Sandwich approximation of univariate convex functions with an application to separable convex programming

In this article an algorithm for computing upper and lower ? approximations of a (implicitly or explicitly) given convex function h defined on an interval of length T is developed. The approximations can be obtained under weak assumptions on h (in particular, no differentiability), and the error decreases quadratically with the number of iterations. To reach an absolute accuracy of ? the number of iterations is bounded by

     

The queueing system MX/G/1 and its ramifications

This paper deals with the bulk arrival queueing system M^X/G/1 and its ramifications. In the system M^X/G/1, customers arrive in groups of size X (a random variable) by a Poisson process, the service times distribution is general, and there is a single server. Although some results for this queueing system have appeared in various books, no unified account of these, as is being presented here, appears to have been reported so far. The chief objectives of the paper are (i) to unify by an elegant procedure the relationships between the p.g.f.'s

     

The iron hat from Shaw House

Abstract

The small unpublished group of armour of the mid 17th century from Shaw House in Berkshire, scene of fighting in the 2nd battle of Newbury in 1644, is preserved in the West Berkshire Museum in Newbury. The group includes an exceedingly rare form of helmet of the period, one made in the form of a broad brimmed hat. The article discusses the small group of known examples, and illustrates the closest comparable iron hat from the Scott collection in Glasgow Museums and Art Galleries.     

The joint signature of coherent systems

We investigate the joint signature of $m$ coherent systems, under the assumption that the components have independent and identically distributed lifetimes. The joint signature, for a particular ordering of failure times, is an $m$‐dimensional matrix depending solely on the composition of the systems and independent of the underlying distribution function of the component lifetimes. The elements of the $m$‐dimensional matrix are formulated based on the joint signatures of numerous series of parallel systems. The number of the joint signatures involved is an exponential function of the number of the minimal cut sets of each original system and may, therefore, be significantly large. We prove that although this number is typically large, a great number of the joint signatures are repeated, or removed by negative signs. We determine the maximum number of different joint signatures based on the number of systems and components. It is independent of the number of the minimal cut sets of each system and is polynomial in the number of components. Moreover, we consider all permutations of failure times and demonstrate that the results for one permutation can be of use for the others. Our theorems are applied to various examples. The main conclusion is that the joint signature can be computed much faster than expected.     

On the minimization of a certain convex function arising in applied decision theory

The author, in an expository paper [4], has presented an algorithm for choosing a non-negative vector

     

The Battle of Mirbat: turning point in the Omani Dhofar rebellion

On 19 July 1972, the pivotal battle of the Dhofar rebellion occurred when over 250 communist guerillas, called adoos,1 ?1. ‘Enemy’ in Arabic. attacked the coastal garrison town of Mirbat2 ?2. Sometimes spelled Marbat. where nine men of the British 22nd Special Air Service Regiment were stationed. Their decisive defense of Mirbat led to decorations three years after the battle, the beginning of the end of the rebellion, and calls for the awarding of Britain's highest honor, the Victoria Cross. The Battle of Mirbat, let alone the Dhofar rebellion are little known outside the UK due3 ?3. Other than papers written for military staff colleges, there is no American written account of the battle. to the covert nature of the SAS deployment, the then Labour government's obsession with secrecy, and the remoteness of the area of operations. Nonetheless, of all the proxy wars of the Cold War this one had the most significance, because had the communist adoos won, Oman and its Musandam Peninsula, which sticks out like a dagger into the Straits of Hormuz and abuts the United Arab Emirates, would have fallen into the communist orbit; threatening the West's oil supply. This is the story of the pivotal battle that was won by Britain and Oman against a communist insurgency.     

