The chance constrained critical path with location-scale distributions

The Chance Constrained Critical Path (CCCP) generally depends on the preassigned minimum probability level. It is shown that for a wide class of probability distributions there always exists a probability value for which the CCCP remains unchanged for all probabilities greater than or equal to that value. This probability value is easily obtained from an optimal solution of a simple network problem. In addition, necessary and sufficient conditions for the CCCP to be unconditionally independent of the minimum probability level are given for that class of probability distributions.     

Proper generating trees and their internal path length

We find the generating function counting the total internal path length of any proper generating tree. This function is expressed in terms of the functions (d(t),h(t)) defining the associated proper Riordan array. This result is important in the theory of Riordan arrays and has several combinatorial interpretations.     

Digraphs without directed path of length two or three

We characterize digraphs without any path of length two or of length three.     

The weight distributions of irreducible cyclic codes of length

Let m be a positive integer and q be an odd prime power. In this paper, the weight distributions of all the irreducible cyclic codes of length 2^m over F_q are determined explicitly.     

Parametrization via secant length and application to path following

Summary A possible way for parametrizing the solution path of the nonlinear systemH(u)=0, H: ^{n+1 n} consists of using the secant length as parameter. This idea leads to a quadratic constraint by which the parameter is introduced. A Newton-like method for computing the solution for a given parameter is proposed where the nonlinear system is linearized at each iterate, but the quadratic parametrizing equation is exactly satisfied. The localQ-quadratic convergence of the method is proved and some hints for implementing the algorithm are givenDedicated to Professor Lothar Collatz on the occasion of his 75th birthday     

Proximity between life distributions and exponential distributions (I)

Many classes of life distributions have been introduced into reliability theory. Because of the importance of exponential distributions in reliability theory, it is interesting to study the difference between life distributions and exponential distributions. In this paper, we study the proximity between the life distribution in various classes and the exponential distribution. We shall give some simple upper bounds.This research was partially supported by the National Natural Science Foundation of China.     

Mapping resolutions of length three I

We produce some interesting families of resolutions of length three by describing certain open subsets of the spectrum of the generic ring for such resolutions constructed in [6].     

Standardization of distributions of the chord length and distance within oval domains

The distributions of the chord length and distance within oval domains are expressed in terms of the distributions of these values in a circle and of some parameters of oval domains. Institute of Mathematics and Informatics, Akademijos 4, 2600 Vilnius, Lithuania. Translated from Lietuvos Matematikos Rinkinys, Vol. 39, No. 4, pp. 469–474, October–December, 1999. Translated by E. Gečiauskas     

Modification of particle distributions by MHD instabilities I

The modification of particle distributions by low amplitude magnetohydrodynamic modes is an important topic for magnetically confined plasmas. Low amplitude modes are known to be capable of producing significant modification of injected neutral beam profiles, and the same can be expected in burning plasmas for the alpha particle distributions. Flattening of a distribution due to phase mixing in an island or due to portions of phase space becoming stochastic is a process extremely rapid on the time scale of an experiment but still very long compared to the time scale of guiding center simulations. Thus it is very valuable to be able to locate significant resonances and to predict the final particle distribution produced by a given spectrum of magnetohydrodynamic modes. In this paper we introduce a new method of determining domains of phase space in which good surfaces do not exist and use this method for quickly determining the final state of the particle distribution without carrying out the full time evolution leading to it.     

On the maximum size of connected hypergraphs without a path of given length

In this note we asymptotically determine the maximum number of hyperedges possible in an $r$-uniform, connected $n$-vertex hypergraph without a Berge path of length $k$, as $n$ and $k$ tend to infinity. We show that, unlike in the graph case, the multiplicative constant is smaller with the assumption of connectivity.     

