bluuebunny/crossref_metadata_2025 huggingface dataset:
Angola: A case study in the challenges of achieving peace and the question of amnesty or prosecution of war crimes in mixed armed conflicts
Authors: Doria José
Published: February 2009

On 22 February 2002, Jonas Malheiro Savimbi, who led the UNITA rebel movement during the bloody armed conflict in Angola and who had battled to take power by force since Angola's independence from Portugal in 1975, was killed in a gun battle with the Angolan Army. During the Cold War, Savimbi was a proxy for the United States against the then-Marxist government of Angola. But after the end of the Cold War, he lost international support for rejecting peace efforts. He was accused of perpetuating a bloody internal conflict to advance his own interests and was exposed to international sanctions. Meanwhile, the government of President José Eduardo dos Santos moved closer to the United States.

The 27-year-long armed conflict is believed to have killed approximately one million people and driven four million others from their homes, creating a humanitarian crisis. In addition, the conflict destroyed almost all of the country's infrastructure, and effectively disrupted every effort by the government to start the long desired national reconstruction after independence, and the building of prosperity for the nation's children.
Developments in the law of genocide
Authors: Schabas William A.
Published: February 2009

Probably more has happened in the past five years to the Convention for the Prevention and Punishment of the Crime of Genocide than in the previous 50, that is, in the half-century following its adoption by the United Nations General Assembly on 9 December 1948.

Indeed, for the first five decades of its existence, the Convention was largely ignored by lawyers, viewed by most of them — as Georg Schwar-zenberger famously remarked — to be ‘unnecessary when applicable and inapplicable when necessary’. Over the years there had been attempts to apply the ‘g-word’ to a wide range of atrocities and gross violations of human rights, including those of China in Tibet, of Iraq against the Kurds, of the United States in Vietnam as well as towards its African-American and aboriginal populations, of Pakistan in Bangladesh, the Khmer Rouge in Cambodia, and Israel in Lebanon. But in each of these cases, some interpretative flair was required in order to stretch the definition to fit the crimes, and the efforts were not always very convincing. In 1990 scholars Frank Chalk and Kurt Jonassohn wrote that ‘the wording of the Convention is so restrictive that not one of the genocidal killings committed since its adoption is covered by it’.
The liability of civilians under international humanitarian law's war crimes provisions
Authors: Arnold Roberta
Published: February 2009

Contemporary international conflicts are witnessing an increasing involvement of civilians — such as, for example, suicide bombers — in the conduct of hostilities. Unlike regular soldiers, however, whose job it is to fight, civilians are not allowed to participate in combat and may be tried under ordinary criminal law for such activity. The question that this paper will attempt to answer is whether in the case where their engagement may lead to gross violations of humanitarian principles, they may be additionally subject to war crimes proceedings pursuant to international humanitarian law (IHL).

In order to assess the applicability of the war crimes' regime to civilians, this paper will be structured as follows. Part 2 will define who is a civilian. Part 3 will examine the position of international jurisprudence and doctrine on the question whether civilians may also be liable for war crimes and under what conditions. The fourth part will draw the conclusions.
The conflict in Western Sahara – an unresolved issue from the decolonization period
Authors: Gasser Hans-Peter
Published: February 2009

The territory of Western Sahara has an area of about 280,000 sq. km and approximately 250,000 inhabitants, known as Sahrawis. It is situated in the north-west of the African continent, where the Sahara Desert meets the Atlantic Ocean, and has a coastline of more than 1,000 km. In the north, Western Sahara has a common border of 443 km with Morocco, and in the south and west it is bordered by Mauritania (1,561 km). The territory also has a short common border of 42 km with Algeria. The climate is predominantly that of the desert: hot and dry in summer, cold in winter, with little or no rainfall. In the coastal regions vegetation may be abundant. While the Sahrawis were originally nomads, most of the population now lives in small towns and villages. The economy is based on agriculture and fishing, primarily destined for local consumption. Rich phosphate deposits are the main export commodity. There seem to be oil deposits off the Atlantic coast.
Off target on the Iraq campaign: a response to Professor Schmitt
Authors: PoKempner Dinah , Garlasco Marc , Docherty Bonnie
Published: February 2009

Law without facts makes a dull subject, and it is one of the peculiarities of international humanitarian law (IHL) that many of the interesting facts are classified or unavailable to those outside the military. This partially explains why IHL until recently has been the redoubt of military lawyers and the International Committee of the Red Cross. That situation is changing, for many reasons.

