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Mathematical problem
In number theory, zero-sum problems are certain kinds of combinatorial problems about the structure of a finite abelian group. Concretely, given a finite
Zero-sum_problem
Situation where total gains match total losses
Zero-sum game is a mathematical representation in game theory and economic theory of a situation that involves two competing entities, where the result
Zero-sum_game
Topics referred to by the same term
Zero-sum problem, Zero-sum thinking, "Zero Sum" (The X-Files episode) Monthly Comic Zero Sum, a monthly shōjo manga published by Ichijinsha "Zero-Sum"
Zero_sum_(disambiguation)
Decision problem in computer science
The subset sum problem (SSP) is a decision problem in computer science. In its most general formulation, there is a multiset S {\displaystyle S} of integers
Subset_sum_problem
Problem in computer science
maximum sum subarray problem, also known as the maximum segment sum problem, is the task of finding a contiguous subarray with the largest sum, within
Maximum_subarray_problem
branch of number theory. Typical topics include covering system, zero-sum problems, various restricted sumsets, and arithmetic progressions in a set
Barycentric-sum_problem
Study of structures where a subset must sum to zero
In mathematics, zero-sum Ramsey theory or zero-sum theory is a branch of combinatorics. It deals with problems of the following kind: given a combinatorial
Zero-sum_Ramsey_theory
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
Problem in number theory
Unsolved problem in mathematics Is there a number that is not 4 or 5 modulo 9 and that cannot be expressed as a sum of three cubes? More unsolved problems in
Sums_of_three_cubes
Topics referred to by the same term
one-point union of topological spaces Whitney sum, of fiber bundles Zero-sum problem in combinatorics Sum (Unix), a program for generating checksums StartUp-Manager
Sum
Algorithmic technique
applied a randomized variant of "fictitious play" to solve two-player zero-sum games efficiently using the multiplicative weights algorithm. In this case
Multiplicative weight update method
Multiplicative_weight_update_method
Seven mathematical problems with a US$1 million prize for each solution
to each problem. The Clay Mathematics Institute officially designated the title Millennium Problem for the seven unsolved mathematical problems, the Birch
Millennium_Prize_Problems
Mathematical problem in number theory
theory, Waring's problem asks whether each natural number k has an associated positive integer s such that every natural number is the sum of at most s natural
Waring's_problem
Mathematical problem
problem may be solved using simple calculation. With 64 squares on a chessboard, if the number of grains doubles on successive squares, then the sum of
Wheat_and_chessboard_problem
Problem in computer science
Unsolved problem in computer science What is the Turing run-time complexity of the square-root sum problem? More unsolved problems in computer science
Square-root_sum_problem
Sum of inverse squares of natural numbers
The Basel problem is a problem in mathematical analysis with relevance to number theory, concerning an infinite sum of inverse squares. It was first posed
Basel_problem
Combinatorial optimization problem
problem using graph theory: The assignment problem consists of finding, in a weighted bipartite graph, a matching of maximum size, in which the sum of
Assignment_problem
the zero-weight cycle problem is the problem of deciding whether a directed graph with weights on the edges (which may be positive or negative or zero) has
Zero-weight_cycle_problem
Israeli mathematician
(aged 72)) was an Israeli mathematician, known for his contributions to the Zero-sum problem as one of the discoverers of the Erdős–Ginzburg–Ziv theorem. Abraham
Abraham_Ziv
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
Probability of shared birthdays
In probability theory, the birthday problem asks for the probability that, in a set of n randomly chosen people, at least two will share the same birthday
Birthday_problem
NP-complete problem in computer science
subsets S1 and S2 such that the sum of the numbers in S1 equals the sum of the numbers in S2. Although the partition problem is NP-complete, there is a pseudo-polynomial
Partition_problem
Approximation method in statistics
minimizing the sum of the squared residuals—the differences between observed values and the values predicted by the model. Least squares problems fall into
Least_squares
Problem in combinatorial optimization
knapsack problem is often used to refer specifically to the subset sum problem. The subset sum problem is one of Karp's 21 NP-complete problems. Knapsack
Knapsack_problem
Chinese mathematician
combinatorial number theory: covering systems, restricted sumsets, and zero-sum problems or EGZ Theorem. With Stephen Redmond, he posed the Redmond–Sun conjecture