Computational results for a stopping rule problem on averages

Suppose x₁, x₂, … are independently distributed random variables with Pr (x_i = 1) = Pr(x_i = ?1) = 1/2, and let s_n =

     

THE FATE OF DISPUTED TERRITORIES: AN ECONOMIC ANALYSIS

This paper presents a simple model to characterize the outcome of a land dispute between two rival parties using a Stackelberg game. Unlike Gershenson and Grossman (2000 Gershenson, D. and Grossman, H.I. 2000. Civil conflict: ended or never ending?. Journal of Conflict Resolution, 44(6): 807–821.  [Google Scholar]), we assume that the opposing parties have access to different technologies for challenging and defending in conflict. We derive the conditions under which territorial conflict between the two parties is less likely to persist indefinitely. Allowing for an exogenous destruction term as in Garfinkel and Skaperdas (2000 Garfinkel, M. and Skaperdas, S. 2000. Conflict without misperceptions or incomplete information: how the future matters. Journal of Conflict Resolution, 44(6): 793–807. [Crossref], [Web of Science ®] , [Google Scholar]), we show that, when the nature of conflict becomes more destructive, the likelihood of a peaceful outcome, in which the territory’s initial possessor deters the challenging party, increases if the initial possessor holds more intrinsic value for the disputed land. Following Siqueira (2003 Siqueira, K. 2003. Conflict and third‐party intervention. Defence and Peace Economics, 14(6): 389–400. [Taylor & Francis Online], [Web of Science ®] , [Google Scholar]), our model has policy implications for peace through third‐party intervention.     

Development of cost effective personnel armour through structural hybridization

The objective of the present study is to develop cost effective thermoplastic hybrid laminate using Dyneema® HB50 and Tensylon®HSBD 30A through structural hybridization method. Laminates having 20 mm thickness were fabricated and subjected to 7.62 × 39 mm mild steel core projectile with an impact velocity of 730 ± 10 ms⁻¹. Parameters such as energy absorption, back face deformation and rate of back face deformation were measured as a function of hybridization ratio. It was observed that hybrid laminate with 50:50 ratio (w/w) of Tensylon® and Dyneema® with Tensylon® as front face showed 200% more energy absorption when compared to 100% Tensylon® laminate and showed equal energy absorption as that of expensive 100% Dyneema® laminate. Moreover, hybrid laminate with TD50:50 ratio showed 40% lower in terms of final back face deformation than Dyneema® laminate. Rate of back face deformation was also found to be slow for hybrid laminate as compared to Dyneema® laminate. Dynamic mechanical analysis showed that, Tensylon® laminate has got higher stiffness and lower damping factor than Dyneema® and hybrid laminates. The interface between Tensylon® and Dyneema® layers was found to be separating during the penetration process due to the poor interfacial bonding. Failure behaviour of laminates for different hybridization ratios were studied by sectioning the impacted laminates. It was observed that, the Tensylon® laminate has undergone shear cutting of fibers as major failure mode whereas the hybrid laminate showed shear cutting followed by tensile stretching, fiber pull out and delamination. These inputs are highly useful for body armour applications to design cost effective armour with enhanced performance.     

Stock control in a many depot system

The chief problems considered are: (1) In a parallel set of warehouses, how should stocks be allocated? (2) In a system consisting of a central warehouse and several subsidiary warehouses, how much stock should be carried in each? The demands may have known, or unknown, distribution functions. For problem (1), the i-th stock n_i should usually be allocated in proportion to the i-th demand m_i; in special cases, a significant improvement is embodied in the formula (N = total allocable stock)

     

Countering global insurgency

This article suggests that the War on Terrorism is actually a campaign against a globalized Islamist 1 1 In this article, the term ‘Islamist’ describes the extremist, radical form of political Islam practiced by some militant groups, as distinct from ‘Islamic’, which describes the religion of Islam, or ‘Muslim’, which describes those who follow the Islamic religion. In this article the term is used to refer primarily to Al Qaeda, its allies and affiliates. View all notes insurgency. Therefore, counterinsurgency approaches are more relevant to the present conflict than traditional terrorism theory. Indeed, a counterinsurgency approach would generate subtly, but substantially different, policy choices in prosecuting the war against Al Qaeda. Based on this analysis, the article proposes a strategy of ‘disaggregation’ that seeks to dismantle, or break, the links in the global jihad.2 2 This article uses the short form of the Islamic term jihad to mean ‘lesser jihad’ (armed struggle against unbelievers), rather than ‘greater jihad’ (jihad fi sabilillah), i.e. moral struggle for the righteousness of God. View all notes Like containment in the Cold War, disaggregation would provide a unifying strategic conception for the war – a conception that has been somewhat lacking to date.     

