Abstract: We present a constructive proof of Tychonoff’s fixed point theorem in a locally convex space for uniformly continuous and sequentially locally non-constant functions.
Abstract: In this paper, by constructing a special non-empty closed convex set and utilizing M¨onch fixed point theory, we investigate the existence of solution for a class of fourth-order singular differential equation in Banach space, which improved and generalized the result of related paper.
Abstract: In this paper, the periodic surveillance scheme has
been proposed for any convex region using mobile wireless sensor
nodes. A sensor network typically consists of fixed number of
sensor nodes which report the measurements of sensed data such as
temperature, pressure, humidity, etc., of its immediate proximity
(the area within its sensing range). For the purpose of sensing an
area of interest, there are adequate number of fixed sensor
nodes required to cover the entire region of interest. It implies
that the number of fixed sensor nodes required to cover a given
area will depend on the sensing range of the sensor as well as
deployment strategies employed. It is assumed that the sensors to
be mobile within the region of surveillance, can be mounted on
moving bodies like robots or vehicle. Therefore, in our
scheme, the surveillance time period determines the number of
sensor nodes required to be deployed in the region of interest.
The proposed scheme comprises of three algorithms namely:
Hexagonalization, Clustering, and Scheduling, The first algorithm
partitions the coverage area into fixed sized hexagons that
approximate the sensing range (cell) of individual sensor node.
The clustering algorithm groups the cells into clusters, each of
which will be covered by a single sensor node. The later
determines a schedule for each sensor to serve its respective cluster.
Each sensor node traverses all the cells belonging to the cluster
assigned to it by oscillating between the first and the last cell for
the duration of its life time. Simulation results show that our
scheme provides full coverage within a given period of time using
few sensors with minimum movement, less power consumption,
and relatively less infrastructure cost.
Abstract: In this paper, free vibration analysis of carbon nanotube (CNT) reinforced laminated composite panels is presented. Three types of panels such as flat, concave and convex are considered for study. Numerical simulation is carried out using commercially available finite element analysis software ANSYS. Numerical homogenization is employed to calculate the effective elastic properties of randomly distributed carbon nanotube reinforced composites. To verify the accuracy of the finite element method, comparisons are made with existing results available in the literature for conventional laminated composite panels and good agreements are obtained. The results of the CNT reinforced composite materials are compared with conventional composite materials under different boundary conditions.
Abstract: This paper describes a new method for affine parameter
estimation between image sequences. Usually, the parameter
estimation techniques can be done by least squares in a quadratic
way. However, this technique can be sensitive to the presence
of outliers. Therefore, parameter estimation techniques for various
image processing applications are robust enough to withstand the
influence of outliers. Progressively, some robust estimation functions
demanding non-quadratic and perhaps non-convex potentials adopted
from statistics literature have been used for solving these. Addressing
the optimization of the error function in a factual framework for
finding a global optimal solution, the minimization can begin with
the convex estimator at the coarser level and gradually introduce nonconvexity
i.e., from soft to hard redescending non-convex estimators
when the iteration reaches finer level of multiresolution pyramid.
Comparison has been made to find the performance of the results
of proposed method with the results found individually using two
different estimators.
Abstract: Let Gα ,β (γ ,δ ) denote the class of function
f (z), f (0) = f ′(0)−1= 0 which satisfied e δ {αf ′(z)+ βzf ′′(z)}> γ i Re
in the open unit disk D = {z ∈ı : z < 1} for some α ∈ı (α ≠ 0) ,
β ∈ı and γ ∈ı (0 ≤γ 0 . In
this paper, we determine some extremal properties including
distortion theorem and argument of f ′( z ) .
Abstract: The paper is concerned with the existence of solution
of nonlinear second order neutral stochastic differential inclusions
with infinite delay in a Hilbert Space. Sufficient conditions for the
existence are obtained by using a fixed point theorem for condensing
maps.
Abstract: In this paper, a necessary and sufficient coefficient are given for functions in a class of complex valued meromorphic harmonic univalent functions of the form f = h + g using Salagean operator. Furthermore, distortion theorems, extreme points, convolution condition and convex combinations for this family of meromorphic harmonic functions are obtained.
Abstract: We present a new algorithm for nonlinear dimensionality reduction that consistently uses global information, and that enables understanding the intrinsic geometry of non-convex manifolds. Compared to methods that consider only local information, our method appears to be more robust to noise. Unlike most methods that incorporate global information, the proposed approach automatically handles non-convexity of the data manifold. We demonstrate the performance of our algorithm and compare it to state-of-the-art methods on synthetic as well as real data.
