GERBER TECHNOLOGY LAUNCHES FIRST OF NEW SERIES OF CUTTING SOLUTIONS

Precision, Productivity and Performance def ine the GERBERcutter? Z7Tolland, Conn., USA – Gerber Technology, a business unit of Gerber Scientific, Inc. (NYSE: GRB), and the world leader in providing innovative integrated software and hardware automation systems to

A Series Solution Approach to the Circular Restricted Gravitational Three-Body Dynamical Problem

The present manuscript examines the circular restricted gravitational three-body problem (CRGTBP) by the introduction of a new approach through the power series method. In addition, certain computational algorithms with the aid of Mathematica software are specifically designed for the problem. The algorithms or rather mathematical modules are established to determine the velocity and position of the third body’s motion. In fact, the modules led to accurate results and thus proved the new approach to be efficient.

Analysis of Formal and Analytic Solutions for Singularities of the Vector Fractional Differential Equations

In this article,we study on the existence of solution for a singularities of a system of nonlinear fractional differential equations(FDE).We construct a formal power series solution for our considering FDE and prove convergence of formal solutions under conditions.We use the Caputo fractional differential operator and the nonlinearity depends on the fractional derivative of an unknown function.

Adomian Modification Methods for the Solution of Chebyshev’s Differential Equations

The current study examines the important class of Chebyshev’s differential equations via the application of the efficient Adomian Decomposition Method (ADM) and its modifications. We have proved the effectiveness of the employed methods by acquiring exact analytical solutions for the governing equations in most cases;while minimal noisy error terms have been observed in a particular method modification. Above all, the presented approaches have rightly affirmed the exactitude of the available literature. More to the point, the application of this methodology could be extended to examine various forms of high-order differential equations, as approximate exact solutions are rapidly attained with less computation stress.

Symmetries and conservation laws associated with a hyperbolic mean curvature flow

Under investigation in this paper is a hyperbolic mean curvature flow for convex evolving curves.Firstly,in view of Lie group analysis,infinitesimal generators,symmetry groups and an optimal system of symmetries of the considered hyperbolic mean curvature flow are presented.At the same time,some group invariant solutions are computed through reduced equations.In particular,we construct explicit solutions by applying the power series method.Furthermore,the convergence of the solutions of power series is certificated.Finally,conservation laws of the hyperbolic mean curvature flow are established via Ibragimov's approach.

CTL Response Suppression in Chronic Phase of Infection:A mathematical study

Human immunodeficiency virus(HIV)has had an insightful impact about the state of healthiness of human immune system.Due to great improvement in drug therapy,HIV infections have been reduced by 17%over the past eight years.It has been proved that most effective treatment HAART(Highly Active Anti Retroviral Therapy)mainly controls the diseases progression but it does not eradicate the diseases completely.Reverse Transcriptase Inhibitor drugs specially associated with virus specific Cytotoxic T-Lymphocyte(CTL)that declines with disease progression. CTL responses against AIDS pathogenesis could be potential in the dynamics of virus replication, recognition and clearance of infected cells.In this research article a mathematical model has been proposed on the basis of CTL response suppression in the chronic phase of infection due to presence of virus.We also consider the growth of the virus population from the infected CD4^+T cells budding process and from the other infected cells like macrophages and thymocytes.Our analytical and numerical studies are consistent with existing observations from allied areas.

Transverse vibrations of arbitrary non-uniform beams

Free and steady state forced transverse vibrations of non-uniform beams are investigated with a proposed method, leading to a series solution. The obtained series is verified to be convergent and linearly independent in a convergence test and by the non-zero value of the corresponding Wronski determinant, respectively. The obtained solution is rigorous, which can be reduced to a classical solution for uniform beams. The proposed method can deal with arbitrary non-uniform Euler-Bernoulli beams in principle,but the methods in terms of special functions or elementary functions can only work in some special cases.

Fundamentals and progress of the manifold method based on independent covers

Aiming to solve mesh generation,computational stability,accuracy control,and other problems encountered with existing numerical methods,such as the finite element method and the finite volume method,a new numerical computational method for continuum mechanics,namely the manifold method based on independent covers(MMIC),is proposed based on the concept of mathematical manifolds,to form partitioned series solutions of partial differential equations.As partitions,the cover meshes have the characteristics of arbitrary shape,arbitrary connection,and arbitrary refinement.They are expected to fundamentally solve the mesh generation problem and can also simulate the precise geometric boundaries of the CAD model and strictly impose boundary conditions.In the selection of series solutions,local analytical solutions(such as series solutions at crack tips and series solutions in infinite domains)or proper forms of complete series can be used to reflect the local or global characteristics of the physical field to accelerate convergence.Various applications are presented.A new method of beam,plate,and shell analysis is proposed.The deformation characteristics of beams,plates,and shells are simulated with polynomial series of suitable forms,and the analysis of curved beams and shells with accurate geometric representation is realized.For the static elastic analysis of two-dimensional structures,a mesh splitting algorithm is proposed,and h-p version adaptive analysis is carried out with error estimation.Thus,automatic computation integrated with CAD is attempted.Adaptive analysis is also attempted for the solution of differential equations of fluids.For the one-dimensional convection-diffusion equation and Burgers equation,calculation results with high precision are obtained in strong convection and shock wave simulations,avoiding nonphysical oscillations.And solving the two-dimensional incompressible Navier-Stokes equation is also attempted.The series solution formula is used to obtain the physical quantity of interest of the material at a space point to eliminate the convection terms.Thus,geometrically nonlinear problems can be analyzed in fixed meshes,and a new method of free surface tracking is proposed.

Numerical investigation of the flow of a micropolar fuid through a porous channel with expanding or contracting walls

In this paper,we study the flow of a micropolar fluid in a porous channel with expanding or contracting walls.First,we use spectral collocation method on the governing equations to obtain an initial approximation for the solution of equations.Then using the obtained initial approximation,we apply the homotopy analysis method to obtain a recursive fomula for the solution.