Models for petroleum field exploitation

This paper presents some models for an early evaluation of a petroleum field. Based on crude assumptions about a reservoir, our models suggest decisions concerning platform capacity, drilling programme and production. We start out with a simple production planning model using linear programming. By mixed integer programming techniques the model is gradually extended. The most sophisticated version of the model can propose platform capacity, where and when wells should be drilled, and the production from the wells. The models are tested on numerical examples, and the results are discussed. From the experiments we conclude that the problems are very hard to solve, and that the size of problems that can be solved is limited by the computational burden. Finally we give some ideas for future work that may provide better solution methods.     

Periodic Solutions for Second Order Differential Inclusions with Nonconvex and Unbounded Multifunction

In this paper we consider a second order multivalued periodic boundary value problem with a nonconvex and unbounded orientor field (set-valued vector field). Using a directionally continuous selector, through its Filippov regularization we produce a convex-valued, bounded multifunction and with this as orientor field we introduce a new multivalued periodic problem. Using the Leray-Schauder principle, we solve the convex problem and then we show that its solutions also solve the original nonconvex problem.     

一类平面三次拟齐次向量场的全局拓扑结构

利用中心投影变换的思想证明一类平面三次拟齐次向量场的几何性质依赖于它的切向量场和诱导向量场.讨论了该系统的拓扑结构,并进行了分类;证明了该系统具有25类不同类的拓扑结构相图.     

Global regularity of generalized magnetic Benard problem

We study the magnetic Bénard problem in two‐dimensional space with generalized dissipative and diffusive terms, namely, fractional Laplacians and logarithmic supercriticality. Firstly, we show that when the diffusive term for the magnetic field is a full Laplacian, the solution initiated from data sufficiently smooth preserves its regularity as long as the power of the fractional Laplacians for the dissipative term of the velocity field and the diffusive term of the temperature field adds up to 1. Secondly, we show that with zero dissipation for the velocity field and a full Laplacian for the diffusive term of the temperature field, the global regularity result also holds when the diffusive term for the magnetic field consists of the fractional Laplacian with its power strictly bigger than 1. Finally, we show that with no diffusion from the magnetic and the temperature fields, the global regularity result remains valid as long as the dissipation term for the velocity field has its strength at least at the logarithmically supercritical level. These results represent various extensions of previous work on both Boussinesq and magnetohydrodynamics systems. Copyright © 2016 John Wiley & Sons, Ltd.     

AN ACCELERATION STRATEGY FOR RANDOMIZE-THEN-OPTIMIZE SAMPLING VIA DEEP NEURAL NETWORKS

Randomize-then-optimize (RTO) is widely used for sampling from posterior distribu-tions in Bayesian inverse problems.However,RTO can be computationally intensive for complexity problems due to repetitive evaluations of the expensive forward model and its gradient.In this work,we present a novel goal-oriented deep neural networks (DNN) sur-rogate approach to substantially reduce the computation burden of RTO.In particular,we propose to drawn the training points for the DNN-surrogate from a local approximated posterior distribution-yielding a flexible and efficient sampling algorithm that converges to the direct RTO approach.We present a Bayesian inverse problem governed by elliptic PDEs to demonstrate the computational accuracy and efficiency of our DNN-RTO ap-proach,which shows that DNN-RTO can significantly outperform the traditional RTO.     

Effective Boundary Conditions for the Heat Equation with Interior Inclusion

Of concern is the scenario of a heat equation on a domain that contains a thin layer, on which the thermal conductivity is drastically different from that in the bulk. The multi-scales in the spatial variable and the thermal conductivity lead to computational difficulties, so we may think of the thin layer as a thickless surface, on which we impose "effective boundary conditions"(EBCs). These boundary conditions not only ease the computational burden, but also reveal the effect of the inclusion. In this paper, by considering the asymptotic behavior of the heat equation with interior inclusion subject to Dirichlet boundary condition, as the thickness of the thin layer shrinks, we derive, on a closed curve inside a two-dimensional domain, EBCs which include a Poisson equation on the curve, and a non-local one. It turns out that the EBCs depend on the magnitude of the thermal conductivity in the thin layer,compared to the reciprocal of its thickness.     

