Preemptive LCFS scheduling in hard real-time applications

We investigate the real-time behaviour of a (discrete time) single server system with preemptive LCFS task scheduling. The main result deals with the probability distribution of a random variable SRD(T), which describes the time the system operates without violating a fixed task service time deadline T. The tree approach, used for the derivation of our results, is also suitable for revisiting problems in queueing theory.

Relying on a simple general probability model, asymptotic formulas concerning all moments of SRD(T) are determined; for instance, the expectation of SRD(T) is proved to grow exponentially in T, i.e., E[SRD(T)]C^TT^3/2 for some > 1.     

Discrete-time system modelling in Lp with orthonormal basis functions

In this paper, model sets for linear time-invariant systems spanned by fixed pole orthonormal bases are investigated. The obtained model sets are shown to be complete in L_p(T) (1<p<∞), the Lebesque spaces of functions on the unit circle T, and in C(T), the space of periodic continuous functions on T. The L_p norm error bounds for estimating systems in L_p(T) by the partial sums of the Fourier series formed by the orthonormal functions are computed for the case 1<p<∞. Some inequalities on the mean growth of the Fourier series are also derived. These results have application in estimation and model reduction.     

Existence of solutions for lower semicontinuous quasi-equilibrium problems

In this paper, we deal with the following quasi-equilibrium problem: given a nonempty subset C of a topological vector space X, a nonempty set D, two functions T : C → D, f : X × D → R and a multifunction S : C → 2^X, find such that , and for all . Such a problem, recently introduced in [1], extends and unifies several variational inequality problems, generalized complementarity problems and Nash equilibrium problems. We prove several existence results in which the upper semicontinuity of the multifunction S is not assumed.     

A double-sequence iteration process for fixed points of continuous pseudocontractions

Let C be a bounded closed convex nonempty subset of a (real) Hilbert space H. The idea of a double-sequence iteration is introduced, and it is proved that a Mann-type double-sequence iteration process converges strongly to a fixed point of a continuous pseudocontractive map T which maps C into C. Related results deal with the strong convergence of the iteration process to fixed points of nonexpansive maps.     

Liquidus calculations for III-N semiconductors

Liquidus curves for III-N semiconducting compounds (AlN, GaN, and InN) are calculated. A quasi-chemical equilibrium approach also known as the first approximation in regular solution theory is used to calculate the T-X data. These calculations are based primarily on the heat and entropy of formation and the heat and entropy of fusion. A semi-empirical method is used to estimate the entropy and temperature of fusion values of the nitrides. The entropy of fusion of AlN is estimated to be 15.2 eu/mole with a melting point of 2800°C; for GaN, ΔS^F = 16.1 eu/mole with T_m = 1700°C; and for InN, ΔS^F = 14.5 eu/mole with T_m = 1200°C. These liquidus calculations are used to compute pressure of N₂ over both the column III rich and nitrogen rich regions of the nitrides. Implications for crystal growth are discussed.     

The foundations of confounding in epidemiology

A statistically coherent view of confounding motivated by the over controversy over the proper control of confounding in the presence of prior knowledge is presented. Confounding by a covariate C in the presence of data on C is distinguished from confounding in the absence of data on C. A covariate C is defined to be a nonconfounder in the absence of data on C if the population parameter of interest can be unbiasedly estimated (asymptotically) absent data on C. Under this definition, C may be a confounder for some parameters of interest and a nonconfounder for others. If C is a confounder for a parameter of interest that has a causal interpretation, we call C a causal confounder. When data on C are available, C is defined to be a nonconfounder for a particular parameter of interest if and only if inference on the parameter of interest does not depend on the data through C. Bayesians, frequentists and pure likelihoodists will in general agree on the prior knowledge necessary to render C a non-confounder. In particular C will in general be a nonconfounder precisely when the crude data ignoring C are S-sufficient for the parameter of interest. The intuitive view held by many practicing epidemiologists that confounding by C represents a bias of the unadjusted crude estimator is in a sense correct provided inference is performed conditional on approximate ancillary statistics that measure the degree to which associations in the data differ due to sampling variability from those population associations known a priori.     