Zhi-Wei_Sun
Linear combination of nth roots
form of a sum of radicals. In 1991, Blömer proposed a polynomial time Monte Carlo algorithm for determining whether a sum of radicals is zero, or more
Sum_of_radicals
Basic integral in elementary calculus
contribution of each ti to the Riemann sum will be at least 0 · ε/n and at most 1 · ε/n. This makes the total sum at least zero and at most ε. So let δ be a positive
Riemann_integral
Lowest possible energy of a quantum system or field
where zero-point cancellations occur in the low-energy universe we observe today. This discrepancy is known as the cosmological constant problem and it
Zero-point_energy
Problem in physics and celestial mechanics
not counted here) If the sum of the energies is negative, then they both trace out ellipses. If the sum of both energies is zero, then they both trace out
N-body_problem
Skolem problem: can an algorithm determine if a constant-recursive sequence contains a zero? The values of g(k) and G(k) in Waring's problem Do the Ulam
List of unsolved problems in mathematics
List_of_unsolved_problems_in_mathematics
Complexity class used to classify decision problems
given subset has sum zero is a verifier. Clearly, summing the integers of a subset can be done in polynomial time, and the subset sum problem is therefore
NP_(complexity)
Analytic function in mathematics
(s)=\sum _{n=0}^{\infty }a_{2n}t^{2n}} which led Riemann to his famous hypothesis. The functional equation shows that the Riemann zeta function has zeros at
Riemann_zeta_function
Algorithm in numerical analysis
is zero the first time around. var y = input[i] - c // Alas, sum is big, y small, so low-order digits of y are lost. var t = sum + y // (t - sum) cancels
Kahan_summation_algorithm
Addition of several numbers or other values
{\displaystyle \sum _{i=1}^{n}i.} For long summations, and summations of variable length (defined with ellipses or Σ notation), it is a common problem to find
Summation
Even integers as sums of two primes
best-known unsolved problems in number theory and all of mathematics. It states that every even natural number greater than 2 is the sum of two prime numbers
Goldbach's_conjecture
Mathematical optimization problem
definition of the problem is to minimize the total cost of the flow over all edges: ∑ ( u , v ) ∈ E a ( u , v ) ⋅ f ( u , v ) {\displaystyle \sum _{(u,v)\in
Minimum-cost_flow_problem
Problem in applied mathematics
or in field theories involving a non-zero density of strongly interacting fermions. In physics the sign problem is typically (but not exclusively) encountered
Numerical_sign_problem
Mathematical algorithm
algorithm is used to solve non-linear least squares problems, which is equivalent to minimizing a sum of squared function values. It is an extension of
Gauss–Newton_algorithm
Combinatorial optimization problem
between the two facilities). The problem is to assign all facilities to different locations with the goal of minimizing the sum of the distances multiplied
Quadratic_assignment_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
Complexity class
salesman problem—is NP-hard. The subset sum problem is another example: given a set of integers, does any non-empty subset of them add up to zero? That is
NP-hardness
Number of nonzero symbols in a string
uint64_t m32 = 0x00000000ffffffff; //binary: 32 zeros, 32 ones const uint64_t h01 = 0x0101010101010101; //the sum of 256 to the power of 0,1,2,3... //This is
Hamming_weight
Mathematical models of strategic interactions
science and computer science. Initially, game theory addressed two-person zero-sum games, in which a participant's gains or losses are exactly balanced by
Game_theory
Algorithmic problem in computer science
knapsack problem, each of the amounts xi must be either zero or wi; the continuous knapsack problem differs by allowing xi to range continuously from zero to
Continuous_knapsack_problem
Four basic unsolved problems about prime numbers
known as Landau's problems. They are as follows: Goldbach's conjecture: Can every even integer greater than 2 be written as the sum of two primes? Twin
Landau's_problems
Mathematical expression with disputed status
Zero to the power of zero, denoted as 00, is a mathematical expression with different interpretations depending on the context. In certain areas of mathematics
Zero_to_the_power_of_zero
j are added. Informally, the problem is to maximize the sum of the values of the items in the knapsack so that the sum of the weights is less than or
Quadratic_knapsack_problem
Concept in graph theory
In graph theory, a nowhere-zero flow or NZ flow is a network flow that is nowhere zero. It is intimately connected (by duality) to coloring planar graphs
Nowhere-zero_flow
FIND-SUBSET-SUM is in NP-equivalent. Given a set of integers, FIND-SUBSET-SUM is the problem of finding some nonempty subset of the integers that adds up to zero
NP-equivalent
Class of ordinary differential equations
