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[
{
"definitions": {
"W": [
{
"Q7913892": "Van der Waerden number"
}
],
"k": [
{
"Q12503": "integer (number that can be written without a fractional or decimal component)"
}
],
"\\varepsilon": [
{
"Q3176558": "positive number (real number strictly greater than zero)"
}
]
},
"formula": {
"qID": "1",
"oldId": "2459",
"fid": "3",
"math_inputtex": "W(2, k) > 2^k/k^\\varepsilon",
"title": "Van_der_Waerden's_theorem"
}
},
{
"definitions": {
"X": [
{
"Q36161": "set (fundamental mathematical concept related to the notions of belonging or inclusion)"
}
],
"\\Sigma": [
{
"Q739925": "Family of sets (a collection of some of the subsets of a set)"
}
]
},
"formula": {
"qID": "2",
"oldId": "4050",
"fid": "189",
"math_inputtex": "(X,\\Sigma)",
"title": "Bounded_variation"
}
},
{
"definitions": {
"p": [
{
"Q49008": " prime number (natural number greater than 1 that has no positive divisors other than 1 and itsel)"
}
],
"n": [
{
"Q12503": "integer (number that can be written without a fractional or decimal component)"
}
]
},
"formula": {
"qID": "3",
"oldId": "4189",
"fid": "50",
"math_inputtex": "(p-1)!^n",
"title": "Lindemann–Weierstrass_theorem"
}
},
{
"definitions": {
"f_{c}": [
{
"Q5156597": "Complex quadratic polynomial"
}
],
"z": [
{
"Q11567": "complex number (number that can be put in the form a + bi, where a and b are real numbers and i is called the imaginary unit )"
}
],
"c": [
{
"Q1413083": "parameter"
},
{
"Q50700": "coefficient (number just before a variable)"
}
]
},
"formula": {
"qID": "4",
"oldId": "15332",
"fid": "68",
"math_inputtex": "f_c(z) = z^2 + c",
"title": "Orbit_portrait"
}
},
{
"definitions": {
"x": [
{
"Q50701": "variable (a value that can change, usually with a context of an equation or operation)"
},
{
"Q935944": "Free variables and bound variables"
}
],
"y": [
{
"Q50701": "variable (a value that can change, usually with a context of an equation or operation)"
},
{
"Q935944": "Free variables and bound variables"
}
],
"P": [
{
"Q1144319": "Predicate"
}
]
},
"formula": {
"qID": "5",
"oldId": "391",
"fid": "114",
"math_inputtex": "\\forall x \\, \\forall y \\, P(x,y) \\Leftrightarrow \\forall y \\, \\forall x \\, P(x,y)",
"title": "First-order_logic"
}
},
{
"definitions": {
"\\alpha": [
{
"Q50700": "coefficient (number just before a variable)"
}
],
"x": [
{
"Q3150667": "Indeterminate "
}
]
},
"formula": {
"qID": "6",
"oldId": "6937",
"fid": "5",
"math_inputtex": "\\alpha(x)",
"title": "Clenshaw_algorithm"
}
},
{
"definitions": {
"\\alpha": [
{
"Q2256802": "Schwellenwert",
"Q729113": "Weighted mean"
}
],
"x": [
{
"Q21199": "natural number (numbers used for counting and ordering)"
}
]
},
"formula": {
"qID": "7",
"oldId": "25610",
"fid": "24",
"math_inputtex": "\\alpha(x)",
"title": "Isolation_lemma"
}
},
{
"definitions": {
"\\alpha": [
"exponent (of the Hölder condition)",
{
"Q33456": "exponentiation (mathematical operation)"
}
],
"x": [
{
"Q44946": "point (fundamental object of Euclidean geometry)"
}
]
},
"formula": {
"qID": "8",
"oldId": "27419",
"fid": "4",
"math_inputtex": "\\alpha(x)",
"title": "Singularity_spectrum"
}
},
{
"definitions": {
"\\Psi": [
{
"Q230883": "quantum state (state of a quantum system )"
}
],
"i_{1}": [
{
"Q21199": "natural number (numbers used for counting and ordering)"
}
],
"i_{2}": [
{
"Q21199": "natural number (numbers used for counting and ordering)"
}
],
"\\alpha_{1}": [
{
"Q50700": "coefficient (number just before a variable)"
}
],
"\\alpha_{2}": [
{
"Q50700": "coefficient (number just before a variable)"
}
],
"\\Gamma": [
{
"Q50700": "coefficient (number just before a variable)"
}
],
"\\lambda": [
{
"Q50700": "coefficient (number just before a variable)"
}
],
"\\Phi": [
"Schmidt vectors"
],
"N": [
{
"Q378201": "Qubit (unit of information)",
"Q302462": "Count"
}
]
},
"formula": {
"qID": "9",
"oldId": "14488",
"fid": "36",