Undecidable properties of monoids with word problem solvable in linear time

Let C₁ be the class of finitely presented monoids with word problem solvable in linear time. Let P be a Markov property of monoids related to class C₁ in some sense. It is undecidable given a monoid in C₁ whether it satisfies P. Let C and C′ be classes of finitely presented monoids with word problem solvable in some time-bounds. If C contains C₁ and C′ properly contains C, then it is undecidable given a monoid in C′ whether it belongs to C.     

On some dynamical subsets of the rauzy fractal

Let ( ,(+1)_n) be the adic system associated to the substitution: 1 → 12,…,(n − 1) → 1n, n → 1. In Sirvent (1996) it was shown that there exist a subset Cⁿ of and a map h_n: C → Cⁿ such that the dynamical system (C, h_n) is semiconjugate to ( ). In this paper we compute the Hausdorff and Billingsley dimensions of the geometrical realizations of the set Cⁿ on the (n− l)-dimensional torus. We also show that the dynamical system (Cⁿ,h_n) cannot be realized on the (n − 1)-torus.     

Asymptotic shape of the Erlang capacity region of a multi-service shared resource

We consider a loss model of an unbuffered resource having C channels, which are shared by several different types of service connections. Connections of each type arrive in a Poisson stream and request a number of channels, which depends on the type. An arriving connection is blocked and lost if there are not enough free channels. Otherwise, the channels are held for the duration of the connection, and the holding period is generally distributed. It is assumed that C and the traffic intensities are proportionately large. The admission control problem is considered for specified upper bounds on the blocking probabilities, and the boundary of the admissible set is investigated asymptotically. Characterization of admissible sets is extremely useful, not only for connection-level admission control, which is the context in which this topic has typically been considered in the past, but also for higher level objectives, such as network economics, network design, and network control. The asymptotic view of the admissible set is particularly appropriate for the higher level objectives, where the fine details are not as important as the qualitative properties of the shape of the set and tractability of the numerical calculations for large systems. Our results are derived by investigating the local behavior with respect to the tangent hyperplane at a point on the boundary of the admissible set. The lowest order results that hold in the asymptotic limit C→∞ are given first. Importantly, the boundary is linear for the key critically loaded and also for the overloaded regimes, and weakly convex for the underloaded regime. Next, refined results that hold for C1 are given, which indicate that the boundary is not convex, although only slightly so.     

Fuzzy plane geometry: triangles

A fuzzy triangle T (with a discrete-valued membership function) can be regarded as a nest of parallel-sided triangles T_i with successively higher membership values. Such a nest is determined by its max projections on any two of its “sides”. The area (perimeter) of T is a weighted sum of the areas (perimeters) of the T_i's. The side lengths and altitudes of T can also be defined as weighted sums obtained from projections; using these definitions, the perimeter of T is the sum of the side lengths, and the side lengths are related to the vertex angles by the Law of Sines, but there is no simple relationship between the area of T and the products of the side lengths and altitudes.     

On renaming a set of clauses as a Horn set

Let S = {C₁, …, C_m} be a set of clauses in the propositional calculus and let n denote the number of variables appearing these clauses. We present and O(mn) time algorithm to test whether S can be renamed as a Horn set.     

An approach to mining bundled commodities

Although bundled commodities are largely existed in supermarket, there are few investigations about bundled commodities mining. In this study, interval-valued association rules as a novel and possible approach to solving the bundled commodities mining issue, is proposed. Properties research based on interval-valued association rules is conducted, and an interval-valued rule pattern: F, ,  is constructed, where F denotes set of interval-valued ruses, and denote the disjunctive operation and conjunctive operation, respectively. Furthermore, one of the properties satisfied by the interval-valued rules: A  C = B  C and A  C = B  C  A = B, where A, B, C are there different rules, is validated and utilized to mine the bundled commodities. Finally, a large-scale software engineering project relative to interval-valued rule mining is implemented to merge flight testing information about aircrafts which validates the technique of mining bundled commodities can be discovered a special relation between objects. These initial investigations provide a researchable framework for bundled commodities mining.     