Popular interest in IHL is growing due to concern with responses to terrorism, interventionism (humanitarian and otherwise) and international justice. Civil society organisations have successfully campaigned for both new standards, such as the Landmines Convention, as well as new mechanisms of enforcement, such as the ad hoc international criminal tribunals and the International Criminal Court. At the same time, technology and globalisation have facilitated both real-time battlefront reporting and post-battle analysis by civilians.
International criminal courts round-up
Authors: Swaak-Goldman Olivia , Nybondas Maria
Published: February 2009

For the International Criminal Court (ICC) 2003 was a crucial year — its first as a functioning institution. With the coming into force of its Statute in July 2002, 2003 was spent establishing the infrastructure and procedures according to which the ICC will function. The ICC also made progress in establishing its four organs: the Chambers, the Presidency, the Office of the Prosecutor and the Registry.
Breaching international law to ensure its enforcement: the reliance by the ICTY on illegal capture
Authors: Sloan James
Published: February 2009

In an address to the United Nations General Assembly on 7 November 1995, Antonio Cassese, then President of the International Criminal Tribunal for the former Yugoslavia (ICTY), highlighted the difficulty of enforcing international criminal justice in the absence of state cooperation. To emphasise his point, Cassese offered an apt — if somewhat inelegant — analogy: he likened the Tribunal to a limbless giant, dependent on the ‘artificial limbs’ of the enforcement agencies of UN Member States. First among the various areas cited by Cassese where the Tribunal depended upon state cooperation was the arrest of suspected criminals living within the borders of those states. Over nine years later the problem remained acute. In a 23 November 2004 address to the Security Council, the Prosecutor of the ICTY, Carla Del Ponte, highlighted failures on the part of the governments of Croatia, Serbia and Montenegro and Bosnia and Herzegovina to arrest indictees and turn them over to the Tribunal. In particular, she mentioned the lack of cooperation by Belgrade as ‘the single most important obstacle faced by the Tribunal’ in the implementation of its strategy to complete its trials by the end of 2008.
The United Nations Convention on Certain Conventional Weapons of 1980: its recent development and increasing significance
Authors: Solomon Steven A.
Published: February 2009

Efforts to regulate warfare, including the use of particular weapons, have a long history, dating back, according to some scholars, thousands of years. But international codification of the rules of war in binding multilateral legal instruments only began in the second half of the nineteenth century. Among the first such efforts was one devoted to the prohibition of the use of a particular weapon in wartime. The St. Petersburg Declaration of 1868 on exploding bullets banned the use of explosive projectiles under 400 grammes in weight and is generally recognised as constituting the first significant international instrument prohibiting a specific weapon. It also incorporated into the conventional law of armed conflict the customary principle prohibiting the use of weapons ‘of a nature to cause superfluous injury or unnecessary suffering’ — a tenet of international humanitarian law and a touchstone for many important international agreements on the use of weapons that have since followed, including the Hague Declaration of 1899 on expanding bullets, the Geneva Gas Protocol of 1925 and, most recently, the United Nations Convention on Conventional Weapons of 1980 (hereafter, CCW).
The International Criminal Court's Trust Fund for Victims: challenges and opportunities
Authors: Ferstman Carla
Published: February 2009

The historic International Criminal Court Statute has come into force against a backdrop of massive atrocities being committed in different parts of the world. Looking at the situations currently under investigation by the Office of the Prosecutor, in the Democratic Republic of the Congo it is estimated that 3.5 million children, women and men have died as a result of the conflict in that country, while in Uganda, the brutal conflict between the rebel Lord's Resistance Army (LRA) and government forces has been characterised by abduction of children to join LRA contingents and for sexual enslavement and large-scale displacement of civilians, among other heinous acts. It is likely that future situations to be dealt with by the Court will similarly impact on hundreds of thousands of victims.

The scale of these atrocities presents a unique challenge for the Court. Thousands of alleged perpetrators may fall within its jurisdiction, although for optimal efficiency and impact the Office of the Prosecutor will need to find a way to focus on the responsibility of key individuals, but without being perceived as detracting from the complexities of any given situation.
The elastodynamic Green's tensor for the 2D half-space
Authors: Buchen Peter W.
Published: February 2009

An exact algebraic representation for the 2D elastodynamic Green's tensor is derived. A new displacement potential decomposition is employed which yields, in conjunction with the Pekeris–Cagniard–de Hoop method, the exact representation. The first motions of the major arrivals are evaluated in terms of their polarizations, radiation patterns, geometrical spreading and wave-front singularities. The tensorial components of the Rayleigh wave on the free surface are found and solutions for dipolar line source discussed. We also investigate diffracted phases first noticed by Lapwood in his 1949 paper [13].
The characteristic identities and reduced matrix elements of the unitary and orthogonal groups
Authors: Gould M. D.
Published: February 2009

Polynomial identities satisfied by the generators of the Lie groups O(n) and U(n) are rederived. Using these identities the reduced matrix elements of the Lie groups U(n) and O(n) are evaluated as rational functions of the IR labels occurring in the canonical chains

This method does not require an explicit realization of the Lie algebras and their representations using bosons. Finally, trace formulae encountered previously by several authors for finite dimensional irreducible representations are shown to hold on arbitrary representations admitting an infinitesimal character.
Variational control problems for linear differential systems with Stieltjes boundary conditions
Authors: Chan W. L. , Ng S. K.
Published: February 2009