Simulation modelling and analysis of a border security system

Border control is vital to the security of a nation and its citizens. All countries look at measures to improve the security of their borders. But increasing security can bring a substantial financial burden. In this study, we analyze the border security problem of Turkey using a simulation approach. Our main objective is to find more efficient ways of improving border control and security along Turkey’s land borders. To achieve this, we examine the structure of the border security system and its major elements, examine the relationships between performance measures, and assess the effectiveness of security elements on each system performance measure. We also look into the issues of planned changes and additional resources, and we evaluate new alternative system designs. The results of simulation experiments are analyzed by statistical methods.     

A new approach for achievement of the equilibrium efficient frontier with fixed-sum outputs

In a recent paper, Yang et al developed an algorithm based on the extended minimal adjustment strategy and the equilibrium competition strategy to achieve a common equilibrium efficient frontier. However, the computational burden of their algorithm is challenging when a sample contains many inefficient decision-making units (DMUs). In this paper, we propose a linear programming model that can achieve a common equilibrium efficient frontier in a single step, regardless of the number of inefficient DMUs. Furthermore, we demonstrate the existence and the non-uniqueness of the equilibrium efficient frontier and identify its shortcomings through an example. Next, we extend our approach to incorporate weight restrictions to indicate the relative importance of the different inputs and outputs and introduce the secondary goal of minimizing the maximal relative deviation for each fixed-sum output, which can result in a unique equilibrium efficient frontier.     

A demonstrative study of a new SQC concept and procedure in the manufacturing industry

A review of the changes in the environment surrounding the manufacturing industry indicated an ever greater necessity for corporate efforts to amplify and capitalize upon the technical prowess of the engineering staff who bear the main burden of these times. In this study, we propose the establishment of a new technical method for conducting scientific SQC as a new concept and procedure that will improve the job quality of the engineering staff in each stage of the business process so as to contribute to production with excellent QCDS. We also try to evaluate and investigate its usefulness on the basis of an actual study example in Toyota.     

Stochastic Jacobi fields and vector fields induced by varying area on path spaces

Summary. We study two classes of vector fields on the path space over a closed manifold with a Wiener Riemannian measure. By adopting the viewpoint of Yang-Mills field theory, we study a vector field defined by varying a metric connection. We prove that the vector field obtained in this way satisfies a Jacobi field equation which is different from that of classical one by taking in account that a Brownian motion is invariant under the orthogonal group action, so that it is a geometric vector field on the space of continuous paths, and induces a quasi-invariant solution flow on the path space. The second object of this paper is vector fields obtained by varying area. Here we follow the idea that a continuous semimartingale is indeed a rough path consisting of not only the path in the classical sense, but also its Lévy area. We prove that the vector field obtained by parallel translating a curve in the initial tangent space via a connection is just the vector field generated by translating the path along a direction in the Cameron-Martin space in the Malliavin calculus sense, and at the same time changing its Lévy area in an appropriate way. This leads to a new derivation of the integration by parts formula on the path space. Received: 8 August 1996 / In revised form: 8 January 1997     

A model for the periodic optimization of bus dispatching times

We model the problem of dispatching time control in rolling horizons following a periodic optimization approach reactionary to travel time and passenger demand disturbances. This model provides more flexibility to transport planners allowing them to adjust the bus schedules during the daily operations. We prove that our periodic optimization model is a convex quadratic program, guaranteeing the global optimality of its solution. To reduce the computational burden, we introduce an iterative algorithm that uses gradient approximations to obtain an approximate dispatching solution. The proposed solution method is found to be significantly faster than exact optimization approaches for quadratic programming and maintains an (almost) negligible optimality gap in realistic bus operation scenarios. Finally, we show that our periodic optimization method outperforms myopic methods that adjust the dispatching time of each bus trip in isolation using operational data from bus line 302 in Singapore.     

Evolution of hypersurfaces by powers of mean curvature minus an external force field

In this paper, we study the evolution of hypersurfaces by powers of mean curvature minus an external force field. We prove that when the power is 2, the flow has a long-time smooth solution for all time under some conditions. Those conditions are that the second fundamental form on the initial submanifolds is not too large, the external force field, with its any order derivatives, is bounded, and the field is convex with its eigenvalues satisfying a pinch inequality.     

