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On short connecting nets with added points
mathematics, the Steiner tree problem, or minimum Steiner tree problem, named after Jakob Steiner, is an umbrella term for a class of problems in combinatorial
Steiner_tree_problem
Topics referred to by the same term
mathematics, Steiner's problem (named after Jakob Steiner) may refer to: Steiner's calculus problem The Steiner tree problem Steiner's conic problem This disambiguation
Steiner's_problem
Geometric inequality applicable to any closed curve
solution to the problem, proving this fact is rather difficult. The first progress toward the solution was made by Swiss geometer Jakob Steiner in 1838, using
Isoperimetric_inequality
In enumerative geometry, Steiner's conic problem is the problem of finding the number of smooth conics tangent to five given conics in the plane in general
Steiner's_conic_problem
Professional wrestling tag team
Doom to wrestle the Steiners at Halloween Havoc, in which the Steiners lost. On November 1, 1989, in Atlanta, Georgia, the Steiners defeated the Freebirds
Steiner_Brothers
Question about single-shape aperiodic tiling
shape is called an einstein, a word play on ein Stein, German for "one stone". Several variants of the problem, depending on the particular definitions of
Einstein_problem
The Steiner traveling salesman problem (Steiner TSP, or STSP) is an extension of the traveling salesman problem. Given a list of cities, some of which
Steiner travelling salesman problem
Steiner_travelling_salesman_problem
Number of digits needed to express a number in a particular base
In mathematics and computer science, optimal radix choice is the problem of choosing the base, or radix, that is best suited for representing numbers
Optimal_radix_choice
Process of achieving a goal by overcoming obstacles
Problem solving is the process of achieving a goal by overcoming obstacles, a frequent part of most activities. Problems in need of solutions range from
Problem_solving
Term in mathematics
the solution of the second Cousin problem. The standard complex space C n {\displaystyle \mathbb {C} ^{n}} is a Stein manifold. Every domain of holomorphy
Stein_manifold
2.71828...; base of natural logarithms
_{b}x} occurs at x = e {\displaystyle x=e} (Steiner's problem, discussed below). This is useful in the problem of a stick of length L that is broken into
E_(mathematical_constant)
Variant of the Steiner tree problem in geometry and combinatorics
The rectilinear Steiner tree problem, minimum rectilinear Steiner tree problem (MRST), or rectilinear Steiner minimum tree problem (RSMT) is a variant
Rectilinear_Steiner_tree
American sci-fi television series
3 Body Problem is an American science fiction television series created by David Benioff, D. B. Weiss, and Alexander Woo. It is the third adaptation of
3_Body_Problem_(TV_series)
Austrian esotericist (1861–1925)
Steiners Geburtstag am 27. Februar 1861 – Neue Dokumente" Archived 28 June 2014 at the Wayback Machine, Das Goetheanum 2009/9, pp. 3ff Rudolf Steiner
Rudolf_Steiner
NP-hard problem in combinatorial optimization
In the theory of computational complexity, the travelling salesman problem (TSP) asks the following question: "Given a list of cities and the distances
Travelling_salesman_problem
Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer
List of unsolved problems in mathematics
List_of_unsolved_problems_in_mathematics
American writer and commentator (born 1944)
mortgage crisis began, Stein wrote a column for the online version of CBS News Sunday Morning. He proclaimed that the foreclosure problem would "blow over and
Ben_Stein
Type of algorithm
in the optimum solution, the problem is W[2]-hard (due to a folklore reduction from the Dominating Set problem). Steiner Tree is also known to be APX-hard
Parameterized approximation algorithm
Parameterized_approximation_algorithm
Educational philosophy
Rudolf Steiners". Archived from the original on 10 February 2021. Retrieved 10 February 2021. J. Vasagard, "A different class: the expansion of Steiner schools"
Waldorf_education
German nun and philosopher (1891–1942)
Problem as it Developed Historically and Considered Phenomenologically) was awarded a doctorate in philosophy with the summa cum laude honor. Stein then
Edith_Stein
Mathematical problem involving optimal stopping theory
known as the marriage problem, the sultan's dowry problem, the fussy suitor problem, the googol game, and the best choice problem. Its solution is also