"math_inputtex": "|{\\Psi}\\rangle=\\sum_{i_1,i_2,\\alpha_1,\\alpha_2}\\Gamma^{[1]i_1}_{\\alpha_1}\\lambda^{[1]}_{\\alpha_1}\\Gamma^{[2]i_2}_{\\alpha_1\\alpha_2}\\lambda^{[2]}_{{\\alpha}_2}|{i_1i_2}\\rangle|{\\Phi^{[3..N]}_{\\alpha_2}}\\rangle",
"title": "Time-evolving_block_decimation"
}
},
{
"definitions": {
"z": [
{
"Q3913": "binary number (a system that represents numeric values using two symbols; 0 and 1)"
}
],
"x": [
{
"Q3913": "binary number (a system that represents numeric values using two symbols; 0 and 1)"
}
],
"y": [
{
"Q3913": "binary number (a system that represents numeric values using two symbols; 0 and 1)"
}
]
},
"formula": {
"qID": "10",
"oldId": "16784",
"fid": "38",
"math_inputtex": "z*x\\le y",
"title": "Monoidal_t-norm_logic"
}
},
{
"definitions": {
"x": [
{
"Q12916": "real number (quantity along a continuous line)"
}
],
"c": [
{
"Q12916": "real number (quantity along a continuous line)"
}
]
},
"formula": {
"qID": "11",
"oldId": "16716",
"fid": "20",
"math_inputtex": " \\frac{d}{dx}\\left( \\log_c x\\right) = {1 \\over x \\ln c} , \\qquad c > 0, c \\ne 1",
"title": "Differentiation_rules"
}
},
{
"definitions": {
"\\theta": [
{
"Q11352": "angle ( figure formed by two rays)"
}
],
"n": [
{
"Q2303886": "index (the numbering of various objects within the mathematical notation)"
}
]
},
"formula": {
"qID": "12",
"oldId": "2875",
"fid": "2",
"math_inputtex": "\\theta = n \\times 137.508^\\circ,",
"title": "Fermat's_spiral"
}
},
{
"definitions": {
"s_{V}": [
"Kemeny-Young score"
],
"\\mathcal{R}": [
{
"Q526719": "ranking (relationship between items in a set)"
}
]
},
"formula": {
"qID": "13",
"oldId": "9319",
"fid": "2",
"math_inputtex": "s_V(\\mathcal{R})",
"title": "Consistency_criterion"
}
},
{
"definitions": {
"\\ell": [
{
"Q11348": "function (binary relation, which is left-total and right-unique)"
}
],
"m": [
{
"Q1027788": "Argument of a function (independent variable of math function)"
}
]
},
"formula": {
"qID": "14",
"oldId": "21982",
"fid": "43",
"math_inputtex": "\\ell(m)",
"title": "Basis_(universal_algebra)"
}
},
{
"definitions": {
"b": [
{
"Q12916": "real number (quantity along a continuous line)"
}
],
"x": [
{
"Q12916": "real number (quantity along a continuous line)"
}
]
},
"formula": {
"qID": "15",
"oldId": "26321",
"fid": "4",
"math_inputtex": "bx-x^2",
"title": "Adequality"
}
},
{
"definitions": {
"\\omega_{k}": [
{
"Q946764": "Natural frequency"
}
]
},
"formula": {
"qID": "16",
"oldId": "13492",
"fid": "85",
"math_inputtex": "\\omega_{k}",
"title": "Mason–Weaver_equation"
}
},
{
"definitions": {
"\\mathbf{m}_{1}": [
"class mean",
{
"Q19033": "arithmetic mean (sum of a collection of numbers divided by the number of numbers in the collection)"
}
]
},
"formula": {
"qID": "17",
"oldId": "27275",
"fid": "2",
"math_inputtex": "\\mathbf{m}_1",
"title": "Kernel_Fisher_discriminant_analysis"
}
},
{
"definitions": {
"r_{ij}": [
{
"Q126017": "distance (straight line that connects two points)"
}
]
},
"formula": {
"qID": "18",
"oldId": "15283",
"fid": "17",
"math_inputtex": "r_{ij}",
"title": "Implicit_solvation"
}
},
{
"definitions": {
"Z": [
"canonical partition function",
{
"Q230963": "Partition function (statistical mechanics) "
}
],
"j": [
{
"Q2303886": "index (the numbering of various objects within the mathematical notation )"
}
],
"g_{j}": [
"degeneracy factor"
],
"\\mathrm{e}": [
{
"Q168698": "exponential function (unique function which is its own derivative and equals one at zero)"
}
],
"\\beta": [
"inverse temperature",
{
"Q917476": "Thermodynamic beta"
}
],
"E_{j}": [
"energy level"
]
},
"formula": {
"qID": "19",
"oldId": "3897",
"fid": "2",
"math_inputtex": " Z = \\sum_{j} g_j \\cdot \\mathrm{e}^{- \\beta E_j}",
"title": "Partition_function_(statistical_mechanics)"
}
},
{
"definitions": {
"S'": [
"tristimulus values"
]
},
"formula": {
"qID": "20",
"oldId": "8808",
"fid": "39",
"math_inputtex": "S'",
"title": "Color_balance"
}
},
{
"definitions": {
"S'": [
{
"Q17285": "plane (flat, two-dimensional surface)"
},
"plane",
"geometric surface",
"area",
"2-dimensional manifold"
