Predictions based on the cumulative curves: Basic principles and nontrivial example

In this paper the new prediction method based on analysis of the integrated (cumulative) curves is suggested. This method includes the procedure of the optimal linear smoothing (POLS) for the finding of optimal trends, independent “reading” of relative fluctuations in terms of β-distribution function that are formed after subtraction of the calculated trend and the recognition of the proper fitting hypothesis for the integrated optimal trends by the eigen-coordinates method. The combined noninvasive approach was applied to analysis of temperature data obtained from the site http://data.giss.nasa.gov/gistemp/ related to the global warming (GW) phenomenon. These data are considered as nontrivial examples of verification of new forecasting method. The available data were combined into six files covering the mean/anomalous temperature 1546 month’s points covering the period from the January of 1880 up to October of 2008. Besides the global registered points the combined files included in themselves the north/south data points measured independently for both the Earth’s hemispheres. The combined new method (preliminary verified on mimic data) applied to these files predicts the changing of the GW period by the global cooling (GC) period that will happen during the years 2038–2136. Besides this important result a new method helps to discover the influence of a small but stable oscillating process with a set of self-similar periods Ω_n = Ω₀ξⁿ, n = 0, ±1, ±2, ±3, ±4 with mean period 〈T〉 = 12.55 year. This fact should present interest for ecologists and meteorologists working in this field.     

Explicit series solution of travelling waves with a front of Fisher equation

In this paper, an analytic technique, namely the homotopy analysis method, is employed to solve the Fisher equation, which describes a family of travelling waves with a front. The explicit series solution for all possible wave speeds 0 < c < +∞ is given. Such kind of explicit series solution has never been reported, to the best of author’s knowledge. Our series solution indicates that the solution contains an oscillation part when 0 < c < 2. The proposed analytic approach is general, and can be applied to solve other similar nonlinear travelling wave problems.     

Existence and asymptotics of traveling waves for nonlocal diffusion systems

In this paper, we deal with the existence and asymptotic behavior of traveling waves for nonlocal diffusion systems with delayed monostable reaction terms. We obtain the existence of traveling wave front by using upper-lower solutions method and Schauder’s fixed point theorem for c > c₁(τ) and using a limiting argument for c = c₁(τ). Moreover, we find a priori asymptotic behavior of traveling waves with the help of Ikehara’s Theorem by constructing a Laplace transform representation of a solution. Especially, the delay can slow the minimal wave speed for ?₂f(0, 0) > 0 and the delay is independent of the minimal wave speed for ?₂f(0, 0) = 0.     

Simulación numérica del flujo turbulento de aire con gotas dispersas de agua a través de separadores de torres de refrigeración

This work presents a numerical study on the turbulent flow of air with dispersed water droplets in separators of mechanical cooling towers. The averaged Navier-Stokes equations are discretised through a finite volume method, using the Fluent and Phoenics codes, and alternatively employing the turbulence models k ? ?, k ? ω and the Reynolds stress model, with low-Re version and wall enhanced treatment refinements. The results obtained are compared with numerical and experimental results taken from the literature. The degree of accuracy obtained with each of the considered models of turbulence is stated. The influence of considering whether or not the simulation of the turbulent dispersion of droplets is analyzed, as well as the effects of other relevant parameters on the collection efficiency and the coefficient of pressure drop. Focusing on four specific eliminators (‘Belgian wave’, ‘H1-V’, ‘L-shaped’ and ‘Zig-zag’), the following ranges of parameters are outlined: 1 ≤ U_e ≤ 5 m/s for the entrance velocity, 2 ≤ D_p ≤ 50 μm for the droplet diameter, 650 ≤ Re ≤ 8.500 for Reynolds number, and 0.05 ≤ P_i ≤ 5 for the inertial parameter. Results reached alternately with Fluent and Phoenics codes are compared. The best results correspond to the simulations performed with Fluent, using the SST k ? ω turbulence model, with values of the dimensionless scaled distance to wall y⁺ in the range 0.2 to 0.5. Finally, correlations are presented to predict the conditions for maximum collection efficiency (100 %), depending on the geometric parameter of removal efficiency of each of the separators, which is introduced in this work.     

Behavior of different ansätze in the generalized projection operator method

Using the recently reported generalized projection operator method for the nonlinear Schrödinger equation, we derive the generalized pulse parameters equations for ansätze like hyperbolic secant and raised cosine functions. In general, each choice of the phase factor θ in the projection operator gives a different set of ordinary differential equations. For θ = 0 or θ = π/2, the corresponding projection operator scheme is equivalent to the Lagrangian variation method or the bare approximation of the collective variable theory. We prove that because of the inherent symmetric property between the pulse parameters of a Gaussian ansätz results the same set of pulse parameters equations for any value of the generalized projection operator parameter θ. Finally we prove that after the substitution of the ansätze function, the Lagrange function simplifies to the same functional form irrespective of the ansätze used because of a special property shared by all the anätze chosen in this work.     