Secretary_problem
Swiss mathematician (1796–1863)
symmetrization Steiner system Steiner surface Steiner conic Steiner's conic problem Steiner's problem Steiner tree Steiner chain Poncelet–Steiner theorem Parallel
Jakob_Steiner
American economist (1916–1999)
stop it through policy is not an insurmountable problem, since it is sure to stop regardless. Herbert Stein (1995). On the Other Hand – Essays on Economics
Herbert_Stein
geometry, a Steiner point is a point that is not part of the input to a geometric optimization problem but is added during the solution of the problem, to create
Steiner point (computational geometry)
Steiner_point_(computational_geometry)
Open problem on 3x+1 and x/2 functions
Unsolved problem in mathematics For even numbers, divide by 2; For odd numbers, multiply by 3 and add 1. With enough repetition, do all positive integers
Collatz_conjecture
Scottish football player and manager (1922–1985)
rejected and there were rumours of financial problems. All but two of the Scottish professionals left. Stein initially left his wife, Jean, and young daughter
Jock_Stein
Estimation problem in physics or engineering
A Fermi problem (or Fermi question, Fermi quiz), also known as an order-of-magnitude problem, is an estimation problem in physics or engineering education
Fermi_problem
Field equation for spin-3/2 fermions
equations for composite particles. For spin 3 / 2 {\displaystyle 3/2} , this problem is subtle because the vector-spinor field contains unphysical spin-1/2
Rarita–Schwinger_equation
Block design in combinatorial mathematics
longer strictly adhered to. Long-standing problems in design theory were whether there exist any nontrivial Steiner systems (nontrivial meaning t < k < n)
Steiner_system
Type of geometric grid
Hanan Grid Problems Networks, vol. 38, 2000, pp. 200-221 Christine R. Leverenz, Miroslaw Truszczynski, The Rectilinear Steiner Tree Problem: Algorithms
Hanan_grid
Theorem on equilateral triangles
ISBN 978-1402788291. Gueron, Shay; Tessler, Ran (2002). "The Fermat-Steiner problem". Amer. Math. Monthly. 109 (5): 443–451. doi:10.2307/2695644. JSTOR 2695644
Viviani's_theorem
Phenomenon in decision theory and estimation theory
In decision theory and estimation theory, Stein's example (also known as Stein's phenomenon or Stein's paradox) is the observation that when three or more
Stein's_example
Computational problem of graph theory
In graph theory, the shortest path problem is the problem of finding a path between two vertices (or nodes) in a graph such that the sum of the weights
Shortest_path_problem
Japanese anime television series
visual novel Steins;Gate 0. It serves as a sequel to Steins;Gate and the 2011 anime adaptation. The series is the final iteration of the Steins;Gate 0 story
Steins;Gate_0_(TV_series)
American author (1874–1946)
is where there is an adversary, a problem. Why Stein is not, finally, a good or helpful writer. There is no problem. It's all affirmation. A rose is a
Gertrude_Stein
Mathematical counting-out question
computer science and mathematics, the Josephus problem (or Josephus permutation) is a theoretical problem related to a certain counting-out game. Such games
Josephus_problem
Stein. Stein originally called the tripods of this problem "semicrosses", and they were also called Stein corners by Solomon W. Golomb. A collection of disjoint
Tripod_packing
German applied mathematician and theoretical computer scientist
algorithms for combinatorial optimization problems including the travelling salesperson problem and the Steiner tree problem. She is an associate professor at
Vera_Traub
American professor of mathematics
developer of SageMath and founder of CoCalc. Stein does computational and theoretical research into the problem of computing with modular forms and the Birch
William_A._Stein
UN agency to protect and support refugees
of Humanitarian Action. Cornell University Press. 2002. Nicholas Steiner. Problems of Protection. Routledge. 2003. Wikimedia Commons has media related
United Nations High Commissioner for Refugees
United_Nations_High_Commissioner_for_Refugees
foundational in the study of the problem of differentiation of integrals. The result is named after the mathematicians Elias M. Stein and Jan-Olov Strömberg. Let
Stein–Strömberg_theorem
Three tangent circles in a triangle
construction of the Malfatti circles was given by Steiner (1826), and many mathematicians have since studied the problem. Malfatti himself supplied a formula for