In mathematics and its applications, a Sturm–Liouville problem is a second-order linear ordinary differential equation of the form d d x [ p ( x ) d y
Sturm–Liouville_theory
Resource problem in machine learning
maximize the sum of the collected rewards. The horizon H {\displaystyle H} is the number of rounds that remain to be played. The bandit problem is formally
Multi-armed_bandit
18 mathematical problems stated in 1998
Smale's problems is a list of eighteen unsolved problems in mathematics proposed by Steve Smale in 1998 and republished in 1999. Smale composed this list
Smale's_problems
Divergent sum of positive unit fractions
infinite series formed by summing all positive unit fractions: ∑ i = 1 ∞ 1 i = 1 1 + 1 2 + 1 3 + 1 4 + 1 5 + ⋯ . {\displaystyle \sum _{i=1}^{\infty }{\frac
Harmonic_series_(mathematics)
Book by Robert Wright
directed first and foremost by "non-zero-sumness" i.e., the prospect of creating new interactions that are not zero-sum. The principal argument of Nonzero
Nonzero: The Logic of Human Destiny
Nonzero:_The_Logic_of_Human_Destiny
Principle in mathematical optimization
linear programming problem. Von Neumann noted that he was using information from his game theory, and conjectured that two person zero sum matrix game was
Duality_(optimization)
Infinite series that is not convergent
the partial sums of the series does not have a finite limit. If a series converges, the individual terms of the series must approach zero. Thus any series
Divergent_series
Numerical optimization process
A sum-of-squares optimization program is an optimization problem with a linear cost function and constraints that certain polynomials constructed from
Sum-of-squares_optimization
On the distribution of prime numbers
attempt the rigorous solution of Goldbach's problem, viz., whether every integer is expressible as the sum of two positive prime numbers; and further to
Hilbert's_eighth_problem
Model for physics of semiconductors
temperature goes to zero. He explained why metal samples containing magnetic impurities have a resistance minimum (see Kondo effect). The problem of finding a
Kondo_model
Mathematics problem
The 100 prisoners problem is a mathematical problem in probability theory and combinatorics. In this problem, 100 numbered prisoners must find their own
100_prisoners_problem
Economical computational problem
computation in two-player zero-sum games is known as min-max optimization. The present page studies the more general problem of non-zero-sum games with many players
Nash_equilibrium_computation
Replacing a number with a simpler value
dealing with a gentle slope from one to zero, the output would be zero for the first few terms until the sum of the error and the current value becomes
Rounding
Polynomial-time algorithm for the assignment problem
method is a combinatorial optimization algorithm that solves the assignment problem in polynomial time and which anticipated later primal–dual methods. It
Hungarian_algorithm
Decision rule used for minimizing the possible loss for a worst-case scenario
to maximize the minimum gain. Originally formulated for several-player zero-sum game theory, covering both the cases where players take alternate moves
Minimax
Natural number
non-trivial zeroes in the Riemann zeta function. It is in equivalence with the sum of ceilings of the first two such zeroes, 15 and 22. The secretary problem is
37_(number)
Millennium Prize Problem
Newtonian fluid—as the sum of contributions by pressure, viscous stress and an external body force. Since the setting of the problem proposed by the Clay
Navier–Stokes existence and smoothness
Navier–Stokes_existence_and_smoothness
2.71828...; base of natural logarithms
anno debeatur? transl.: This is a problem of another kind: The question is, if some lender were to invest [a] sum of money [at] interest, let it accumulate
E_(mathematical_constant)
On dissections between polyhedra
which all of three-dimensional space can be tiled periodically is zero. Unsolved problem in mathematics In spherical or hyperbolic geometry, must polyhedra
Hilbert's_third_problem
2007 studio album by Nine Inch Nails
Year Zero is the fifth studio album by the American industrial rock band Nine Inch Nails, released by Interscope Records on April 17, 2007. Conceived while
Year_Zero_(album)
Polynomial whose coefficients are all 1 or −1
Mahler measure, zero distribution, and autocorrelation remain active. A polynomial P ( z ) = ∑ j = 0 n a j z j {\displaystyle P(z)=\sum _{j=0}^{n}a_{j}z^{j}}
Littlewood_polynomial
Problem in computer science
computational complexity theory and quantum computing, Simon's problem is a computational problem that is proven to be solved exponentially faster on a quantum
Simon's_problem
Choosing the fewest coins to make a given amount of money
as w1 through wn. The problem is: given an amount W, also a positive integer, to find a set of non-negative (positive or zero) integers {x1, x2, ...
