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id stringlengths 40 40	title stringlengths 15 120	text stringlengths 41 3.14k	source stringclasses 2 values
8e987f148358fdcc0a3996f6d6283e83b1679e10	the unit distance graph on the three-dimensional integer	the unit distance graph on the three-dimensional integer lattice has a vertex for each lattice point; each vertex has exactly six neighbors. it is possible to remove some of the points from the lattice, so that each remaining point has exactly three remaining neighbors, and so that the induced subgraph of these points ...	wikipedia
6c7cd4444353f445678190241bab2f280d963d48	using the same construction, the hexagonal tiling of	using the same construction, the hexagonal tiling of the plane is the maximal abelian covering graph of the three-edge dipole graph, and the diamond cubic is the maximal abelian covering graph of the four-edge dipole. the d {\displaystyle d} -dimensional integer lattice (as a graph with unit-length edges) is the maxima...	wikipedia
a8c2f68561eaded2e7e5f4fddfb69768ea899aa5	a maximal abelian covering graph can be constructed	a maximal abelian covering graph can be constructed from any finite graph g {\displaystyle g}; applied to k 4 {\displaystyle k_{4}}, the construction produces the (abstract) laves graph, but does not give it the same geometric layout. choose a spanning tree of g {\displaystyle g}, let d {\displaystyle d} be the number ...	wikipedia
99745c805f90bff66d8d71e5c730374b9dbc41fb	as an abstract graph, the laves graph can	as an abstract graph, the laves graph can be constructed as the maximal abelian covering graph of the complete graph k 4 {\displaystyle k_{4}}. being an abelian covering graph of k 4 {\displaystyle k_{4}} means that the vertices of the laves graph can be four-colored such that each vertex has neighbors of the other thr...	wikipedia
aa7122df82133791e2350c8434b0b7cfbea5ee42	it is possible to choose a larger set	it is possible to choose a larger set of one out of every four points of the integer lattice, so that the graph of distance- 2 {\displaystyle {\sqrt {2}}} pairs of this larger set forms two mirror-image copies of the laves graph, disconnected from each other, with all other pairs of points farther than 2 {\displaystyle...	wikipedia
a9f18dd0fa7471c047f1bdd4e7700b70cfc94e9d	and all the other points formed by adding	and all the other points formed by adding multiples of four to these coordinates. the edges of the laves graph connect pairs of points whose euclidean distance from each other is the square root of two, 2 {\displaystyle {\sqrt {2}}}, as the points of each pair differ by one unit in two coordinates, and are the same in ...	wikipedia
7a4fdd90b42f0b3ca4d21cdd86c744d52e74bc2b	several crystalline chemicals have known or predicted structures	several crystalline chemicals have known or predicted structures in the form of the laves graph. thickening the edges of the laves graph to cylinders produces a related minimal surface, the gyroid, which appears physically in certain soap film structures and in the wings of butterflies.	wikipedia
e44be2bcee0a8ae3b7215e8acd3bcf4d9b60d72a	h. s. m. coxeter (1955) named this graph	h. s. m. coxeter (1955) named this graph after fritz laves, who first wrote about it as a crystal structure in 1932. it has also been called the k crystal, (10,3)-a network, diamond twin, triamond, and the srs net. the regions of space nearest each vertex of the graph are congruent 17-sided polyhedra that tile space. i...	wikipedia
33622ad99f8ea84d88d197f2f0f13ea4bb71dd08	in geometry and crystallography, the laves graph is	in geometry and crystallography, the laves graph is an infinite and highly symmetric system of points and line segments in three-dimensional euclidean space, forming a periodic graph. three equal-length segments meet at 120° angles at each point, and all cycles use ten or more segments. it is the shortest possible trip...	wikipedia