Abstract: In this paper, we investigate dynamics of 2n almost periodic attractors for Cohen-Grossberg neural networks (CGNNs) with variable and distribute time delays. By imposing some new assumptions on activation functions and system parameters, we split invariant basin of CGNNs into 2n compact convex subsets. Then the existence of 2n almost periodic solutions lying in compact convex subsets is attained due to employment of the theory of exponential dichotomy and Schauder-s fixed point theorem. Meanwhile, we derive some new criteria for the networks to converge toward these 2n almost periodic solutions and exponential attracting domains are also given correspondingly.
Abstract: The contact width is important design parameter for
optimizing the design of new metal gasket for asbestos substitution
gasket. The contact width is found have relationship with the helium
leak quantity. In the increasing of axial load value, the helium leak
quantity is decreasing and the contact width is increasing. This study
provides validity method using simulation analysis and the result is
compared to experimental using pressure sensitive paper. The results
denote similar trend data between simulation and experimental result.
Final evaluation is determined by helium leak quantity to check
leakage performance of gasket design. Considering the phenomena of
position change on the convex contact, it can be developed the
optimization of gasket design by increasing contact width.
Abstract: In this paper, by introducing twice continuously differentiable mappings, we develop an interior path following following method, which enables us to give a constructive proof of the general Brouwer fixed point theorem and thus to solve fixed point problems in a class of non-convex sets. Under suitable conditions, a smooth path can be proven to exist. This can lead to an implementable globally convergent algorithm. Several numerical examples are given to illustrate the results of this paper.
Abstract: In this paper, we propose a robust controller design method for discrete-time systems with sector-bounded nonlinearities and time-varying delay. Based on the Lyapunov theory, delaydependent stabilization criteria are obtained in terms of linear matrix inequalities (LMIs) by constructing the new Lyapunov-Krasovskii functional and using some inequalities. A robust state feedback controller is designed by LMI framework and a reciprocally convex combination technique. The effectiveness of the proposed method is verified throughout a numerical example.
Abstract: In this paper, we consider an iteration process for
approximating common fixed points of two asymptotically quasinonexpansive
mappings and we prove some strong and weak convergence
theorems for such mappings in uniformly convex Banach
spaces.
Abstract: In this paper we investigate numerically positive solutions of the equation -Δu = λuq+up with Dirichlet boundary condition in a boundary domain ╬® for λ > 0 and 0 < q < 1 < p < 2*, we will compute and visualize the range of λ, this problem achieves a numerical solution.
Abstract: In this paper, we use a one-step iteration scheme to approximate common fixed points of two quasi-asymptotically nonexpansive mappings. We prove weak and strong convergence theorems in a uniformly convex Banach space. Our results generalize the corresponding results of Yao and Chen [15] to a wider class of mappings while extend those of Khan, Abbas and Khan [4] to an improved one-step iteration scheme without any condition and improve upon many others in the literature.
Abstract: We study the problem of reconstructing a three dimensional binary matrices whose interiors are only accessible through few projections. Such question is prominently motivated by the demand in material science for developing tool for reconstruction of crystalline structures from their images obtained by high-resolution transmission electron microscopy. Various approaches have been suggested to reconstruct 3D-object (crystalline structure) by reconstructing slice of the 3D-object. To handle the ill-posedness of the problem, a priori information such as convexity, connectivity and periodicity are used to limit the number of possible solutions. Formally, 3Dobject (crystalline structure) having a priory information is modeled by a class of 3D-binary matrices satisfying a priori information. We consider 3D-binary matrices with periodicity constraints, and we propose a polynomial time algorithm to reconstruct 3D-binary matrices with periodicity constraints from two orthogonal projections.
Abstract: This paper presents a novel algorithm for path planning of mobile robots in known 3D environments using Binary Integer Programming (BIP). In this approach the problem of path planning is formulated as a BIP with variables taken from 3D Delaunay Triangulation of the Free Configuration Space and solved to obtain an optimal channel made of connected tetrahedrons. The 3D channel is then partitioned into convex fragments which are used to build safe and short paths within from Start to Goal. The algorithm is simple, complete, does not suffer from local minima, and is applicable to different workspaces with convex and concave polyhedral obstacles. The noticeable feature of this algorithm is that it is simply extendable to n-D Configuration spaces.
Abstract: This paper describes a probabilistic method for
three-dimensional object recognition using a shared pool of surface
signatures. This technique uses flatness, orientation, and convexity
signatures that encode the surface of a free-form object into three
discriminative vectors, and then creates a shared pool of data by
clustering the signatures using a distance function. This method
applies the Bayes-s rule for recognition process, and it is extensible
to a large collection of three-dimensional objects.
Abstract: In this paper, we present a new method for solving quadratic programming problems, not strictly convex. Constraints of the problem are linear equalities and inequalities, with bounded variables. The suggested method combines the active-set strategies and support methods. The algorithm of the method and numerical experiments are presented, while comparing our approach with the active set method on randomly generated problems.