Necessary and sufficient conditions for optimality in the control of linear differential systems ẋ = Ax + Bu with Stieltjes boundary conditions , where ν is an r × n matrix valued measure of bounded variation, are obtained, Feedback-like control is given in the case of quadratic performance.
Steady Prandtl-Batchelor flows past a circular cylinder
Authors: Hocking G. C.
Published: February 2009

The high Reynolds number flow past a circular cylinder with a trailing wake region is considered when the wake region is bounded and contains uniform vorticity. The formulation allows only for a single vortex pair trapped behind the cylinder, but calculates solutions over a range of values of vorticity. The separation point and length of the region are determined as outputs. It was found that using this numerical method there is an upper bound on the vorticity for which solutions can be calculated for a given arclength of the cavity. In some cases with shorter cavities, the limiting solutions coincide with the formation of a stagnation point in the outer flow at both separation from the cylinder and reattachment at the end of the cavity.
Sub-supersolutions in a variational inequality related to a sandpile problem
Authors: Le Vy Khoi
Published: February 2009

In this paper we study a variational inequality in which the principal operator is a generalised Laplacian with fast growth at infinity and slow growth at 0. By defining appropriate sub-and super-solutions, we show the existence of solutions and extremal solutions of this inequality above the subsolutions or between the sub- and super-solutions.
On the stability of solutions for thep(x)-Laplacian equation and some applications to optimisation problems with state constraints
Authors: Galewska Elżbieta , Galewski Marek
Published: February 2009

We consider the stability of solutions for a family of Dirichlet problems with (p, q)-growth conditions. We apply the results obtained to show continuous dependence on a functional parameter and the existence of an optimal solution in a control problem with state constraints governed by thep(x)-Laplacian equation.
Robust stability of impulsive switched systems with disturbance
Authors: Liu Xinzhi , Zhang Hongtao
Published: February 2009

This paper studies a class of impulsive switched systems with persistent bounded disturbance using robust attractor analysis and multiple Lyapunov functions. Some sufficient conditions for internal stability of the systems are obtained in terms of linear matrix inequalities (LMI). Based on the results, a simple approach for the design of a feedback controller is presented to achieve a desired level of disturbance attenuation. Numerical examples are also worked out to illustrate the obtained results.
Stability analysis of a k-out-of-N:G reparable system
Authors: Xu Houbao
Published: February 2009

A k-out-of-N:G reparable system with an arbitrarily distributed repair time is studied in this paper. We translate the system into an Abstract Cauchy Problem (ACP). Analysing the spectrum of the system operator helps us to prove the well-posedness and the asymptotic stability of the system.
Using Modified Proper Orthogonal Decomposition (MPOD) for reducing ecosystem models
Authors: Lawrie J. , Hearne J. W.
Published: February 2009

In this paper we consider simplifying a model of the nitrogen cycle in Port Phillip Bay, Victoria, Australia. The approach taken is to aggregate state variables that are linearly related using a projection in state space. The technique involved is a modification of proper orthogonal decomposition and was developed so that a resulting simplified model retains an ecological interpretation. It can be applied automatically, and enables insights into the system to be gained that were not obvious beforehand. In the case of the Port Phillip Bay model, we find that the variables representing water and sand are unaffected by the remaining variables, while only variables on the same trophic level can be grouped together. The validity of the aggregation under several nutrient loads is also discussed.
Thermodynamics, Mnemonic Matrices and Generalized Inverses
Authors: Leipnik R. B. , Pearce C. E. M.
Published: February 2009

We present an alternative matrix mnemonic for the basic equations of simple thermodynamics. When normalized, this permits an explicit generalized inverse, allowing inversion of the mechanical and chemical thermodynamic equations. As an application, the natural variablesS, V, PandTare derived from the four energiesE(internal),F(free),G(Gibbs) andH(enthalpy).
Extension of a short-time solution of the diffusion equation with application to micropore diffusion in a finite system
Authors: Haynes P. D. , Lucas S. K.
Published: February 2009

The diffusion equation is used to model and analyze sorption, a process used in the purification or separation of fluids. For the diffusion inside a spherical porous solid immersed in a limited-volume and well-stirred fluid, Ruthven [5], Crank [3] and, for the analogous flow of heat, Carslaw and Jaeger [2] give an eigenfunction expansion solution to the diffusion equation that provides accurate long-time solutions when only a few terms are used. However, to obtain the same accuracy for short-time solutions the number of eigenfunction terms required increases exponentially. An alternative error function solution of Carman and Haul [1] is accurate for sufficiently short times but not for long times. Although their solution is well quoted [3, 4, 6], Carman and Haul do not provide a derivation in their paper. This paper provides a full derivation of the short-time solution of Carman and Haul that uses only the first term of a negative exponential series in the Laplace domain. It is shown that the accuracy and range of the short-time result is improved by the inclusion of additional terms of the negative exponential series. An analysis of short-time and long-time resultsis presented, together with recommendations as to their use.
Hermite interpolation visits ordinary two-point boundary value problems
Authors: Grundy R. E.
Published: February 2009

