TheO(n3) algorithm for a special case of the maximum cost-to-time ratio cycle problem and its coherence with an eigenproblem of a matrix

Let twon×n matrices be given, namely a real matrixA=(a_ij) and a (0, 1)-matrixT=(t_ij). For a cyclic permutation=(i ₁,i ₂,...,i _k) of a subset of N={1, 2, ..., n} we define _A;T(), the cost-to-time ratio weight of, as . This paper presents an O(n³) algorithm for finding (A;T)=max _A;T(), the maximum cost-to-time ratio weight of the matricesA andT. Moreover a generalised eigenproblem is proposed.     

Discretization of solutions to a wave equation, numerical differentiation, and function recovery with the help of computer (computing) diameter

We study three concretizations of the notion of computer (computing) diameter, namely, the discretization of solutions to the Klein-Gordon equation, numerical differentiation, and function recovery.     

Remarks on Nonassociative Structures in Quantum Projective Field Theory: the Central Extension jl(2,C) of the Double sl(2,C)+sl(2,C) of the Simple Lie Algebra sl(2,C) and Related Topics

This paper is a revised and expanded version of two notes devoted to nonassociative structures in quantum projective field theory.     

Hydrogeochemical modeling for groundwater management in arid and semiarid regions using MODFLOW and MT3DMS: A case study of the Jeffara of Medenine coastal aquifer,South-Eastern Tunisia

The study of water quality and the quantification of reserves and their variations according to natural and anthropogenic forcing is necessary to establish an adequate management plan for groundwater resources. For this purpose, a modeling approach is a useful tool that allows, after calibration phase and verification of simulation, and under different scenarios of forcing and operational changes, to estimate and control the groundwater quantity and quality. The main objective of this study is to collect all available data in a model that simulates the Jeffara of Medenine coastal aquifer system functioning. To achieve this goal, a conceptual model was constructed based on previous studies and hydrogeological investigations. The regional groundwater numerical flow model for the Jeffara aquifer was developed using MODFLOW working under steady-state and transient conditions. Groundwater elevations measured from the piezometric wells distributed throughout the study area in 1973 were selected as the target water levels for steady state (head) model calibration. A transient simulation was undertaken for the 42 years from 1973 to 2015. The historical transient model calibration was satisfactory, consistent with the continuous piezometric decline in response to the increase in groundwater abstraction. The developed numerical model was used to study the system's behavior over the next 35 years under various constraints. Two scenarios for potential groundwater extraction for the period 2015–2050 are presented. The predictive simulations show the effect of the increase of the exploitation on the piezometric levels. To study the phenomenon of salinization, which is one of the most severe and widespread groundwater contamination problems, especially in coastal regions, a solute transport model has been constructed by using MT3DMS software coupled with the groundwater flow model. The best calibration results are obtained when the connection with the overlying superficial aquifer is considered suggesting that groundwater contamination originates from this aquifer. Recommendations for water resource managers

• The results of this study show that Groundwater resources of Jeffara of Medenine coastal aquifer in Tunisia are under immense pressure from multiple stresses.
• The water resources manager must consider the impact of economic and demographic development in groundwater management to avoid the intrusion of saline water.
• The results obtained presented some reference information that can serve as a basis for water resources planning.
• The model runs to provide information that managers can use to regulate and adequately control the Jeffara of Medenine water resources.

     

2‐(v,k,1) Designs Admitting a Primitive Rank 3 Automorphism Group of Affine Type: The Extraspecial and the Exceptional Classes

2‐(v,k,1) designs admitting a primitive rank 3 automorphism group , where G₀ belongs to the Extraspecial Class, or to the Exceptional Class of Liebeck's Theorem in [23], are classified.     

Mathematical study of the small oscillations of a pendulum containing an almost homogeneous, incompressible, inviscid liquid and a barotropic gas (Oscillations of a pendulum with almost homogeneous liquid and gas)

The authors study the small oscillations of a pendulum containing an almost homogeneous, incompressible, inviscid liquid (i.e. a liquid whose density in equilibrium is practically a linear function of the height, which differs very little from a constant) and a moving gas. Using functional analysis, they prove that the spectrum is comprised of a countable set of real eigenvalues and an essential spectrum, which fills an interval, and they give an existence and uniqueness theorem for the solution of the evolution problem.     