]
},
"formula": {
"qID": "21",
"oldId": "17336",
"fid": "30",
"math_inputtex": "S'",
"title": "Hilbert's_theorem_(differential_geometry)"
}
},
{
"definitions": {
"k": [
{
"Q1663694": "inclusion map"
}
],
"l": [
{
"Q1663694": "inclusion map"
}
],
"i": [
{
"Q1663694": "inclusion map"
}
],
"j": [
{
"Q1663694": "inclusion map"
}
]
},
"formula": {
"qID": "22",
"oldId": "4416",
"fid": "4",
"math_inputtex": "\\text{Ker} (k_* - l_*) \\cong \\text{Im} (i_*, j_*).",
"title": "Mayer–Vietoris_sequence"
}
},
{
"definitions": {
"D": [
"relative graphlet frequency distance"
],
"G": [
"graphlets",
"graphs",
"graph",
{
"Q5597315": "Graphlets"
}
],
"H": [
"graphlets",
"graphs",
"graph",
{
"Q5597315": "Graphlets"
}
],
"i": [
"number",
{
"Q2303886": "index (the numbering of various objects within the mathematical notation)"
}
]
},
"formula": {
"qID": "23",
"oldId": "25343",
"fid": "3",
"math_inputtex": "D(G,H) = \\sum_{i=1}^{29} | F_i(G) - F_i(H) |",
"comments": "F_i is a substitution",
"title": "Graphlets"
}
},
{
"definitions": {
"E_{\\mathrm{k}}": [
"total kinetic energy",
{
"Q46276": "kinetic energy"
}
],
"E_{\\mathrm{r}}": [
"rotational energy",
"angular kinetic energy",
{
"Q2140940": "Rotational energy"
}
],
"E_{\\mathrm{t}}": [
"translational kinetic energy"
]
},
"formula": {
"qID": "24",
"oldId": "566",
"fid": "28",
"math_inputtex": " E_\\text{k} = E_t + E_\\text{r} \\, ",
"title": "Kinetic_energy"
}
},
{
"definitions": {
"\\lambda": [
"length",
{
"Q36253": "length (measured dimension of an object)"
}
],
"L": [
{
"Q1096885": "lattice (subgroup of a real vector space or a Lie group)"
},
"lattice"
],
"B": [
{
"Q189569": "basis"
}
],
"d": [
"number",
{
"Q3176558": "positive number (real number strictly greater than zero)"
}
]
},
"formula": {
"qID": "25",
"oldId": "22618",
"fid": "22",
"math_inputtex": "\\lambda(L(B)) \\leq d",
"title": "Lattice_problem"
}
},
{
"definitions": {
"L": [
"weighted path length"
],
"C": [
{
"Q188889": "code (system of rules to convert information (codification))"
}
],
"T": [
{
"Q188889": "code (system of rules to convert information (codification))"
}
]
},
"formula": {
"qID": "26",
"oldId": "485",
"fid": "10",
"math_inputtex": "L\\left(C\\right) \\leq L\\left(T\\right)",
"title": "Huffman_coding"
}
},
{
"definitions": {
"v": [
{
"Q13824": "phase velocity (rate at which the phase of the wave propagates in space)"
}
],
"c": [
{
"Q2111": "speed of light (speed at which all massless particles and associated fields travel in vacuum)"
}
],
"n": [
{
"Q174102": "Refractive index (optical characteristic of a material)"
}
]
},
"formula": {
"qID": "27",
"oldId": "2623",
"fid": "0",
"math_inputtex": "v = \\frac{c}{n}",
"title": "Dispersion_(optics)"
}
},
{
"definitions": {
"\\sigma_{y}": [
"Allan deviation",
{
"Q1440227": "Allan variance"
}
],
"\\tau": [
"observation time"
],
"\\pi": [
{
"Q167": "pi (ratio of the circumference of a circle to its diameter)"
}
],
"h_{-2}": [
"Power coefficient"
]
},
"formula": {
"qID": "28",
"oldId": "1227",
"fid": "93",
"math_inputtex": "\\sigma_y^2(\\tau) = \\frac{2\\pi^2\\tau}{3}h_{-2}",
"title": "Allan_variance"
}
},
{
"definitions": {
"R_{\\text{s normal}}": [
"surface resistance"
],
"\\omega": [
"resonant frequency"
],
"\\mu_{0}": [
{
"Q1515261": "vacuum permeability (physical constant)"
}
],
"\\sigma": [
"electrical conductivity"
]
},
"formula": {
"qID": "29",
"oldId": "21692",
"fid": "5",
"math_inputtex": " R_{s\\ normal} = \\sqrt{ \\frac{\\omega \\mu_0} {2 \\sigma} }",
"title": "Superconducting_radio_frequency"
}
},
{
"definitions": {
"\\phi_{1}": [
"phase-range"
]
},
"formula": {
"qID": "30",
"oldId": "24277",
"fid": "5",
"math_inputtex": " \\phi_1 = -30^\\circ...+30^\\circ",
"title": "Vienna_rectifier"
}
},
{
"definitions": {
"T_{c}": [
{
"Q1128317": "tax rate (ratio (usually expressed as a percentage) at which a business or person is taxed)"
}
]
},
"formula": {
"qID": "31",
"oldId": "3625",
"fid": "19",
"math_inputtex": "T_c",
"title": "Modigliani–Miller_theorem"