This paper is concerned with constructing polynomial solutions to ordinary boundary value problems. A semi-analytic technique using two-point Hermite interpolation is compared with conventional methods via a series of examples and is shown to be generally superior, particularly for problems involving nonlinear equations and/or boundary conditions.
Monotonicity of the error term in Gauss-Turán quadratures for analytic function
Authors: Milovanović Gradimir V. , Spalević Miodrag M.
Published: February 2009

For Gauss–Turán quadrature formulae with an even weight function on the interval [−1, 1] and functions analytic in regions of the complex plane which contain in their interiors a circle of radius greater than I, the error term is investigated. In some particular cases we prove that the error decreases monotonically to zero. Also, for certain more general cases, we illustrate how to check numerically if this property holds. Some ℓ2-error estimates are considered.
The exponential of a constant matrix on time scales
Authors: Zafer A.
Published: February 2009

In this paper we describe an elementary method for calculating the matrix exponential on an arbitrary time scale. An example is also given to illustrate the result.
Facility location via continuous optimization with discontinuous objective functions
Authors: Ugon J. , Kouhbor S. , Mammadov M. , Rubinov A. , Kruger A.
Published: February 2009

Facility location problems are one of the most common applications of optimization methods. Continuous formulations are usually more accurate, but often result in complex problems that cannot be solved using traditional optimization methods. This paper examines theuse of a global optimization method—AGOP—for solving location problems where the objective function is discontinuous. This approach is motivated by a real-world application in wireless networks design.
The multivariate Faà di Bruno formula and multivariate Taylor expansions with explicit integral remainder term
Authors: Leipnik Roy B. , Pearce Charles E. M.
Published: February 2009

The Faà di Bruno formulæ for higher-order derivatives of a composite function are important in analysis for a variety of applications. There is a substantial literature on the univariate case, but despite significant applications the multivariate case has until recently received limited study. We present a succinct result which is a natural generalization of the univariate version. The derivation makes use of an explicit integralform of the remainder term for multivariate Taylor expansions.
On the dynamics of a family of third-order iterative functions
Authors: Amat Sergio , Busquier Sonia , Plaza Sergio
Published: February 2009

We study the dynamics of a family of third-order iterative methods that are used to find roots of nonlinear equations applied to complex polynomials of degrees three and four. This family includes, as particular cases, the Chebyshev, the Halley and the super-Halleyroot-finding algorithms, as well as the so-called c-methods. The conjugacy classes of theseiterative methods are found explicitly.
What is the discrete analogue of the Painlevé property?
Authors: Ramani A. , Grammaticos B.
Published: February 2009

We analyse the various integrability criteria which have been proposed for discrete systems, focusing on the singularity confinement method. We present the exact procedure used for the derivation of discrete Painlevé equations based on the deautonomisation of integrable autonomous mappings. This procedure is then examined in the light of more recent criteria based on the notion of the complexity of the mapping. We show that the low-growth requirements lead, in the case of the discrete Painlevé equations, to exactly the same results as singularity confinement. The analysis of linearisable mappings shows that they have special growth properties which can be used in order to identify them. A working strategy for the study of discrete integrability based on singularity confinement and low-growth considerations is also proposed.
Integrability, random matrices and Painlevé transcendents
Authors: Witte N. S. , Forrester P. J. , Cosgrove Christopher M.
Published: February 2009

The probability that an interval I is free of eigenvalues in a matrix ensemble with unitary symmetry is given by a Fredholm determinant. When the weight function in the matrix ensemble is a classical weight function, and the interval I includes an endpoint of the support, Tracy and Widom have given a formalism which gives coupled differential equations for the required probability and some auxiliary quantities. We summarize and extend earlier work by expressing the probability and some of the auxiliary quantities in terms of Painlevé transcendents.
Nonlinear electron solutions and their characteristics at infinity
Authors: Booth Hilary
Published: February 2009

The Maxwell-Dirac equations model an electron in an electromagnetic field. The two equations are coupled via the Dirac current which acts as a source in the Maxwell equation, resulting in a nonlinear system of partial differential equations (PDE's). Well-behaved solutions, within reasonable Sobolev spaces, have been shown to exist globally as recently as 1997 [12]. Exact solutions have not been found—except in some simple cases.

