Math 2.0

Subjects

26 Real functions

See MSC 26 on zbMATH Open.

NameTagKindMSC
Sequential characterization of limits000MXHEY22statement26A03
Power series are differentiable inside the radius of convergence002X7EK91Hstatement30B10, 26A24
A function with zero derivative is constant003QDZ4T16statement26A24
Natural logarithm0044CPHJBVdefinition33B10, 26A09
Jump discontinuity004FH91BN5concept26A15
A differentiable function is convex iff its derivative is increasing005JT76HCKstatement26A51
Local maximum00999TYPXBdefinition26A24
One-sided limit00BE2J8H05concept26A03
The logarithm grows slower than any power00DGYY10FVstatement26A12, 33B10
Intermediate value theorem00KAFBR32Estatement26A15
Saddle point00N3T18QNAdefinition26B05
Change of variables in multiple integrals00N5FHP1CVstatement26B15
Derivative of sine00R4MWW532statement33B10, 26A24
Absolute value00S7C68D51definition26A03
Additivity of line integrals under concatenation00ZEBSMNNVstatement26B12
Strictly monotone function011EJQWWJSconcept26A48
A convex function on an open interval is continuous011HV2GAWFstatement26A51
1 + x is at most exp x012C7GFF20statement33B10, 26D15
Hölder continuity012PBA0FMDconcept26A16
Reduction formula012RYET5E2concept26A36
Differentiable function of several variables0135XZZQ8Mdefinition26B05
Strict differentiability0146MBQNNEdefinition26B05
Riemann's criterion for integrability017DH8WXTEstatement26A42
Vector-valued function018GTRS7A4concept26B12
Rolle's theorem0194DY35BGstatement26A24
Weierstrass function01A0MK1730counterexample26A27
First derivative test01A2EGXJEMstatement26A24
Function with unequal mixed partial derivatives01NN8NY497counterexample26B05
Tangent line01R1HW3Y42concept26A24
Symmetry of second derivatives01V9FPBBVKstatement26B05
Limit at infinity01YYRV7S9Zconcept26A03
Definite integral021WEM680Wdefinition26A42
Darboux and Riemann integrals agree021XJAQVDCstatement26A42
A function with nonnegative derivative is increasing026BJBQNGJstatement26A24
Uniformly continuous functions map Cauchy sequences to Cauchy sequences026FDZFRXSstatement26A15
Flux through a surface026J1MG2NWconcept26B15
Derivative function027K9RMZ43definition26A24
Vector field0299VCW1THconcept26B12
Mean value inequality02CYB184RCstatement26B05
Divergence02NSMQVQWKdefinition26B12
Line integral of a scalar field02QJVFCNYDconcept26B12
Higher partial derivatives02RSXVM1ZNdefinition26B05
Cauchy mean value theorem02SYZAWM2Kstatement26A24
Partial fraction decomposition030VFEREKGconcept26C15
Order on the reals0337CYB0VDdefinition26A03
Tangent plane to a graph035V802J58concept26B05
Multivalued function03CPD1HGF3concept26E25
Chain rule for Jacobian matrices03GGQEAG9Sstatement26B10
Triangle inequality03HF5PMY5Tstatement26A03
Mean value theorem in several variables03HGK7EW6Rstatement26B05
Indefinite integral03VHANA6ZKdefinition26A36
Jacobian determinant03W6Q1MFR5definition26B10
The Dirichlet function is not Riemann integrable03Z4JC4YRJcounterexample26A42
Jacobian matrix047NDTEPCVconcept26B10
log x is at most x - 104CBRA4JRKstatement33B10, 26D15
Local maximum and minimum04CPG9K1C4definition26B99
Natural logarithm04DXAFN2ESconcept33B10, 26A09
Mesh of a partition04GM4NYXJBdefinition26A42
Density of the irrationals04J6G4H78Jstatement26A03
Dedekind cut04QNZZ4HHYdefinition26A03
Classification of discontinuities04R9K5H562concept26A15
Higher derivative04TKTF8KDKconcept26A24
Definite integral04TMP0XGMJconcept26A42
Integral of cosine04WTBQ7APQstatement26A36