Change as a cost driver in defence procurement

This paper discusses change transactions that occur in connection with the procurement of defence systems. The bases for the reasoning are the ideas of Miller and Vollman (1985 Miller JG Vollman TE (1985) The hidden factory – cutting the explosive growth of overhead costs requires mastery of more than just what happens on the shop floor Harvard Business Review Sept–Oct 142 150  [Google Scholar]) and Eppinger (2001 Eppinger DE (2001) Innovation at the speed of information Harvard Business Review January 149 158  [Google Scholar]). These researchers argue that unplanned flows of information lead to change transactions, causing significant overhead costs. According to this paper, change transactions in defence procurement could be caused by (a) the changes in technology taking place during the long lifetime of a defence system and (b) the structure and contents of the agreements between the defence agent (the procurer) and the defence industry (the supplier).     

Defense spending and economic growth: Extended empirical analysis for the European Union

Previous empirical studies on the defense spending-economic growth nexus such as Kollias et al. (2007 Kollias, C., N. Mylonidis, and S. Paleologou. 2007. “A panel data analysis of the nexus between defense spending and growth in the European Union.” Defense and Peace Economics 18 (1): 75–85.[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]), Mylonidis (2008 Mylonidis, N. 2008. “Revisiting the nexus between military spending and growth in the European Union.” Defense and Peace Economics 19 (4): 265–272.[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]), Dunne and Nikolaidou (2012 Dunne, J. P., and E. Nikolaidou. 2012. “Defense spending and economic growth in the EU15.” Defense and Peace Economics 23 (6): 537–548.[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) analyzed this relationship in the case of the EU15. This study extends the analysis with the inclusion of more EU members and investigates the long run causal ordering between the two variables. Findings reported herein are not uniformed across all EU members. It is also found that end of Cold War has significant negative impact on defense expenditures of former east-European countries.     

Ho Chi Minh and the origins of the Vietnamese doctrine of guerrilla tactics

In a very important sense, the Vietnamese military history of the communist era began in 1941, when Ho Chi Minh prepared ‘Guerrilla Tactics’ (Cach Danh Du Kich).1 ?1. Ministry of Defense Center for the Military Encyclopedia Ministry of Defense Center for the Military Encyclopedia. 1996. Tu Dien Bach Hoa Quan Su Vietnam, Hanoi: People's Army Publishing Company.  [Google Scholar], Tu Dien Bach Hoa Quan Su Vietnam, 69. The publication of this essay, which was a manual on the tactics, techniques, and procedures of guerrilla warfare, preceded the founding of the first armed propaganda unit (Tuyen Truyen Doi Vo Trang) on 22 December 1944, which later became the People's Army of Vietnam (PAVN, Quan Doi Nhan Dan); as well as the revolutionary writings of Truong Chinh (1946–1947) and Vo Nguyen Giap (1959). The fact that ‘Tactics’ was published by the Viet Minh reinforces the claim made by the PAVN that it was the first authoritative Vietnamese writing on this important subject.     

Proportionate flow shop: New complexity results and models with due date assignment

It is known that the proportionate flow shop minimum makespan $Fm/prpt/C_{\max }$ problem is solved optimally by any permutation job sequence. We show that the $Fm/prpt/C_{\max }$ problem is at least ordinary NP‐hard when missing operations are allowed and present some solvable cases. We then consider the standard proportionate flow shop problem (with no missing operations) and show that the solution algorithms for a class of single‐machine due date assignment problems can be extended/generalized to the corresponding proportionate flow shop problems. © 2015 Wiley Periodicals, Inc. Naval Research Logistics 62: 98–106, 2015     

AN ENDOGENOUS GROWTH MODEL OF CAPITAL AND ARMS ACCUMULATION

This paper attempts to examine the effect of an anticipated foreign military threat on the steady‐state growth rate and the transitional behavior of the economy. The modeling strategy follows the Sandler and Hartley (1995 Sandler, T. and Hartley, K. 1995. The Economics of Defense, Cambridge: Cambridge University Press.  [Google Scholar]) and Dunne et al. (2005 Dunne, J.P., Smith, R.P. and Willenbockel, D. 2005. Models of military expenditure and growth: a critical review. Defence and Peace Economics, 16: 449–461. [Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) viewpoints to emphasize the role of national defense in affecting growth from the perspective of both the demand and the supply sides. We thus combine the public capital version of endogenous growth with a framework of competitive arms accumulation. It is found that the key factor determining the steady state and the transitional effects of a rise in the foreign military threat on the home weapon–capital ratio, the consumption–capital ratio, and the rate of economic growth, is the degree of relative risk aversion.     

