Narrow Results

In this paper we compare various parallel preconditioners for solving large sparse nonsymmetric linear systems. They are Block Jacobi, Point-SSOR, ILU(0) in the wavefront order, ILU(0) in the multi-color order, SPAI(SParse Approximate Inverse), and Multi-Color Block SOR. The Block Jacobi and Point-SSOR are well-known, and ILU(0) is one of the most popular preconditioners, but it is inherently serial. ILU(0) in the wavefront order maximizes the parallelism, and ILU(0) in the multi-color order achieves the parallelism of order (N), where N is the order of the matrix. The SPAI tries to capture the approximate inverse in sparse form, which, then, is expected to be a scalable preconditioner. Finally, we implemented the Multi-Color Block SOR preconditioner combined with direct sparse matrix solver. For the Laplacian matrix the SOR method is known to have a non-deteriorating rate of convergence when used with Multi-Color ordering. Since most of the time is spent on the diagonal inversion, which is done on each processor, we expect it to be a good scalable preconditioner. Finally, due to the blocking effect, it will be effective for ill-conditioned problems. Experiments were conducted for the Finite Difference discretizations of two problems with various meshsizes varying up to 1024×1024, and for an ill-conditioned matrix from the shell problem from the Harwell–Boeing collection. CRAY-T3E with 128 nodes was used. MPI library was used for interprocess communications. The results show that Multi-Color Block SOR and ILU(0) with Multi-Color ordering give the best performances for the finite difference matrices and for the shell problem only the Multi-Color Block SOR and Block Jacobi converges. Based on this we recommend that the Multi-Color Block SOR is the most robust preconditioner out of the preconditioners considered.

A signed n-permutation is a permutation on {1,2,…,n} in which each element is labelled by a positive or negative sign. Here we consider the problem of sorting signed permutations by fixed-length reversals. Indeed, limiting the transformations to reversals of length exactly k can be very restrictive, for example, (+1,+3,+2,+4,…,+n) can never be sorted to (+1,+2,+3,+4,…,+n) by 2-reversals. That is, for given two signed permutations it is not obvious whether they can be sorted to each other by k-reversals. Thus in 1996, Chen and Skiena gave the following open problem: what is the connectedness of signed permutations under fixed-length reversals? In this paper, we resolve this open problem when "fixed-length" is even, and give a characterization of the connectedness of signed n-permutations under 2l-reversal, for both linear and circular permutations.

In this paper we consider the problem of computing the longest common abelian factor (LCAF) between two given strings. We present a simple $𝒪\left(\sigma n^2\right)$ time algorithm, where n is the length of the strings and $\sigma$ is the alphabet size, and a sub-quadratic running time solution for the binary string case, both having linear space requirement. Furthermore, we present a modified algorithm applying some interesting tricks and experimentally show that the resulting algorithm runs faster.

In this paper, an extended cubic B Spline scheme (CBS) is utilized to solve linear 10th-order boundary value problems (BVPs). Such types of BVPs occur in stability analysis of electrically conducting fluid in a magnetic field. The key concept is that we switched the BVPs to recreate a system that consists of all linear equations. We will alter our problem into such a form that converts the system of 10th-order BVPs and we are struck on a new system of 2nd-order BVPs. The appropriate outcome given by using CBS is contrasted with the accurate root to each problem. For each and every iteration, absolute error is also premeditated. The rule originated here aside from the estimation of the 10th-order BVPs also evaluates derivative from 1st-order to 10th-order of the accurate root. Couple of examples are demonstrated to evidence the adequacy and aptitude of the proffered strategy.

The untested assumption of linear relationship between stocks and bonds in previous empirical studies may lead to an invalid conclusion if the actual relationship is non-linear. The emphasis of this paper is on the effect of non-linearities on causal relationships between stocks and bonds in the cases of Malaysia and Singapore. Results from linearity tests indicate the existence of non-linearities in the dynamic relationship between stocks and bonds. Non-linear causality test results based on Taylor expansion suggest that non-linear causality flows from stocks to bonds and vice versa. The test further confirms that bonds with different maturity dates have different relationships with stocks.

In this paper, an innovative approach to achieve broadband linear power amplifier (PA) with a continuous broadband is presented. The proposed method mainly depends on the theory of control of intermodulation products and harmonics. This method results in a continuous sweet spots over a wide bandwidth. Based on the continuous sweet spots, a suboptimal solution is derived for improving the efficiency and linearity of broadband PAs. To verify the effectiveness of this method, one broadband PA operating over 4.5–5.5GHz is developed and measured, it indicates that the peak output power of the PA is 35–57dBm for a small signal input with a gain of 12dB, and the peak drain efficiency (DE) of the PA is larger than 57% over the whole working band. However, when the PA is stimulated by a 5MHz two-tone signal input, we observe that the DE keeps above 38% under the condition of the measured third-order intermodulation distortion (IMD3) is not larger than $-30$dBc.