Monotone functions are Riemann integrable04YKAYDQPWstatement26A42
Lipschitz condition055VVSN00Vdefinition26A16, 34A12
Sequential continuity055Z15H69Gconcept26A15
Lebesgue's criterion for Riemann integrability0565EGK6XPstatement26A42
Partition of an interval05A6PKMAJ9concept26A42
Partial derivative05AXG3QRKRdefinition26B05
Jump discontinuity05B0FKFXQAdefinition26A15
Having a directional derivative05EGFBZTGCdefinition26B05
Improper integral05KQ3F99BQconcept26A42, 40A10
Derivative of arctangent05P4B4Q22Vstatement33B10, 26A24
Conservative vector field05R9NF2J49definition26B12
Additivity of the integral over intervals05RCDKHZM6statement26A42
Harmonic numbers grow like log n05S2GSPMGAstatement11B83, 26A12
Jacobian of spherical coordinates05WKRC7HWTstatement26B15
First fundamental theorem of calculus063H5KJC69statement26A42
Surface integral065HE5V98Econcept26B15
Existence of square roots of nonnegative reals068BZBXE0Cstatement26A09
Hessian matrix0693Y2METTconcept26B05
Triple integral0698M7C7AXconcept26B15
Comparison of a series and an integral069HKV4X1Estatement26A42
Partition of an interval069P20KYQTdefinition26A42
Strictly convex function06BA5JZKTQdefinition26A51
Integral of the exponential function06D0EWR2DVstatement26A36
Directional derivative06KWGHDN2Jconcept26B05
Inflection point06MG208MGRconcept26A51
Continuous functions are Riemann integrable06SESV7GQYstatement26A42
Continuously differentiable function06SKCHDQT5definition26A24
Continuous image of a closed interval is a closed interval06ZARTQTQEstatement26A15
Uniqueness of the derivative0762WAE49Pstatement26B05
Continuity of the inverse of a strictly monotone continuous function07BY47HG5Sstatement26A48
Lipschitz maps are uniformly continuous07DCKDXRBPstatement26A16
Limit point of a set07EGCNHAVWdefinition26A03
Grönwall's inequality07EJHQYR9Astatement26D10, 34A40
Convex function on R^n07GR3TNW4Hconcept26B25
A function with positive derivative is strictly increasing07J5X2T1ZXstatement26A24
Convex function07Q7CNM5WFconcept26A51
Uniform continuity on a set07RB7B04HXconcept26A15
Derivatives of the hyperbolic functions07T2TKGZ4Jstatement33B10, 26A24
Young's inequality for products07VHQ31EYJstatement26D15
Derivative of the logarithm07X1QA6BRWstatement33B10, 26A24
Differentiable functions are continuous07ZMX4ANJSstatement26A24
Linearity of the integral080RWVVSB6statement26A42
Analytic function081WKEDK6Cconcept26E05
Higher derivative084NGSTWM7definition26A24
Periodic function089KWVYD69definition26A09
Moment of inertia08ANASGBXVconcept26B15, 70E15
Floor function08GR54CKEAconcept26A09
Real numbers08J2M1JYAGobject26A03
Infinite limit08NM8KQPDQdefinition26A03
Differentiable on an open set08S7FDRS5Zdefinition26B05
Sine and cosine08WFZP6P89concept33B10, 26A09
Integration by parts08Y1BBQTK9statement26A42
One-sided limit0909PWZR62definition26A03
Real exponentiation091AV9YHZYconcept26A09, 33B10
Mesh of a partition093SAXPJ9Pconcept26A42
Heaviside step function09C4JP7Y0Mobject26A06, 44A10
Area of a region as a line integral09CBQB6V67statement26B20
Partial derivative09EGC6F8PTconcept26B05
Upper and lower Darboux integrals09FQT057T7definition26A42
Smooth non-analytic function09RTYYHXKAcounterexample26E10
Local minimum09WRNGPTMVconcept26A24
Higher partial derivatives09ZXGX55DMconcept26B05
Uniform continuity on a set0A3CK6DVVBdefinition26A15
The reals are Archimedean0A3GWZ86AYstatement26A03
Differentiable function0A61B60B5Rdefinition26A24
Derivative gives the directional derivatives0A6PMR20N4statement26B05