RAISING THE COST OF REBELLION: THE ROLE OF THIRD‐PARTY INTERVENTION IN INTRASTATE CONFLICT

This paper presents a simple model to characterize explicitly the role that an intervening third party plays in raising the cost of rebellion in an intrastate conflict. Extending the Gershenson‐Grossman (2000 Gershenson, D. and Grossman, H.I. 2000. Civil conflict: ended or never ending?. Journal of Conflict Resolution, 44(6): 807–821.  [Google Scholar]) framework of conflict in a two‐stage game to the case involving outside intervention in a three‐stage game as in Chang et al. (2007b Chang, Y.‐M., Potter, J. and Sanders, S. 2007b. War and peace: third‐party intervention in conflict. European Journal of Political Economy, 23(4): 954–974.  [Google Scholar]), we examine the conditions under which an outside party optimally intervenes such that (i) the strength of the rebel group is diminished or (ii) the rebellion is deterred altogether. We also find conditions in which a third party optimally intervenes but at a level insufficient to deter rebellion. Such behavior, which improves the incumbent government’s potential to succeed in conflict, is overlooked in some conflict studies evaluating the effectiveness of intervention. One policy implication of the model is that an increase in the strength of inter‐governmental trade partnerships increases the likelihood that third‐party intervention deters rebellion.     

RAIN,GROWTH, AND CIVIL WAR: THE IMPORTANCE OF LOCATION

We re‐examine the Miguel et al. (2004 Miguel, E., Satyanath, S. and Sergenti, E. 2004. Economic shocks and civil conflict: an instrumental variables approach. Journal of Political Economy, 112(4): 725–753. [Crossref], [Web of Science ®] , [Google Scholar]) study of the impact of growth on civil war, using growth in rainfall as an instrument. Miguel et al. (2004 Miguel, E., Satyanath, S. and Sergenti, E. 2004. Economic shocks and civil conflict: an instrumental variables approach. Journal of Political Economy, 112(4): 725–753. [Crossref], [Web of Science ®] , [Google Scholar]) – in our view, erroneously – include countries participating in civil wars in other states. Restricting the conflict data to states with conflict on their own territory reduces the estimated impact of economic growth on civil war. We show how spatial correlations in rainfall growth and participation in civil conflicts induce a stronger apparent relationship in the mis‐classified data.     

Estimating a survival curve when new is better than used with respect to a distinguished set

Hollander, Park, and Proschan define a survival function S of a positive random variable X to be new better than used at age t₀ (NBU-{t₀}) if S satisfies $ \begin{array}{*{20}c} {\frac{{S(x + t_0)}}{{S\left({t_0} \right)}} \le S\left(x \right),} & {{\rm for}\,{\rm all}\,x\, \ge \,0,} \\ \end{array}$ where S(x) = P(X > x). The NBU-{t₀} class is a special case of the NBU-A family of survival distributions, where A is a subset of [0, ∞). These families introduce a variety of modeling possibilities for use in reliability studies. We treat problems of nonparametric estimation of survival functions from these classes by estimators which are themselves members of the classes of interest. For a number of such classes, a recursive estimation technique is shown to produce closed-form estimators which are strongly consistent and converge to the true survival distribution at optimal rates. For other classes, additional assumptions are required to guarantee the consistency of recursive estimators. As an example of the latter case, we demonstrate the consistency of a recursive estimator for S ∈ NBU-[t₀, ∞) based on lifetime data from items surviving a preliminary “burn-in” test. The relative precision of the empirical survival curve and several recursive estimators of S are investigated via simulation; the results provide support for the claim that recursive estimators are superior to the empirical survival curve in restricted nonparametric estimation problems of the type studied here.