The rational canonical form via the splitting field

It is clear that a given rational canonical form can be further resolved to a Jordan canonical form with entries from the splitting field of its minimal polynomial. Conversely, with an a priori knowledge of the existence and uniqueness of the rational canonical form of a matrix with entries from a general field, one can modify its Jordan canonical form in the splitting field of its minimal polynomial to construct its rational canonical form in the original field. No author has tried this converse with the a priori existence–uniqueness condition removed. It is feared that “in many occasions when, after a result has been established for a matrix with entries in a given field, considered as a matrix with entries in a finite extension of that field, we cannot go back from the extension field to get the desired information in the original field” [I.N. Herstein, Topics in Algebra, Ginn and Company, Waltham, MA, 1964 (pp. 262–263)]. The present paper removes this a priori condition and uses a “symmetrization” to “integrate” back the Jordan canonical form of a matrix to its rational canonical form in the original field.     

适合无限维实零点定理的序域之结构Ⅱ

在本文的第二部分中,我们研究了适合无限维实零点定理的序域的结构．通过嵌入,我们证明了,一个序域适合无限维实零点定理,当且仅当它的实闭包同构于域的某个具有无限维逼近性质的子域,这里是一个无裂缝的可除序群,｛Γ｝是指数在中,系数为实数的形式幂级数域．     

Green fields

We introduce Green fields, as commutative Green biset functors with no non-trivial ideals. We state some of their properties and give examples of known Green biset functors which are Green fields. Among the properties, we prove some criterions ensuring that a Green field is semisimple. Finally, we describe a type of Green field for which its category of modules is equivalent to a category of vector spaces over a field.     

Continuous Time Finite State Mean Field Games

In this paper we consider symmetric games where a large number of players can be in any one of d states. We derive a limiting mean field model and characterize its main properties. This mean field limit is a system of coupled ordinary differential equations with initial-terminal data. For this mean field problem we prove a trend to equilibrium theorem, that is convergence, in an appropriate limit, to stationary solutions. Then we study an N+1-player problem, which the mean field model attempts to approximate. Our main result is the convergence as N→∞ of the mean field model and an estimate of the rate of convergence. We end the paper with some further examples for potential mean field games.     

Learning from incomplete data in Bayesian networks with qualitative influences

Domain experts can often quite reliably specify the sign of influences between variables in a Bayesian network. If we exploit this prior knowledge in estimating the probabilities of the network, it is more likely to be accepted by its users and may in fact be better calibrated with reality. We present two algorithms that exploit prior knowledge of qualitative influences in learning the parameters of a Bayesian network from incomplete data. The isotonic regression EM, or irEM, algorithm adds an isotonic regression step to standard EM in each iteration, to obtain parameter estimates that satisfy the given qualitative influences. In an attempt to reduce the computational burden involved, we further define the qirEM algorithm that enforces the constraints imposed by the qualitative influences only once, after convergence of standard EM. We evaluate the performance of both algorithms through experiments. Our results demonstrate that exploitation of the qualitative influences improves the parameter estimates over standard EM, and more so if the proportion of missing data is relatively large. The results also show that the qirEM algorithm performs just as well as its computationally more expensive counterpart irEM.     

Diameter estimates for submanifolds in manifolds with nonnegative curvature

Given a closed connected manifold smoothly immersed in a complete noncompact Riemannian manifold with nonnegative sectional curvature, we estimate the intrinsic diameter of the submanifold in terms of its mean curvature field integral. On the other hand, for a compact convex surface with boundary smoothly immersed in a complete noncompact Riemannian manifold with nonnegative sectional curvature, we can estimate its intrinsic diameter in terms of its mean curvature field integral and the length of its boundary. These results are supplements of previous work of Topping, Wu-Zheng and Paeng.     

Ricci solitons and odd-dimensional spheres

As a real hypersurface in a complex space, we prove two criterion inequalities for an odd-dimensional sphere in terms of the shape operator, the Reeb vector field and its associated 1-form. Also, we determine a real hypersurface in a complex space which admits a Ricci soliton with the Reeb vector field the potential vector field.