##### The Significance of Non-ergodic Property of Statistical Mechanics Systems for Understanding Resting State of a Living Cell

D. V. Prokhorenko ., V. V. Matveev

Journal of Advances in Mathematics and Computer Science, Page 46-86
DOI: 10.9734/BJMCS/2011/160

A better grasp of the physical foundations of life is necessary before we can understand the processes occurring inside a living cell. In his physical theory of the cell, American physiologist Gilbert Ling introduced an important notion of the resting state of the cell. He describes this state as an independent stable thermodynamic state of a living substance in which it has stored all the energy it needs to perform all kinds of biological work. This state is characterized by lower entropy of the system than in an active state. The main contribution to this reduction in entropy is made by the cellular water (the dominant component with a concentration of 14 M) which remains in a bound quasi-crystallized state in a resting cell. When the cell becomes active the water gets desorbed and the system’s entropy goes up sharply while the free energy of the system decreases as it is used up for biological work. However, Ling’s approach is primarily qualitative in terms ofh thermodynamics and it needs to be characterized more specifically. To this end, we propose a new thermodynamic approach to studying Ling’s model of the living cell (Ling’s cell), the centrepiece off which is the non-ergodicity property which has recently been proved for a wide range of systems in statistical mechanics (Prokhorenko, 2009). In many ways this new thermodynamics overlaps with the standard quasi-stationary thermodynamics and is therefore compatible with the principles of the Ling cell, however a number of new specific results take into account the existence of several non-trivial motion integrals communicating with each other, whose existence follows from the nonergodicity of the system (Ling’s cell). These results allowed us to develop general thermodynamic approaches to explaining some of the well-known physiological phenomena, which can be used for further physical analysis of these phenomena using specific physical models.

##### Functioning of Divine Ratio on Conformal Einstein Spaces

S. Kumar, K. C. Petwal

Journal of Advances in Mathematics and Computer Science, Page 87-100
DOI: 10.9734/BJMCS/2011/133

Albert Einstein, during the development of his precious theory of relativity evoked a fascinating proverb; ”Two things are infinite in this world! One is the beauty of universe and the other is human stupidity. Though! I am not sure about the beauty of universe.” Perhaps, the inspirational notion from the aforementioned proverb may yield in the form of DIVINE RATIO, the magical proportion. When one talks about the beauty of universe from the stand point of Mathematics, one would probably think about this enthusiastic number. The present article is intended to discuss the compatibility of Divin structure in Einstein as well as conformal Einstein spaces. A brief research on the compatibility of Divine structure with many well known Einstein as well as conformal Einstein equations has been carried out and based on the compatibility conditions, new kinds of spaces e.g., Divine Einstein and conformally Divine Einstein spaces have been generated. Moreover, some new tensor fields e.g., Divine Yang, Divine Bach etc. and the three new looking conformally Divine Einstein equations have also been established.

##### Use of Stochastic Asset-liability Model to Find Unique Price of Asset

Bright O. Osu, Silas A. Ihedioha

Journal of Advances in Mathematics and Computer Science, Page 101-111
DOI: 10.9734/BJMCS/2011/183

‘Asset–liability control’ is meant for managing the risk arising from changes in the relationship between assets and liabilities, due to volatile interest rate in critical situations like economic recession, inflation, etc. A stochastic asset-liability model (ALM), if adopted, and the market, though incomplete, is in equilibrium, a unique price can be obtained that is consistent both with the ALM and with the market. This paper presents a stochastic asset-liability model. A unique price, consistent with the ALM and the market, is obtained given a precise condition. The present market value of asset is also obtained with the given unique price. This classical problem considers an amount of money which an institution has in the bank that grows deterministically and a risky asset such as a stock whose value follows a geometric Brownian motion with a drift.

##### Identification and Removal of Impulsive Noise from Corrupted Images Using Hypergraph Model

D. Aradhana, K. G. Karibasappa, A. Channa Keshav Reddy, K. Karibasappa

Journal of Advances in Mathematics and Computer Science, Page 112-120
DOI: 10.9734/BJMCS/2011/189

Image noise is unwanted information of an image. Noise can occur during image capture, transmission, or processing and it may depend or may not depend on image content. In order to remove the noise from the noisy image, prior knowledge about the nature of noise must be known otherwise noise removal causes the image blurring. Identifying nature of noise is a challenging problem. Many researchers have proposed their ideas on image denoising and each of them has its assumptions, advantages and limitations. In this paper, we are proposing a new algorithm for identifying and removing the impulsive noise using hypergraph concept.