This note suggests that near earth objects and Central Force Optimization have something in common, that NEO theory may hold the key to solving some vexing problems in deterministic optimization: local trapping and proof of convergence. CFO analogizes Newton’s laws to locate the global maxima of a function. The NEO-CFO nexus is the striking similarity between CFO’s D_{avg} and an NEO’s ΔV curves. Both exhibit oscillatory plateau-like regions connected by jumps, suggesting that CFO’s metaphorical “gravity” indeed behaves like real gravity, thereby connecting NEOs and CFO and being the basis for speculating that NEO theory may address difficult issues in optimization.

H. Vazquez-Leal, A. Sarmiento-Reyes, U. Filobello-Nino, Y. Khan, A. L. Herrera-May, R. Castaneda-Sheissa, V. M. Jimenez-Fernandez, M. Vargas-Dorame, J. Sanchez-Orea

The increase of complexity on integrated circuits has also raised the demand for new testing methodologies capable to detect functional failures within circuits before they reach the market. Hence, this work proposes to explore the use of homotopy as a tool for testing a basic analog circuit. The homotopy path is influenced by nonlinearities from the equilibrium equation of the circuit; this situation can be used to infer faults by detecting changes on the homotopy path. The concept was explored using numerical simulation of a simple test circuit; then comparing results for the circuit with and without faults, obtaining modifications on the homotopy path like: the final point, number of iterations, and the number of turning points.

Central Force Optimization is a deterministic metaheuristic for an evolutionary algorithm that searches a decision space by flying probes whose trajectories are computed using a gravitational metaphor. CFO benefits from the inclusion of a pseudorandom component (a numerical sequence that is precisely known by specification or calculation but otherwise arbitrary). The essential requirement is that the sequence is uncorrelated with the decision space topology, so that its effect is to pseudorandomly distribute probes throughout the landscape. While this process may appear to be similar to the randomness in an inherently stochastic algorithm, it is in fact fundamentally different because CFO remains deterministic at every step. Three pseudorandom methods are discussed (initial probe distribution, repositioning factor, and decision space adaptation). A sample problem is presented in detail and summary data included for a 23-function benchmark suite. CFO’s performance is quite good compared to other highly developed, state-of-the-art algorithms.

We consider the braid group on three strands, B3and construct a complex valued representation of it with degree 6, namely, First, we show that this representation is irreducible and not equivalent to either Burau or Krammer’s representations. Second, we prove that the representation is unitary relative to an invertible hermitian matrix.

The existence of at least three weak solutions is established for a class of quasilinear elliptic systems involving the (p(x); q(x))-biharmonic operators with Navier boundary value conditions. The technical approach is mainly based on a three critical points theorem due to Ricceri [12].

The problem of deﬁning products of distributions is a difﬁcult and not completely understood problem, studied from several points of views since Schwartz established the theory of distributions around 1950. Many ﬁelds, such as wave propagation or quantum mechanics, require such multiplications. The product of an inﬁnitely differentiable function (x) and distribution 4(x) inRn is well deﬁned by since Using an induction, we derive an interesting formula for and hence we are able to write out an explicit expression of the product In particular, we imply the product with a few applications in further simplifying existing distributional products. Furthermore, we obtain an asymptotic expression for which isequivalent to the well-known Pizzetti’s formula. Several asymptotic products including as wellasthemore generalized are calculated and presented as inﬁnitely series.

We study the existence and nonexistence of entire positive solutions for quasilinear elliptic system with gradient term

on where nonlinearities f and g are positive and continuous, the potentials a and b are continuous, c-positive and satisfy appropriate growth conditions at inﬁnity. We have that entire large positive solutions fail to exist if f and g are sublinear and a and b have fast decay at inﬁnity, while if f and g satisfy some growth conditions at inﬁnity, and a; b are of slow decay or fast decay at inﬁnity, then the system has inﬁnitely many entire solutions, which are large or bounded.

