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Let ℕ0 denote the set of all non-negative integers and 풫(ℕ0) be its power set. An integer additive set-indexer (IASI) of a graph G is an injective function f : V(G) → 풫(ℕ0) such that the induced function f+ : E(G) → 풫(ℕ0) defined by f+ (uv) = f(u) + f(v) is also injective. A graph G which admits an IASI is called an integer additive set-indexed graph (IASI-graph). An IASI of a graph G is said to be an arithmetic IASI if the elements of the set-labels of all vertices and edges of G are in arithmetic progressions. In this paper, we discuss about two special types of arithmetic IASIs. [ABSTRACT FROM AUTHOR]

Let G = (V(G), E(G)) be a simple, finite and undirected graph of order n. Given a bijection f: V(G) ∪ E(G) → Zk such that for each edge uv ∈ E(G), f(u) + f(v) + f(uv) is constant C( k). Let nf(i) be the number of vertices and edges labeled by i under f. If |nf(i) - nf(j)| ≤ 1 for all 0 ≤ i < j ≤ k - 1, we say f is a k-totally magic cordial (k-TMC) labeling of G. A graph is said to be k-totally cordial magic if it admits a k-TMC labeling. In this paper, we give some ways to construct new families of k-TMC graphs from a known k-totally cordial magic graphs. We also give a sufficient condition for an odd graph to admit no k-TMC labeling. As a by-product, we determine the k-totally magic cordiality of many families of graphs. [ABSTRACT FROM AUTHOR]

In this paper, we introduce new definitions of the Gray weight and the Gray map for linear codes over ℤ9 + uℤ9 with u2 = u. Some results on self-dual codes over this ring are investigated. Further, the structural properties of quadratic residue codes are also considered. Two self-dual codes with new parameters [22, 11, 5] and [24, 12, 9] over ℤ9 are obtained. [ABSTRACT FROM AUTHOR]

A finite word w ∈ {0, 1}* is balanced if for every equal-length factors u and v of every cyclic shift of w we have ||u|1 - |v|1| ≤ 1. This new class of finite words was defined in [O. Jenkinson and L. Q. Zamboni, Characterisations of balanced words via orderings, Theoret. Comput. Sci. 310(1-3) (2004) 247-271]. In [O. Jenkinson, Balanced words and majorization, Discrete Math. Algorithms Appl. 1(4) (2009) 463-484], there was proved several results considering finite balanced words and majorization. One of the main results was that the base-2 orbit of the balanced word is the least element in the set of orbits with respect to partial sum. It was also proved that the product of the elements in the base-2 orbit of a word is maximized precisely when the word is balanced. It turns out that the words 0q-p1p have similar extremal properties, opposite to the balanced words, which makes it meaningful to call these words the most unbalanced words. This paper contains the counterparts of the results mentioned above. We will prove that the orbit of the word u = 0q-p1p is the greatest element in the set of orbits with respect to partial sum and that it has the smallest product. We will also prove that u is the greatest element in the set of orbits with respect to partial product. [ABSTRACT FROM AUTHOR]

In this paper, four three-node triangular finite element models which can readily be incorporated into the standard finite element program framework are devised via a multi-field variational functional for the bounded plane Helmholtz problem. In the models, boundary and domain fields are independently assumed. The former is constructed by nodal interpolation and the latter comprises nonsingular solutions of the Helmholtz equation. The equality of the two fields are enforced along the element boundary. Among the four devised models, the most accurate one is 1/3 to 1/2 less erroneous than the conventional single-field model in most examples. [ABSTRACT FROM AUTHOR]

An increasing amount of attention has been paid on the study of thermodiffusion effects on mass transport. This paper presents a novel mathematical model for an entire proton exchange membrane fuel cell (PEMFC) with focus placed on the modeling and assessment of the role of thermodiffusion that has been usually neglected in previous fuel cell research work. Built upon the equations of continuity, momentum, energy, species concentrations, and electric potentials in different regions of a PEMFC, a set of nonlinear partial differential equations are numerically solved using finite element methods. The simulation results demonstrate that the thermodiffusion has a noticeable impact on transport of species in an operational PEMFC. [ABSTRACT FROM AUTHOR]

This paper deals with a time-domain mathematical model for dissipative acoustics and is organized as follows. First, the equations of this model are written in terms of displacement and temperature fields and an energy equation is obtained. The resulting initial-boundary value problem is written in a functional framework allowing us to prove the existence and uniqueness of solution. Next, two different time-discretization schemes are proposed, and stability and error estimates are proved for both. Finally, numerical results are reported which were obtained by combining these time-schemes with Lagrangian and Raviart–Thomas finite elements for temperature and displacement fields, respectively. [ABSTRACT FROM AUTHOR]

In this paper, we consider a 1D inviscid model to simulate river flows whose unknown are the water elevation, the flow rate and the wet area. We rewrite this model in terms of the wet area and the flow rate. Next, by using a weak formulation and a discretization by characteristics, we derive an implicit semidiscretized scheme that involves a variational inequality. Under suitable hypothesis, we prove that this scheme has at least one solution. We present an algorithm for the numerical solution of the fully discretized problem and the numerical results obtained for channels with parabolic and rectangular sections and variable depth. Finally, we perform a stability analysis for the semidiscretized scheme applied to a similar problem where the convection term has been omitted. [ABSTRACT FROM AUTHOR]

In this paper, we consider the numerical method for the voice generation problem. The basic mathematical model for the voice generation is the Helmholtz equation in an unbounded region. Introducing an artificial boundary, we divide the unbounded region into a bounded region and the rest unbounded one with a simple shape. We apply the finite element method for the equation in the bounded region imposing an artificial boundary condition given through the Dirichlet to Neumann (DtN) mapping on the artificial boundary. We then compute the frequency response function or the formant curve by which we can simulate the voice generation process for various vowels. The complex eigenvalues related to the Helmholtz equation control the peaks of the frequency response function known as formants. We give the variational formulas for the complex eigenvalues with respect to the variation of vocal tract boundary. [ABSTRACT FROM AUTHOR]

In this paper we analyze the Residual-Free Bubble (RFB) method applied to the linear diffusion­advection­reaction problem. We propose a new a priori error analysis for the method and for its practical implementation in a quite general context, which allows, e.g. linear or quadratic elements on the resolvable scales. We also perform some numerical tests, showing in both cases the advantages of the method. [ABSTRACT FROM AUTHOR]