Malfatti_circles
American politician and physician (born 1950)
December 16, 2016. Thrush, Glenn (September 19, 2016). "Jill Stein: Trump may have 'memory problem'". Politico. Archived from the original on June 22, 2025
Jill_Stein
Conjecture on zeros of the zeta function
Unsolved problem in mathematics Do all non-trivial zeros of the Riemann zeta function have a real part equal to one half? More unsolved problems in mathematics
Riemann_hypothesis
Austrian-born British concert pianist
1959, there were serious problems in the marriage. Harewood began an affair with the violinist Patricia Tuckwell, but Stein rejected the idea of divorce
Marion_Stein
Combinatorial optimization problem
assignment problem is a fundamental combinatorial optimization problem. In its most general form, the problem is as follows: The problem instance has
Assignment_problem
Gospels of Matthew, Mark, and Luke
the Synoptic Problem is "practically insoluble". Nearly every conceivable theory has been advanced as a solution to the synoptic problem. The most notable
Synoptic_Gospels
Sequence of operations for a task
mathematically rigorous instructions, typically used to solve a class of specific problems or to perform a computation. Algorithms are used as specifications for
Algorithm
Topics referred to by the same term
geometry), a point added in solving a geometric optimization problem to make its solution better Steiner point (triangle), a certain point on the circumcircle
Steiner_point
Type of mathematical functions
Cousin problem. This is called the classic Cousin problem. From this condition, we can see that the Stein manifold is not compact. Levi problem is not
Function of several complex variables
Function_of_several_complex_variables
Geometric problems involving the partition of a figure
In geometry, a dissection problem is the problem of partitioning a geometric figure (such as a polytope or ball) into smaller pieces that may be rearranged
Dissection_problem
Combinatorics problem proposed by Thomas Penyngton Kirkman
shall walk twice abreast. A solution to this problem is an example of a Kirkman triple system, which is a Steiner triple system having a parallelism, that
Kirkman's_schoolgirl_problem
Question in abstract algebra
Whitehead's problem cannot be resolved in ZFC. J. H. C. Whitehead, motivated by the second Cousin problem, first posed the problem in the 1950s. Stein answered
Whitehead_problem
Iranian-American mathematician
undirected graphs, for formulating the Steiner tree problem on networks, and for his work on facility location problems on networks. Hakimi, S. L. (1963),
S._L._Hakimi
connector problem is the problem of finding the minimum Wiener connector. It can be thought of as a version of the classic Steiner tree problem (one of
Wiener_connector
1971 book by George Steiner
University Press. Retrieved 12 July 2014. Siegel, Lee. "Our George Steiner Problem -- and Mine". The New York Times. Retrieved 12 July 2014. Makaryk,
In_Bluebeard's_Castle
Shape that blocks all lines of sight
forests. Opaque sets were introduced by Stefan Mazurkiewicz in 1916, and the problem of minimizing their total length was posed by Frederick Bagemihl in 1959
Opaque_set
Swiss painter, anthroposophical philosopher and writer
durch Eurythmie. Zu Rudolf Steiners „Eurythmie“, Besazio 1976 Die Aktie, Symbol der Schande, Besazio 1976 Rudolf Steiners Philosophie der Freiheit als
Karl_Ballmer
World Wrestling Federation pay-per-view event
(Samu and Fatu). The Steiners and The Headshrinkers had faced each other at WrestleMania in a match won by the Steiners. The Steiners then moved on to feud
King_of_the_Ring_(1993)
American computer scientist (born 1965)
Scholar Record for C. Stein". Stein, Clifford (1992). "Approximation algorithms for multicommodity flow and shop scheduling problems." Doctoral dissertation
Clifford_Stein
In mathematics, the Minkowski–Steiner formula is a formula relating the surface area and volume of compact subsets of Euclidean space. More precisely
Minkowski–Steiner_formula
In mathematics, a semi-infinite programming (SIP) problem is an optimization problem with a finite number of variables and an infinite number of constraints
Generalized semi-infinite programming
Generalized_semi-infinite_programming
Subset of a graph's vertices, including at least one endpoint of every edge
the graph. In computer science, the problem of finding a minimum vertex cover is a classical optimization problem. It is NP-hard, so it cannot be solved
