We calculate the mean fitness for evolution models, when the fitness is a function of the Hamming distance from a reference sequence, and there is a probability that this fitness is nullified (Eigen model case) or tends to the negative infinity (Crow-Kimura model case). We calculate the mean fitness of these models. The mean fitness is calculated also for the random fitnesses with logarithmic-n...

Abstract We express the Crow-Kimura and Eigen models of quasispecies theory in a functional integral representation. We formulate the spin coherent state functional integrals using the Schwinger Boson method. In this formulation, we are able to deduce the long-time behavior of these models for arbitrary replication and degradation functions. We discuss the phase transitions that occur in these ...

The problem of scattering of capillary waves by a semi-infinite dock with a porous undulatory sea bed is attempted using perturbation technique. Two different eigen function expansions of the velocity potential function on the two sides of the surface discont inuity are constructed. An integral expression for first order reflection coefficient is arrived at involving the bottom shape function. ...

In this paper the buckling coefficient of FGM rectangular plates calculated by the new version of differential quadrature method (DQM). At the first the governing differential equation for plate has been calculated and then according to the new version of differential quadrature method (DQM) the existence derivatives in equation , convert to the amounts of function in the grid points inside of ...

In this paper, we propose a new optimized PID controller to stabilize the synchronous machine connected to an infinite bus. The model for the synchronous machine is 4-ordered linear Philips-Heffron synchronous machine. In this research, the parameters of the PID controller are optimally achieved by minimizing a definite fitness function to removes the unstable Eigen-value to the left side of im...

The present study investigates the peristaltic flow of couple stress fluid in a non-uniform rectangular duct with compliant walls. Mathematical modeling is based upon the laws of mass and linear momentum. Analytic solutions are carried out by the eigen function expansion method under long-wavelength and low-Reynolds number approximations. The features of the flow characteristics are analyzed by...

Unreasonable control parameters of the Line Commutated Converter based High Voltage Direct Current (LCC-HVDC) system may induce small-signal instability. This paper studies impact inverter controller on steady response LCC-HVDC under weak AC grid condition. Firstly, according to a practical project, model is established switching function. Then, eigen-analysis method adopted study side oscillat...

Let K be an imaginary quadratic field where p splits, $$p\ge 5$$ a prime number and f eigen-newform of even weight level $$N>3$$ that is coprime to p. Under the Heegner hypothesis, Kobayashi–Ota showed one inclusion Iwasawa main conjecture involving Bertolini–Darmon–Prasanna p-adic L-function holds after tensoring by $$\mathbb {Q}_p$$ . certain hypotheses, we improve upon Kobayahsi–Ota’s result...

Vibrations of structures subjected to concentrated point loads have many applications in mechanical engineering. Experiments are expensive and numerical methods often used for simulations. In this paper, we consider the plate vibration with nonlinear dependence on eigen-parameter. The problem is formulated as eigenvalue a holomorphic Fredholm operator function. Bogner–Fox–Schmit element discret...