This paper presents a fast algorithm for solving the n-queens problem. The basic idea of this algorithm is to use pre-computed solutions in 75% of the cases, while the remaining cases are solved by calling the Sosic's algorithm. The novelty of this algorithm is in the observation that these pre-computable cases exhibit a modular nature. In addition, the pre-computed solutions run 100 times faster than Sosic's algorithm in most cases.

Various theorems for classical piecewise-linear (PL) knots are shown to carry over to PL virtual knots. We then classify PL virtual knots up to edge index six.

A statement of hyperarithmetic analysis is a sentence of second order arithmetic S such that for every Y⊆ω, the minimum ω-model containing Y of RCA₀ + S is HYP(Y), the ω-model consisting of the sets hyperarithmetic in Y. We provide an example of a mathematical theorem which is a statement of hyperarithmetic analysis. This statement, that we call INDEC, is due to Jullien [13]. To the author's knowledge, no other already published, purely mathematical statement has been found with this property until now. We also prove that, over RCA₀, INDEC is implied by and implies ACA₀, but of course, neither ACA₀, nor ACA₀⁺ imply it.

We introduce five other statements of hyperarithmetic analysis and study the relations among them. Four of them are related to finitely-terminating games. The fifth one, related to iterations of the Turing jump, is strictly weaker than all the other statements that we study in this paper, as we prove using Steel's method of forcing with tagged trees.

Let $R$ be a commutative ring, $I$ an ideal of $R$ and $k\ge 2$ a fixed integer. The ideal-based $k$-zero-divisor hypergraph${\mathcal{H}}_I^k(R)$ of $R$ has vertex set $Z_I(R,k)$, the set of all ideal-based $k$-zero-divisors of $R$, and for distinct elements $x_1,x_2,\dots ,x_k$ in $Z_I(R,k)$, the set $\{x_1,x_2,\dots ,x_k\}$ is an edge in ${\mathcal{H}}_I^k(R)$ if and only if $x_1{x}_2\cdots x_k\in I$ and the product of the elements of any $(k-1)$-subset of $\{x_1,x_2,\dots ,x_k\}$ is not in $I$. In this paper, we show that ${\mathcal{H}}_I^3(R)$ is connected with diameter at most 4 provided that $x^2\notin I$ for all ideal-based 3-zero-divisor hypergraphs. Moreover, we find the chromatic number of ${\mathcal{H}}_I^k(R)$ when $R$ is a product of finite fields. Finally, we find some necessary conditions for a finite ring $R$ and a nonzero ideal $I$ of $R$ to have ${\mathcal{H}}_I^3(R)$ planar.

How do brand and product development processes interact? How do brands and branding strategies influence product development? Moreover, does a branding strategy facilitate or impede the development process? So far, research on product development has focused on the development of new products and services, whereas research on marketing and especially branding has emphasized what types of line extensions to create rather than on how to integrate brands and product development processes.

The present models of the product development process mostly distinguish between the process of innovation and that which follows, and also distinguish between the company as a sender and the user as a receiver of the communicated values. In the present study we suggest an alternative understanding of the innovation process: A network process perspective (NPP) as derived from the actor network theory (ANT), is used to explore the co-created relationship between the new product development process and branding.

The network process perspective is used to analyse and understand the innovation process and represents a constructivist theory that departs from an ontological assumption that the 'world' is the relations and networks among heterogeneous human and non-human actors and that these networks are not per se stable, but are created, negotiated and dynamic. This theory is especially suitable for comprehending 'branding' where the 'ing' underscores the dynamic nature of this concept and to explore the dynamics in innovation.

The empirical analysis identified four incidents as critical to the co-construction of the product and the brand in two companies. The effects are measured using the framework provided by Kapferer. The present analysis indicates that branding and innovation processes are interrelated in more subtle and complex ways than indicated in prior research on the subject. It further shows that even with well-organized marketing departments, consistent branding strategies and skilled project managers, the product development process is not easily managed. The brand and the branding strategies are non-human actors among other actors in the process, and it requires skill, persistence and energy if the 'brand' wants to become an influential 'actor'. Sometimes, the processes may even be reversed.