x^2 is not uniformly continuous on the real line0A8JXHYTJCcounterexample26A15
Chain rule for a composition with a curve0A8TJ0VHC7statement26B05
Gradient0ABK9V9Y64concept26B12
Strictly convex function0AEAHMFSCAconcept26A51
sin(1/x) has no limit at 00AFWQZ1PKFcounterexample26A15
Step function0AJXYH4DDQconcept26A42
Stokes' theorem0AKRKVHW94statement26B20
Differentiation under the integral sign0AR06W1E1Bstatement26B15
Ceiling function0ASM4EPMB2definition26A09
Periodic function0ATF6Q0633concept26A09
Boundedness theorem0ATVXC3NCCstatement26A15
Lipschitz condition0AW1E6YTJYconcept26A16
Completeness axiom0AXWET80YWstatement26A03
Curl-free vector field on a convex set is conservative0B22P010D6statement26B12
Level set0B2RZ0778Nconcept26B99
Strict differentiability0B6QWX3086concept26B05
Mean value theorem0BARQY52N5statement26A24
Smooth function0BE3QDH73Adefinition26E10
Path independence of line integrals0BFN21TF5Fstatement26B20
Infinite limit0BH9JH7HBYconcept26A03
Limit along different paths0BJ6H85DRQconcept26B05
Hölder's inequality for sums0BKDAGMGX9statement26D15
Quotient rule0BS0NJPKVEstatement26A24
Antiderivative0BW9N5CDSBdefinition26A36
Uniform limits commute with integration0BWGW68B66statement40A30, 26A42
Implicit function theorem0BXBADR94Cstatement26B10
Having a gradient0BXE0S1XERdefinition26B12
Slopes of a convex function are increasing0BY5FTHEEEstatement26A51
Antiderivative0BYWRWFT4Fconcept26A36
Zero derivative on a connected open set implies constant0BYZTFM0DJstatement26B05
Separately continuous but not continuous function0C0KPAKK9Ycounterexample26B05
Rectifiable curve0C28RT5BG7definition26A45
Polynomial functions are continuous0C5TP6RYSVstatement26A15
Reverse triangle inequality0C9S13WKMFstatement26A03
Work done by a force field0CDZ684TCDconcept26B12
Absolute value is continuous but not differentiable at 00CQ9ZM383Ncounterexample26A24
Uniform convergence of derivatives allows term-by-term differentiation0CS42KEM5Cstatement40A30, 26A24
Exponential growth beats polynomial growth0CT6CBGTYYstatement26A12, 33B10
Improper multiple integral0CWK2NFSEWconcept26B15
Linearity of the derivative0CXZ217QDPstatement26B05
Derivative of a continuous linear map0CYYAF8AD2statement26B05
Integration by substitution0D37QFPEZEstatement26A42
A continuous injective function on an interval is strictly monotone0D6FCW80A0statement26A48
The exponential function is convex0D7GRZ2ADXstatement26A51
Construction of the reals from Cauchy sequences0D8HE681SCconcept26A03
Gaussian integral0DFT1GP1JPexample26A42, 40A10
Surface integral0DQ8ERJZNSdefinition26B15
Inequality of arithmetic and geometric means0DRF0F3XC9statement26E60
Square root function0E10E0NW9Vconcept26A09
Ceiling function0EA4XFB0EYconcept26A09
Chain rule in several variables0EAAS2EHDRstatement26B05
Trigonometric substitution0EAR3KNRTNconcept26A36
Existence of the infimum0EDH403M21statement26A03
Continuity at a point0EEE2CZB2Adefinition26A15
Refinement of a partition0EEKF7YFBWdefinition26A42
Concave function0EF2VG8XKQdefinition26A51
The exponential function is its own derivative0EX9GFJ0B3statement33B10, 26A24
Iterated derivative0EY05Z9RPNdefinition26B05
x sin(1/x) is continuous at 00EZMAY1FQDexample26A15
Derivative0F1WR9C83Kdefinition26A24
Riemann integrable function0F2QCWVFT7concept26A42
Iterated derivative0F32S73FJNconcept26B05
Derivative vanishes at a local extremum0F405477F8statement26B05
Divergence of a curl is zero0F56CMMC5Pstatement26B12
Square root0F7FQS6XY6concept26A09
Local maximum0FBETJR0JGconcept26A24
