The Inequality 8pg < μ for Hypersurface Two-dimensional Isolated Double Points

The Milnor number μ and the geometric genus p_g of normal 2-dimensional double points are studied by using Zariski's canonical resolution. By using formulas due to E. HORIKAWA and H. LAUFER, we represent μ ? 8p_g in terms of the number of blowing-ups along ?¹ and the number l of ?even”? components in the resolution process. A key point of our arguments is the fact that if l is small then the resolution process is restricted very much. For rational double points and double points with p_a = 1, each classes are characterized by numerical invariants appearing in this resolution process. For the case p_a = 1, we can make our inequality sharper and can prove 12 · p_g ? 3 ≤ μ. This is an another proof of Xu-Yau's inequality for the singularity with p_a = 1 in our situation.     

Preconditioning of the Stiffness Matrix of Local Refined Triangulation

A preconditioning method for the finite element stiffness matrix is given in this paper. The triangulation is refined in a subregion; the preconditioning process is composed of resolution of two regular subproblems; the condition number of the preconditioned matrix is O(1 logH/h), where H and h are mesh sizes of the unrefined and local refined triangulations respectively.     

拟遗传代数的诱导模与广义Betti数

本文引入了模的广义Betti数,给出了经典Betti数与广义Betti数之间的关系,证明了具有纯粹强正合Borel子代数的零关系拟遗传代数的诱导模的极小投射分解可通过其正合Borel子代数的相应模的极小投射分解的诱导给出,从而两者具有相同的广义Betti数.     

On the index of powers of edge ideals

The index of a graded ideal measures the number of linear steps in the graded minimal free resolution of the ideal. In this paper, we study the index of powers and squarefree powers of edge ideals. Our results indicate that the index as a function of the power of an edge ideal I is strictly increasing if I is linearly presented. Examples show that this needs not to be the case for monomial ideals generated in degree greater than two.     

Simulating cardiac electrophysiology using anisotropic mesh adaptivity

The simulation of cardiac electrophysiology requires small time steps and a fine mesh in order to resolve very sharp, but highly localized, wavefronts. The use of very high resolution meshes containing large numbers of nodes results in a high computational cost, both in terms of CPU hours and memory footprint. In this paper an anisotropic mesh adaptivity technique is implemented in the Chaste physiological simulation library in order to reduce the mesh resolution away from the depolarization front. Adapting the mesh results in a reduction in the number of degrees of freedom of the system to be solved by an order of magnitude during propagation and 2–3 orders of magnitude in the subsequent plateau phase. As a result, a computational speedup by a factor of between 5 and 12 has been obtained with no loss of accuracy, both in a slab-like geometry and for a realistic heart mesh with a spatial resolution of 0.125 mm.     

有向Kirkman填充设计的谱

§ 1　IntroductionLet X be a set of v points.A packing(directed packing) of X is a collection of subsets(ordered subsets) of X(called blocks) such that any pair(ordered pair) of distinct pointsfrom X occur together in atmostone block in the collection.A packing(directed packing)is called resolvable ifitsblock setadmitsa partition into parallel classes,each parallel classbeing a partition of the pointset X.A Kirkman triple system KTS(v) is a collection Tof3 -subsets of X(triples) suchthat …     

On the number of elementary particles in a resolution dependent fractal spacetime

We reconsider the fundamental question regarding the number of elementary particles in a minimally extended standard model. The main conclusion is that since the dimension of E-infinity spacetime is resolution dependent, then the number of elementary particles is also resolution dependent. For D = 10 of superstrings, D = 11 of M theory and D = 12 of F theory one finds N(SM) equal to (6)(10) = 60, (6)(11) = 66 and (6)(12) = 72 particles, respectively. This is in perfect agreement with prediction made previously by Mohamed Saladin El-Naschie and Marek-Crnjac.     

BOUND ON THE MAXIMUM NUMBER OF CLEAR TWO-FACTOR INTERACTIONS FOR 2^n-（n-k） DESIGNS

Clear effects criterion is an important criterion for selecting fractional factorial designs[1].Tang et al.[2]derived upper and lower bounds on the maximum number of clear two-factor interactions（2fi＇s）in 2^n-（n-k）designs of resolution Ⅲ and Ⅳ by constructing 2^n-（n-k）designs.But the method in[2]does not perform well sometimes when the resolution is Ⅲ.This article modifies the construction method for 2^n-（n-k） designs of resolution Ⅲ in[2].The modified method is a great improvement on that used in[2].     

