scholarly journals On M-unambiguity of Parikh matrices

2020 ◽  
Vol 4 (1) ◽  
pp. 1
Author(s):  
Wen Chean Teh
Keyword(s):  
Title Page ◽  
Ambiguous Words ◽  
Matrix Mapping ◽  
Initial Results

<div class="page" title="Page 1"><div class="layoutArea"><div class="column"><p><span>The Parikh matrix mapping was introduced by Mateescu <em>et al</em>. in 2001 as a canonical generalization of the classical Parikh mapping. The injectivity problem of Parikh matrices, even for ternary case, has withstanded numerous attempts over a decade by various researchers, among whom is Serbanuta. Certain </span><em>M</em><span>-ambiguous words are crucial in Serbanuta's findings about the number of </span><em>M</em><span>-unambiguous prints. We will show that these words are in fact strongly </span><em>M</em><span>-ambiguous, thus suggesting a possible extension of Serbanuta’s work to the context of strong </span><span>M</span><span>-equivalence. In addition, initial results pertaining to a related conjecture by Serbanuta will be presented.</span></p></div></div></div>

Parikh q-Matrices and q-Ambiguous Words

2020 ◽  
Vol 31 (01) ◽  
pp. 23-36
Author(s):  
Somnath Bera ◽  
Rodica Ceterchi ◽  
Kalpana Mahalingam ◽  
K. G. Subramanian
Keyword(s):  
Binary Alphabet ◽  
Ambiguous Words ◽  
Matrix Mapping

The Parikh matrix mapping plays an important role in the study of words through numerical properties. The Parikh [Formula: see text]-matrix mapping, introduced by Egecioglu and Ibarra (2004) as an extension of the Parikh matrix mapping, maps words to matrices with polynomial entries in [Formula: see text] A word [Formula: see text] over an ordered alphabet [Formula: see text] is said to be [Formula: see text]-ambiguous if there exists another word [Formula: see text] over [Formula: see text] such that both the words have same Parikh [Formula: see text]-matrix. Here we derive several properties of [Formula: see text]-ambiguous words, in particular, for a binary alphabet.

Electron Probe Analysis of Vertebrate Smooth Muscle: Distribution of Ca and Ci

1976 ◽  
Vol 34 ◽  
pp. 334-335 ◽  
Author(s):  
Avril V. Somlyo ◽  
H. Shuman ◽  
A.P. Somlyo
Keyword(s):  
Smooth Muscle ◽  
Electron Probe ◽  
Preliminary Report ◽  
Cell Damage ◽  
Electron Probe Analysis ◽  
Perinuclear Space ◽  
Probe Analysis ◽  
High K ◽  
Low K ◽  
Initial Results

This is a preliminary report of electron probe analysis of rabbit portal-anterior mesenteric vein (PAMV) smooth muscle cryosectioned without fixation or cryoprotection. The instrumentation and method of electron probe quantitation used (1) and our initial results with cardiac (2) and skeletal (3) muscle have been presented elsewhere.In preparations depolarized with high K (K2SO4) solution, significant calcium peaks were detected over the sarcoplasmic reticulum (Fig 1 and 2) and the continuous perinuclear space. In some of the fibers there were also significant (up to 200 mM/kg dry wt) calcium peaks over the mitochondria. However, in smooth muscle that was not depolarized, high mitochondrial Ca was found in fibers that also contained elevated Na and low K (Fig 3). Therefore, the possibility that these Ca-loaded mitochondria are indicative of cell damage remains to be ruled out.

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