We study the finite groups G with a faithful irreducible character whose square is a linear combination of algebraically conjugate irreducible characters of G. In conclusion, we offer another proof of one theorem of Isaacs-Zisser. There are a few papers treating the finite groups possessing an irreducible character whose powers are linear combinations of appropriate irreducible characters, for ...

Syndrome decoding is a more efficient method of decoding linear codes over finite fields over a noisy channel [5]. Thus, in this paper we investigate the generalization of the syndrome decoding to linear codes over finite commutative rings. A first generalization was given in [1] via Pontryagin duality. In the same direction we give another generalization using linear functional-based duality. ...

The aim of this paper is to compute the rational character tables of the dicyclic group $T_{4n}$, the groups of order $pq$ and $pqr$. Some general properties of rational character tables are also considered into account.The aim of this paper is to compute the rational character tables of the dicyclic group $T_{4n}$, the groups of order $pq$ and $pqr$. Some general properties of rational charact...

We propose an algorithm to find piecewise linear skeletons of hand-written characters by using principal curves. The development of the method was inspired by the apparent similarity between the definition of principal curves (smooth curves which pass through the “middle” of a cloud of points) and the medial axis (smooth curves that go equidistantly from the contours of a character image). The ...

OBJECTIVE To study the effects of smoking in a film trailer. DESIGN Experimental study. SETTING Ten secondary schools in Northern Germany. PARTICIPANTS A sample of 1051 adolescents with a mean (SD) age of 14.2 (1.8) years. Main Exposures Participants were randomized to view a 42-second film trailer in which the attractive female character either smoked for about 3 seconds or did not smoke...

In recent papers we have refined a conjecture of Lehrer and Solomon expressing the character of the representation of a finite Coxeter group W on the pth graded piece of its Orlik-Solomon algebra as a sum of characters induced from linear characters of centralizers of elements of W . Our refined conjecture relates the character of W on the pth graded piece of its Orlik-Solomon algebra with the ...

Example 1.1. A field homomorphism K → F is a character by restricting it to the nonzero elements of K (that is, using G = K×) and ignoring the additive aspect of a field homomorphism. In particular, when L/K is a field extension any element of Aut(L/K) is a field homomorphism L→ L and therefore is a character of L× with values in L×. Example 1.2. For any α ∈ F×, the map Z→ F× by k 7→ αk is a ch...

 ‎Let $V$ be an $n$-dimensional complex inner product space‎. ‎Suppose‎ ‎$H$ is a subgroup of the symmetric group of degree $m$‎, ‎and‎ ‎$chi‎ :‎Hrightarrow mathbb{C} $ is an irreducible character (not‎ ‎necessarily linear)‎. ‎Denote by $V_{chi}(H)$ the symmetry class‎ ‎of tensors associated with $H$ and $chi$‎. ‎Let $K(T)in‎ (V_{chi}(H))$ be the operator induced by $Tin‎ ‎text{End}(V)$‎. ‎Th...