Symbolic Solving of Partial Differential Equation Systems and Compatibility Conditions

An algorithm is produced for the symbolic solving of systems of partial differential equations by means of multivariate Laplace–Carson transform. A system of K equations with M as the greatest order of partial derivatives and right-hand parts of a special type is considered. Initial conditions are input. As a result of a Laplace–Carson transform of the system according to initial condition we obtain an algebraic system of equations. A method to obtain compatibility conditions is discussed.

A Refinement of some Overrelaxation Algorithms for Solving a System of Linear Equations

In this paper we propose a refinement of some successive overrelaxation methods based on the reverse Gauss–Seidel method for solving a system of linear equations Ax = b by the decomposition A = Tm − Em − Fm, where Tm is a banded matrix of bandwidth 2m + 1. We study the convergence of the methods and give software implementation of algorithms in Mathematica package with numerical examples. ACM Computing Classification System (1998): G.1.3.

Variable Neighborhood Search for Solving the Capacitated Single Allocation Hub Location Problem

In this paper a Variable Neighborhood Search (VNS) algorithm for solving the Capacitated Single Allocation Hub Location Problem (CSAHLP) is presented. CSAHLP consists of two subproblems; the first is choosing a set of hubs from all nodes in a network, while the other comprises finding the optimal allocation of non-hubs to hubs when a set of hubs is already known. The VNS algorithm was used for the first subproblem, while the CPLEX solver was used for the second. Computational results demonstrate that the proposed algorithm has reached optimal solutions on all 20 test instances for which optimal solutions are known, and this in short computational time.

On the Critical Points of Kyurkchiev’s Method for Solving Algebraic Equations

This paper is dedicated to Prof. Nikolay Kyurkchiev on the occasion of his 70th anniversary This paper gives sufficient conditions for kth approximations of the zeros of polynomial f (x) under which Kyurkchiev’s method fails on the next step. The research is linked with an attack on the global convergence hypothesis of this commonly used in practice method (as correlate hypothesis for Weierstrass–Dochev’s method). Graphical examples are presented.

A general Approach to Methods with a Sparse Jacobian for Solving Nonlinear Systems of Equations

2000 Mathematics Subject Classification: 65H10.

An Iterative Procedure for Solving Nonsmooth Generalized Equation

2000 Mathematics Subject Classification: 47H04, 65K10.

Steffensen Methods for Solving Generalized Equations

2000 Mathematics Subject Classification: 65G99, 65K10, 47H04.

Effective decision making and problem solving in projects

Processing information and forming opinions pose special challenges when attempting to effectively manage the new or complex tasks that typically arise in projects. Based on research in organizational and social psychology, we introduce mechanisms and strategies for collective information processing which are important for forming opinions and handling information in projects.

A költségvetési korlát megkeményítése a posztszocialista országokban = Hardening of the budget constraint in the post-socialist countries

A költségvetési korlát megkeményítése nem egyforma mértékben ment végbe minden posztszocialista gazdaságban. Egyes országokban messzire jutottak ebben a tekintetben, másokban viszont alig változott az indulóállapot. A tanulmány áttekinti a költségvetési korlát puhaságának különböző megnyilvánulásait: az állami támogatásokat, a puha adózást, a nem teljesítő bankkölcsönöket, a vállalatközi tartozások felgyülemlését és a kifizetetlen béreket. A jelenséget sokféle tényező okozza, amelyek többnyire együttesen jelentkeznek. Az állami tulajdon fenntartása kedvez a puha költségvetési szindróma megrögződésének, a privatizálás elősegíti a keményítést, de nem elégséges feltétele a kemény korlát érvényesítésének. Ehhez megfelelő politikai, jogi és gazdasági környezetet kell céltudatosan kialakítani. A posztszocialista átmenet kezdetén sokan azt hitték, hogy a hatékony piacgazdaság létrehozásához elegendő lesz megvalósítani a liberalizáció, privatizáció és stabilizáció "szentháromságát". Mára már kiderült, hogy a költségvetési korlát megkeményítése az említett három feladattal egyenrangúan fontos. Ahol ez nem valósul meg (például Oroszország), ott a privatizáció nem hozza meg a várt eredményt. ___________________ The budget constraint has not hardened to equal degrees in the various post-socialist countries. In some of them, a great deal has been done in this respect, while in others there has been hardly any change from the initial state. This study surveys the typical manifestations of softness of the budget constraint, such as state subsidies, soft taxation, non-performing loans, the accumulation of trade arrears between firms, and the build-up of wage arrears. Softness of the budget constraint is caused by several factors that tend to act in combination. Thus retention of state ownership helps to preserve the soft budget-constraint syndrome, while privatization encourages the budget constraint to harden, although it does not form a sufficient condition for it to happen. Purposeful development of the requisite political, legal and economic conditions is also required. It was widely maintained at the outset of the post-socialist transition that the 'Holy Trinity' of liberalization, privatization and stabilization would suffice to produce an efficient market economy. Since then, it has become clear that hardening the budget constraint needs to be given equal priority with these. Otherwise, the effects of privatization will fall short of expectations, as they have in Russia, for example.