An extended rational interpolation method

To interpolate function, f(x), a ? x ? b, when we have some information about the values of f(x) and their derivatives in separate points on {x₀, x₁, … , x_n} ? [a, b], the Hermit interpolation method is usually used. Here, to solve this kind of problems, extended rational interpolation method is presented and it is shown that the suggested method is more efficient and suitable than the Hermit interpolation method, especially when the function f(x) has singular points in interval [a, b]. Also for implementing the extended rational interpolation method, the direct method and the inverse differences method are presented, and with some examples these arguments are examined numerically.     

Maple packages for computing Hirota’s bilinear equation and multisoliton solutions of nonlinear evolution equations

The Hirota method for generating Hirota’s bilinear equation and constructing soliton solutions of nonlinear evolution equations is discussed and illustrated. Two Maple programs Bilinearization and Multisoliton are presented to automatically calculate Hirota’s bilinear equations for nonlinear evolution equations and to compute their N-soliton solutions for N = 1, 2 or 3, respectively. Different kinds of examples are used to demonstrate the effectiveness of the packages.     

RBFs approximation method for time fractional partial differential equations

In this paper, radial basis functions (RBFs) approximation method is implemented for time fractional advection–diffusion equation on a bounded domain. In this method the first order time derivative is replaced by the Caputo fractional derivative of order α ∈ (0, 1], and spatial derivatives are approximated by the derivative of interpolation in the Kansa method. Stability and convergence of the method is discussed. Several numerical examples are include to demonstrate effectiveness and accuracy of the method.     

Existence of quasibounded solutions for the higher order dynamic equations on measure chains

By using the exponential dichotomy and Schauder’s fixed point theorem, some new criteria are established for the existence of quasibounded solutions of the inhomogeneous system x^Δ = A(t)x + g(t, x) + h(t), which generalize the previous results in [15], [19].     

Lower bounds for minimum semidefinite rank from orthogonal removal and chordal supergraphs

The minimum semidefinite rank (msr) of a graph is the minimum rank among positive semidefinite matrices with the given graph. The OS-number is a useful lower bound for msr, which arises by considering ordered vertex sets with some connectivity properties. In this paper, we develop two new interpretations of the OS-number. We first show that OS-number is also equal to the maximum number of vertices which can be orthogonally removed from a graph under certain nondegeneracy conditions. Our second interpretation of the OS-number is as the maximum possible rank of chordal supergraphs who exhibit a notion of connectivity we call isolation-preserving. These interpretations not only give insight into the OS-number, but also allow us to prove some new results. For example we show that msr(G) = |G| ? 2 if and only if OS(G) = |Gzsfnc ? 2.     

On the stability of fractional neutron point kinetics (FNPK)

The aim of this work is investigate the stability of fractional neutron point kinetics (FNPK). The method applied in this work considers the stability of FNPK as a linear fractional differential equation by transforming the s − plane to the W − plane. The FNPK equations is an approximation of the dynamics of the reactor that includes three new terms related to fractional derivatives, which are explored in this work with an aim to understand their effect in the system stability. Theoretical study of reactor dynamical systems plays a significant role in understanding the behavior of neutron density, which is important in the analysis of reactor safety. The fractional relaxation time (τ^α) for values of fractional-order derivative (α) were analyzed, and the minimum absolute phase was obtained in order to establish the stability of the system. The results show that nuclear reactor stability with FNPK is a function of the fractional relaxation time.     

On Pauli’s principles of “Zweiteilung und symmetrie verminderung” in Higgs physics and non-linear dynamics

Pauli’s principle of bi-division and symmetry reduction “Zweiteilung und symmetrie verminderung” is generalized to cover maximally symmetric spaces specified by Killing’s vector fields and its successive symmetry breaking to yield the particles of the standard model of high energy physics.An analogous picture borrowed from non-linear dynamics and complexity theory will be used to illustrate the conceptual aspect of the procedure from which one could infer, the existence not only of one, but several Higgs particles, possibly three neutral and two charged Higgs with masses not that far from the presently accessible electro-weak energy scale. A tree level estimation with one Higgs to approximate the mass was found to give m_H ≃ 162 Gev.     

Generation of n × m-scroll attractors in a two-port RCL network with hysteresis circuits

In this paper, the generation of n × m-scroll attractors based on a two-port network is presented. The two-port network is built according to the RCL circuit suggested in the conventional Chua’s circuit. By appending hysteresis voltage controlled devices on this two-port network, n-scroll and n × m-scroll attractors can be duly obtained both in simulations and experiments.     

Global chaos synchronization of new chaotic systems via nonlinear control

Nonlinear control is an effective method for making two identical chaotic systems or two different chaotic systems be synchronized. However, this method assumes that the Lyapunov function of error dynamic (e) of synchronization is always formed as V (e) = 1/2e^Te. In this paper, modification based on Lyapunov stability theory to design a controller is proposed in order to overcome this limitation. The method has been applied successfully to make two identical new systems and two different chaotic systems (new system and Lorenz system) globally asymptotically synchronized. Since the Lyapunov exponents are not required for the calculation, this method is effective and convenient to synchronize two identical systems and two different chaotic systems. Numerical simulations are also given to validate the proposed synchronization approach.     

