the Royal Society every three years "for an outstandingly significant contribution in the field of pure or applied chemistry or engineering, including chemical engineering".  It was created in 1960 after a donation by the Leverhulme Trust to mark the 300-year anniversary of the foundation of the Royal Society, and is accompanied by a £2000 gift.  Since its creation it has been awarded 17 times, and unlike other Royal Society medals such as the Royal Medal, it has never been awarded to a woman or to the same person multiple times.  Citizens of the United Kingdom have won the medal 16 out of the 17 times; the only foreign recipient was Man Mohan Sharma, an Indian citizen who was awarded the medal in 1996 "for his work on the dynamics of multi-phase chemical reactions in industrial processes".  Two of the Leverhulme Medal winners also won the Nobel Prize in Chemistry: Archer John Porter Martin, who won the medal in 1963 for "his distinguished and fundamental discoveries in chromatography and its application" and the Nobel Prize in 1952, and Cyril Norman Hinshelwood, who won the medal in 1960 for "his outstanding contributions to physical chemistry" and the Nobel Prize in 1956.

Christian IX of Denmark: Christian IX (8 April 181829 January 1906) was King of Denmark from 1863 to 1906.  From 1863 to 1864, he was concurrently Duke of Schleswig, Holstein and Lauenburg.

Supporting paragraphs: Royal Medal of Recompense Christian IX of Denmark
Answer: 1863 to 1864