e as the limit of (1 + 1/n)^n0FEMF8JKAFstatement26A09
Absolute value0FFXKTKKQCconcept26A03
Total derivative0FNKFT8H6Econcept26B05
Even and odd functions0FP31SX5EAconcept26A09
Scalar potential0FP4BVDAAQdefinition26B12
Reversing a path changes the sign of a line integral0FSCXYG856statement26B12
Second derivative test0FZFHK97P7statement26A24
Dedekind cut0G3RRM41X9concept26A03
Derivative of the inverse function0G65751VSWstatement26B10
Derivative of arcsine0GA6G43EA9statement33B10, 26A24
Epsilon-delta definition of a limit0GBZDAFPX8statement26A03
Concave function0GCM7B6PBKconcept26A51
Curl0GDNHS9J2Xdefinition26B12
Critical point0GEQ42PTGBdefinition26A24
Function for which the iterated integrals differ0GJZE2E4RXcounterexample26B15
Absolute value is multiplicative0GMV7GP8W0statement26A03
Quotient of continuous functions is continuous0GR2APWTACstatement26A15
Curl-free field that is not conservative0GRM3BS0DDcounterexample26B12
Extended real number line0GSZ7B0CGRobject26A03
Triple integral0GTBGMZXV8definition26B15
Moment of inertia0GVMR0C3S6definition26B15, 70E15
Area under a curve0GXA8Z205Econcept26A42
Integral of sine0GXCXCX3QNstatement26A36
Divergence theorem on a rectangle in the plane0GZ3D8F921statement26B20
Dirichlet integral0GZNSHMG4Qexample26A42, 40A10
Line integral of a vector field0H5MR9B6GTconcept26B12
Changing the order of integration0H60H1Q0SXstatement26B15
Del operator0H6DP8CHNDconcept26B12
Scalar potential0H7C3T1GJYconcept26B12
Rectifiable curve0HATW2VWAZconcept26A45
Riemann sum0HBY48G8G1definition26A42
Differentiable function of several variables0HHHDCXZV4concept26B05
Thomae's function0HJ28H9Y95example26A15
Centre of mass0HNK6KT05Kconcept26B15
Green's theorem0HR3N02317statement26B20
One-sided derivative0HXEX0DPRAdefinition26A24
Exponential function0J0FCWV32Dconcept33B10, 26A09
Existence of nth roots by the intermediate value theorem0J29GM30Z7example26A15
Taylor's theorem in several variables0J8T4K4YTEstatement26B12
Limit of a function of several variables0J8Y1NCY0Kconcept26B05
Riemann sum0JAEHXTVV5concept26A42
Vector calculus identities0JC5X4HWR2statement26B12
Analytic function0JD5ZNW0F4definition26E05
Continuity in R^n0JEJATBVD7concept26B05
Function of several variables0JPCHTXWG0concept26B99
Saddle point0JW6MDHAZDconcept26B05
L'Hôpital's rule0JWT4PPQ7Bstatement26A24
Divergence theorem0JX86PSSA9statement26B20
Power rule0JZGW75C5Zstatement26A24
Upper and lower Darboux sums0K0A06X2MQconcept26A42
Lipschitz functions are uniformly continuous0K1EWAR6AFstatement26A16
Integral of 1/x0K1N1Y4EGZstatement26A36
Differentiable function0K57YG3BB8concept26A24
Removable discontinuity0K96Z2S699concept26A15
Inverse function theorem0K9HSJFCMJstatement26B10
General Leibniz rule0K9QCK6WJCstatement26A24
Upper and lower Darboux integrals0KABP2HWMQconcept26A42
One-sided limits of a monotone function exist0KJXHN0TW0statement26A48
Continuous partial derivatives imply differentiability0KXSK8TEEBstatement26B05
Derivative of x^a0KY08TWDMQstatement26A24, 26A09
Derivative of an inverse function0M0RZ3HSB0statement26A24
Linearity of differentiation0M0TKFRX2Astatement26A24
Convex function on R^n0M1GJSWZDAdefinition26B25
Bernoulli's inequality0M1MX28VXKstatement26D05
Curl of a gradient is zero0M2JRW1J0Nstatement26B12
Uniform continuity0M4JJT780Xconcept26A15
Line integral of a scalar field0M50E4WYWJdefinition26B12
Approximation property of the supremum0M8TGGP9JPstatement26A03
Step function0M9XEDF1HJdefinition26A42