An interval nonlinear program for the planning of waste management systems with economies-of-scale effects—A case study for the region of Hamilton,Ontario, Canada

In practical environmental systems with the effects of economies-of-scale (EOS), most relationships among different system components are nonlinear in nature, which can be described precisely only if a nonlinear model is employed. In this study, an interval nonlinear programming (INLP) model is developed and applied to the planning of a municipal solid waste (MSW) management system with EOS effects on system costs. The INLP has a nonlinear objective function and linear constraints. It handles nonlinearity presented as exponential functions. When exponential term p = 1 (in the INLP’s objective function), the model becomes an interval linear program; when p = 2, it becomes an interval quadratic program. Therefore, the INLP is flexible in reflecting a variety of system complexities. A solution algorithm with satisfactory performance is proposed. Application of the proposed method to the planning of waste management activities in the Hamilton-Wentworth Region, Ontario, Canada, indicated that reasonable solutions have been generated. In general, the INLP model could reflect uncertain and nonlinear characteristics of MSW management systems with EOS effects. The modeling results provided useful decision support for the Region’s waste management activities.     

The stochastic soliton-like solutions of stochastic KdV equations

By means of a generalized method and symbolic computation, we consider a stochastic KdV equation U_t + f(t)U ♢ U_x + g(t)U_xxx = W(t) ♢ R^♢(t, U, U_x, U_xxx). We construct new and more general formal solutions. At the same time, we recover all the solutions found by Xie [Phys. Lett. A 310 (2003) 161]. The solutions obtained include the nontravelling wave and coefficient function’s stochastic soliton-like solutions, singular stochastic soliton-like solutions, stochastic triangular functions solutions.     

Special Functions on the Sphere with Applications to Minimal Surfaces

A function which is homogeneous in x, y, z of degree n and satisfies V_xx + V_yy + V_zz = 0 is called a spherical harmonic. In polar coordinates, the spherical harmonics take the form rⁿf_n, where f_n is a spherical surface harmonic of degree n. On a sphere, f_n satisfies ▵ f_n + n(n + 1)f_n = 0, where ▵ is the spherical Laplacian. Bounded spherical surface harmonics are well studied, but in certain instances, unbounded spherical surface harmonics may be of interest. For example, if X is a parameterization of a minimal surface and n is the corresponding unit normal, it is known that the support function, w = X · n, satisfies ▵w + 2w = 0 on a branched covering of a sphere with some points removed. While simple in form, the boundary value problem for the support function has a very rich solution set. We illustrate this by using spherical harmonics of degree one to construct a number of classical genus-zero minimal surfaces such as the catenoid, the helicoid, Enneper's surface, and Hennenberg's surface, and Riemann's family of singly periodic genus-one minimal surfaces.     

Intersection of Yager’s implications with QL and D-implications

The intersection of the different classes of implications is one of the most popular topics nowadays due to the large number of construction methods of these operators. In this paper, we deal with the characterization of the intersection of Yager’s implications with QL and D-implications. Some initial steps have already been made with the intersection of Yager’s implications with (S, N), R and QL-implications, however some questions remain unanswered. In particular, we solve an open problem related to the characterization of those implications that are both QL-implications and f-generated implications with f(0) < ∞, fully determining the expression of the QL-implications generated by a continuous t-conorm that belong to the considered intersection. Furthermore, we perform a similar study for D-implications and finally, we study the intersection of Yager’s implications with their φ-conjugates.     

Approximate solutions of a nonlinear oscillator typified as a mass attached to a stretched elastic wire by the homotopy perturbation method

The homotopy perturbation method is used to solve the nonlinear differential equation that governs the nonlinear oscillations of a system typified as a mass attached to a stretched elastic wire. The restoring force for this oscillator has an irrational term with a parameter λ that characterizes the system (0 ? λ ? 1). For λ = 1 and small values of x, the restoring force does not have a dominant term proportional to x. We find this perturbation method works very well for the whole range of parameters involved, and excellent agreement of the approximate frequencies and periodic solutions with the exact ones has been demonstrated and discussed. Only one iteration leads to high accuracy of the solutions and the maximal relative error for the approximate frequency is less than 2.2% for small and large values of oscillation amplitude. This error corresponds to λ = 1, while for λ < 1 the relative error is much lower. For example, its value is as low as 0.062% for λ = 0.5.     

Wave propagation in nonlocal elastic continua modelled by a fractional calculus approach

In the present paper, the wave propagation in one-dimensional elastic continua, characterized by nonlocal interactions modeled by fractional calculus, is investigated. Spatial derivatives of non-integer order 1 < α < 2 are involved in the governing equation, which is solved by fractional finite differences. The influence of long-range interactions is then analyzed as α varies: the resonant frequencies and the standing waves of a nonlocal bar are evaluated and the deviations from the classical (local) ones, recovered by imposing α = 2, are discussed.