1b68e83ee14de3598142e4f850f3f2b8dae291d2	light bullets are localized pulses of electromagnetic energy	light bullets are localized pulses of electromagnetic energy that can travel through a medium and retain their spatiotemporal shape in spite of diffraction and dispersion which tend to spread the pulse. this is made possible by a balance between the non-linear self-focusing and spreading effects brought about by the me...	wikipedia
5c777218e3da6dd2d47ddfdf76f8e501650bce54	spatial and temporal stability which are the characteristics	spatial and temporal stability which are the characteristics of a soliton have been achieved in light bullets using alternative refractive index models. an experiment which exploited the discrete spreading and self-focusing effects on 170-femtosecond pulses at 1550-nanometre wavelengths by a two-dimensional hexagonal a...	wikipedia
1b68e83ee14de3598142e4f850f3f2b8dae291d2	light bullets are localized pulses of electromagnetic energy	light bullets are localized pulses of electromagnetic energy that can travel through a medium and retain their spatiotemporal shape in spite of diffraction and dispersion which tend to spread the pulse. this is made possible by a balance between the non-linear self-focusing and spreading effects brought about by the me...	wikipedia
7e20f906f86d44186d421f6f9f0539fc12ffa026	humphreys' hobbies included gardening and reading.she was an	humphreys' hobbies included gardening and reading.she was an active member of the natural bridge appalachian trail club.she lived in lynchburg, virginia, through her retirement in 1980 until her death on october 6, 2006.	wikipedia
a8ce895036350a2c5bb5db75428bfc12292d89f9	humphreys was born on october 22, 1911 in	humphreys was born on october 22, 1911 in south vancouver, british columbia. her mother, mabel jane thomas (1885-1963), was born in london, england, and worked as a dressmaker and a florist.her father was richard humphreys (1880-1969), a machinist who was born in pwllheli, wales. her parents were married in 1910, and h...	wikipedia
7cfad15c1dc5dc249f870dc13578cb24a74d0744	in the summers, humphreys taught high school teachers	in the summers, humphreys taught high school teachers at nsf summer institutes.from 1965 to 1969, humphreys worked for the educational testing service.she was also a consultant in 1975 for the american council on education regarding mathematics course credit given by nonacademic organizations.humphreys was an active me...	wikipedia
843a91249f9801e45ef919f92e8b9483ecbe5126	in 1949, humphreys became an associate professor at	in 1949, humphreys became an associate professor at randolph-macon woman's college.after one year at randolph-macon, she was named gillie a. larew professor and head of the mathematics department. she was head of the department until 1979. for the 1955-1956 academic year, humphreys went on sabbatical leave to the unive...	wikipedia
df3557efcc22f0f41a4f596e5d59eb1aa22c934c	from 1935 to 1936, humphreys was an instructor	from 1935 to 1936, humphreys was an instructor of mathematics and physics at mount st. scholastica college. she began teaching at h. sophie newcomb memorial college in 1936 and was promoted to assistant professor in 1941. she was also an assistant professor at barnard college in the summer of 1944, and an assistant pro...	wikipedia
a3d483f4d45b8e917074b6689f009ffad03badb2	i had hoped that the university of chicago	i had hoped that the university of chicago would hear about a job for me, but only one came through, and the male candidate who got his thesis at the same time got that job. in the meantime, i had registered at a teacher’s agency in downtown chicago, and many cards came in for the sum of something like $900, and you ta...	wikipedia
9c3c1dd5b04a12fec8f7b9b6a8962e9f159363c3	humphreys attended north vancouver high school from 1925	humphreys attended north vancouver high school from 1925 to 1928.she received her bachelor of arts with honors in mathematics from the university of british columbia in 1932, where she held scholarships for all four years. she studied at smith college under susan miller rambo, among others. she earned a master's degree...	wikipedia