We have shown analytically in [6, 18] that any spherical solution surrounds a Coulomb field and any cylindrical solution surrounds a central charged wire; and in [3] and [19] that in any stationary case, the surrounding electron field must be equal and opposite to the central (external) field. Here we extend the numerical solutions in [6] to a family of orbits all of which are well-behaved numerical solutions satisfying the analytic results in [6] and [11]. These solutions die off exponentially with increasing distance from the central axis of symmetry. The results in [18] can be extended in the same way. A third case is included, with dependence on z only yielding a related fourth-order ordinary differential equation (ODE) [3].
Black holes and solitons of the quantized dispersionless NLS and DNLS equations
Authors: Pashaev Oktay K. , Lee Jyh-Hao
Published: February 2009

The classical dynamics of non-relativistic particles are described by the Schrödinger wave equation, perturbed by quantum potential nonlinearity. Quantization of this dispersionless equation, implemented by deformation of the potential strength, recovers the standard Schrödinger equation. In addition, the classically forbidden region corresponds to the Planck constant analytically continued to pure imaginary values. We apply the same procedure to the NLS and DNLS equations, constructing first the corresponding dispersionless limits and then adding quantum deformations. All these deformations admit the Lax representation as well as the Hirota bilinear form. In the classically forbidden region we find soliton resonances and black hole phenomena. For deformed DNLS the chiral solitons with single event horizon and resonance dynamics are constructed.
Numerical solitary wave interaction: the order of the inelastic effect
Authors: Marchant T. R.
Published: February 2009

Solitary wave interaction is examined using an extended Benjamin-Bona-Mahony (eBBM) equation. This equation includes higher-order nonlinear and dispersive effects and is is asymptotically equivalent to the extended Korteweg-de Vries (eKdV) equation. The eBBM formulation is preferable to the eKdV equation for the numerical modelling of solitary wave collisions, due to the stability of its finite-difference scheme. In particular, it allows the interaction of steep waves to be modelled, which due to numerical instability, is not possible using the eKdV equation.

Numerical simulations of a number of solitary wave collisions of varying nonlinearity are performed for two special cases corresponding to surface water waves. The mass and energy of the dispersive wavetrain generated by the inelastic collision is tabulated and used to show that the change in solitary wave amplitude after interaction is of O(α4), verifying previously obtained theoretical predictions.
Propagation of an electromagnetic soliton in a ferromagnetic medium
Authors: Veerakumar V. , Daniel M.
Published: February 2009

We study the propagation of electromagnetic waves (EMWs) in both isotropic and anisotropic ferromagnetic material media. As the EMW propagates through linear charge-free isotropic and anisotropic ferromagnetic media, it is found that the magnetic field and the magnetic induction components of the EMW and the magnetization excitations of the medium are in the form of solitons. However, the electromagnetic soliton gets damped and decelerates in the case of a charged medium. In the case of a charge-free nonlinear ferromagnetic medium we obtain results similar to those for the linear case.
On the geometry of the Painlevé V equation and a Bäcklund transformation
Authors: Schief W. K.
Published: February 2009

It is shown that an integrable class of helicoidal surfaces in Euclidean space E3 is governed by the Painlevé V equation with four arbitrary parameters. A connection with sphere congruences is exploited to construct in a purely geometric manner an associated Bäcklund transformation.
Inverse scattering for the matrix Schrödinger operator and Schrödinger operator on graphs with general self-adjoint boundary conditions
Authors: Harmer M. S.
Published: February 2009

Using a parameterisation of general self-adjoint boundary conditions in terms of Lagrange planes we propose a scheme for factorising the matrix Schrödinger operator and hence construct a Darboux transformation, an interesting feature of which is that the matrix potential and boundary conditions are altered under the transformation. We present a solution of the inverse problem in the case of general boundary conditions using a Marchenko equation and discuss the specialisation to the case of a graph with trivial compact part, that is, with diagonal matrix potential.
Global existence for the generalised 2D Ginzburg-Landau equation
Authors: Gao Hongjun , Kwek Keng-Huat
Published: February 2009

Ginzburg-Landau type complex partial differential equations are simplified mathematical models for various pattern formation systems in mechanics, physics and chemistry. Most work so far has concentrated on Ginzburg-Landau type equations with one spatial variable (1D). In this paper, the authors study a complex generalised Ginzburg-Landau equation with two spatial variables (2D) and fifth-order and cubic terms containing derivatives. Based on detail analysis, sufficient conditions for the existence and uniqueness of global solutions are obtained.
Nonresonance conditions and extremal solutions for first-order impulsive problems under weak assumptions
Authors: Franco Daniel , Pouso Rodrigo L.
Published: February 2009

In this work we shall study the existence of extremal solutions for an impulsive problem with functional-boundary conditions and weak regularity assumptions, not only on the right-hand side of the equation and on the functions that define the boundary conditions, but also on the impulse functions, which will be required to be nondecreasing, but not continuous as well, as is customary in the literature.