Minimizing the size of an identifying or locating-dominating code in a graph is NP-hard

Let G=(V,E) be an undirected graph and C a subset of vertices. If the sets B_r(v)∩C, vV (respectively, vVC), are all nonempty and different, where B_r(v) denotes the set of all points within distance r from v, we call C an r-identifying code (respectively, an r-locating-dominating code). We prove that, given a graph G and an integer k, the decision problem of the existence of an r-identifying code, or of an r-locating-dominating code, of size at most k in G, is NP-complete for any r.     

Sampling frequency and controllability region

In order to decide on the sampling frequency in a digital control system, a measure V is introduced for the subset of states, which can be transferred to the origin within a given time interval θ by a constrained control input. V increases with the number N of samplings in the interval θ = NT, but at the same time the required computer time increases. It is shown, how V(T) can be computed for multi-variable systems. A plot of V(T) allows a trade-off between controllability region and computer time by choice of the sampling interval T.     

Foundations of a theory of synchronous systems

A semantic algebra construction is introduced to model the stepwise behavior of synchronous systems in an arbitrary pointed algebraic theory T. The theory T is extended to a feedback theory F^∞T in which the bottom morphism is the designated point of T. The feedback theory F^∞T is obtained as the inverse limit of the theories n-res T that describe the stepwise behavior of systems in T restricted to the first n clock cycles. It is shown that in F^∞T, iteration satisfies the functorial dagger condition. Some suggestions are made about how to generalize the construction to handle infinite systems.     

Assignment of Complete Structural Properties of Linear Systems via Sensor Selection

For x =Ax + Bu , the problem of structural assignment via sensor selection is to find an output equation, y = Cx + Du , such that the resulting system (A, B, C, D) has the pre-specified structural properties, such as the finite and infinite zero structures as well as the invertibility properties. In this paper, we establish a set of necessary and sufficient conditions under which a complete set of system structural properties can be assigned, and an explicit algorithm for constructing the required matrix pair (C, D).     

Hankel norm approximation for well-posed linear systems

The sub-optimal Hankel norm approximation problem is solved for a well-posed linear system with generating operators (A,B,C) and transfer function G satisfying some mild assumptions. In the special case of the sub-optimal Nehari problem, an explicit parameterization of all solutions is obtained in terms of the system parameters A, B, C and G(0).     

Biquartic C-surface splines over irregular meshes

C¹-surface splines define tangent continuous surfaces from control points in the manner of tensor-product (B-)splines, but allow a wider class of control meshes capable of outlining arbitrary free-form surfaces with or without boundary. In particular, irregular meshes with non-quadrilateral cells and more or fewer than four cells meeting at a point can be input and are treated in the same conceptual frame work as tensor-product B-splines; that is, the mesh points serve as control points of a smooth piecewise polynomial surface representation that is local and evaluates by averaging. Biquartic surface splines extend and complement the definition of C¹-surface splines in a previous paper (Peters, J SLAM J. Numer. Anal. Vol 32 No 2 (1993) 645–666) improving continuity and shape properties in the case where the user chooses to model entirely with four-sided patches. While tangent continuity is guaranteed, it is shown that no polynomial, symmetry-preserving construction with adjustable blends can guarantee its surfaces to lie in the local convex hull of the control mesh for very sharp blends where three patches join. Biquartic C¹-surface splines do as well as possible by guaranteeing the property whenever more than three patches join and whenever the blend exceeds a certain small threshold.     

A homeomorphism between observable pairs and conditioned invariant subspaces

A bijective correspondence between similarity classes of observable systems (C,A) and n-codimensional conditioned invariant subspaces of a pair (C,A) is constructed that leads to a homeomorphism of the spaces. This is applied to the parametrization of inner functions of fixed McMillan degree. Proofs using state space methods as well as using polynomial models are given.     

High-order implicit blending surfaces of low degree

The applicability of the so-called potential method for blending implicitly defined surfaces is extended. The extended method is able to produce blendings which are C^k-continuous, where k may be chosen arbitrarily large. The blendings consist of piecewise algebraic surfaces of low degree. Specifically, the degree is k + 1 for so-called convex corners, and 2k for an important class of non-convex corners. In general the degree is linear in k, the constant of proportionality depending on the geometry of the corner. The method is illustrated by a concrete example, where a C² blending surface of degree 4 is constructed for a certain non-convex corner.