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1.
In this paper, we consider multipleclass queueing systems with Npolicy in which the idle server starts service as soon as the number of customers in the startup class reaches threshold N. We consider the cases of FCFS and nonpreemptive priority. We obtain the Laplace–Stieltjes transform of the waiting times of each class of customers. We also show some results for the general behavior of such systems. 相似文献
2.
Abstract We establish the global existence and uniqueness of mild solutions for a class of first‐order abstract stochastic Sobolev‐type integro‐differential equations in a real separable Hilbert space in which we allow the nonlinearities at a given time t to depend not only on the state of the solution at time, t, but also on the corresponding probability distribution at time t. Results concerning the continuous dependence of solutions on the initial data and almost sure exponential stability, as well as an extension of the existence result to the case in which the classical initial condition is replaced by a so‐called nonlocal initial condition, are also discussed. Finally, an example is provided to illustrate the applicability of the general theory. 相似文献
3.
The coefficients in the stochastic differential equation that the short interest rate follows are of vital importance in the subsequent modelling of bond prices and other interest rate products. Empirical tests have previously been performed by various authors who compare a variety of popular short‐rate models. Most recently, Ahn and Gao compared their model with affine‐drift models and showed that their model with a non‐linear drift function outperforms the others. This paper compares the model developed by Goard, which is a time‐dependent generalization of the Ahn–Gao model, with the Ahn–Gao model itself. It is found that the time‐dependent model using a second‐order Fourier series in time, outperforms the Ahn–Gao model for all data sets considered. 相似文献
4.
The paper studies arbitrage opportunities and possible speculative opportunities for diffusion mean‐reverting market models. It is shown that the Novikov condition is satisfied for any time interval and for any set of parameters. It is non‐trivial because the appreciation rate has Gaussian distribution converging to a stationary limit. It follows that the mean‐reverting model is arbitrage‐free for any finite time interval. Further, it is shown that this model still allows some speculative opportunities: a gain for a wide enough set of expected utilities can be achieved for a strategy that does not require any hypothesis on market parameters and does not use estimation of these parameters. 相似文献
5.
In this paper we describe the notion of the centre of a BCI‐algebra and show that it is a p‐semisimple subalgebra. Various properties of BCI‐ideals have been studied, and necessary and sufficient conditions for certain ideals to be closed have been investigated. 相似文献
6.
This article reports a test of theories of payoff allocation in n‐person game‐theoretic systems. An experimental study was conducted to test the relative predictive accuracy of three solution concepts (imputation set, stable set, core) in the context of 4‐person, 2‐strategy non‐sidepayment games. Predictions from each of the three solution concepts were computed on the basis of both α‐effectiveness (von Neumann‐Morgenstern) and β‐effectiveness (Aumann), making a total of six predictive theories under test. Two important results emerged. First, the data show that the g‐imputation set was more accurate than the a‐imputation set, the β‐stable set was more accurate than the α‐stable set, and the (3‐core was more accurate than the α‐core; in other words, for each of the solutions tested, the prediction from any solution concept based on (β‐effectiveness was more accurate than the prediction from the same solution based on a‐effectiveness. Second, the β‐core was the most accurate of the six theories tested. Results are interpreted as showing that β‐effectiveness is superior to a‐effectiveness as a basis for payoff predictions in cooperative non‐sidepayment games. 相似文献
7.
Let G denote a complex linear algebraic group. In this paper we establish several forms of equivariant Riemann–Roch valid for the category of Gquasiprojective complex varieties. The main application is to the operation of convolution that appears in the construction of modules over convolution algebras, for example the Hecke algebras associated to a complex reductive group as well as in the representation theory of quantum groups. The paper concludes with a discussion of some of these applications. The results in this paper hold mostly at the level of Grothendieck groups. The second part of this paper will discuss the extension to higher Ktheory in detail. 相似文献
8.
