What is missing in canonical models for proper normal algebraic surfaces?

Smooth surfaces have finitely generated canonical rings and projective canonical models. For normal surfaces, however, the graded ring of multicanonical sections is possibly nonnoetherian, such that the corresponding homogeneous spectrum is noncompact. I construct a canonical compactification by adding finitely many non-ℚ-Gorenstein points at infinity, provided that each Weil divisor is numerically equivalent to a ℚ-Cartier divisor. Similar results hold for arbitrary Weil divisors instead of the canonical class.     

Generating low-discrepancy sequences from the normal distribution: Box–Muller or inverse transform?

Quasi-Monte Carlo simulation is a popular numerical method in applications, in particular, economics and finance. Since the normal distribution occurs frequently in economic and financial modeling, one often needs a method to transform low-discrepancy sequences from the uniform distribution to the normal distribution. Two well known methods used with pseudorandom numbers are the Box–Muller and the inverse transformation methods. Some researchers and financial engineers have claimed that it is incorrect to use the Box–Muller method with low-discrepancy sequences, and instead, the inverse transformation method should be used. In this paper we prove that the Box–Muller method can be used with low-discrepancy sequences, and discuss when its use could actually be advantageous. We also present numerical results that compare Box–Muller and inverse transformation methods.     

The coherence of ?ukasiewicz assessments is NP-complete

The problem of deciding whether a rational assessment of formulas of infinite-valued ?ukasiewicz logic is coherent has been shown to be decidable by Mundici [1] and in PSPACE by Flaminio and Montagna [10]. We settle its computational complexity proving an NP-completeness result. We then obtain NP-completeness results for the satisfiability problem of certain many-valued probabilistic logics introduced by Flaminio and Montagna in [9].     

Asymptotically optimal empirical Bayes estimators for the parameters of normal distribution family

There have been a lot of discussions in the literature concerning the empirical Bayes (EB) estimation of a single parameter, wihle the multi-parameter case is still rarely touched upon.In some circumstances this case is important,as evidenced by the well-known example of normal distribution N(μ, σ~2).     

The distribution of sublattices of ℤ m

Lattices , are similar if one can be transformed into the other by an angle-preserving linear map. Similarity classes of lattices of rankn may be parametrized by a fundamental domain of the action ofGL _n () on the generalized upper half-plane _n . Given 1<nm and, letN(D,T) be the number of sublattices of _n which have rankn, similarity class inD, and determinant T. Our most basic result will be thatN(D,T)c ₁(m, n)(D)T ^m asT for suitable setsD, where is the invariant measure on _n . The casen=2 had been dealt with by Roelcke and by Maass using the theory of modular forms.Herrn Professor Hlawka zum achtzigsten Geburtstag gewidmetSupported in part by NSF-DMS-9401426     

Lipschitz and differentiability properties of quasi-concave and singular normal distribution functions

The paper provides a condition for differentiability as well as an equivalent criterion for Lipschitz continuity of singular normal distributions. Such distributions are of interest, for instance, in stochastic optimization problems with probabilistic constraints, where a comparatively small (nondegenerate-) normally distributed random vector induces a large number of linear inequality constraints (e.g. networks with stochastic demands). The criterion for Lipschitz continuity is established for the class of quasi-concave distributions which the singular normal distribution belongs to.     

What is The Squeeze (or Sandwich) Theorem?

<正>Let's do an exercise as warming up.Ex:Find lim x→0sin1/x.lim x→0sin1/x=lim1/x→∞sin1/x=lim t→∞sint(Let t=1/x).We know lim t→∞sint does not exist,so lim x→0sin1/x DNE.We can use graphing calculator to show the result is DNE(from figure 1to figure 8).     

On distribution of Grubbs’ statistics in case of normal sample with outlier

We investigate one-sided Grubbs’ statistics for a normal sample. Those statistics are standardized maximum and standardized minimum, i.e., studentized extreme deviation statistics. We consider the case of the sample when there is one abnormal observation (outlier), unknown to what number according. The outlier differs from other observations in values of population mean and dispersion. We obtain recursive relationships for the marginal distribution function of one-sided Grubbs’ statistics. We find asymptotic formulas for marginal distribution functions. We obtain recursive relationships for the joint distribution function of one-sided Grubbs’ statistics and investigate its properties.     

Wiener–Hopf equation whose kernel is a probability distribution

We prove the existence of a solution of an inhomogeneous generalized Wiener–Hopf equation whose kernel is a probability distribution on R generating a random walk drifting to +∞, while the inhomogeneous term f of the equation belongs to the space L ₁(0,∞) or L _∞(0,∞). We establish the asymptotic properties of the solution of this equation under various assumptions about the inhomogeneity f.     

The normal ΔH-matrices with connection to some Jacobi-like methods

The ΔH-matrices appear in the context of certain maximization and minimization problems. The following purely algebraic problem, arising in connection with certain norm-reducing Jacobi-type algorithms is treated: When is a normal ΔH-matrix diagonal? Final results are obtained in the cases n = 3 and n = 4, and in general for the attractive normal ΔH-matrices.     

The Baum–Welch algorithm with limiting distribution constraints

We present a method of incorporating limiting distribution information in the Baum–Welch algorithm for estimating parameters of discrete-time, finite-state, Hidden Markov Models. We find that having, even imperfect, limiting distribution information can dramatically improve transition probability estimates. Additionally, we find that when (1) the underlying process is weakly correlated with the observable signal, and (2) the length of the data sequence is short, the additional information provided by the limiting distribution is substantial.     

The existence of TU α-core in normal form games

This paper provides a TU α-core existence result in a large class of normal form games. In the oligopoly markets of a homogeneous good, the TU α-core is non-empty if all profit functions are continuous and concave. In a general game, the existence of TU α-core follows from the weak separability, the compactness and convexity of choice sets, and the concavity and continuity of payoff functions. Received: November 1997/final version: August 1998     

Can time-homogeneous diffusions produce any distribution?

Given a centred distribution, can one find a time-homogeneous martingale diffusion starting at zero which has the given law at time 1? We answer the question affirmatively if generalized diffusions are allowed.     

How Relevant is Operational Research to Development? The Case of Kenyan Industry

This paper proposes that the debate over O.R.'s role in development can be advanced by looking at a specific industrial environment. The Kenyan example suggests that for O.R. to make a contribution to this developing society it must: first, be defined as broadly as possible so as to include the most basic problem-solving techniques, and second, contribute to the diffusing of these techniques throughout the economy. O.R. should be viewed less as the province of an elite group of specialists— and more as a common resource available to managers at any level of industry. O.R. educators in developing nations can "democratise" quantitative techniques by incorporating them into such traditional business disciplines as accounting, marketing, and production. These courses should stress problem-solving and rely on cases drawn from local experiences. The paper ends by describing a pilot project, the Case Research and Documentation Centre, which is designed to promote more pragmatic management education and research in Kenya.