Moreover, in order to prove one of our results we shall study a general impulsive linearproblem, giving a complete characterisation of resonance for it.
On some noncoercive variational inequalities containing degenerate elliptic operators
Authors: Le Vy Khoi
Published: February 2009

We are concerned with the solvability of variational inequalities that contain degenerate elliptic operators. By using a recession approach, we find conditions on the boundary conditions such that the inequality has at least one solution. Existence results of Landesman-Lazer type for a nonsmooth inequality and a resonance problem for a weightedp-Laplacian are discussed in detail.
On the condition number of integral equations in linear elasticity using the modified Green's function
Authors: Argyropoulos E. , Gintides D. , Kiriaki K.
Published: February 2009

In this work the modified Green's function technique for an exterior Dirichlet and Neumann problem in linear elasticity is investigated. We introduce a modification of the fundamental solution in order to remove the lack of uniqueness for the solution of the boundary integral equations describing the problems, and to simultaneously minimise their condition number. In view of this procedure the cases of the sphere and perturbations of the sphere are examined. Numerical results that demonstrate the effect of increasing the number of coefficients in the modification on the optimal condition number are also presented.
Effects of an axisymmetric rigid punch on a nonhomogeneous transversely isotropic half-space
Authors: Chaudhuri P. K. , Ray Subhankar
Published: February 2009

Elastic behaviour of a nonhomogeneous transversely isotropic half-space is studied under the action of a smooth rigid axisymmetric indentor. Hankel transforms of different orders have been used. It is observed that in contrast to a homogeneous medium, the pressure distribution in the contact region in a nonhomogeneous medium is not directly available, rather it is obtainable from the solution of a Fredholm integral equation. The integral equation is solved for a flat-ended punch and paraboloidal indentations for various values of the nonhomogeneity parameter, and the effects of nonhomogeneity in elastic behaviour on stresses have been shown graphically. The results of the associated homogeneous case are readily available from the results of the present study.
A certain class of generating functions involving bilateral series
Authors: Srivastava H. M. , Pathan M. A. , Bin-Saad M. G.
Published: February 2009

The authors derive a general theorem on partly bilateral and partly unilateral generating functions involving multiple series with essentially arbitrary coefficients. By appropriately specialising these coefficients, a number of (known or new) results are shown to follow as applications of the theorem.
Direction of vorticity and a new regularity criterion for the Navier-Stokes equations
Authors: Zhou Yong
Published: February 2009

In this paper, we prove a new regularity criterion in terms of the direction of vorticity for the weak solution to 3-D incompressible Navier-Stokes equations. Under the framework of Constantin and Fefferman, a more relaxed regularity criterion in terms of the direction of vorticity is established.
Impulsive control of rumours with two broadcasts
Authors: Belen Selma , Kaya C. Yalçin , Pearce C. E. M.
Published: February 2009

In this paper we introduce an impulsive control model of a rumour process. The spreaders are classified as subscriber spreaders, who receive an initial broadcast of a rumour and start spreading it, and nonsubscriber spreaders who change from being an ignorant to being a spreader after encountering a spreader. There are two consecutive broadcasts. The first starts the rumour process. The objective is to time the second broadcast so that the final proportion of ignorants is minimised. The second broadcast reactivates as spreaders either the subscriber stiflers (Scenario 1) or all individuals who have been spreaders (Scenario 2). It is shown that with either scenario the optimal time for the second broadcast is always when the proportion of spreaders drops to zero.
Duality for linear multiplicative programs
Authors: Scott Carlton H. , Jefferson Thomas R.
Published: February 2009

Linear multiplicative programs are an important class of nonconvex optimisation problems that are currently the subject of considerable research as regards the development of computational algorithms. In this paper, we show that mathematical programs of this nature are, in fact, a special case of more general signomial programming, which in turn implies that research on this latter problem may be valuable in analysing and solving linear multiplicative programs. In particular, we use signomial programming duality theory to establish a dual program for a nonconvex linear multiplicative program. An interpretation of the dual variables is given.
Bifurcation phenomena for an oxidation reaction in a continuously stirred tank reactor. III The inhibiting effect of an inert species
Authors: Nelson M. I.
Published: February 2009

We extend an investigation into the static and dynamic multiplicity exhibited by the reaction of a fuel/air mixture in a continuously stirred tank reactor by considering the effect of adding a chemically inert species to the reaction mixture. The primary bifurcation parameter is taken to be the fuel fraction as this is the most important case from the perspective of fire-retardancy. We show how the addition of the inert species progressively changes the steady-state diagrams and flammability limits. We also briefly outline how heat-sink additives can be incorporated into our scheme.
Growth estimates for solutions of nonlinear second-order difference equations
Authors: Stević Stevo
Published: February 2009

We prove several growth theorems for solutions of certain nonlinear second-order difference equations.
A robust linearisation scheme for a nonlinear elliptic boundary value problem: Error estimates
Authors: Slodička Marian
Published: February 2009

We consider a nonlinear second-order elliptic boundary value problem in a bounded domain Ω ⊂ RN with mixed boundary conditions. The solution is found via linearisation. We design a robust and efficient approximation scheme. Error estimates for the linearisation algorithm are derived in L2(Ω), H1(Ω) and L∞(Ω) spaces under the minimal regularity assumptions of the exact solution.
Robust H∞ stabilisation with definite attenuance of an uncertain impulsive switche system
Authors: Xu Honglei , Liu Xinzhi , Teo Kok Lay
Published: February 2009