}
},
{
"definitions": {
"T_{c}": [
"critical Temperature",
{
"Q111059": "critical point (critical point where phase boundaries disappear)"
}
]
},
"formula": {
"qID": "32",
"oldId": "17517",
"fid": "2",
"math_inputtex": "T_c",
"title": "Proximity_effect_(superconductivity)"
}
},
{
"definitions": {
"T_{c}": [
"critical surface",
{
"Q111059": "critical point (critical point where phase boundaries disappear)"
}
]
},
"formula": {
"qID": "33",
"oldId": "22538",
"fid": "9",
"math_inputtex": "T_c",
"title": "Multicritical_point"
}
},
{
"definitions": {
"P_{1}": [
{
"Q43260": "polynomial (mathematical expression consisting of variables and coefficients)"
}
],
"X": [
{
"Q3150667": "Indeterminate "
}
],
"P": [
{
"Q43260": "polynomial (mathematical expression consisting of variables and coefficients)"
}
],
"\\alpha_{1}": [
{
"Q11567": "complex number (number that can be put in the form a + bi, where a and b are real numbers and i is called the imaginary unit )"
}
]
},
"formula": {
"qID": "34",
"oldId": "17497",
"fid": "55",
"math_inputtex": "P_1(X)=P(X)/(X-\\alpha_1)",
"title": "Jenkins–Traub_algorithm"
}
},
{
"definitions": {
"k": [
{
"Q2095069": "normalizing constant"
}
],
"n": [
{
"Q21199": "natural number (numbers used for counting and ordering)"
}
]
},
"formula": {
"qID": "35",
"oldId": "5626",
"fid": "4",
"math_inputtex": "= \\frac{k}{n}.",
"title": "Doomsday_argument"
}
},
{
"definitions": {
"n": [
{
"Q21199": "natural number (numbers used for counting and ordering)"
}
],
"i": [
{
"Q2303886": "index (the numbering of various objects within the mathematical notation)"
}
],
"r": [
{
"Q2303886": "index (the numbering of various objects within the mathematical notation)"
}
],
"p_{i}": [
{
"Q1137759": "prime factor ( prime number dividing an integer )"
}
],
"a_{i}": [
"maximum power"
]
},
"formula": {
"qID": "36",
"oldId": "4630",
"fid": "12",
"math_inputtex": "n = \\prod_{i=1}^r p_i^{a_i}",
"title": "Divisor_function"
}
},
{
"definitions": {
"H": [
"system function",
"system response",
"transfer function"
],
"j": [
{
"Q193796": "imaginary unit (square root of negative one, used to define complex numbers)"
}
],
"\\omega": [
{
"Q12916": "real number (quantity along a continuous line)"
}
],
"\\mathcal{F}": [
{
"Q6520159": "Fourier transform (mathematical transform that expresses a mathematical function of time as a function of frequency)"
}
],
"h": [
"impulse response"
],
"t": [
{
"Q11471": "time (dimension in which events can be ordered from the past through the present into the future)"
}
]
},
"formula": {
"qID": "37",
"oldId": "8338",
"fid": "87",
"math_inputtex": "H(j \\omega) = \\mathcal{F}\\{h(t)\\}",
"title": "LTI_system_theory"
}
},
{
"definitions": {
"\\pi": [
{
"Q167": "pi (ratio of the circumference of a circle to its diameter)"
}
]
},
"formula": {
"qID": "38",
"oldId": "1320",
"fid": "31",
"math_inputtex": "\\pi/4",
"title": "Phase-shift_keying"
}
},
{
"definitions": {
"x": [
{
"Q12916": "real number (quantity along a continuous line)"
}
],
"y": [
{
"Q12916": "real number (quantity along a continuous line)"
}
],
"n": [
{
"Q21199": "natural number (numbers used for counting and ordering)"
}
],
"k": [
{
"Q21199": "natural number (numbers used for counting and ordering)"
}
]
},
"formula": {
"qID": "39",
"oldId": "133",
"fid": "6",
"math_inputtex": "(x+y)^n = \\sum_{k=0}^n {n \\choose k}x^{n-k}y^k = \\sum_{k=0}^n {n \\choose k}x^{k}y^{n-k}.\n",
"title": "Binomial_theorem"
}
},
{
"definitions": {
"A": [
{
"Q3686031": "concentration (type of physical property)"
}
],
"t": [
{
"Q11471": "time (dimension in which events can be ordered from the past through the present into the future)"
}
],
"k": [
"reaction rate coefficient"
]
},
"formula": {
"qID": "40",
"oldId": "9082",
"fid": "33",
"math_inputtex": "\\ [A]_t = -kt + [A]_0",
"title": "Rate_equation"
}
},
{
"definitions": {
"q": [
{
"Q9492": "probability (measure of the expectation that an event will occur or a statement is true)"
}
]
},
"formula": {