Enhanced algorithms for implementing the spectral discretization of the vorticity‐velocity‐pressure formulation of Stokes problem

In this paper, we deal with the numerical resolution of spectral discretization of the vorticity‐velocity‐pressure formulation of Stokes problem in a square or a cube provided with nonstandard boundary conditions, which involve the normal component of the velocity and the tangential components of the vorticity. Therefore, we propose two algorithms: the Uzawa algorithm and the global resolution. We implemented the two algorithms and compared their results. With global resolution, we obtained a very good accuracy with a small number of iteration.     

On minquantile and maxcovering optimisation

In this paper we introduce the parametric minquantile problem, a weighted generalisation ofkth maximum minimisation. It is shown that, under suitable quasiconvexity assumptions, its resolution can be reduced to solving a polynomial number of minmax problems.It is also shown how this simultaneously solves (parametric) maximal covering problems. It follows that bicriteria problems, where the aim is to both maximize the covering and minimize the cover-level, are reducible to a discrete problem, on which any multiple criteria method may be applied.Corresponding author.Visiting researcher at the Center for Industrial Location of the Vrije Universiteit Brussel during this research.     

Timed Petri nets and prediction to improve the Chandy–Misra conservative-distributed simulation

The main contribution of this paper shows that distributed simulation of timed Petri nets (TPN) can take advantage of their structure to obtain a significant lookahead which is usually difficult to compute with other models. In this paper, we introduce a conservative-distributed simulation with a reduced number of control messages and without deadlock resolution. This approach is based on a part of optimism computed on the prediction time each logical process can determine for its advancement. Obviously this prediction time must be computed easily according to the structure of the simulated logical process. Timed Petri nets meet these requirements and we use their structure to evaluate the depth of the prediction. In conservative-distributed simulation, it is known that the deeper the prediction, the better the efficiency of the simulation. We present a method we have devised based on channel time prediction. We compare its performance to the Chandy–Misra method and to some related Petri nets approaches (Chiola). Experiments carried out on Sun stations show that there is more parallelism and a reduced number of null messages in the cases of deadlock avoidance. Moreover, considering deadlock detection and resolution technique we observe that in many cases no deadlock occurs with less control messages.     

Cohen-Macaulay types of subgroup lattices of finite abelianp-groups

For a minimal free resolution of a Stanley-Reisner ring constructed from the order complex of a modular lattice. T. Hibi showed that its last Betti number (called the Cohen-Macaulay type) is computed by means of the Möbius function of the given modular lattice. Using this result, we consider the Stanley-Reisner ring of the subgroup lattice of a finite abelianp-group associated with a given partition, and show that its Cohen-Macaulay type is a polynomial inp with integer coefficients.     

Hazard Rate Regression Using Ordinary Nonparametric Regression Smoothers

Abstract

This article proposes a method for nonparametric estimation of hazard rates as a function of time and possibly multiple covariates. The method is based on dividing the time axis into intervals, and calculating number of event and follow-up time contributions from the different intervals. The number of event and follow-up time data are then separately smoothed on time and the covariates, and the hazard rate estimators obtained by taking the ratio. Pointwise consistency and asymptotic normality are shown for the hazard rate estimators for a certain class of smoothers, which includes some standard approaches to locally weighted regression and kernel regression. It is shown through simulation that a variance estimator based on this asymptotic distribution is reasonably reliable in practice. The problem of how to select the smoothing parameter is considered, but a satisfactory resolution to this problem has not been identified. The method is illustrated using data from several breast cancer clinical trials.     

Dilation coefficient, plane-width, and resolution coefficient of graphs

In this paper we investigate the relations between three graph invariants that are related to the ‘compactness’ of graph drawing in the plane: the dilation coefficient, defined as the smallest possible quotient between the longest and the shortest edge length; the plane-width, which is the smallest possible quotient between the largest distance between any two points and the shortest length of an edge; and the resolution coefficient, the smallest possible quotient between the longest edge length and the smallest distance between any two points. These three invariants coincide for complete graphs. More specifically, we show that the plane-width and the dilation coefficient are equivalent graph parameters in the sense that they are bounded on the same sets of graphs, while bounded resolution coefficient implies bounded plane-width (or dilation coefficient) but not conversely. It is known that the one-dimensional analogues of the plane-width and the resolution coefficient are closely related to the chromatic number and the bandwidth respectively. We complete this picture by showing that a graph of one-dimensional dilation coefficient $d$ is exactly the same as a graph of circular chromatic number  $d+1$ . Finally, we complement the result that a graph of resolution coefficient less than $\sqrt{2}$ is planar by constructing a family of graphs of resolution coefficient $\sqrt{2}$ not contained in any nontrivial minor-closed graph family.     

