The Lie symmetry method is applied to derive the point symmetries for N-dimensional fractional heat equation. We find that numbers of and brackets are reduced significantly as compared integer order all dimensions. In fact linear equation number solution equal product space dimension, whereas case, it half on dimension. algebras equations mentioned using subsequent computations by inspection. I...

Let Mn be the set of n × n complex matrices, and for every A ∈ Mn, let Sp(A) denote the spectrum of A. For various types of products A1 ∗ · · · ∗ Ak on Mn, it is shown that a mapping φ : Mn → Mn satisfying Sp(A1 ∗ · · · ∗ Ak) = Sp(φ(A1) ∗ · · · ∗ φ(Ak)) for all A1, . . . , Ak ∈ Mn has the form X → ξS−1XS or A → ξS−1XtS for some invertible S ∈ Mn and scalar ξ. The result covers the special cases...

in this article, we characterize the involutiveness of the linear combination of the forma1a1 +a2a2 when a1, a2 are nonzero complex numbers, a1 is a quadratic or tripotent matrix,and a2 is arbitrary, under certain properties imposed on a1 and a2.

background: in this study, the effects of three structural analogues of adenosine upon proliferation of human tumor cells were investigated. previous research showed a cytotoxic effect of adenosine via a3 receptor and a1 receptor and sometimes this effect was receptor independent. the researches showed a differential cytotoxic effect of adenosine and its a3 agonists on cancerous cells, while ot...

6,798,120 B1 9/2004 Fearing et al. 7,267,150 B2 * 9/2007 Shimizu et a1. ............. .. 156/378 7,446,423 B2 * 11/2008 Sakai et a1. ...... .. 257/783 7,678,211 B2 * 3/2010 Takasaki et a1. 156/64 7,896,047 B2 * 3/2011 Yamamoto ....... .. 156/378 7,988,803 B2 * 8/2011 Takasaki et a1. ....... .. 156/64 8,091,764 B2 * 1/2012 Suga et a1. ............. .. 228/18021 2006/0264086 A1 11/2006 Nolan 2008...

In this study, it was aimed to find out whether electroencephalographic (EEG) frequency bands can be used distinguish people with obstructive sleep apnea (OSA) from those who do not have it. 11842 different cases taken 121 patients suffering OSA were combined the case study of 30-person control group without apnea. Apneas highlighted at respiration-record channels and EEG records which are conc...