We analyze a novel twolevel queueing network with blocking, consisting of N level1 parallel queues linked to M level2 parallel queues. The processing of a customer by a level1 server requires additional services that are exclusively offered by level2 servers. These level2 servers are accessed through blocking and nonblocking messages issued by level1 servers. If a blocking message is issued, the level1 server gets blocked until the message is fully processed at the level2 server. The queueing network is analyzed approximately using a decomposition method, which can be viewed as a generalization of the wellknown twonode decomposition algorithm used to analyze tandem queueing networks with blocking. Numerical tests show that the algorithm has a good accuracy. 相似文献
9.
Misconceptions caused by misunderstanding mathematical language are of different types, e.g. interference of mathematical and non‐mathematical meanings, complexity or unfamiliarity of words, improper use of symbols, syntactical misunderstandings and redundancy or inadequacy of data. Fifteen mathematical words were presented to 84 students of 8th grade and the responses of students were analysed. Mathematical items of a Science Talent Search Test were also analysed from the answers of 100 candidates of 8th grade. The analysis casts light on the processes of the development of mathematical concepts which the students learn through the vicissitudes of the interaction of mathematical and non‐mathematical meanings of words which may be familiar or unfamiliar, relevant or irrelevant, and/or distinct or difficult, to the learners. Complications in understanding mathematical concepts for individual students are pointed out from these experiments. Acquaintance with such communication processes of learners can also help in detecting strategies of imparting mathematical instructions to the learners. Roles of the uses of common, mathematical, transformational, and story‐telling language have also been discussed. The paper concludes with some comments on the importance of guided discovery learning, error analysis by teachers, and the preparation of a register of mathematical language. 相似文献
10.
Abstract The main aim of this paper is to describe the space of operator‐valued predictable processes, which are integrable with respect to a Hilbert space valued quasi‐left continuous semimartingale. The space of integrable processes is a randomized Musielak‐Orlicz space with a modular explicitely expressed in terms of Jacod‐Grigelionis characteristics. 相似文献
11.
It is well known that the degree‐raised Bernstein–Bézier coefficients of degree n of a polynomial g converge to g at the rate 1/ n. In this paper we consider the polynomial A
n( g) of degree ⩼ n interpolating the coefficients. We show how A
n can be viewed as an inverse to the Bernstein polynomial operator and that the derivatives A
n( g)( r) converge uniformly to g( r) at the rate 1/ n for all r. We also give an asymptotic expansion of Voronovskaya type for A
n( g) and discuss some shape preserving properties of this polynomial.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
12.
Multi‐person versions of Prisoner's Dilemma are widely applicable in the social sciences. Examination of two important classes of real‐world situations reveals that although both can appropriately be called Prisoner's Dilemma, they have incompatible payoff structures. Thus Prisoner's Dilemma games constitute an important but apparently ambiguous set of models. We therefore undertake a taxonomy of multi‐person Prisoner's Dilemma. Some aspects of the well‐studied two‐person case provide a useful beginning for the task. In the general multi‐person form, however, some properties of the two‐person game are found incompatible with others and so are dropped. Additional properties are suggested by strategic considerations and the associated social phenomena. We demonstrate interdependencies among the various properties and relate some of them to a simple graphical representation. 相似文献
14.
We deal with the 2‐orthogonal, 2‐symmetric self‐associated sequence (2‐orthogonal Tchebychev polynomials) and its cubic components.
We prove that all the forms (linear functionals) arising are third degree forms. Therefore, an introduction to third degree
forms is provided. We look for the connection between these components which are 2‐orthogonal with respect to the functional
vector t(w 0{ μ},w 1
μ) and orthogonal sequences with respect to w 0
μ, μ=0,1,2. Associated forms w 0
μ) 1) and their inverse w 0
μ) -1 are also studied through the symmetrized w 0} 0
μ, μ=0,1,2. Further, we give integral representations for some of these forms.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
15.
Within the framework of finite element methods, the paper investigates a general approximation technique for the nonlinear
convective term of the Navier–Stokes equations. The approach is based on an upwind method of finite volume type. It is proved
that the discrete convective term satisfies a well‐known collection of sufficient conditions for convergence of the finite
element solution.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
16.
