Other Mathematics Commons^™

Grundlagenreflexionen Zur Thematik Anthropomorpher Schnittstellen, Rudolf Kaehr

Rudolf Kaehr

Report for the EMBASSI Project

Almost Periodic Factorization Of Certain Block Triangular Matrix Functions, Ilya M. Spitkovsky, Darryl H. Yong

All HMC Faculty Publications and Research

Let

where , and . For rational such matrices are periodic, and their Wiener-Hopf factorization with respect to the real line always exists and can be constructed explicitly. For irrational , a certain modification (called an almost periodic factorization) can be considered instead. The case of invertible and commuting , was disposed of earlier-it was discovered that an almost periodic factorization of such matrices does not always exist, and a necessary and sufficient condition for its existence was found. This paper is devoted mostly to the situation when is not invertible but the commute pairwise (). The complete description is …

The Best Way To Knock 'M Down, Arthur T. Benjamin, Matthew T. Fluet '99

All HMC Faculty Publications and Research

"Knock 'm Down" is a game of dice that is so easy to learn that it is being played in classrooms around the world. Although this game has been effective at developing students' intuition about probability [Fendel et al. 1997; Hunt 1998], we will show that lurking underneath this deceptively simple game are many surprising and highly unintuitive results.

Martin Gardner = Mint! Grand! Rare!, Jeremiah Farrell

Scholarship and Professional Work - LAS

Jeremiah Farrell's contirbution to "The Mathemagician and Pied Puzzler: A Collection in Tribute to Martin Gardner"

Related works:

The puzzle from figure one is also available in Colloquy (Wordways 14,2) online at: http://digitalcommons.butler.edu/wordways/vol14/iss2/8/

Cube Puzzles, Jeremiah Farrell

Scholarship and Professional Work - LAS

Jeremiah Farrell's contribution to "The Mathemagician and Pied Puzzler: A Collection in Tribute to Martin Gardner"

Bounds On A Bug, Arthur T. Benjamin, Matthew T. Fluet '99

All HMC Faculty Publications and Research

In the game of Cootie, players race to construct a "cootie bug" by rolling a die to collect component parts. Each cootie bug is composed of a body, a head, two eyes, one nose, two antennae, and six legs. Players must first acquire the body of the bug by rolling a 1. Next, they must roll a 2 to add the head to the body. Once the body and head are both in place, the remaining body parts can be obtained in any order by rolling two 3s for the eyes, one 4 for the nose, two 5s for the …

(Ω, Ξ)-Logic: On The Algebraic Extension Of Coalgebraic Specifications, Rolf Hennicker, Alexander Kurz

Engineering Faculty Articles and Research

We present an extension of standard coalgebraic specification techniques for statebased systems which allows us to integrate constants and n-ary operations in a smooth way and, moreover, leads to a simplification of the coalgebraic structure of the models of a specification. The framework of (Ω,Ξ)-logic can be considered as the result of a translation of concepts of observational logic (cf. [9]) into the coalgebraic world. As a particular outcome we obtain the notion of an (Ω, Ξ)- structure and a sound and complete proof system for (first-order) observational properties of specifications.

Asupra Unor Noi Functii În Teoria Numerelor, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Performantele matematicii actuale,ca si descoperirile din viitor isi au,desigur, inceputul in cea mai veche si mai aproape de filozofie ramura a matematicii, in teoria numerelor. Matematicienii din toate timpurile au fost, sunt si vor fi atrasi de frumusetea si varietatea problemelor specifice acestei ramuri a matematicii. Regina a matematicii, care la randul ei este regina a stiintelor, dupa cum spunea Gauss, teoria numerelor straluceste cu lumina si atractiile ei, fascinandu-ne si usurandu-ne drumul cunoasterii legitatilor ce guverneaza macrocosmosul si microcosmosul. De la etapa antichitatii, cand teoria numerelor era cuprinsa in aritmetica, la etapa aritmeticii superioare din perioada Renasterii, cand teoria …

Smarandache Type Functions Obtained By Duality, Florentin Smarandache, C Dumitrescu, N Varlan, St Zamfir, E Radescu, N Radescu

Branch Mathematics and Statistics Faculty and Staff Publications

we extend the Smarandache function from the set N* of positive integers to the set Q of rationals