応用および計算数学ジャーナル

In this paper, we derive equivalent equations of integration of secant and cosecant functions. Furthermore, we derive reduction formula for integration of product of integer powers of cosine and sine functions.

Viscoelasticity with regular relaxation functions has attracted the attention of many researchers over the last half century or so. Several results concerning existence and long-time behavior of solutions have been established. In particular the exponential, polynomial decay and recently what so called the general decay have been proved. For viscoelasticity, with singular kernels, less attention has been given and few results of existence and exponential decay have been established. In this paper we extend the general decay result, established for regularkernel viscoelasticity, to that with singular kernels. We also present some numerical test to illustrate our theoretical result.

Textual point of view, generate in a series of rotational dynamics experiment. Initial research, is wish find a method overcome the momentum conservation. But further study, again detected inside the classical mechanics, the error of the principle of force moment. Then a series of, momentous the error of inside classical theory, all discover come out. The momentum conservation law is wrong? the newton third law is wrong? the energy conservation law is also can surpass. After redress these error, the new theory namely perforce bring. This will involve the classical physics and mechanics the foundation fraction, textbooks of physics foundation part should proceed the grand modification.

In this work, we discover groups of similar users of a topic recommendation system. The data sets used are from Tipster Newsgroups, which are used in the annual TREC (Text Retrieval Conference) competition. The users are simulated, represented by tag/rating pairs. The documents in the Tipster data sets are clustered with a topic clustering algorithm that is a subset of the topic recommendation system being proposed in this paper. The users query the clusters derived from the topic clustering algorithm with tags, then rate the degree of relevance the content returned by the system has to their tag. It is shown in this work that, starting from a random sampling of the clusters by the users, and a random initial distribution of ratings per user, that a topic recommendation engine powered by a Boltzmann machine with nearest neighbor interactions results in two distinct clusters of users: those that converge quickly to a particular single topic, and those who explore a few different topics in a way that is periodic in time. This allows new users entering the system to be clustered and hence given a more relevant experience earlier in the process.

This note is for finding a polynomial time solution for the "Travelling Salesman Problem" for a "Complete" graph for any number of vertices. The solutions that I am getting for the examples given in the textbooks are giving the correct answers. If new examples are tried to further test the algorithm and the answers are approximately very near to the correct answer, then this algorithm can be considered as a new type of heuristic algorithm.

The space χ (F) of all entire functions ( ) =Σ k k k f z x z of exponential order 1 and type 0 have been defined by Sirajudeen. In the present paper we characterize the matrix class concerning the space χ (F) . 2010 AMS Mathematical Subject Classification: 46A45; 40C05; 46A35.

Recently, Samet, Vetro and Vetro introduced α-ψ-contractive mappings and gave some results on fixed points of the mappings . In fact, their technique generalized some ordered fixed point results . Also they have proved some results on coupled fixed points of α-ψ-contractive mappings. In 1974 Ciric introduced quasicontractive mappings and obtained an important generalization of Banach’s contraction principle. Recently Mohammadi, Rezapour and Shahzad have proved some fixed point results on α-ψ-contractive and α-ψ-quasicontractive multifunction’s. By using the main idea of, we give some new results for coupled fixed points of α-ψ-contractive multifunction.

We present a local convergence analysis for a regula falsi-type method for solving nonlinear equations. In the earlier studies such as hypotheses on the second derivative have been used to show convergence of this method. In this paper we show convergence under hypotheses only on the first derivative. Moreover, we provide a radius of convergence and computable error bounds on the distances involved. Numerical examples are also given in this study.

Wavelet has wide range of use in the present scientific universe. At present using wavelet through MATLAB different types of tasks are done. For instance biometric recognition (fingerprint recognition, voice recognition, iris recognition, face recognition, pattern recognition and signature recognition), signal processing, human voice activity detection etc. are done using wavelet and wavelet transform. Among these here I have discussed about “Human Voice Activity Detection”. At first a human voice is taken as the input sound to MATLAB command window using a good headphone for a few second. Then the sound taken as input give a graphical representation that is saved for future activities. After that using the wavelet toolbox of MATLAB the image of the input sound is taken for analyzing it. Using discrete wavelet transform the image is analyzed. During this analysis a “10 level wavelet” tree is generated by Haar wavelet with 10 decomposition level. At the same time the original signal is reconstructed. At the first time six different human voice activities of the same persons are analyzed. The Norm and the SNR (Signal to Noise Ratio) are counted. The data of the SNR are counted in decibel (db.) unit. Also the bit rates of the three different voice are counted. In this way total 18 different experiments are done for the different five persons where except the first person for all the person three experiments are dine.. The numerical data of the experiments are shown as graphical representation as well as in histogram analysis. In this process the whole experiments are done for the activity detection of human voice.