A method for solving LSM problems of small size in the AHP

The Analytic Hierarchy Process (AHP) is one of the most popular methods used in Multi-Attribute Decision Making. It provides with ratio-scale measurements of the prioirities of elements on the various leveles of a hierarchy. These priorities are obtained through the pairwise comparisons of elements on one level with reference to each element on the immediate higher level. The Eigenvector Method (EM) and some distance minimizing methods such as the Least Squares Method (LSM), Logarithmic Least Squares Method (LLSM), Weighted Least Squares Method (WLSM) and Chi Squares Method (X2M) are of the tools for computing the priorities of the alternatives. This paper studies a method for generating all the solutions of the LSM problems for 3 × 3 matrices. We observe non-uniqueness and rank reversals by presenting numerical results.

Solving the Least Squares Method problem in the AHP for 3 X 3 and 4 X 4 matrices

The Analytic Hierarchy Process (AHP) is one of the most popular methods used in Multi-Attribute Decision Making. The Eigenvector Method (EM) and some distance minimizing methods such as the Least Squares Method (LSM) are of the possible tools for computing the priorities of the alternatives. A method for generating all the solutions of the LSM problem for 3 × 3 and 4 × 4 matrices is discussed in the paper. Our algorithms are based on the theory of resultants.

A puha költségvetési korlát szindrómája a kórházi szektorban = The soft budget constraint syndrome in the hospital sector

A kutatások eddig főképpen azt vizsgálták, hogyan jelenik meg a puha költségvetési korlát szindrómája a vállalati szférában és a hitelrendszerben. A jelen cikk a kórházi szektorra összpontosítja a figyelmet. Leírja az események öt főszereplőjének, a betegnek, az orvosnak, a kórházigazgatónak, a politikusnak és a kórház tulajdonosának motivációit és magatartásuk ellentmondásos jellegét. A motivációk magyarázzák, miért olyan erőteljes a túlköltési hajlam és a költségvetési korlát felpuhulásának tendenciája. A döntési és finanszírozási folyamatok minden szintjén felfelé hárítják a túlköltés és eladósodás terheit. A cikk kitér a különböző tulajdonformák (állami, nonprofit és forprofit nem állami tulajdonformák) és a puha költségvetési korlát szindrómájának kapcsolatára. Végül normatív szempontból vizsgálja a jelenséget: melyek a költségvetési korlát megkeményítésének kedvező és kedvezőtlen következményei, és hogyan tükröződnek a normatív dilemmák az események résztvevőinek tudatában. ___________ Researches so far have examined mainly how the soft budget constraint syndrome appears in the corporate sphere and the credit system. This article concentrates on the hospital sector. It describes the motivations and the contradictory behaviour of the five main types of participant in the events: patients, doctors, hospital managers, politicians, and hospital owners. The motivations explain why the propensity to overspend and the tendency to soften the budget constraint are so strong. The burdens of overspending and indebtedness are pushed upwards at every level of the decision-making and funding processes. The article considers the connection between the soft budget constraint syn-drome and the various forms of ownership (state ownership and the non-profit and for-profit forms of non-state ownership). Finally, the phenomenon is examined from the normative point of view: what are the favourable and unfavourable consequences of hardening the budget constraint and how these are reflected in the consciousness of the participants in the normative dilemmas and events.

The Soft Budget Constraint. An introductory study to volume IV of the Life’s Work series

The author’s ideas on the soft budget constraint (SBC) were first expressed in 1976. Much progress has been made in understanding the problem over the ensuing four decades. The study takes issue with those who confine the concept to the process of bailing out loss-making socialist firms. It shows how the syndrome can appear in various organizations and forms in many spheres of the economy and points to the various means available for financial rescue. Single bailouts do not as such generate the SBC syndrome. It develops where the SBC becomes built into expectations. Special heed is paid to features generated by the syndrome in rescuer and rescuee organizations. The study reports on the spread of the syndrome in various periods of the socialist and the capitalist system, in various sectors. The author expresses his views on normative questions and on therapies against the harmful effects. He deals first with actual practice, then places the theory of the SBC in the sphere of ideas and models, showing how it relates to other theoretical trends, including institutional and behavioural economics and theories of moral hazard and inconsistency in time. He shows how far the intellectual apparatus of the SBC has spread in theoretical literature and where it has reached in the process of “canonization” by the economics profession. Finally, he reviews the main research tasks ahead.

Introduction of soft budget constraint as an analyzing tool into public management. The case of the Hungarian public administration reform

Public management reforms are usually underpinned by arguments that they will make the public administration system more effective and efficient. In practice, however, it is very hard to determine whether a given reform will improve the efficiency and effectiveness of the public administration system in the long run. Here, I shall examine how the concept of the soft budget constraint (SBC) introduced by János Kornai (Kornai 1979, 1986; Kornai, Maskin & Roland 2003) can be applied to this problem. In the following, I shall describe the Hungarian public administration reforms implemented by the Orbán government from 2010 onward and analyze its reforms, focusing on which measures harden and which ones soften the budget constraint of the actors of the Hungarian public administration system. In the literature of economics, there is some evidence-based knowledge on how to harden/soften the budget constraint, which improves/reduces the effectiveness and hence the efficiency of the given system. By using the concept of SBC, I also hope to shed some light on the rationale behind the Hungarian government’s introduction of such a contradictory reform package. Previously, the concept of SBC was utilized narrowly in public management studies, mostly in the field of fiscal federalism. My goal is to apply the concept to a broader area of public management studies. My conclusion is that the concept of SBC can significantly contribute to public management studies by deepening our knowledge on the reasons behind the success and failure of public administration reforms.