A Comparison of Classical Holomorphic Dynamics and Holomorphic Semigroup Dynamics-II

In this paper, we prove that the escaping set of a transcendental semi group is S-forward invari-ant. We also prove that if a holomorphic semi group is a belian, then the Fatou, Julia, and escaping sets are S-completely invariant. We also investigate certain cases and conditions that the holomorphic semi group dynamics exhibits the similar dynamical behavior just like a classical holomorphic dynamics. Frequently, we also examine certain amount of connections and contrasts between classical holomorphic dynamics and holomorphic semi group dynamics.

Approximation of a Function Belonging to Lip (ɑ, θ, w) by (C, 1) (E, q)

Available with fulltext.

Improved Upper Bound to Product Rate Variation Problem

The sequencing problem which minimizes the deviation between the actual (integral) and the ideal (rational) cumulative production of a variety of models of a common base product is called the product rate variation problem. If the objective is to minimize the maximum deviation, the problem is bottleneck product rate variation problem and the problem with the objective of minimizing all the deviations is the total product rate variation problem. The problem has been widely studied with several pseudo-polynomial time exact algorithms and heurism-tics. The lower bound of a feasible solution to the problem has been investigated to be tight. However, the upper bound of a feasible solution had been established in the literature which could further be improved. In this paper, we propose the improved upper bound for BPRVP and TPRVP.

Approximating the Sum of Infinite Series of Non Negative Terms with reference to Integral Test

This paper describes a method of obtaining approximate sum of infinite series of positive terms by using integrals under its historical background. It has shown the application of improper integrals to determine whether the given innate series is convergent or divergent. Here, the limits of the integrals and the series usually extend to infinity though they may be slowly convergent. We have also established a relation to approximate the sum of infinite series of positive terms with a suitable example.

Rheological Parameter Analysis in Generalized Bulk Mixture Mass Flow Model

Pokhrel et al. recently developed a generalized quasi two-phase bulk mixture model for mass flow. This model has been constructed by employing full dimensional two-phase mass flow model equations. The model is a set of coupled partial differential equations which is characterized by some new mechanical and dynamical aspects of generalized bulk and shear viscosities, pressure, velocities and effective friction for the mixture where all these are evolving as functions of several dynamical variables, physical parameters, inertial and dynamical coefficients and drift factors. They formulated pressure and rate-dependent Coulumbviscoplastic rheology of the mixture mass flow to describe the model equation. Rheological behavior of the flow dynamics affects the whole dynamics of mixture mass flow. So, in this paper, the relations of mixture pressure and viscosity with respect to pressure drifts and solid volume fractions are studied to describe the rheological behavior of the generalized bulk mixture mass flow model. Moreover, the behaviour of mixture viscosities with respect to isotrophic drifts are also analyzed. We also present the simulation result for the time evolution of the drift induced full dynamical mixture pressure of the material exited from a silo gate that moves down slope along a channel.

Optimal Methods for Finding Simple and Multiple Roots of Nonlinear Equations and their Basins of Attraction

In this paper, using the variant of Frontini-Sormani method, some higher order methods for finding the roots (simple and multiple) of nonlinear equations are proposed. In particular, we have constructed an optimal fourth order method and a family of sixth order method for finding a simple root. Further, an optimal fourth order method for finding a multiple root of a nonlinear equation is also proposed. We have used different weight functions to a cubically convergent For ntini-Sormani method for the construction of these methods. The proposed methods are tested on numerical examples and compare the results with some existing methods. Further, we have presented the basins of attraction of these methods to understand their dynamics visually.

On the Transit-Based Evacuation Strategies in an Integrated Network Topology

Evacuation planning problem deals with sending the maximum number of evacuees from the danger zone to the safe zone in minimum time as eciently as possible. The dynamic network flow models for various evacuation network topology have been found suitable for the solution of such a problem. Bus based evacuation planning problem (BEPP), as an important variant of the vehicle routing problem (VRP), is one of the emerging evacuation planning problems. In this work, an organized overview of this problem with a focus on their solution status is compactly presented. Arrival patterns of the evacuees including their transshipments at different pickup locations and their assignments are presented. Finally, a BEPP model and a solution for a special network are also proposed.

Absolute Summability for N-Tupled Triangle Matrices on Sequence Space

Available with fulltext.

Approximate Algorithms for Continuous-Time Quickest Multi-Commodity Contraflow Problem

Multi-commodity flow problem appears when several distinct commodities are shipped from supply nodes to the demand nodes through a network without violating the capacity constraints. The quickest multi-commodity flow problem deals with the minimization of time satisfying given demand. Ingeneral, the quickest multi-commodity flow problems are computationally hard. The outbound lane capacities can be increased through reverting the orientation of lanes towards the demand nodes. We present two approximation algorithms by introducing partial contraow technique in the continuous-time quick estmulti-commodity ow problem: one polynomial-time with the help of length-bounded flow and another FPTAS by using _-condensed time-expanded graph. Both algorithms reverse only necessary arc capacities to get the optimal solutions and save unused arc capacities which may be used for other purposes.

Efficient algorithm for Minimum cost flow problem with partial lane reversals

In this paper, we investigate the minimum cost flow problem in two terminal series parallel network. We present modified minimum cost flow algorithm that computes the maximum dynamic and the earliest arrival flows in strongly polynomial time and also preserves all unused arc capacities. We also present strongly polynomial time minimum cost partial contraflow algorithm that solves both problems with partial reversals of arc capacities on two terminal series parallel networks.