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Identifying palindromes in sequences has been an interesting line of research in combinatorics on words and also in computational biology, after the discovery of the relation of palindromes in the DNA sequence with the HIV virus. Efficient algorithms for the factorization of sequences into palindromes and maximal palindromes have been devised in recent years. We extend these studies by allowing gaps in decompositions and errors in palindromes, and also imposing a lower bound to the length of acceptable palindromes.

We first present an on-line algorithm for obtaining a palindromic decomposition of a string of length $n$ with the minimal total gap length in time ${𝒪}(nlogn\cdot g)$ and space ${𝒪}(n\cdot g)$, where $g$ is the number of allowed gaps in the decomposition. We then consider a decomposition of the string in maximal $\delta$-palindromes (i.e. palindromes with $\delta$ errors under the edit or Hamming distance) and $g$ allowed gaps. We present an algorithm to obtain such a decomposition with the minimal total gap length in time ${𝒪}(n\cdot (g+\delta ))$ and space ${𝒪}(n\cdot g)$. Finally, we provide an implementation of our algorithms.

We discuss approximations of the vertex coupling on a star-shaped quantum graph of n edges in the singular case when the wave functions are not continuous at the vertex and no edge-permutation symmetry is present. It is shown that the Cheon–Shigehara technique using δ interactions with nonlinearly scaled couplings yields a 2n-parameter family of boundary conditions in the sense of norm resolvent topology. Moreover, using graphs with additional edges, one can approximate the -parameter family of all time-reversal invariant couplings.

The zero-width approximation (ZWA) restricts the intermediate unstable particle state to the mass shell and, when combined with the decorrelation approximation, fully factorizes the production and decay of unstable particles. The ZWA uncertainty is expected to be of , where M and Γ are the mass and width of the unstable particle. We review the ZWA and demonstrate that errors can be much larger than expected if a significant modification of the Breit–Wigner lineshape occurs. A thorough examination of the recently discovered candidate Standard Model Higgs boson is in progress. For M_H≈125 GeV, one has Γ_H/M_H < 10^-4, which suggests an excellent accuracy of the ZWA. We show that this is not always the case. The inclusion of off-shell contributions is essential to obtain an accurate Higgs signal normalization at the 1% precision level. For gg→H→VV, V = W, Z, corrections occur due to an enhanced Higgs signal in the region M_VV > 2M_V, where also sizable Higgs-continuum interference occurs. We discuss how experimental selection cuts can be used to suppress this region in search channels where the Higgs mass cannot be reconstructed. We note that H→VV decay modes in non-gluon-fusion channels are similarly affected.

New formulae for the resonant scattering and the production amplitudes near an inelastic threshold are derived. It is shown that the Flatté formula, frequently used in experimental analyses, is not sufficiently accurate. Its application to data analysis can lead to a substantial distortion of the effective mass spectra and of the resonance pole positions.

A unitary parameterization, satisfying a generalized Watson theorem for the production amplitudes, is proposed. It can be easily applied to study production processes, multichannel meson-meson interactions and the resonance properties, including among others the scalar resonances a₀(980) and f₀(980).

The goal of this paper is to solve mathematical model equations on solid tumour growth and compute their parameter values by applying growth rates of prostate cancer cell lines in vivo. For these computations, we investigate previously developed C3(1)/Tag transgenic models of prostate cancer. To make the computations fast, we have constructed an algorithm, which is based on small amounts of spatial grid-points and obtained a correspondence between the in vivo growth of tumours and the solutions of the model equations.

We consider Eigen-functions of the Laplace–Beltrami Operator on n-Spheres and characterize them in terms of their local plane wave behavior. We estimate the local spectrum of wave numbers by approximating the Spherical harmonics in the locally flat neighborhood around a point on the Spheres. These local wave numbers are shown to obey an interesting Pythagorean type relation. Based on this relation, we propose a question whether there are integer triples for 2-spheres and their generalization to n-spheres. We apply the local spectrum to define quantities such as phase velocity and group velocity on a sphere and outline the relevance of the analysis for the case fields on de Sitter space.

This paper reports on a study of a methodology to procure semiconductor components for subassemblies used in mainframe computers assembled in IBM. The demand for the subassemblies is highly uncertain as a result of the uncertain mainframe model demands. The demands for mainframe models are dependent on each other. There is also dependency among demands in several time periods. The component personalization process is several weeks long and hence orders for components have to be placed in advance. There is a lot of commonality of components in subassemblies and subassemblies in mainframe models. A software tool to perform procurement planning as well as some what-if analyses has been developed. Results are reported on the use of this tool to generate component requirements by considering set requirements for components, component commonality and dependency of product demands. The results, when compared with the traditional materials requirements planning (MRP) method, suggest that equal or higher service levels can be achieved for a given inventory budget; conversely, a specified service level can be achieved with equal or lower component procurement.

We develop a general theory of partial morphisms in additive exact categories which extends the model theoretic notion introduced by Ziegler in the particular case of pure-exact sequences in the category of modules over a ring. We relate partial morphisms with (co-)phantom morphisms and injective approximations and study the existence of such approximations in these exact categories.

The aim of this note is to improve an approximation formula of Ramanujan-type discussed by Hirschhorn and Villarino.

We review recent progress in understanding the physical meaning of quantum graph models through analysis of their vertex coupling approximations.