1cae3d87cb8b09f1fa390582ed7ccb221cd74ae1	mabel gweneth humphreys (1911-2006) was a canadian-american mathematician	mabel gweneth humphreys (1911-2006) was a canadian-american mathematician and professor of mathematics at randolph-macon woman's college. the m. gweneth humphreys award of the association for women in mathematics was established in her honor.	wikipedia
0211260bc4f346ff85a78b5828d5d9099a9b46c6	this is a list of launches performed by	this is a list of launches performed by ariane carrier rockets between 1979, when the type first flew, and 1989. this period includes all flights of the ariane 1, ariane 2 and ariane 3, as well as early ariane 4 launches.	wikipedia
0211260bc4f346ff85a78b5828d5d9099a9b46c6	this is a list of launches performed by	this is a list of launches performed by ariane carrier rockets between 1979, when the type first flew, and 1989. this period includes all flights of the ariane 1, ariane 2 and ariane 3, as well as early ariane 4 launches.	wikipedia
e9b29e2e0662df3e8edfc3b3d9042dc496214e4c	by noting the corresponding compass vector, walking along	by noting the corresponding compass vector, walking along the contour one can line up a hand held compass aligning the expected direction, and eye-balling the line of contour's estimated level, move up or down along the bearing faster — to closely locate a desired point (planned point) along the hillside. pragmatically...	wikipedia
04a1295eee3a1de0956e25ba2bd356926507bd23	the line of greatest slope has practical significance	the line of greatest slope has practical significance in map reading. on the terrain it is often far more discernible, even intuitively obvious, rather than accurately picking out the consistent height level on what is likely the undulating uneven ground along the ground represented on the contour line. but knowing tha...	wikipedia
1397d2a088b0c27c720582aef76d88bb325edcc0	in mountain biking the line of greatest slope	in mountain biking the line of greatest slope defines the fall line, which is the path a trail will follow to descend a hill or mountain with the shortest path, and will also cause the rider to gain the most velocity (assuming brakes are not used, and other factors such as rolling resistance are equal).	wikipedia
3ac91524e0cdd1e3dd083ef4b3c48d8f8352fc6f	mathematically, the line (or path) of greatest slope	mathematically, the line (or path) of greatest slope from a point is determined by the gradient of height, taken as a potential field with respect to an acceleration from the force of gravity. lines of greatest slope are analogous to lines of force acting to accelerate an object downward at that point. these lines are ...	wikipedia
5db0005b4edf4e038d6cebd7cbc591f29c09fa55	the following is a list of indefinite integrals	the following is a list of indefinite integrals (antiderivatives) of expressions involving the inverse hyperbolic functions. for a complete list of integral formulas, see lists of integrals. in all formulas the constant a is assumed to be nonzero, and c denotes the constant of integration.	wikipedia
c061707b251ee49fde59fd8ab91094e27c0d3539	in analytic number theory, the kuznetsov trace formula	in analytic number theory, the kuznetsov trace formula is an extension of the petersson trace formula. the kuznetsov or relative trace formula connects kloosterman sums at a deep level with the spectral theory of automorphic forms. originally this could have been stated as follows. let be a sufficiently "well behaved" ...	wikipedia
1eaa0e72bb1fd8971ba1c84ba1a31acae444bb08	it was later translated by jacquet to a	it was later translated by jacquet to a representation theoretic framework. let g {\displaystyle g} be a reductive group over a number field f and h ⊂ g {\displaystyle h\subset g} be a subgroup. while the usual trace formula studies the harmonic analysis on g, the relative trace formula is a tool for studying the harmo...	wikipedia
cfbbfab00651ad5f629c65afe662cca7cf1d506d	the integral transform part is some integral transform	the integral transform part is some integral transform of g and the spectral part is a sum of fourier coefficients, taken over spaces of holomorphic and non-holomorphic modular forms twisted with some integral transform of g. the kuznetsov trace formula was found by kuznetsov while studying the growth of weight zero au...	wikipedia