Vertex_cover
Theory of rapid universe expansion
horizon problem are also solved by inflation theory. The flatness problem (also known as the oldness problem) is a cosmological fine-tuning problem within
Cosmic_inflation
Method in probability theory
distribution; therefore the Stein method applied to the problem of Poisson approximation is often referred to as the Stein–Chen method. Probably the most
Stein's_method
Rule for estimating the mean of a dataset
called Stein's phenomenon, and has been demonstrated for several different problem settings, some of which are briefly outlined below. James and Stein demonstrated
James–Stein_estimator
Cognitive science issue
The symbol grounding problem is a concept in the fields of artificial intelligence, cognitive science, philosophy of mind, and semantics. It addresses
Symbol_grounding_problem
Task of computing complete subgraphs
In computer science, the clique problem is the computational problem of finding cliques (subsets of vertices, all adjacent to each other, also called complete
Clique_problem
Logic problem
cannibals problem, and the closely related jealous husbands problem, are classic river-crossing logic puzzles. The missionaries and cannibals problem is a
Missionaries and cannibals problem
Missionaries_and_cannibals_problem
Randomized algorithm for minimum cuts
263872. S2CID 15220291. Karger, David R.; Stein, Clifford (1996). "A new approach to the minimum cut problem" (PDF). Journal of the ACM. 43 (4): 601. doi:10
Karger's_algorithm
Famous sentence
emotions associated with it, an idea also intensively discussed in the problem of universals debate where Peter Abelard and others used the rose as an
Rose is a rose is a rose is a rose
Rose_is_a_rose_is_a_rose_is_a_rose
Problems which attempt to find the most efficient way to pack objects into containers
Packing problems are a class of optimization problems in mathematics that involve attempting to pack objects together into containers. The goal is to
Packing_problems
American mathematician (1931–2018)
Theorems and Applications to Non-elliptic Problems. Princeton University Press. ISBN 978-0-691-08247-9. Stein, Elias (1993). Harmonic Analysis: Real-variable
Elias_M._Stein
Set of computational problems stated by Richard Karp (1973)
NP-complete problems are a set of computational problems which are NP-complete. In his 1972 paper, "Reducibility Among Combinatorial Problems", Richard
Karp's 21 NP-complete problems
Karp's_21_NP-complete_problems
Computational problem in graph theory
maximum flow problems involve finding a feasible flow through a flow network that obtains the maximum possible flow rate. The maximum flow problem can be seen
Maximum_flow_problem
Complexity class
theory, NP-complete problems are the hardest of the problems to which solutions can be verified quickly. Somewhat more precisely, a problem is NP-complete
NP-completeness
South African – Israeli biophysicist
Stein (Hebrew: זאב וילפרד שטיין) is a writer and biophysicist who has applied mathematical principles to medical, biologic, and oncologic problems. Wilfred
Wilfred_Stein
Unsolved problem in computational complexity theory
Unsolved problem in computer science Can the graph isomorphism problem be solved in polynomial time? More unsolved problems in computer science The graph
Graph_isomorphism_problem
Classical problem in combinatorics
The set cover problem is a classical question in combinatorics, computer science, operations research, and complexity theory. Given a set of elements
Set_cover_problem
Set of circles related by tangency
the Pappus chain, the problem of Apollonius, and the three-dimensional Soddy's hexlet. Similarly, if some circles of the Steiner chain are externally tangent
Steiner_chain
American-Canadian professional wrestler, rock musician, and actor (born 1970)
"Enemy" by Fozzy (2005) Sample from "Enemy" by Fozzy, with Jericho on vocals Problems playing this file? See media help. Jericho is the lead singer for the heavy
Chris_Jericho
Problem of solving a partial differential equation subject to prescribed boundary values
In mathematics, a Dirichlet problem asks for a function which solves a specified partial differential equation (PDE) in the interior of a given region
Dirichlet_problem
Unique ellipse tangent to all 3 midpoints of a given triangle's sides
"Steiner Inellipse", MathWorld Dörrie, Heinrich (1965), "Steiner's ellipse problem", 100 Great Problems of Elementary Mathematics, translated by Antin, David