In this paper, we study the problem of robust H∞ stabilisation with definite attenuance for a class of impulsive switched systems with time-varying uncertainty. A norm-bounded uncertainty is assumed to appear in all the matrices of the state model. An LMI-based method for robust· H∞ stabilisation with definite attenuance via a state feedback control law is developed. A simulation example is presented to demonstrate the effectiveness of the proposed method.
Ramaswami's duality and probabilistic algorithms for determining the rate matrix for a structured GI/M/1 Markov chain
Authors: Hunt Emma
Published: February 2009

We show that Algorithm H* for the determination of the rate matrix of a block-GI/M/1 Markov chain is related by duality to Algorithm H for the determination of the fundamental matrix of a block-M/G/1 Markov chain. Duality is used to generate some efficient algorithms for finding the rate matrix in a quasi-birth-and-death process.
Sharp integral inequalities based on general Euler two-point formulae
Authors: Pečarić J. , Perić I. , Vukelić A.
Published: February 2009

We consider a family of two-point quadrature formulae, using some Euler-type identities. A number of inequalities, for functions whose derivatives are either functions of bounded variation, Lipschitzian functions orR-integrable functions, are proved.
Point-joint coordinate formulation for the dynamic analysis of generalised planar linkages
Authors: Attia Hazem Ali
Published: February 2009

This paper presents a two-step formulation for the dynamic analysis of generalised planar linkages. First, a rigid body is replaced by a dynamically equivalent constrained system of particles and Newton's second law is used to study the motion of the particles without introducing any rotational coordinates. The translational motion of the constrained particles represents the general motion of the rigid body both translationally and rotationally. The simplicity and the absence of any rotational coordinates from the final form of the equations of motion are considered the main advantages of this formulation. A velocity transformation is then used to transform the equations of motion to a reduced set in terms of selected relative joint variables. For an open-chain, this process automatically eliminates all of the non-working constraint forces and leads to efficient integration of the equations of motion. For a closed-chain, suitable joints should be cut and some cut-joint constraint equations should be included. An example of a closed-chain is used to demonstrate the generality and efficiency of the proposed method.
Plane poloidal-toroidal decomposition of doubly periodic vector fields. Part 2. The Stokes equations
Authors: McBain G. D.
Published: February 2009

We continue our study of the adaptation from spherical to doubly periodic slot domains of the poloidal-toroidal representation of vector fields. Building on the successful construction of an orthogonal quinquepartite decomposition of doubly periodic vector fields of arbitrary divergence with integral representations for the projections of known vector fields and equivalent scalar representations for unknown vector fields (Part 1), we now present a decomposition of vector field equations into an equivalent set of scalar field equations. The Stokes equations for slow viscous incompressible fluid flow in an arbitrary force field are treated as an example, and for them the application of the decomposition uncouples the conservation of momentum equation from the conservation of mass constraint. The resulting scalar equations are then solved by elementary methods. The extension to generalised Stokes equations resulting from the application of various time discretisation schemes to the Navier-Stokes equations is also solved.
Existence of solutions and optimal control problems for hyperbolic hemivariational inequalities
Authors: Parks Jong Yeoul , Park Sun Hye
Published: February 2009

In this paper we prove the existence of solutions for hyperbolic hemivariational inequalities and then investigate optimal control problems for some convex cost functionals.
Symmetry analysis of rotating fluid
Authors: Fakhar K. , Chen Zu-Chi , Ji Xiaoda
Published: February 2009

The machinery of Lie theory (groups and algebras) is applied to the unsteady equations of motion of rotating fluid. A special-function type solution for the steady state is derived. It is then shown how the solution generates an infinite number of time-dependent solutions via three arbitrary functions of time. This algebraic structure also provides the mechanism to search for other solutions since its character is inferred from the basic equations.
Existence of seamount steady vortex flows
Authors: Emamizadeh B. , Bahrami F.
Published: February 2009

In this paper we will study a feature of a localised topographic flow. We will prove existence of an ideal fluid containing a bounded vortex, approaching a uniform flow at infinity and passing over a localised seamount. The domain of the fluid is the upper half-plane and the data prescribed is the rearrangement class of the vorticity field.
The existence of periodic and subharmonic solutions to subquadratic discrete Hamiltonian systems
Authors: Zhou Zhan , Yu Jianshe , Guo Zhiming
Published: February 2009

In this paper, by using critical point theory, we establish some results for the existence of periodic and subharmonic solutions to subquadratic discrete Hamiltonian systems.
On constant-sign periodic solutions in modelling the spread of interdependent epidemics
Authors: Agarwal Ravi P. , O'Regan Donal , Wong Patricia J. Y.
Published: February 2009

We consider the following model that describes the spread of n types of epidemics which are interdependent on each other:

Our aim is to establish criteria such that the above system has one or multiple constant-sign periodic solutions (u1, u2, …, un), that is, for each 1 ≤ i ≤ n, ui, is periodic and θiui ≥ 0 where θi, ε (1, −1) is fixed. Examples are also included to illustrate the results obtained.
Explicit bounds for third-order difference equations
Authors: Berenhaut Kenneth S. , Goedhart Eva G. , Stević Stevo
Published: February 2009

