No abstract

Given a list of real numbers      , we determine the conditions under which  will form the spectrum of a dense n × n singular symmetric matrix. Based on a solvability lemma, an algorithm to compute the elements of the matrix is derived for a given list and dependency parameters. Explicit computations are performed for  5 n  and to illustrate the result.

Data obtained from electrocardiogram (ECG) signals provides invaluable tools for diagnosing cardiac disorders. However, ECG signals recorded from electrocardiograph are usually corrupted by noise attributed to several factors. To help solve these problems, we develop a simple but inexpensive and easy-to-implement MATLAB T M model that generates ECG signals and gives us mathematical control over the ECG signal. Our model fuses Mathematical functions in MATLAB T M with physiological data.

In topological dynamical systems (TDS), recurrence (periodic–like recurrence) is one of the important concepts in its studies but one major problem is the inability to demonstrate and/or illustrate its formation in the orbit structure of system from a topological point of view. In this paper, the logistic function was applied to demonstrate the periodic point as a recurrent formation (periodic–like recurrence) in the topological dynamical system and dynamical system. The Wolfram Alpha computational knowledge engine was used in obtaining the tables and the figures for the study through various examples of the logistic function. The study shows that period – 2 recurrence is formed when the trajectory of the function is made up of two different values that keep repeating after successive iterations as a result of the period – 2 orbits when the parameter of the function is between 3 and 3.45. The study again shows that when the parameter of the function is greater than 3.83 there is a period – 3 point hence the formation of other periodic points. Convincingly, beyond this period – 3 is another subsequent period called the period-doubling cascade leading into chaos. This period-doubling asserts that other periodic–like recurrences are also present, hence period –n  recurrent exists.

The goal of this paper is to investigate whether the Ext-groups of all pairs ( ) , M N of modules over Nakayama algebras of type ( )achieve that by discussing the Ext-groups of Nakayama algebra with projectives of lengths 3 1 n + and 3 2 n + using combinations of modules of different lengths.