"qID": "41",
"oldId": "3545",
"fid": "1",
"math_inputtex": "q^{42}",
"title": "Martingale_(betting_system)"
}
},
{
"definitions": {
"\\alpha": [
{
"Q12916": "real number (quantity along a continuous line)"
}
],
"d": [
{
"Q4440864": "dimension (minimum number of coordinates within a space needed to specify any point)"
}
],
"\\varepsilon": [
{
"Q12916": "real number (quantity along a continuous line)"
}
]
},
"formula": {
"qID": "42",
"oldId": "15433",
"fid": "5",
"math_inputtex": "\\alpha(d) \\le \\left(\\sqrt{3/2} + \\varepsilon\\right)^d",
"title": "Borsuk's_conjecture"
}
},
{
"definitions": {
"f^{\\mu}": [
"4-acceleration"
],
"G": [
{
"Q18373": " gravitational constant (empirical physical constant)"
}
],
"c": [
{
"Q2111": "speed of light (speed at which all massless particles and associated fields travel in vacuum)"
}
],
"A": [
{
"Q1289248": "scalar (real numbers in the context auf linear algebra)"
}
],
"T_{\\alpha\\beta}": [
{
"Q876346": "Stress–energy tensor"
}
],
"B": [
{
"Q1289248": "scalar (real numbers in the context auf linear algebra)"
}
],
"T": [
"trace of the stress energy tensor"
],
"\\eta_{\\alpha\\beta}": [
"Minkowski metric",
{
"Q464794": "Minkowski spacetime (mathematical space setting which eases explanation of special relativity)"
}
],
"\\delta _{\\nu}^{\\mu}": [
{
"Q193794": "identity matrix (n × n square matrix with ones on the main diagonal and zeros elsewhere)"
},
{
"Q192826": "Kronecker delta (function)"
}
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{
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{
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{
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},
{
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},
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},
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},
{
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},
{
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}
},
{
"definitions": {
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{
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},
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{
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},
{
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{
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"title": "Stochastic_volatility"
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},
{
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{
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},
{
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},
{
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"direction"
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{
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{
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],
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{
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},
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},
{
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{
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{
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],
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}
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{
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{
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],
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},
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},
{
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},
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},
{
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},
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"oldId": "6392",
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{
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},
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"oldId": "2482",
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},
{