Discrete -convex extremal distributions: Theory and applications

Given a nondegenerate moment space with s fixed moments, explicit formulas for the discrete s-convex extremal distribution have been derived for s=1,2,3 (see [M. Denuit, Cl. Lefèvre, Some new classes of stochastic order relations among arithmetic random variables, with applications in actuarial sciences, Insurance Math. Econom. 20 (1997) 197–214]). If s=4, only the maximal distribution is known (see [M. Denuit, Cl. Lefèvre, M. Mesfioui, On s-convex stochastic extrema for arithmetic risks, Insurance Math. Econom. 25 (1999) 143–155]). This work goes beyond this limitation and proposes a method for deriving explicit expressions for general nonnegative integer s. In particular, we derive explicitly the discrete 4-convex minimal distribution. For illustration, we show how this theory allows one to bound the probability of extinction in a Galton–Watson branching process. The results are also applied to derive bounds for the probability of ruin in the compound binomial and Poisson insurance risk models.     

Comparing different metaheuristic approaches for the median path problem with bounded length

In this paper we consider the Bounded Length Median Path Problem which can be defined as the problem of locating a path-shaped facility that departures from a given origin and arrives at a given destination in a network. The length of the path is assumed to be bounded by a given maximum length. At each vertex of the network (customer-point) the demand for the service is given and the cost to reach the closest service-point is computed. The objective is to minimize the sum of these costs over all the customer-points in the network.     

Queue length distributions in a markov model of a multistage clocked queueing network

In [4], we treated the problem of passage through a discrete-time clock-regulated multistage queueing network by modeling the input time series {a_n} to each queue as a Markov chain. We showed how to transform probability transition information from the input of one queue to the input of the next in order to predict mean queue length at each stage. The Markov approximation is very good for p = E(a_n) ≦ ½, which is in fact the range of practical utility. Here we carry out a Markov time series input analysis to predict the stage to stage change in the probability distribution of queue length. The main reason for estimating the queue length distribution at each stage is to locate “hot spots”, loci where unrestricted queue length would exceed queue capacity, and a quite simple expression is obtained for this purpose.     

Conditional limit results for type I polar distributions

Let (S ₁,S ₂) = (R cos(Θ), R sin(Θ)) be a bivariate random vector with associated random radius R which has distribution function F being further independent of the random angle Θ. In this paper we investigate the asymptotic behaviour of the conditional survivor probability when u approaches the upper endpoint of F. On the density function of Θ we impose a certain local asymptotic behaviour at 0, whereas for F we require that it belongs to the Gumbel max-domain of attraction. The main result of this contribution is an asymptotic expansion of , which is then utilised to construct two estimators for the conditional distribution function . Furthermore, we allow Θ to depend on u.      

Theory of shapes. I

In this survey there are contained the principal results and problems in the area of the fundamental theory of shapes of Borsuk-Fox-Mardesic. This is the first sufficiently detailed survey on the theory of shapes not only in the USSR but also abroad. There is given the necessary bibliography of 199 citations.     

Exact completion of path categories and algebraic set theory: Part I: Exact completion of path categories

We introduce the notion of a “category with path objects”, as a slight strengthening of Kenneth Brown's classical notion of a “category of fibrant objects”. We develop the basic properties of such a category and its associated homotopy category. Subsequently, we show how the exact completion of this homotopy category can be obtained as the homotopy category associated to a larger category with path objects, obtained by freely adjoining certain homotopy quotients. In a second part of this paper, we will present an application to models of constructive set theory. Although our work is partly motivated by recent developments in homotopy type theory, this paper is written purely in the language of homotopy theory and category theory, and we do not presuppose any familiarity with type theory on the side of the reader.     

Quaternary Golay sequence pairs I: even length

The origin of all 4-phase Golay sequences and Golay sequence pairs of even length at most 26 is explained. The principal techniques are the three-stage construction of Fiedler, Jedwab and Parker involving multi-dimensional Golay arrays, and a ??sum?Cdifference?? construction that modifies a result due to Eliahou, Kervaire and Saffari. The existence of 4-phase seed pairs of lengths 3, 5, 11, and 13 is assumed; their origin is considered in (Gibson and Jedwab, Des Codes Cryptogr, 2010).     

Irregularities of point distributions relative to homothetic convex bodies I

The uniformity and irregularities of point distributions can be measured by various kinds of geometric objects. In this paper we prove the existence of point sets that have relatively small irregularities with respect to homothetic copies of a fixed convex body. The results give higher dimensional alternatives to a theorem of Beck.Supported by the Alexander von Humboldt Foundation.