For a given nonderogatory matrix A, formulas are given for functions of A in terms of Krylov matrices of A. Relations between the coefficients of a polynomial of A and the generating vector of a Krylov matrix of A are provided. With the formulas, linear transformations between Krylov matrices and functions of A are introduced, and associated algebraic properties are derived. Hessenberg reductio...

An algorithm for reduction of a regular matrix pair (A; B) to block Hessenberg-triangular form is presented. This condensed form Q T (A; B)Z = (H; T), where H and T are block upper Hessenberg and upper triangular, respectively, and Q and Z orthogonal, may serve as a rst step in the solution of the generalized eigenvalue problem Ax = Bx. It is shown how an elementwise algorithm can be reorganize...

A new proof of the general representation for the entries of the inverse of any unreduced Hessenberg matrix of finite order is found. Also this formulation is extended to the inverses of reduced Hessenberg matrices. Those entries are given with proper Hessenbergians from the original matrix. It justifies both the use of linear recurrences for such computations and some elementary properties of ...

We consider a standard matrix ow on the set of unitary upper Hessenberg matrices with nonnegative subdiagonal elements. The Schur parametrization of this set of matrices leads to ordinary diier-ential equations for the weights and the parameters that are analogous with the Toda ow as identiied with a ow on Jacobi matrices. We derive explicit diierential equations for the ow on the Schur paramet...

In his 2011 autobiography, A Serendipitous Life [1] , Karl Rickels describes how in 2008 in Munich at the 50th anniversary of the Collegium Internationale NeuroPharmacologicum (CINP) he looked around at the President’s Dinner, ‘... a special event held in the Emperor’s Hall at the residence of Bavaria’s famous king. I saw only one person I remembered from the first congress in Rome. I had been ...

One of the most widely used techniques for water content determination in food is Karl Fischer (KF) titration. Compared to other methods based on loss of weight, the primary advantage of the Karl Fischer titration method is its high selectivity to water. The aim of the study was to develop and validate the Karl Fischer method for moisture determination in pollen loads, royal jelly, bee venom an...

We prove that certain Gibbs measures on subshifts of nite type are nonsingular and ergodic for certain countable equivalence relations, including the orbit relation of the adic transformation (the same as equality after a permutation of nitely many coordinates). The relations we consider are deened by cocycles taking values in groups, including some nonabelian ones. This generalizes (half of) t...

This article investigates the historical method of Karl Sudhoff (1853- 1938), Germany's first professor of medical history. It argues that in order to understand his ideas more fully, we need to step outside the historiography of medical history and assess his methodology in relation to the norms and ideals of German academic history writing in general. The article demonstrates that the philolo...

their holdings of multiple copies. A handful of later lists are included, the most substantial from the seventeenth century being that of John Nidd, dated 1659, with a high proportion of medical books. Where the books were bequeathed to College libraries, as Nidd's were to Trinity and Andrew Perne's to Peterhouse, those still to be found on the College shelves have been identified. The owners f...

Çal??mada, Türkiye sigortac?l?k sektöründe karl?l???n firmaya özel, endüstriye özel ve makroekonomik belirleyenlerinin firma karl?l??? üzerine etkileri panel veri yöntemi kullan?larak tahmin edilmeye çal???lm??t?r. De?i?kenlerin ölçümünde kullan?lan veriler, hayat d??? sigorta alan?nda faaliyet gösteren toplam 30 i?letmenin 2009Q4-2019Q3 dönemine ait üç ayl?k verilerdir. Karl?l?k modelinin tahm...