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{
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},
{
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{
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{
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],
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{
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{
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{
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{
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{
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{
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],
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{
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{
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{
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],
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},
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"oldId": "28184",
"fid": "6",
"math_inputtex": " F = \\{ (x,y) : x \\in \\mathcal{R}^b,\\, y \\in \\mathcal{R}^n,\\; x=y \\}.",
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}
},
{
"definitions": {
"X_{i}": [
{
"Q176623": "random variable (variable whose value is subject to variations due to chance)"
}
],
"\\omega": [
{
"Q10290214": "event (in statistics, a set of outcomes to which a probability is assigned)"
}
],
"\\omega_{i}": [
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]
},
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"oldId": "4212",
"fid": "21",
"math_inputtex": "X_i(\\omega)=\\omega_i",
"title": "Almost_surely"
}
},
{
"definitions": {
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{
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},
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],
"q_{i}": [
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}
],
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}
],
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"math_inputtex": "\n{\\partial{L}\\over \\partial q_i} = {\\mathrm{d} \\over \\mathrm{d}t}{\\partial{L}\\over \\partial{\\dot{q_i}}}.\n",
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}
},
{
"definitions": {
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}
]
},
"formula": {
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"oldId": "24263",
"fid": "100",
"math_inputtex": "x_7",
"title": "Near_sets"
}
},
{
"definitions": {
"\\Pi_{n}": [
{
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}
]
},
"formula": {
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"oldId": "2926",
"fid": "30",
"math_inputtex": "\\Pi_n",
"title": "Polynomial_interpolation"
}
},
{
"definitions": {
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{
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}
],
"X": [
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],
"T": [
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],
"V": [
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},
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"oldId": "26177",
"fid": "10",
"math_inputtex": "\\sigma^2 = X^TVX,",
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}
},
{
"definitions": {
"\\mathbb{R}": [
{
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}
],
"n": [
{
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}
],
"f": [
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],
"x": [
"variable"
],
"B": [
{
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}
],
"x_{0}": [
{
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}
],
"r": [
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],
"S": [
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},
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"oldId": "22382",
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"math_inputtex": "\\int_{\\mathbb{R}^n}f\\,dx = \\int_0^\\infty\\left\\{\\int_{\\partial B(x_0;r)} f\\,dS\\right\\}\\,dr.",
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}