Change-making_problem
Sequence in computer science
functional programming languages. Prefix sums have also been much studied in parallel algorithms, both as a test problem to be solved and as a useful primitive
Prefix_sum
Numerical method for solving physical or engineering problems
v_{j}\cdot \nabla v_{k}\,ds} are both zero. If we write u ( x ) = ∑ k = 1 n u k v k ( x ) {\displaystyle u(x)=\sum _{k=1}^{n}u_{k}v_{k}(x)} and f ( x )
Finite_element_method
Probability puzzle
The Monty Hall problem is a brain teaser, in the form of a probability puzzle, based nominally on the American television game show Let's Make a Deal
Monty_Hall_problem
23 mathematical problems stated in 1900
Hilbert's problems are 23 problems in mathematics published by German mathematician David Hilbert in 1900. They were all unsolved at the time, and several
Hilbert's_problems
Russian mathematician (1937–2008)
{\displaystyle S=\sum _{x=1}^{P}e^{2\pi i(a_{1}x/p^{n}+\cdots +a_{n}x^{n}/p)},\quad (a_{s},p)=1,\quad 1\leq s\leq n,} led to the new bounds for zeros of the Dirichlet
Anatoly_Karatsuba
Game theory scenario
for two or more parties. It is also called a positive-sum game as it is the opposite of a zero-sum game. If a win–win scenario is not achieved, the scenario
Win–win_game
Type of mathematical expression
{\displaystyle \sum _{k=0}^{n}a_{k}x^{k}} That is, a polynomial can either be zero or can be written as the sum of a finite number of non-zero terms. Each
Polynomial
Geometry problem about finding touching circles
Since zero bend's a dead straight line And concave bends have minus sign, The sum of the squares of all four bends Is half the square of their sum. Sundry
Problem_of_Apollonius
Problem in computational complexity theory
n} real numbers contains three elements that sum to zero. A generalized version, k {\displaystyle k} -SUM, asks the same question on k {\displaystyle k}
3SUM
Infinite sum
{\displaystyle 0+0+0+\cdots ,} which has partial sums equal to zero at every term and thus sums to zero. Grouping its elements in pairs starting after the
Series_(mathematics)
Sums vector sets A and B by adding each vector in A to each vector in B
ball, centered at 0 (the non-zero assumption is needed because the open ball of radius 0 is the empty set). The Minkowski sum of a closed ball and an open
Minkowski_addition
Natural number
integers n ≥ 34 {\displaystyle n\geq 34} can be expressed as the sum of five non-zero squares. There are five countably infinite Ramsey classes of permutations
5
the zeroes of those polynomials; the sum of the zeroes is the Möbius function evaluated at (in the very last case above) 21; only half of the zeroes are
List of trigonometric identities
List_of_trigonometric_identities
Concept in cosmology
problem in physics Why is the vacuum energy density much smaller than a zero-point energy suggested by quantum field theory? More unsolved problems in
Cosmological_constant_problem
Concept in mathematical optimization
instance, in utility maximization problems. With an extra multiplier μ 0 ≥ 0 {\displaystyle \mu _{0}\geq 0} , which may be zero (as long as ( μ 0 , μ , λ )
Karush–Kuhn–Tucker_conditions
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
the sum of reciprocals (or sum of inverses) is defined as the sum of reciprocals of some series of positive integers (counting numbers). It is a sum of
List_of_sums_of_reciprocals
Problem in statistical estimation
simplifying series relating to the German Tank Problem. ∑ n = m ∞ 1 ( n k ) = k k − 1 1 ( m − 1 k − 1 ) {\displaystyle \sum _{n=m}^{\infty }{\frac {1}{\binom {n}{k}}}={\frac
German_tank_problem
Technique to make a model more generalizable and transferable
defined as the number of non-zero elements in w {\displaystyle w} . Solving a L 0 {\displaystyle L_{0}} regularized learning problem, however, has been demonstrated
Regularization_(mathematics)
Inverse of a finite difference
calculus of finite differences, the indefinite sum (or antidifference operator), denoted by ∑ x {\textstyle \sum _{x}} or Δ − 1 {\displaystyle \Delta ^{-1}}
Indefinite_sum
Arithmetic operation
and division. The addition of two whole numbers results in the total or sum of those values combined. For example, the adjacent image shows two columns
Addition
On solvability of Diophantine equations
Hilbert's tenth problem is the tenth on the list of mathematical problems that the German mathematician David Hilbert posed in 1900. It is the challenge
Hilbert's_tenth_problem
Extremes of a linear function over a convex polygonal region occur at the region's corners
solution, all terms in the sum are nonnegative. Since the sum is equal to zero, we must have that each individual term is equal to zero. Hence, c T x ∗ = c T
Fundamental theorem of linear programming
Fundamental_theorem_of_linear_programming
Zero-sum game where competitions between strategies contain a cycle
An intransitive or non-transitive game is a zero-sum game in which pairwise competitions between the strategies contain a cycle. If strategy A beats strategy
Intransitive_game
Smooth approximation to the maximum function
convex. We can define a strictly convex log-sum-exp type function by adding an extra argument set to zero: L S E 0 + ( x 1 , . . . , x n ) = L S E ( 0
LogSumExp
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
Methodic assignment of colors to elements of a graph
Vertex coloring is often used to introduce graph coloring problems, since other coloring problems can be transformed into a vertex coloring instance. For
Graph_coloring
Equivalence of optimization problems
\min\{g'\}=\sum _{p_{i}\in P}r(p_{i})+\sum _{q_{j}\in Q}c(q_{j}).} The above minimization problem can then be formulated as a minimum-cut problem by constructing
Max-flow_min-cut_theorem
ZERO SUM-PROBLEM
ZERO SUM-PROBLEM
Girl/Female
Latin
Mother of Asopus.
