1. χtrivial(x) = 1 for every x ∈ G is a character. It is called the trivial character. 2. If χ1 and χ2 are characters of G then so is χ1 · χ2 (where χ1 · χ2(x) = χ1(x)χ2(x)). 3. For every character χ of G and x ∈ G, |χ(x)| = 1 (the absolute norm is of course in C). In particular, if we define χ1(x) = χ1(x), then χ1 is also a character and χ · χ = χtrivial. 4. This implies that Ĝ = {χ ∈ C[G] | χ...

We summerize the status of factorization hypothesis in the color-suppressed B meson decays : B → J/ψK (*). We present the general formalism for decay rates and polarization fractions with considering all possible non-factorizable contributions which also include the color-octet contributions, and a new factorization scheme comes appear when the universality is exist : χ F 1 = χ A1 = χ A2 = χ V ...

Let p be a puncture of a punctured sphere, and let Q be the set of all other punctures. We prove that the maximal cardinality of a set A of arcs pairwise intersecting at most once, which start at p and end in Q, is |χ|(|χ| + 1). We deduce that the maximal cardinality of a set of arcs with arbitrary endpoints pairwise intersecting at most twice is |χ|(|χ|+ 1)(|χ|+ 2).

This paper is a contribution to the theory of substructural logics. We introduce the notions of (MP)-based and almost (MP)-based logics (w.r.t. a special set of formulae D), which leads to an alternative proof of the well-known forms of the local deduction theorems for prominent substructural logics (FL, FLe, FLew , etc.). Roughly speaking, we decompose the proof of the local deduction theorem ...

The oxidation of Nb-silicide-based alloys is improved with Al, Cr, Ge or Sn addition(s). Depending on addition(s) and its(their) concentration(s), alloyed C14-AB₂ Laves and A15-A₃X phases can be stable in the microstructures of the alloys. In both phases, A is the transition metal(s), and B and X respectively can be Cr, Al, Ge, Si or Sn, and Al, Ge, Si or Sn. The alloying, creep and hardness of...

We investigate the values of several types of Dirichlet series D(s) for certain integer values of s, and give explicit formulas for the value D(s) in many cases. The easiest types of D are Dirichlet L-functions and their variations; a somewhat more complex case involves elliptic functions. There is one new type that includes ∑∞ n=1(n +1) for which such values have not been studied previously. 2...

BACKGROUND To compare mental health and well-being in different levels of the perceived discrimination among Iranian people living in Tehran. METHOD Using multi-stage sampling, 1255 subjects with the average age of 45 years and 9 months (including 672 women and 583 men) were selected and they completed all items of the general health questionnaire (GHQ), the social well-being inventory (SWI),...