On the convergence rate and optimization of a numerical method with splitting of boundary conditions for the stokes system in a spherical layer in the axisymmetric case: Modification for thick layers

The convergence rate of a fast-converging second-order accurate iterative method with splitting of boundary conditions constructed by the authors for solving an axisymmetric Dirichlet boundary value problem for the Stokes system in a spherical gap is studied numerically. For R/r exceeding about 30, where r and R are the radii of the inner and outer boundary spheres, it is established that the convergence rate of the method is lower (and considerably lower for large R/r) than the convergence rate of its differential version. For this reason, a really simpler, more slowly converging modification of the original method is constructed on the differential level and a finite-element implementation of this modification is built. Numerical experiments have revealed that this modification has the same convergence rate as its differential counterpart for R/r of up to 5 × 10³. When the multigrid method is used to solve the split and auxiliary boundary value problems arising at iterations, the modification is more efficient than the original method starting from R/r ～ 30 and is considerably more efficient for large values of R/r. It is also established that the convergence rates of both methods depend little on the stretching coefficient η of circularly rectangular mesh cells in a range of η that is well sufficient for effective use of the multigrid method for arbitrary values of R/r smaller than ～ 5 × 10³.     

A note on the paper “characterization of all optimal solutions and parametric maximal flows in networks” of G. Ruhe (optimization 16 (1985) 1, 51-61)

First it is shown that the implementation of the algorithm proposed in the considered paper may cause some problems if no further specification is made as to one of its steps. Secondly, such a specification is suggested.     

Partial geometries pg (s, t, 2) with an abelian Singer group and a characterization of the van Lint-Schrijver partial geometry

Let be a proper partial geometry pg(s,t,2), and let G be an abelian group of automorphisms of acting regularly on the points of . Then either t≡2±od s+1 or is a pg(5,5,2) isomorphic to the partial geometry of van Lint and Schrijver (Combinatorica 1 (1981), 63–73). This result is a new step towards the classification of partial geometries with an abelian Singer group and further provides an interesting characterization of the geometry of van Lint and Schrijver.The author is Postdoctoral Fellow of the Fund for Scientific Research Flanders (FWO-Vlaanderen).     

Reliability of a consecutive (r, s)-out-of-(m, n):F lattice system with conditions on the number of failed components in the system

A consecutive(r, s)-out-of-(m, n):F lattice system which is defined as a two-dimensional version of a consecutive k-out-of-n:F system is used as a reliability evaluation model for a sensor system, an X-ray diagnostic system, a pattern search system, etc. This system consists of m × n components arranged like an (m, n) matrix and fails iff the system has an (r, s) submatrix that contains all failed components. In this paper we deal a combined model of a k-out-of-mn:F and a consecutive (r, s)-out-of-(m, n):F lattice system. Namely, the system has one more condition of system down, that is the total number of failed components, in addition to that of a consecutive (r, s)-out-of-(m, n):F lattice system. We present a method to obtain reliability of the system. The proposed method obtains the reliability by using a combinatorial equation that does not depend on the system size. Some numerical examples are presented to show the relationship between component reliability and system reliability.     

The <Emphasis Type="Italic">R</Emphasis>-matrix factorization, <Emphasis Type="Italic">Q</Emphasis>-operator,and variable separation in the case of the XXX spin chain with the <Emphasis Type="Italic">SL</Emphasis>(2, C) symmetry group

We show a connection between the R-matrix factorization, the Baxter Q-operator, and separation of variables in the example of an integrable spin chain with the SL(2, ℂ) symmetry group.     

An extension of a bound for functions in Sobolev spaces,with applications to (<Emphasis Type="Italic">m</Emphasis>, <Emphasis Type="Italic">s</Emphasis>)-spline interpolation and smoothing

Given a function f on a bounded open subset Ω of with a Lipschitz-continuous boundary, we obtain a Sobolev bound involving the values of f at finitely many points of . This result improves previous ones due to Narcowich et al. (Math Comp 74, 743–763, 2005), and Wendland and Rieger (Numer Math 101, 643–662, 2005). We then apply the Sobolev bound to derive error estimates for interpolating and smoothing (m, s)-splines. In the case of smoothing, noisy data as well as exact data are considered.