6. Theorem of Ceva, Menelaus and Van Aubel. Theorem 1 (Menelaus). If A1 , B1 , C1 are points on the sides BC, CA and AB of a triangle ABC, then the points are collinear if and only if |A1 B| |B1 C| |C1 A|

Source URL: www.irmo.ie

A QUASI-ERGODIC THEOREM FOR EVANESCENT PROCESSES L.A. BREYER AND G.O. ROBERTS Abstract. We prove a conditioned version of the ergodic theorem for Markov processes, which we call a quasi-ergodic theorem. We also prove a c

Source URL: www.lbreyer.com

U NIVERSITÉ PARIS D IDEROT – PARIS VII S ORBONNE PARIS C ITÉ É COLE D OCTORALE S CIENCES M ATHÉMATIQUES DE PARIS C ENTRE THÈSE en vue d’obtenir le grade de

Source URL: ludovicpatey.com

• Computability theory
• Ramsey theory
• Theorem
• Graph coloring
• Reverse mathematics

THEOREM OF THE DAY The Six-Circles Theorem Consider a triangle with vertices A, B and C, with opposite sides a, b and c, respectively. Construct six circles, C0, . . . , C5, in the triangle, with the tangencies shown in

Source URL: theoremoftheday.org

Games and Economic Behavior–47 www.elsevier.com/locate/geb Strategic learning in games with symmetric information Olivier Gossner a,b,∗ and Nicolas Vieille c

Source URL: ogossner.free.fr

• Decision theory
• Gaming
• Mathematics
• Game theory
• Theorems
• Folk theorem
• Nash equilibrium
• Epsilon-equilibrium
• Extensive-form game
• Normal-form game
• Outcome
• Correlated equilibrium

THEOREM OF THE DAY Le Porisme de Poncelet Consid´erons deux ellipses dans le plan euclidien, l’une d’elles compl`etement entour´ee par l’autre. Si une ligne polygonale ferm´ee a` n cˆot´es peut eˆ tre inscrit

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THEOREM OF THE DAY Green’s Theorem Let C be a closed, anticlockwise-oriented curve in the xy-plane enclosing a region D. Let F(x, y) = (P(x, y), Q(x, y)) be a 2-valued function having continuous partial derivatives on

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MUltlog and MUltseq Reanimated and Married M. Baaz1 C.G. Ferm¨ uller1 1

Source URL: www.preining.info

• Proof theory
• Sequent calculus
• Sequent
• First-order logic
• Propositional calculus
• Intuitionistic logic
• Many-valued logic
• Cut-elimination theorem
• Method of analytic tableaux
• Mathematical logic
• Rule of inference
• Boolean algebra

THEOREM OF THE DAY Taylor’s Theorem Let c be a real number and f a real-valued function which is (n+1)-times differentiable in some interval I around c. Then for x ∈ I, there is some value θ lying between x and c, s

Source URL: www.theoremoftheday.org

THEOREM OF THE DAY The Lutz-Nagell Theorem For the elliptic curve y2 = x3 + ax2 + bx + c, with a, b, and c integers and having (non-zero) discriminant function D = −4a3c + a2b2 + 18abc − 4b3 − 27c2, let P = (X, Y)

Source URL: www.theoremoftheday.org