Steiner_inellipse
Antisemitic set of publications of the 1920s
Independent newspaper, beginning with The International Jew: The World's Problem, published on May 22, 1920. At the beginning of 1920, Ford's personal newspaper
The_International_Jew
American artist (1877–1967)
abruptly with the death of Stein. Toklas's later years were very difficult because of poor health and financial problems. She converted to the Catholic
Alice_B._Toklas
List of unsolved computational problems
NP? NC = P problem NP = co-NP problem P = BPP problem P = PSPACE problem L = NL problem PH = PSPACE problem L = P problem L = RL problem Unique games
List of unsolved problems in computer science
List_of_unsolved_problems_in_computer_science
Unsolved problem in graph theory
2/{\sqrt {3}}} times the length of the Steiner minimum tree. Unsolved problem in computer science Is the Steiner ratio of the Euclidean plane equal to
Gilbert–Pollak_conjecture
French and American Writer, literary critic and philosopher (1929–2020)
Steiner's Post-Holocaust Fiction" Archived February 18, 2020, at the Wayback Machine. Jewish Social Studies, 1999. "George Steiner's Jewish Problem"
George_Steiner
Complexity class used to classify decision problems
Unsolved problem in computer science P = ? N P {\displaystyle {\mathsf {P\ {\overset {?}{=}}\ NP}}} More unsolved problems in computer science In
NP_(complexity)
American computer scientist
"When trees collide: An approximation algorithm for the generalized Steiner problem on networks". SIAM Journal on Computing. 24 (3): 440–456. doi:10
Philip_N._Klein
Most populous city in California, US
city has an urban population of bobcats (Lynx rufus). Mange is a common problem in this population. Although Serieys et al. 2014 find selection of immune
Los_Angeles
Periodic spatial graph
Karsten (2017), Periodic Steiner networks minimizing length, arXiv:1705.02471; Alex, Jerome (2019), The Periodic Steiner Problem (Doctoral dissertation)
Laves_graph
Triangle center minimizing sum of distances to each vertex
The Fermat point gives a solution to the geometric median and Steiner tree problems for three points. The Fermat point of a triangle with largest angle
Fermat_point
Japanese visual novel game
Lensenmayer said that this was a smaller problem than it had been with the first Steins;Gate, due to Steins;Gate 0's more serious tone and lesser focus
Steins;Gate_0
Geometry problem about finding touching circles
In Euclidean plane geometry, Apollonius's problem is to construct circles that are tangent to three given circles in a plane (Figure 1). Apollonius of
Problem_of_Apollonius
Ability to make choices voluntarily
Rudolf Steiner, who collaborated in a complete edition of Arthur Schopenhauer's work, wrote The Philosophy of Freedom, which focuses on the problem of free
Free_will
Choosing the fewest coins to make a given amount of money
List of knapsack problems Coin problem The coin collector's problem Cormen, Thomas H.; Leiserson, Charles E.; Rivest, Ronald L.; Stein, Clifford (2009)
Change-making_problem
Minimum-cost tree with exactly k vertices
tree problem has been shown to be NP-hard by a reduction from the Steiner tree problem. The reduction takes as input an instance of the Steiner tree problem:
K-minimum_spanning_tree
American singer and songwriter (born 1981)
operatic style to perform the 18th-century aria Caro mio ben on "Daughter". Problems playing these files? See media help. Beyoncé possesses a mezzo-soprano
Beyoncé
Concern for the well-being of others
such as the teletransportation paradox to illustrate the philosophical problems with personal identity. Effective altruism is a philosophy and social movement
Altruism
STEINERS PROBLEM
STEINERS PROBLEM
Surname or Lastname
English (Sussex)
English (Sussex) : topographic name for someone who lived in a stone-built house (see Stone), with the habitational or agent suffix -er.Translation of German Steiner.
Girl/Female
Muslim/Islamic
Away from all Problems
Boy/Male
Arabic, Indian, Muslim
Problem Solver
Surname or Lastname
English
English : occupational name for a stonemason or stonecutter, or a topographic name for someone who lived on stony ground, from a derivative of Middle English stene ‘stony place’. Compare Stone.
Boy/Male
German
Sone.
Surname or Lastname
English
English : habitational name from a place on the Thames west of London, apparently named with the plural of Old English stÄn ‘stone’. The reference may be to milestones on the Roman road that ran through the town.