On the challenges of healthcare modelling and a proposed project life cycle for successful implementation

OR methods and tools are being increasingly applied within the health services domain to support objective decision-making for the effective and efficient provision of resources. Healthcare modelling, however, is beset with many challenges and this paper examines a number of issues that define the primary challenges faced by the modeller in this field. It is fair to say that their resolution determines the likely success or failure of healthcare modelling in general. Working with a number of participating health service organizations, a proposed framework towards successful implementation has evolved and is presented in this paper     

关于二阶椭圆方程区域分裂法的最优预处理

§0.引言 区域分裂是与微分方程数值解的并行计算的数学基础密切相关的,预处理共轭梯度法是区域分裂的一个主要途径,寻找好的预处理子是关键问题,本文给出一个较一般性的方法,预处理过程包括一个整体小规模问题和若干个独立的局部子问题,整体问题和局部问题的选取均有极大的任意性,预处理条件数的估计是由整体问题和局部问题的一些特     

Complexity of solving parametric polynomial systems

In this paper, we present three algorithms: the first one solves zero-dimensional parametric homogeneous polynomial systems within single exponential time in the number n of unknowns; it decomposes the parameter space into a finite number of constructible sets and computes the finite number of solutions by parametric rational representations uniformly in each constructible set. The second algorithm factirizes absolutely multivariate parametic polynomials within single exponential time in n and in the upper bound d on the degree of the factorized polynomials. The third algorithm decomposes algebraic varieties defined by parametric polynomial systems of positive dimension into absolutely irreducible components uniformly in the values of the parameters. The complexity bound for this algorithm is double exponential in n. On the other hand, the lower bound on the complexity of the problem of resolution of parametric polynomial systems is double exponential in n. Bibliography: 72 titles.     

Numerical study of liquid/liquid slug flow in a capillary microreactor

The great advantage of microreactors is associated with an extremely large surface-to-volume ratio. Hence, microreactors permit promising operating conditions, such as almost-perfect heat or mass transfer. This, of course, requires that the hydrodynamics is well understood. The hydrodynamics of a liquid/liquid slug flow in a micro-capillary is characterized by a complex vortex structure in both the disperse and the continuous phase. The disperse phase, in our investigations, is not wetting the walls and, thus, a thin film of the continuous phase persist between the disperse phase and the wall. Due to this phenomenon, a relative movement between disperse and continuous phase is possible and, indeed, observed. Understanding of these complex phenomena allows for a control of the hydrodynamics, and thus, to tailor the heat and mass transport in a desired manner. Apparently, several effects influence the hydrodynamics. The main dimensionless groups are a Reynolds number, a Capillary number, and the ratio of viscosities and densities of both phases. To study the physics of this complex two-liquid system, a modified level-set method in conjunction with an immersed-boundary formulation is engaged. Presently, the simulations are time-dependent and axially-symmetric in nature. The mesh resolution represents a challenge, as the spatial resolution has to resolve the thin film between the disperse phase and the wall adequately. All simulations are implemented within the software OpenFOAM. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

“Miniaturized” Linearizations for Quadratic 0/1 Problems

In order to solve a quadratic 0/1 problem, some techniques, consisting in deriving a linear integer formulation, are used. Those techniques, called “linearization”, usually involve a huge number of additional variables. As a consequence, the exact resolution of the linear model is, in general, very difficult. Our aim, in this paper, is to propose “economical” linear models. Starting from an existing linearization (typically the so-called “classical linearization”), we find a new linearization with fewer variables. The resulting model is called “Miniaturized” linearization. Based on this approach, we propose a new linearization scheme for which numerical tests have been performed.     

Minimal projective resolutions

In this paper, we present an algorithmic method for computing a projective resolution of a module over an algebra over a field. If the algebra is finite dimensional, and the module is finitely generated, we have a computational way of obtaining a minimal projective resolution, maps included. This resolution turns out to be a graded resolution if our algebra and module are graded. We apply this resolution to the study of the -algebra of the algebra; namely, we present a new method for computing Yoneda products using the constructions of the resolutions. We also use our resolution to prove a case of the ``no loop' conjecture.