Monotonicity of the integral0MBWQKM8QRstatement26A42
Derivative of a polynomial0MH1WK89PPstatement26A24
Derivative as a little-o approximation0MN882VJ4Pstatement26B05
Centre of mass0MPZGAZ2GKdefinition26B15
Order on the reals0MSSD1VCW9concept26A03
Sequential continuity0MVDQEAB60definition26A15
Exponentials dominate powers in sequences0MVTCFW42Kstatement26A12
Divergence0MWV6ZTK6Sconcept26B12
Riemann integrable function0N1JQXZXHCdefinition26A42
Vector field0N67NBKQ5Tdefinition26B12
Mean value theorem for integrals0N91N98EG5statement26A42
The integral of a continuous function is an antiderivative0NC2A3HWGTstatement26A36
Implicit function theorem for a surjective derivative0NE2W2XPQJstatement26B10
Curl0NF6GQNXMYconcept26B12
Fundamental theorem of calculus0NHGY0N0JBstatement26A42
Double integral0NKBMFC18Rdefinition26B15
Schwarz's theorem for C^2 functions0NNQY8WCW6statement26B05
Triangle inequality for integrals0NR82KMYKDstatement26A42
Composition of continuous functions is continuous0NRQPQX3VAstatement26A15
Derivative of a map into R^n by components0NS0X75RS1statement26B05
Gradient0NS2QYVC4Ydefinition26B12
Local minimum0NS8BP96QXdefinition26A24
Discrete Grönwall inequality0NTM3J5MFEstatement26D15, 39A22
Continuous function0P27W9RW0Gdefinition26A15
Second-order Taylor expansion0P30YYZN85statement26B12
Iterated integral0P4WX7Y502definition26B15
A function with bounded derivative is Lipschitz0P64VE79X3statement26A16
Continuity is equivalent to sequential continuity0PAQM3H57Xstatement26A15
Fermat's theorem on stationary points0PCVBRV9VJstatement26A24
Multi-index notation0PJXBR6QA3concept26B99
Conservative vector field0PKG97PX9Yconcept26B12
Limit of a function0PKRYB8ATMconcept26A03
Interval0Q1D85B8G6concept26A03
Integral of a power0Q3HYFT9RQstatement26A36
Uniform continuity0Q4DR37DVEdefinition26A15
Second derivative0Q4QJWEHW3concept26A24
Darboux's theorem0Q5A47J48Dstatement26A24
Reciprocal rule0QD4E5JYPTstatement26A24
Contour line0QD83RAN8Gconcept26B99
Removable discontinuity0QG9C579SRdefinition26A15
Implicit differentiation0QKA345AW1concept26B10
Derivative function0QKJ6NT0R9concept26A24
Riemann integral0QM4TXT3DRdefinition26A42
Lipschitz continuity0QNVQ4VD9Tdefinition26A16
Derivative of a map into a product0QQMXFTX0Astatement26B05
Upper and lower Darboux sums0QRQVH0CRWdefinition26A42
Continuity of the sum of a uniformly convergent series of functions0R0MYT0BJDstatement40A30, 26A15
Fubini's theorem0R0T1VWH5Xstatement26B15
Characterization of the floor0R9B0B5458statement26A09
One-sided derivative0R9PHTGVNWconcept26A24
Exponential function0RMVS7RXZXdefinition33B10, 26A09
Jensen's inequality0RWMRTPC87statement26D15
A continuous nowhere differentiable function0RXK2Z808Qcounterexample26A27
Chain rule0RXX2PT1MQstatement26A24
Indeterminate form0S7G92KKA7concept26A03
Continuity in R^n0S9EK5MQPEdefinition26B05
Derivative of tangent0SAMR34WXCstatement33B10, 26A24
Hessian matrix0SCSQWXRA4definition26B05
Gradient theorem0SD237FEJDstatement26B20
Product rule in several variables0SF85PY0QNstatement26B05
Refinement of a partition0SPZ1H3N9Vconcept26A42
C^1 functions are strictly differentiable0STPPDXGMEstatement26B05
Density of the rationals0STX0WRDNGstatement26A03
Cauchy principal value0SYR10HD4Rconcept26A42
Dirichlet function0T4EJ8ZJM9counterexample26A15
Integration in polar coordinates0T89W1QZ9Kstatement26B15
C^k function characterised by continuous derivatives0TCBZMEYGNstatement26B05
Arc length0TH78S7GBZconcept26A42, 53A04
Term-by-term differentiation0TJ8QBJX5Kstatement40A30, 26A24