},
{
"definitions": {
"x": [
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],
"p_{x}": [
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],
"y": [
"y coordinate"
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"p_{y}": [
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},
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"oldId": "18056",
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"math_inputtex": "\n\\{x, p_x\\}_{DB} = \\{y, p_y\\}_{DB} = \\frac{1}{2}\n",
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}
},
{
"definitions": {
"G_{k,\\sigma}": [
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],
"y": [
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}
],
"k": [
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}
],
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}
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},
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"oldId": "26815",
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"math_inputtex": "G_{k, \\sigma} (y)= 1-(1+ky/\\sigma)^{-1/k} ",
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},
{
"definitions": {
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],
"H_{B}": [
{
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},
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],
"C": [
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],
"X": [
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]
},
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"oldId": "7260",
"fid": "15",
"math_inputtex": "L(H_B) \\otimes C(X)",
"title": "Quantum_channel"
}
},
{
"definitions": {
"\\pi_{i}": [
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],
"N": [
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],
"i": [
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},
"formula": {
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"oldId": "22755",
"fid": "2",
"math_inputtex": "\\pi_i = 2^{-N} \\tbinom Ni",
"title": "Ehrenfest_model"
}
},
{
"definitions": {
"p_{1}": [
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}
],
"p_{n}": [
{
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}
]
},
"formula": {
"qID": "95",
"oldId": "14285",
"fid": "1",
"math_inputtex": "(\\sqrt{p_1}, \\cdots ,\\sqrt{p_n})",
"title": "Fidelity_of_quantum_states"
}
},
{
"definitions": {
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]
},
"formula": {
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"oldId": "15596",
"fid": "27",
"math_inputtex": "\\boldsymbol{s}",
"title": "Yield_surface"
}
},
{
"definitions": {
"J": [
{
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}
],
"T": [
{
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}
],
"W": [
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"y": [
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},
"formula": {
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"oldId": "21658",
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"math_inputtex": "\\mathbf{J^TW\\ \\Delta y}",
"title": "Non-linear_least_squares"
}
},
{
"definitions": {
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},
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"oldId": "7629",
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"math_inputtex": "\\bar V^*",
"title": "Markov_decision_process"
}
},
{
"definitions": {
"n": [
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],
"\\delta": [
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},
"formula": {
"qID": "99",
"oldId": "14812",
"fid": "9",
"math_inputtex": "\\;\\frac{(n+\\delta-1)(n+\\delta-2)\\cdots n}{(\\delta-1)!}\\;",
"title": "Hilbert_series_and_Hilbert_polynomial"
}
},
{
"definitions": {
"y_{k}": [
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"n": [
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},
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"oldId": "17319",
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]