d1a9000611b3d1a15e250664715c087a4b21cef4	johann gottlieb was remembered as a passionate researcher,	johann gottlieb was remembered as a passionate researcher, restless worker and an excellent rhetorician. his guide to qualitative chemical analysis (leitfaden der qualitativen analyse (1869)) provided insights to his didactic experiences and counts among some rare documents of university teaching and laboratory exercis...	wikipedia
ed897dc6b1580e14636e059baa92568c52db051c	in 1867/68 gottlieb was elected director of the	in 1867/68 gottlieb was elected director of the joanneum, and served as its rector again in 1874/75 when the joanneum acquired its new status of a royal technical college. gottlieb heavily contributed to the reorganisation coming with that new status. on 3rd march 1875, gottlieb broke down in his office and died the ne...	wikipedia
b7e13b60ee2a0bb24a5e33a7f4d2f81b6db92f7a	at the joanneum in graz, the chair of	at the joanneum in graz, the chair of physics and chemistry held by anton schrötter was split into one for physics and one for chemistry following schrötter’s appointment at the vienna polytechnic in 1843. in early 1846, gottlieb was appointed professor for general and technical chemistry to that newly created chair. h...	wikipedia
951db0537be3ab40f1c4562c929d43b76978eb87	gottlieb was born in brno as son to	gottlieb was born in brno as son to a pharmacist. he completed his matura at the local gymnasium and was supposed to take over his father’s business. he studied thus first pharmacy then chemistry under professor adolf martin pleischl in vienna. he later continued his studies also in prague. his plans to pursue a scient...	wikipedia
582c1164156b1e52eaf70ed9fc2fd4ba6d7767c8	after playing for piráti chomutov for four seasons	after playing for piráti chomutov for four seasons in the czech extraliga, valach became a free agent at the end of the 2018-19 season. he decided to sign his first contract in the ebel and agreed to a one-year deal with ehc black wings linz on 1 july 2019.	wikipedia
dfe904e42bfa4759ef046fb20310e63e2e6f0327	during her career, corrick collected over 10,000 specimens,	during her career, corrick collected over 10,000 specimens, of which nearly 6,000 are held in the national herbarium of victoria. she was an authority on the genus pultenaea and published six names, despite being a "self-taught amateur". she collaborated with photographer bruce furhrer on two books, wildflowers of sout...	wikipedia
3340594266525da0e9a240fc8702191751c52cd8	corrick was employed as a technical assistant by	corrick was employed as a technical assistant by the national herbarium of victoria from 1975 to 1986, before being promoted to technical officer from 1986 until her retirement in 1987. she was then appointed honorary associate at the herbarium.	wikipedia
d7a9a0d6c2d8bc481bdcff3d601142a86c9a56de	margaret georgina corrick was born in hobart, tasmania	margaret georgina corrick was born in hobart, tasmania on 11 october 1922. her parents were members of the tasmanian field naturalists club and she and her sisters joined as children. she was educated at the friends' school in hobart. before her marriage she worked as a bank clerk, while afterwards she moved with her b...	wikipedia
9777acd7a9e85c52fd302c755a43f9244cf09ec6	kazuki watanabe is a japanese motorcycle racer. he	kazuki watanabe is a japanese motorcycle racer. he competes in the mfj all japan road race jsb1000 championship, aboard a suzuki gsx-r1000. he has previously competed in the mfj all japan road race jsb1000 championship, the mfj all japan road race gp250 championship and the mfj all japan road race j-gp2 championship, w...	wikipedia
b00575118ea50fd289a15c73a2f19b88d710d246	kazuki watanabe (渡辺一樹, watanabe kazuki, born 2	kazuki watanabe (渡辺一樹, watanabe kazuki, born 2 october 1990) is a japanese motorcycle racer. he competes in the mfj all japan road race jsb1000 championship, aboard a suzuki gsx-r1000. he has previously competed in the mfj all japan road race jsb1000 championship, the mfj all japan road race gp250 championship and the...	wikipedia