Interval0TK8Y3J5RWdefinition26A03
Bounded derivative on a convex set implies Lipschitz0TKG7T3K0Estatement26B35
Lipschitz map0TMZ21WKCNdefinition26A16
Partial derivatives do not imply differentiability0TNZC55X3Jcounterexample26B05
Strictly monotone function0TR9SR9FTBdefinition26A48
Real exponentiation0TV07AQT62definition26A09, 33B10
Integration over a non-rectangular region0TXCQ9CST1concept26B15
Limit of a function0TXTSEMHR5definition26A03
Derivative0V1EJCT8G6concept26A24
Derivative of cosine0V2DV29EGTstatement33B10, 26A24
Smooth function0V33BNKZ9Sconcept26E10
Cauchy principal value0V3RDQV3ZXdefinition26A42
Square root function0V7E9KP6Q2definition26A09
Product rule0V9A43H7WVstatement26A24
Square root0VB8BFRABHdefinition26A09
Improper integral0VCTBJMEJFdefinition26A42, 40A10
Product of continuous functions is continuous0VGMHCF4SCstatement26A15
Limit of a function of several variables0VMG8TA8VFdefinition26B05
Convex function0VV0HSW1ZSdefinition26A51
Continuously differentiable function0VW90BBSJ4concept26A24
Gradient is orthogonal to level sets0VXYV3NQQ1statement26B12
Continuous functions on a closed bounded interval are uniformly continuous0W0TZDRF9Cstatement26A15
Linear approximation0W276SSSCGconcept26B05
Riemann integral0W29TBTY12concept26A42
Line integral as an integral over the parameter interval0W3W1VYWBPstatement26B12
Tangent half-angle substitution0W8ETY2AZ6concept26A36
Epsilon-delta definition of continuity0W8YHHGCJGstatement26A15
Double integral0WAR4F23B4concept26B15
Sine and cosine0WB57D9488definition33B10, 26A09
Integration by partial fractions0WBTWFXJQGconcept26A36
Rational function0WCZH4AFMTdefinition26A09
x^2 sin(1/x) is differentiable with discontinuous derivative0WDAKKN4NCcounterexample26A24
Local maximum and minimum0WFBH1Q3WCconcept26B99
There is a natural number n with 1/n below any positive epsilon0WH916TJNYstatement26A03
Volume of a ball in R^30WMDV48VSNstatement26B15
Indefinite integral0WN1QXR7R3concept26A36
Extreme value theorem0WS1A8E2P9statement26A15
A monotone function has countably many discontinuities0WYTM4C9QGstatement26A48
Iterated integral0WZCHE1ZF9concept26B15
Hölder continuity0WZTM0EFR6definition26A16
Continuous function0X3WGX95FEconcept26A15
Arc length0X7G61297Xdefinition26A42, 53A04
Uniform limit theorem0X9XT05JVCstatement40A30, 26A15
Rational function0XDK9CGYKJconcept26A09
Even and odd functions0XE690QF65definition26A09
Second fundamental theorem of calculus0XYAFCN0PTstatement26A42
Inflection point0Y0WS5BCJ7definition26A51
Limit at infinity0Y12QYTJK3definition26A03
Level set0Y5Q8Q9WJ7definition26B99
Directional derivative0Y7PVW4Q44definition26B05
Second derivative0Y9D2FJRQ4definition26A24
Term-by-term integration0YBY3VYX0Kstatement40A30, 26A42
Jacobian matrix0YF0VXKXGBdefinition26B10
Flux through a surface0YPRY7T4PKdefinition26B15
Line integral of a vector field0YS8RX87F4definition26B12
Critical point0YTCMFB4HCconcept26A24
Floor function0YVRNEDSVGdefinition26A09
Homotopy invariance of line integrals of closed forms0YVVN6R715statement26B20
Tangent plane to a graph0YXEHVA93Rdefinition26B05
A function with nonnegative second derivative is convex0Z41C17TGPstatement26A51
Local homeomorphism from the inverse function theorem0Z8CSYVHDJstatement26B10
Constant multiple rule0Z9JB71BS0statement26A24
Gradient points in the direction of steepest ascent0ZC78099PAstatement26B12
Jacobian determinant0ZCSMYHTBPconcept26B10
The logarithm is strictly concave0ZS54B9GJFstatement26A51