We introduce wavelet bases consistent with the eigenspaces of the action of rotation by the angle 2π / N in dimension d = 2. Our particular construction yields wavelets that are momentrum-entire (a property weaker than the compact support property). The orthogonality of wavelets in a given eigenspace is based on an inner product that depends on the eigenspace, while the eigenspaces themselves form a super-orthogonal system over a certain family of Hilbert spaces. (We describe this notion in the Introduction.) The existence of a gradient-orthonormal basis of momentum-entire wavelets is an issue that remains open.

In this paper, necessary and sufficient conditions are obtained so that the neutral functional difference equation $$\Delta^{m}\big(y_n-y_{\tau(n)}\big) + q_nG(y_{\sigma(n)})=f_n,\quad n\geq n_0,$$ admits a positive bounded solution, where $$m \geq 1$$ is an odd integer, $$\Delta$$ is the forward difference operator given by $$\Delta y_n = y_{n+1}-y_n$$; $$\{f_n\}$$, $$\{q_n\}$$, are sequences of real numbers with $$q_n \geq 0$$, $$G \in C(\mathbb{R},\mathbb{R}).$$ The results of this paper improve and extend some recent work [6,15].

The paper analyses transmission lines terminated by nonlinear loads situated as follows: GC-loads are connected parallel and L-load is connected in series to them (Fig. 1). First, we formulate boundary conditions for a lossless transmission line system on the basis of Kirchhoff’s law. Then, we reduce the mixed problem for the system in question to initial value problem for a neutral system on the boundary. We introduce an operator in a suitable function space whose fixed point is a periodic solution of the neutral system. The obtained conditions are easily verifiable. We demonstrate the advantages of our method in Numerical example.

Let H be a graph on n vertices and let G be a collection of n subgraphs of H, one for each vertex, G is an orthogonal double cover (ODC) of H if every edge of H is contained in exactly two members of G and any two members share an edge whenever the corresponding vertices are adjacent in H and share no edges whenever the corresponding vertices are non-adjacent in H. In this paper, we are concerned with the symmetric starter vectors of the orthogonal double covers of the complete bipartite graphs and using this method to construct ODCs by the disjoint union of path and a complete bipartite graph. Here, we consider P_{m} the path on m vertices where 4 ≤ m ≤ 11:

In this paper, we discuss the numerical integration with exponential fitting factor for singularly perturbed two-point boundary value problems. It is based on the fact that: the given SPTPBVP is replaced by an asymptotically equivalent delay differential equation. Then, numerical integration with exponential fitting factor is employed to obtain a tridiagonal system which is solved efficiently by Thomas algorithm. We discussed convergence analysis of the method. Model examples are solved and the numerical results are compared with exact solution.

We introduce a new class of nonlinear mappings, the class of generalized strongly successively Φ - pseudocontractive mappings in the intermediate sense and prove the convergence of Mann type iterative scheme to their fixed points. Our results improves and generalizes several other results in literature.

An orthogonal double cover (ODC) of a graph is a collection of subgraphs of such that every edge of is contained in exactly two members of and for any two members and in , is 1 if and it is 0 if . An ODC of is cyclic (CODC) if the cyclic group of order is a subgroup of the automorphism group of . In this paper, the CODCs of certain circulants with a specific regularity by certain infinite graph classes are concerned.

In this paper, we establish some strong convergence and stability results of multistep iterative scheme for a general class of operators introduced by Bosede and Rhoades [5] in a Banach space. As corollaries, some convergence and stability results for the Noor, Ishikawa, Mann and Picard iterative schemes are also established. Our convergence results generalize and extend the results of Berinde [3], Bosede [4], Olaleru [16], Rafiq [21, 22] among others, while our stability results are extensions and generalizations of multitude of results in the literature, including the results of Berinde [1], Bosede and Rhoades [5], Imoru and Olatinwo [9] and Osilike [18].

It is well known that the problem of fractional differentiation n is an ill-posed problem. So far there exists many approximation methods for solving this problem. In this paper we prove a stability estimate for a problem of fractional differentiation. Based on the obtained stability estimate, we present a Tikhonov regularization method and obtain the error estimate. According to the optimality theory of regularization, the error estimates are order optimal. Numerical experiment shows that the regularization works well.