Abstract:
The main theorem of the present paper is the bistability theorem for a four dimensional cancer model, in the variables？？representing primary cancer C, metastatic cancer ？, growth factor GF and growth inhibitor GI, respectively. It says that for some values of the para- meters this system is bistable, in the sense that there are exactly two positive singular points of this vector field. And one is stable and the other unstable. We also find an expression for？ for the discrete model T of the introduction, with variables , where C is cancer, are growth factors and growth inhibitors respectively. We find an affine vector field Y whose time one map is T^{2} and then compute ？, where ？is an integral curve of Y through ？. We also find a formula for the first escape time for the vector field associated to T, see section four.

Writing
in 1943, renowned Austrian physicist Edwin Schrodinger asked “What is Life?”
thereby invigorating the debate which preoccupied biologists at the time. He
proposed an answer to this question rooted in considerations borrowed from
Thermodynamics and Statistical Mechanics. To reveal the missing link in Biology-Physics,
the present Note investigates an alternate answer in which dynamical action,
rather than thermodynamics and energy, plays the fundamental role. It reviews
in particular the process of biological cell replication which may be
considered to define “Life” and might be the macroscopic manifestation of an
underlying quantum physical process in which xons, conveyors of dynamical
action, are the determining agents.

Abstract:
Gibson developed the affordance concept to complement his theory of direct perception that stands in sharp contrast with the prevalent inferential theories of perception. A comparison of the two approaches shows that the distinction between them also has an ontological aspect. We trace the history and newer formalizations of the notion of affordance and discuss some competing opinions on its scope. Next, empirical work on the affordance concept is reviewed in brief and the relevance of dynamical systems theory to affordance research is demonstrated. Finally, the striking but often neglected convergence of the ideas of Gibson and those of certain Continental philosophers is discussed.

Abstract:
In this paper, surface photometry and dynamical properties of Lenticular galaxies will be developed and applied to NGC3245. In this respect, we established new relation between the intensity distribution I and the semi-major axis a Moreover, some basic statistics of both independent and the dependent variables of the relation are also given. In addition to the I(a) relation , the Sérsic r^{1/n} model is applied for the intensity profile I(r) resulting in an estimation of the effective radius, re, and the surface brightness it encloses, μe. Both relations (I(a) and I(r)) are accurate as judged by the precision criteria which are: the probable errors for the coefficients , the estimated variance of the fit and the Q value (the square distance between the exact solution and the least square estimated solution) where all very satisfactory. Correlation coefficients between some parameters of the isophotes are also computed. Finally as examples of applications of surface photometry we determined the dynamical properties: mass, density, potential distributions, as well as distributions of escape and circular speeds in terms of Sérsic model.

In dynamical systems, the system suddenly becomes unstable due to
parameter perturbation which corresponds to environmental changes or major
incidents. To avoid such instabilities in engineering systems, tuning system
parameters is very important. In this paper, we propose a method for obtaining
optimal parameter values in a parameterized dynamical system. Here, the optimal
value means the farthest point from the bifurcation curves in a bounded
parameter plane. As illustrated examples, we show the results of
continuous-time and discrete-time systems. Our algorithm can find the optimal
parameter values in both systems.

Abstract:
We examine through the lens of dynamical systems a “one dimensional” time mapping of emergent VEV from Pre-Planckian space time conditions. As it is, we will from first principles examine what adding acceleration does as to the HUP previously derived. In doing so, we will be trying it in our discussion with the earlier work done on the HUP. not equal to zero, constant, but large would frequently imply which would have three dissimilar real valued roots. And the situation with not equal to zero yields more tractable result for which will have implications for the HUP inequality in Pre-Planckian space-time, and buttresses an analysis of a 1 dimensional “time” mapping for emergent VEV (vacuum expectation values).

We calculate the core-hole spectral density in a pristine graphene, where the density of states of itinerant electrons goes linearly to zero at the Fermi level. We consider explicitly two models of electron-hole interaction. In the unscreened Coulomb interaction model, the spectral density is similar to that in metal (for local interaction). Thus there is no δ-function singularity in the core-hole spectral density. In the local interaction model, the δ-function singularity survives, but the interaction leads to the appearance of the background in the spectral density.

In this paper, we derive an explicit form in terms of
end-point data in space-time for the classical action, i.e. integration of the Lagrangian
along an extremal, for the nonlinear quartic oscillator evaluated on extremals.

We present
a new family of percolation models. We show, using theory and computer
simulations, that these represent a new universality class. Interestingly,
systems in this class appear to violate the Harris criterion, making model
systems within these class ideal systems for studying the influence of disorder
on critical behavior. We argue that such percolative systems have already been
realized in practice in strongly correlated electron systems that have been
driven to the quantum critical point by means of chemical substitution.

Abstract:
The Jablonowski test case is widely used for debugging and evaluating the numerical characteristics of global dynamical cores that describe the fluid dynamics component of Atmospheric General Circulation Models. The test is defined in terms of a steady-state solution to the equations of motion and an overlaid perturbation that triggers a baroclinically unstable wave. The steady-state initial conditions are zonally symmetric. Therefore, the test case design has the potential to favor models that are built upon regular latitude-longitude or Gaussian grids. Here we suggest rotating the computational grid so that the balanced flow is no longer aligned with the computational grid latitudes. Ideally the simulations should be invariant under rotation of the computational grid. Note that the test case only requires an adjustment of the Coriolis parameter in the model code. The rotated test case has been exercised by six dynamical cores. In addition, two of the models have been tested with different vertical coordinates resulting in a total of eight model variants. The models are built with different computational grids (regular latitude-longitude, cubed-sphere, icosahedral hexagonal/triangular) and use very different numerical schemes. The test case is useful for debugging, assessing the degree of anisotropy in the numerical methods and grids, and evaluating the numerical treatment of the pole points since the rotated test case directs the flow directly over the geographical poles. It thereby challenges the polar treatments like polar filters in some models.