Boy/Male
Indian, Tamil
People with this Name are Preferably Intelligent and Very Generous; Highly Knowledgeable in Problem Solving Skills
Girl/Female
Indian, Telugu
Destroyer of Problems
Boy/Male
Hindu, Indian
Problem
Boy/Male
Muslim
Problem solver
Surname or Lastname
English
English : patronymic from Wick 2, or variant of the habitational name Wick, with genitive or plural -s. There has been much confusion between this name and Weeks.In 1638 Richard Wickes (also known as Richard Atwick), of Staines, Middlesex, England, died, leaving a bequest to “my son John Wickes now living in New England.†This John Wickes came from London, England, to Plymouth, MA, in 1635, and subsequently settled at Portsmouth, RI.
Surname or Lastname
English
English : variant of Stevens.
Surname or Lastname
English
English : from Old English stÄn ‘stone’, in any of several uses. It is most commonly a topographic name, for someone who lived either on stony ground or by a notable outcrop of rock or a stone boundary-marker or monument, but it is also found as a metonymic occupational name for someone who worked in stone, a mason or stonecutter. There are various places in southern and western England named with this word, for example in Buckinghamshire, Gloucestershire, Hampshire, Kent, Somerset, Staffordshire, and Worcestershire, and the surname may also be a habitational name from any of these.Translation of various surnames in other languages, including Jewish Stein, Norwegian Steine, and compound names formed with this word.This name was brought independently to New England by many bearers from the 17th century onward. Thomas Scott was one of the founders of Hartford, CT, (coming from Cambridge, MA, with Thomas Hooker) in 1635.
Girl/Female
Bengali, Indian
Eternity; Problem Solver
Surname or Lastname
English
English : patronymic from Steer.
Boy/Male
Australian, Danish, Norwegian, Swedish
Stone Fighter
STEINERS PROBLEM
STEINERS PROBLEM
Girl/Female
Australian, Slavic
Beloved of the People
Girl/Female
Latin Spanish
Delightful. Gives pleasure.
Boy/Male
Muslim
Fertile, Winner, Provider
Boy/Male
Australian, British, English
He who Holds Christ in his Heart
Boy/Male
Indian, Kannada
God of Starts
Surname or Lastname
English
English : habitational name from Dilworth, a place in Lancashire named from Old English dile ‘dill’ (a medicinal and culinary herb) + wor{dh} ‘enclosure’.Irish : English surname adopted by bearers of the Gaelic name Ó Dubhluachra ‘descendant of Dubhluachra’, a compound of dubh ‘black’ + luachair ‘rushes’.
Boy/Male
Muslim/Islamic
Successful
Boy/Male
Indian, Sanskrit
Beautiful
Boy/Male
Indian, Tamil
Lord of Men
Girl/Female
English American
A(influenced by Beryl) or Carys which has been used throughout the English-speaking world in the...
STEINERS PROBLEM
STEINERS PROBLEM
STEINERS PROBLEM
STEINERS PROBLEM
STEINERS PROBLEM
n.
A director.
n.
One who steers; the helmsman of a vessel.
a.
Sourness or severity of countenance; sterness.
v. i.
To be directed and governed; to take a direction, or course; to obey the helm; as, the boat steers easily.
n.
One who fishes with a seine.
a.
Alt. of Problematical
n.
A large fish pound used for the capture of the tunny in the Mediterranean; also applied to the seines used for the same purpose.
n.
One who steers; steersman.
v. t.
To have just and adequate ideas of; to apprehended the meaning or intention of; to have knowledge of; to comprehend; to know; as, to understand a problem in Euclid; to understand a proposition or a declaration; the court understands the advocate or his argument; to understand the sacred oracles; to understand a nod or a wink.
n.
One who proposes problems.
v. i.
To poke or stir up a fire; hence, to tend the fires of furnaces, steamers, etc.
n.
A kind of woolen, or woolen and cotton, cloth, often highly glazed, -- used for curtains, sieves, strainers, etc.
n.
One who steers; as, a boat steerer.
n.
A trussed frame extending fore and aft, usually above deck, and intended to increase the longitudinal strength and stiffness. Used chiefly in American river and lake steamers. Called also hogging frame, and hogback.
n.
A workman who stains; as, a stainer of wood.
n.
A boat or vessel propelled by steam power; -- generally used of river or coasting craft, as distinguished from ocean steamers.
v. t.
To propose problems.
n.
One who stains or tarnishes.
a.
Having the nature of a problem; not shown in fact; questionable; uncertain; unsettled; doubtful.
n.
A certain function relating to a system of forces and their points of application, -- first used by Clausius in the investigation of problems in molecular physics.