We show that, for a (not necessarily continuous) weakly contractive mean-type mapping $\mathbf{M} \colon I^p\to I^p$ (where $I$ is an interval and $p \in \mathbb{N}$), the functional equation $K \circ \mathbf{M}=K$ has at most one solution in family of continuous means I^p \to I$. Some general approach to latter also given.

• The Employee Benefit Research Institute (EBRI) and the Investment Company Institute (ICI) have collaborated to develop the EBRI/ICI 401(k) Accumulation Projection Model. This model examines how 401(k) assets might contribute to retirement income for future retirees based on decisions workers make throughout their careers and finds that the median replacement rate from 401(k) accumulations dep...

This paper examines and compares various manufacturing policies which manufacturer may adopt so as to improve the performance of a vendor managed inventory (VMI) partnership. The goal is to maximize the combined cumulative profit of supply chain while minimizing relevant inventory management costs. The supply chain is a two-level system with a single manufacturer and single retailer at each lev...

context-dependent modeling is a well-known approach to increase modeling accuracy in continuous speech recognition. the most common way to implement this approach is via triphone modeling. nevertheless, the large number of such models results in several problems in model training, whilst the robust training of such models is often hardly obtained. one approach to solve this problem is via param...

Given a continuous transformation on a compact space we call a point normal if the ergodic averages of any continuous functions converge. For example, the familiar notion of a normal number 0 < ξ < 1 in the context of number theory is one which is normal in the above sense for all of the transformations T : [0, 1) → [0, 1) given by T (ξ) = dξ (mod 1) for each d ≥ 2. In this note, we want to con...

We study regularity properties of weak solutions of the degenerate parabolic equation ut + f(u)x = K(u)xx, where Q(u) := K ′(u) > 0 for all u 6= 0 and Q(0) = 0 (e.g., the porous media equation, K(u) = |u|m−1u, m > 1). We show that whenever the solution u is nonnegative, Q(u(·, t)) is uniformly Lipschitz continuous and K(u(·, t)) is C-smooth and note that these global regularity results are opti...

For the usual norm on spaces C(K) and C b (Ω) of all continuous functions on a compact Hausdorff space K (all bounded continuous functions on a locally compact Hausdorff space Ω), the following equalities are proved: lim t→0+ ||f + tg|| C(K) − ||f || C(K) t = max x∈{z | |f (z)|=||f ||} Re(e −i arg f (x) g(x)). and lim t→0+ ||f + tg|| C b (Ω) − ||f || C b (Ω) t = inf δ>0 sup x∈{z | |f (z)|≥||f |...

The first part of the course is devoted to the study of solutions to the Laplace equation in Ω \ K , where Ω is a two-dimensional smooth domain and K is a compact one-dimensional subset of Ω. The solutions are required to satisfy a homogeneous Neumann boundary condition on K and a nonhomogeneous Dirichlet condition on (part of) ∂Ω. The main result is the continuous dependence of the solution on...

Let ω = {0, 1, . . . , n − 1} be a finite alphabet, DN = {1, 2, . . . ,N}, and BN = {x ∈ [0, 1] | ∃k ∈ ! : x = k/nN}. A configuration is a function of the form: ξ : DN → ω, and CN is the set of all configurations. Two configurations ξ1 and ξ2 are near if d(ξ1, ξ2) = (N −A)/N is small, where A = sup{p | ∃i ∈ {0, 1, . . . ,N} : ∀k = i + 1, i + 2, . . . , i + p ≤ N ξ1(k) = ξ2(k)}. The following re...

Let K be a compact set in the complex plane having connected and regular complement, and let / be any function continuous on K and analytic in the interior of K. For the polynomials pn(¡) of respective degrees at most n of best uniform approximation to / on K, we investigate the density of the sets of extreme points And) :={zeK: \f{z) p*n{f)(z)\ = \\f Pn(¡)\\K} in the boundary of K.