This paper gives explicit, applicable bounds for solutions of a wide class of third-order difference equations with nonconstant coefficients. The techniques used are readily adaptable for higher-order equations. The results extend recent work of the authors for second-order equations.
Generalisation of a corrected Simpson's formula
Authors: Pečarić J. , Franjić I.
Published: February 2009

The results obtained by A. J. Roberts and N. Ujević in a recent paper are generalised. A number of inequalities for functions whose derivatives are either functions of bounded variation or Lipschitzian functions or R-integrable functions are derived. Also, some error estimates for the derived formulae are obtained.
On the low frequency asymptotics for the 2-D electromagnetic transmission problem
Authors: Anestopoulos C. N. , Argyropoulos E. E.
Published: February 2009

We examine the transmission problem in a two-dimensional domain, which consists of two different homogeneous media. We use boundary integral equation methods on the Maxwell equations governing the two media and we study the behaviour of the solution as the two different wave numbers tend to zero. We prove that as the boundary data of the general transmission problem converge uniformly to the boundary data of the corresponding electrostatic transmission problem, the general solution converges uniformly to the electrostatic one, provided we consider compact subsets of the domains.
Stability analysis of resource-consumer dynamic models
Authors: Hari Rao V. Sree , Sekhara Rao P. Raja
Published: February 2009

A nutrient-consumer model involving a distributed delay in material recycling and a discrete delay in growth response has been analysed. Various easily verifiable sets of sufficient conditions for global asymptotic stability of the positive equilibrium solution of the model equations have been obtained and the length of the delay in each case has been estimated.
Optimal control on an infinite domain
Authors: Craven B. D.
Published: February 2009

For an optimal control problem with an infinite time horizon, assuming various terminal state conditions (or none), terminal conditions for the costate are obtained when the state and costate tend to limits with a suitable convergence rate. Under similar hypotheses, the sensitivity of the optimum to small perturbations is analysed, and in particular the stability of the optimum when the infinite horizon is truncated to a large finite horizon. An infinite horizon version of Pontryagin's principle is also obtained. The results apply to various economic models.
Analysis of the Michaelis-Menten mechanism in an immobilised enzyme reactor
Authors: Nelson M. I. , Chen X. D. , Sexton M. J.
Published: February 2009

We investigate the behaviour of a reaction described by Michaelis-Menten kinetics in an immobilised enzyme reactor (IER). The IER is treated as a well-stirred flow reactor, with the restriction that bounded and unbounded enzyme species are constrained to remain within the reaction vessel. Our aim is to identify the best operating conditions for the reactor.

The cases in which an iminobilised enzyme reactor is used to either reduce pollutant emissions or to synthesise a product are considered. For the former we deduce that the reactor should be operated using low flow rates whereas for the latter high flow rates are optimal. It is also shown that periodic behaviour is impossible.
A comparison principle and stability for large-scale impulsive delay differential systems
Authors: Liu Xinzhi , Shen Xuemin , Zhang Yi
Published: February 2009

This paper studies the stability of large-scale impulsive delay differential systems and impulsive neutral systems. By developing some impulsive delay differential inequalities and a comparison principle, sufficient conditions are derived for the stability of both linear and nonlinear large-scale impulsive delay differential systems and impulsive neutral systems. Examples are given to illustrate the main results.
Periodic solutions of a nonlinear oscillatory system with two degrees of freedom
Authors: Zhang Zhengqiu , Zhu Yusen , Li Biwen
Published: February 2009

We study a nonlinear oscillatory system with two degrees of freedom. By using the continuation theorem of coincidence degree theory, some sufficient conditions are obtained to establish the existence of periodic solutions of the system.
Flowshop/no-idle scheduling to minimise the mean flowtime
Authors: Narain Laxmi , Bagga P. C.
Published: February 2009

This paper deals with n-job, 2-machine flowshop/mean flowtime scheduling problems working under a “no-idle” constraint, that is, when machines work continuously without idle intervals. A branch and bound technique has been developed to solve the problem.
Sufficient global optimality conditions for multi-extremal smooth minimisation problems with bounds and linear matrix inequality constraints
Authors: Huy N. Q. , Jeyakumar V. , Lee G. M.
Published: February 2009

In this paper, we present sufficient conditions for global optimality of a general nonconvex smooth minimisation model problem involving linear matrix inequality constraints with bounds on the variables. The linear matrix inequality constraints are also known as “semidefinite” constraints which arise in many applications, especially in control system analysis and design. Due to the presence of nonconvex objective functions such minimisation problems generally have many local minimisers which are not global minimisers. We develop conditions for identifying global minimisers of the model problem by first constructing a (weighted sum of squares) quadratic underestimator for the twice continuously differentiable objective function of the minimisation problem and then by characterising global minimisers of the easily tractable underestimator over the same feasible region of the original problem. We apply the results to obtain global optimality conditions for optinusation problems with discrete constraints.