Suppose λ is a positive number. Basic theory of cardinal interpolation ensures the existence of the Gaussian cardinal function \(L_\lambda (x) = \sum\nolimits_{k \in \mathbb{Z}} {c_k \exp ( - \lambda (x - k)^2 ),x \in \mathbb{R}} ,\) satisfying the interpolatory conditions \(L_\lambda (j) = \delta _{0j} ,j \in \mathbb{Z}.\) The paper considers the Gaussian cardinal interpolation operator
$(\mathcal{L}_\lambda {\text{y}})(x): = \sum\limits_{k \in \mathbb{Z}} {y_k L_\lambda (x - k),{\text{ y}} = (y_k )_{k \in \mathbb{Z}} ,{\text{ }}x \in \mathbb{R}} ,$
as a linear mapping from ℓp(ℤ) into L
p(ℝ), 1≤ p ∞, and in particular, its behaviour as λ→0+. It is shown that \(\left\| {\mathcal{L}_\lambda } \right\|_p \) is uniformly bounded (in λ) for 1 < p < ∞, and that \(\left\| {\mathcal{L}_\lambda } \right\|_1 \asymp \log (1/\lambda )\) as λ→0+. The limiting behaviour is seen to be that of the classical Whittaker operator
$\mathcal{W}:{\text{y}} \mapsto \sum\limits_{k \in \mathbb{Z}} {y_k \frac{{\sin \pi (x - k)}}{{\pi (x - k)}}} ,$
in that \(\lim _{\lambda \to 0^ + } \left\| {\mathcal{L}_\lambda {\text{y}} - \mathcal{W}{\text{y}}} \right\|_p = 0,\) for every \({\text{y}} \in \ell ^p (\mathbb{Z}){\text{ and }}1 < p < \infty .\) It is further shown that the Gaussian cardinal interpolants to a function f which is the Fourier transform of a tempered distribution supported in (-π,π) converge locally uniformly to f as λ→0+. Multidimensional extensions of these results are also discussed. 相似文献
17.
The ordered K 0-group of the universal, unital free product C *-algebra M k()*M l()is calculated in the case where k is prime and not a divisor in l. It is shown that the positive cone of K 0(M k()*M l())is as small as possible in this case. The article also contains results (full and partial) on the ordered K 00-group of more general universal, unital free product C * algebras. 相似文献
18.
In this paper we consider the problem of maximizing a non‐linear or linear objective function subject to non‐linear and/or linear constraints. The approach used is an adaptive random search with some non‐random searches built‐in. The algorithm begins with a given point which is replaced by another point if the latter satisfies each of the constraints and results in a bigger functional value. The process of moving from one point to a better point is repeated many times. The value of each of the coordinates of the next point is determined by one of several ways; for example, a coordinate is sometimes forced to have the same value as the value of the corresponding coordinate of the current feasible point. In this algorithm, a candidate point receives no further computational considerations as soon as it is found to be unfeasible; this makes the algorithm general. Computer programs illustrating the details of the new algorithm are given and computational results of two numerical test problems from the literature are presented. Optimality was reached in each of these two problems. 相似文献
19.
Animated motion pictures can be produced by digital computers. The advantages of this method over hand animation are discussed and examples of films made are given to illustrate the techniques and thinking that go into the production. Other work in this field is described. 相似文献
20.
It is my firm belief that mathematics is methodology. The briefer is the method, the more effective it is in treating problems. The novel methodized treatment in this article features all the concepts of conics relating to transformation between coordinate systems and standard forms with graphic illustrations. Denote O’ as the centre of an ellipse or a hyperbola or the vertex of a parabola and F as a focus of a conic. Let O'F= cu, u=[cos θ, sin θ], v = [‐sin θ, cos θ] and P( x,y), then the transformation x’ = u.O'P, y‘ = v.O'P which leads to the standard form for each conic relative to x’ — O'—y‘ The theorem on normal projection in this article is very important in analytic geometry and especially useful for problems involving conies when a directrix or an axis is given. 相似文献
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