Boy/Male
Hebrew American
Sun child; bright sun.
Female
Greek
(ἩÏá½¼) Greek name derived form the word hÄ“rÅs, HERO means "hero." In mythology, this is the name of the lover of Leandros (Latin Leander).
Male
Finnish
Finnish form of German Erich, EERO means "ever-ruler."Â
Boy/Male
Arabic
Empty.
Male
Finnish
Short form of Finnish Antero, TERO means "man; warrior."
Male
Spanish
Spanish name derived from Latin juniperus, JUNÃPERO means "juniper tree."
Boy/Male
Hindu, Indian, Marathi
Fragrance; Flower; Sum; Total
Female
Thai/Siamese
Thai name SOM means "orange (the fruit)."
Boy/Male
Sikh
Sun, Godly, Warrior, Brave, A musical note
Female
English
Short form of English Susan, SUE means "lily."
Boy/Male
Arabic, Australian, German, Greek, Kurdish
Empty; Void
Girl/Female
Australian, Danish, Swedish
Sun
Male
English
Short form of English Humbert, possibly HUM means "bright support."Â
Boy/Male
American, Arabic, British, Czechoslovakian, Danish, Dutch, English, Finnish, French, German, Hawaiian, Hebrew, Hindu, Indian, Iranian, Jamaican, Malayalam, Parsi, Sanskrit, Swedish, Tamil, Telugu, Urdu
Told by God; God has Listen; To Hear; Sun; His Name is God; Sun Child; Little Sun; Strong Person; Heard of God; God; Good Person
Male
English
Short form of English Simon, SIM means "hearkening."
Boy/Male
Biblical
Root, that straitens or binds, that keeps tight.
Boy/Male
Australian, Biblical, Danish, German, Swedish
Mame; Renown; Sun Child; Little Sun
Male
Italian
 Short form of Italian Raniero, NERO means "wise warrior." Compare with another form of Nero.
Girl/Female
Indian, Kannada, Korean, Telugu
The Sun; Obedient
ZERO SUM-PROBLEM
ZERO SUM-PROBLEM
ZERO SUM-PROBLEM
ZERO SUM-PROBLEM
ZERO SUM-PROBLEM
ZERO SUM-PROBLEM
ZERO SUM-PROBLEM
n.
A vegetable secretion of many trees or plants that hardens when it exudes, but is soluble in water; as, gum arabic; gum tragacanth; the gum of the cherry tree. Also, with less propriety, exudations that are not soluble in water; as, gum copal and gum sandarac, which are really resins.
n.
A quantity of money or currency; any amount, indefinitely; as, a sum of money; a small sum, or a large sum.
n.
Fig.: The lowest point; the point of exhaustion; as, his patience had nearly reached zero.
v. i.
To form a scum; to become covered with scum. Also used figuratively.
n.
A cipher; zero.
n.
See Gum tree, below.
n.
The point from which the graduation of a scale, as of a thermometer, commences.
pl.
of Zero
n.
A cipher; nothing; naught.
v. i.
To exude or from gum; to become gummy.
v. t.
To smear with gum; to close with gum; to unite or stiffen by gum or a gumlike substance; to make sticky with a gumlike substance.
n.
The aggregate of two or more numbers, magnitudes, quantities, or particulars; the amount or whole of any number of individuals or particulars added together; as, the sum of 5 and 7 is 12.
pl.
of Zero
n.
A large and valuable fish of the Mackerel family, of the genus Scomberomorus. Two species are found in the West Indies and less commonly on the Atlantic coast of the United States, -- the common cero (Scomberomorus caballa), called also kingfish, and spotted, or king, cero (S. regalis).
a.
Old-fashioned; queer; odd; as, a rum idea; a rum fellow.
n.
The principal points or thoughts when viewed together; the amount; the substance; compendium; as, this is the sum of all the evidence in the case; this is the sum and substance of his objections.
v. t.
To expose to the sun's rays; to warm or dry in the sun; as, to sun cloth; to sun grain.