scholarly journals A Dynamic Knowledge Model of Project Time-Cost Analysis Based on Trend Modelling

2019 ◽  
Vol 28 (1) ◽  
pp. 18-28
Author(s):  
Karel Doubravský ◽  
Radek Doskočil ◽  
Mirko Dohnal

This paper investigates the application of trend quantifiers of project time-cost analysis as a tool for decision-making support in the project management. Practical project management-related problems are solved under information shortages. It means that methods of statistical analysis cannot be easily used as they are based on the law of large numbers of observations. Numbers are information intensive quantifiers. The least information intensive quantifier is a trend; its values are increasing, constant, decreasing. If a derivative cannot be quantified by a trend, then nothing is known and therefore nothing can be analyzed/predicted. For this reason, the trend model M was created. The model M is based on a degraded set of differential equations or heuristics. A trend analysis of the model M is an evaluation of the relevant discrete set of solutions/scenarios S. A trend reconstruction is an evaluation of the model M if a (sub)set of scenarios S is given. The paper studies linear reconstruction, i.e. the model M is a set of linear differential equations. The trend reconstruction is partially reverse process to trend analysis. A case study has 7 variables (e.g. Project duration, Direct personnel costs, Indirect personal costs etc.) and the reconstructed set of linear differential equations has 7 equations. The set of 243 scenarios is obtained if this reconstructed set of trend linear equations is solved. Any future or past behavior of the model M can be described by a sequence of obtained scenarios.

Author(s):  
N. Parhi

AbstractIn this paper sufficient conditions have been obtained for non-oscillation of non-homogeneous canonical linear differential equations of third order. Some of these results have been extended to non-linear equations.


2012 ◽  
Vol 34 (1) ◽  
pp. 7-17
Author(s):  
Dao Huy Bich ◽  
Nguyen Dang Bich

The present paper deals with a class of non-linear ordinary second-order differential equations with exact solutions. A procedure for finding the general exact solution based on a known particular one is derived. For illustration solutions of some non-linear equations occurred in many problems of solid mechanics are considered.


The differential equations arising in most branches of applied mathematics are linear equations of the second order. Internal ballistics, which is the dynamics of the motion of the shot in a gun, requires, except with the simplest assumptions, the discussion of non-linear differential equations of the first and second orders. The writer has shown in a previous paper* how such non-linear equations arise when the pressure-index a in the rate-of-burning equation differs from unity, although only the simplified case of non-resisted motion was there considered. It is proposed in the present investigation to examine some cases of resisted motion taking the pressure-index equal to unity, to give some extensions of the previous work, and to consider, so far as is possible, the nature and the solution of the types of differential equations which arise.


1864 ◽  
Vol 13 ◽  
pp. 423-432

In the preceding memoirs on the Calculus of Symbols, systems have been constructed for the multiplication and division of non-commutative symbols subject to certain laws of combination; and these systems suffice or linear differential equations. But when we enter upon the consideration of non-linear equations, we see at once that these methods do not apply. It becomes necessary to invent some fresh mode of calculation, and a new notation, in order to bring non-linear functions into a condition which admits of treatment by symbolical algebra. This is the object of the following memoir. Professor Boole has given, in his 'Treatise on Differential Equations,’ a method due to M. Sarrus, by which we ascertain whether a given non-linear function is a complete differential. This method, as will be seen by anyone who will refer to Professor Boole s treatise, is equivalent to finding the conditions that a non-linear function may be externally divisible by the symbol of differentiation. In the following paper I have given a notation by which I obtain the actual expressions for these conditions, and for the symbolical remainders arising in the course of the division, and have extended my investigations to ascertaining the results of the symbolical division of non-linear functions by linear functions of the symbol of differentiation. Let F ( x, y, y 1 , y 2 , y 3 . . . . y n ) be any non-linear function, in which y 1 , y 2 , y 3 . . . . y n denote respectively the first, second, third, . . . . n th differential of y with respect to ( x ).


1994 ◽  
Vol 16 (4) ◽  
pp. 11-14
Author(s):  
Nguyen Dang Bich ◽  
Nguyen Vo Thong

This article proposes some forms of aerodynamic forces, looks for accurate solutions of core - pendent non-linear differential equations and analyses the characteristics of aerodynamic forces and of equation's solution. Found solutions proves that aerodynamic forces are formed from two elements: element of non-linear and dispersion, that single solutions are usually found and aerodynamic instability easy occurs.


Mathematics ◽  
2019 ◽  
Vol 7 (11) ◽  
pp. 1078 ◽  
Author(s):  
Asifa Tassaddiq ◽  
Aasma Khalid ◽  
Muhammad Nawaz Naeem ◽  
Abdul Ghaffar ◽  
Faheem Khan ◽  
...  

This study deals with the numerical solution of the non-linear differential equations (DEs) arising in the study of hydrodynamics and hydro-magnetic stability problems using a new cubic B-spline scheme (CBS). The main idea is that we have modified the boundary value problems (BVPs) to produce a new system of linear equations. The algorithm developed here is not only for the approximation solutions of the 10th order BVPs but also estimate from 1st derivative to 10th derivative of the exact solution as well. Some examples are illustrated to show the feasibility and competence of the proposed scheme.


2018 ◽  
Vol 16 (1) ◽  
pp. 507-521 ◽  
Author(s):  
Petr Hasil ◽  
Michal Veselý

AbstractThe paper belongs to the qualitative theory of half-linear equations which are located between linear and non-linear equations and, at the same time, between ordinary and partial differential equations. We analyse the oscillation and non-oscillation of second-order half-linear differential equations whose coefficients are given by the products of functions having mean values and power functions. We prove that the studied very general equations are conditionally oscillatory. In addition, we find the critical oscillation constant.


2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Xiaobin Guo ◽  
Dequan Shang

The approximate solution ofnth-order fuzzy linear differential equations in which coefficient functions maintain the sign is investigated by the undetermined fuzzy coefficients method. The differential equations is converted to a crisp function system of linear equations according to the operations of fuzzy numbers. The fuzzy approximate solution of the fuzzy linear differential equation is obtained by solving the crisp linear equations. Some numerical examples are given to illustrate the proposed method. It is an extension of Allahviranloo's results.


1980 ◽  
Vol 21 (2) ◽  
pp. 175-188 ◽  
Author(s):  
L. Erbe

Integral comparison theorems of Hille-Wintner type of second order linear equations are shown to be valid for the third order linear equation y‴ + q(t)y = 0.


2017 ◽  
Vol 7 (2) ◽  
pp. 286-305
Author(s):  
Jingjun Zhao ◽  
Teng Long ◽  
Yang Xu

AbstractExponential additive Runge-Kutta methods for solving semi-linear equations are discussed. Related order conditions and stability properties for both explicit and implicit schemes are developed, according to the dimension of the coefficients in the linear terms. Several examples illustrate our theoretical results.


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