A new computational method for solving two‐dimensional Stratonovich Volterra integral equation

This paper presents a method for computing numerical solutions of two‐dimensional Stratonovich Volterra integral equations using one‐dimensional modification of hat functions and two‐dimensional modification of hat functions. The problem is transformed to a linear system of algebraic equations using the operational matrix associated with one‐dimensional modification of hat functions and two‐dimensional modification of hat functions. The error analysis of the method is given. The method is computationally attractive, and applications are demonstrated by a numerical example. Copyright © 2017 John Wiley & Sons, Ltd.     

A Note on Convex Reformulation Schemes for Mixed Integer Quadratic Programs

This paper examines a convex reformulation scheme for mixed integer quadratic programs, which was recently developed in the literature. A modification to the scheme, based on a linear transformation, is presented. The modification improves performance for problems which have more continuous variables than integer variables. Numerical results are presented showing the effectiveness of the modification.     

King type modification of Meyer-König and Zeller operators based on the -integers

In the present paper, introducing a King type modification of the Meyer-König and Zeller (MKZ) operators, we prove that the error estimation of these operators is better than the classical MKZ operators. Furthermore, a King type modification of the q-MKZ is also introduced and the rate of convergence of this modification is examined.     

Supplement: Efficient weak second order stochastic Runge-Kutta methods for non-commutative Stratonovich stochastic differential equations

This paper gives a modification of a class of stochastic Runge-Kutta methods proposed in a paper by Komori (2007). The slight modification can reduce the computational costs of the methods significantly.     

Cost estimation algorithm and decision-making model for curriculum modification in educational organization

The decision about curriculum modification usually takes place at the knowledge level, mainly with consideration of individual academic staff competences and qualifications. However, traditional approaches to cost estimation of curriculum modification are focused on material resources only. In this paper we present a cost estimation method and decision model for curriculum modification in educational organizations. The proposed method works at the knowledge level and employs competence sets as knowledge representation models in educational organizations. Authors used the theory of hierarchical, multilevel systems in order to define the model of the decision-making process of curriculum modification and its dimension. Basing on this and also using a fuzzy competence model the cost estimation algorithm in the form of a group competences expansion algorithm is proposed. The algorithm focuses on the cost of staff competence expansion caused by the knowledge development process.     

A new modification of the variational iteration method for van der Pol equations

In this paper, we provide a new modification of the variational iteration method (MVIM) for solving van der Pol equations. The modification couples the classical variational iteration method with He’s polynomials, where the He’s polynomials are applied to the approximate solution and the initial condition to eliminate secular terms. For the large ?, the numerical results demonstrate that the modification method get an accurate approximate period than the other presented methods.     

On lattice embeddings of a lattice into its intervals

The notion of idempotent modification of an algebra was introduced by Ježek; he proved that the idempotent modification of a group is always subdirectly irreducible. In the present note we show that the idempotent modification of a generalized MV -algebra having more than two elements is directly irreducible if and only if there exists an element in A which fails to be boolean. Some further results on idempotent modifications are also proved.     

Modified Taylor approximation of functions with periodic behaviour

We approximate a function with periodic behaviour by means of a small modification of its Taylor polynomial. This modification is based on the work of Scheifele and will simplify the construction of special numerical methods for differential equations with near periodic solutions.     

The Nash modification and hyperplane sections on surfaces

We prove that the planar components of the tangent cone of a complex analytic surface at a point correspond to the base points of hyperplane sections by the Nash modification. This correspondence is then used to characterize domination relations between the normalized Nash modification and the normalized blow-up of a point.     

On idempotent modifications of generalized <Emphasis Type="Italic">MV</Emphasis>-algebras

The notion of idempotent modification of an algebra was introduced by Je?ek; he proved that the idempotent modification of a group is always subdirectly irreducible. In the present note we show that the idempotent modification of a generalized MV -algebra having more than two elements is directly irreducible if and only if there exists an element in A which fails to be boolean. Some further results on idempotent modifications are also proved.     

Une amelioration de la methode de Dijkstra pour la recherche d'un plus court chemin dans un reseau

A slight modification of Dijkstra's original method is presented. If a lower bound on the length of the shortest path between two nodes of a network is known, this modification allows to save up to 35% of the computing time which would be required for the original method.     

Compound modification of globoidal worm drive with variable parameters

The meshing theory is built for the globoidal worm drive systematically. Several modification parameters, including the center distance, the transmitting ratio and the height of the cutter frame, are taken into account concurrently and they are all variable. Many types of modification in the foregoing study can be viewed as the special cases of this work. A new method is proposed to obtain the velocity ratio modification function. The height modification function is recommended to adopt a linear function, whose coefficients may be determined by the trial method. The meshing function of the worm pair is deduced by virtue of the vector rotation approach. In the case of the modification with single constant parameter, the classification standard of the drive type is proved strictly. The computing methods of the contact zone, the contact line, and the instantaneous meshing point are expounded explicitly. The reason why a globoidal worm drive can implement the double-line contact between the teeth is uncovered clearly. The reason why a modified globoidal worm gearing can shun the curvature interference is discovered. The comparative researches on the mesh characters of the diverse modified drives are implemented adequately. Some kinds of the modified drive, containing the compound modified drive with variable parameters, are recommended to be utilized in practice for the excellent mesh performances.     

Iterative algorithm for the inverse problem of electrocardiography in a medium with piecewise-constant electrical conductivity

The article presents a modification of the algorithm for the inverse problem of electrocardiography originally proposed in [6]. The modification is intended to improve the computation accuracy and to reduce the computing time.     

The local asymptotic minimax adaptive property of a recursive estimate

A locally asymptotically normal estiamtion problem generated by independent and identically distributed generalized random variables is considered. A recursive estimate based on a stochastic approximation method, a modification of an estimate proposed by Sakrison, is shown to be locally asymptotically minimax. For a nonparametric generalization of the estimation problem, a modification of the estimate is shown locally asymptotically minimax adaptive.     

Different types of solutions to a multivalued model of granular flow

We deal with a modification of the Savage–Hutter model describing granular material with multivalued friction force. The multivalued structure of this model requires a modification of known definitions of a solution. The connections between definitions of three different types of solutions: entropy, measure‐valued and kinetic are shown. Copyright © 2013 John Wiley & Sons, Ltd.     

Time Regularity of Generalized Ornstein–Uhlenbeck Processes with Lévy Noises in Hilbert Spaces

In this paper we first obtain a necessary condition for \(H\)-càdlàg modification and \(H\)-weakly càdlàg modification of generalized Ornstein–Uhlenbeck processes with Lévy noises in Hilbert spaces \(H\). Then we give a necessary and sufficient condition for the \(H\)-càdlàg modification and \(H\)-weakly càdlàg modification of Ornstein–Uhlenbeck processes driven by cylindrical \(\alpha \)-semistable processes. Secondly, we investigate the properties of cylindrical càdlàg modification and \(V\)-cylindrical càdlàg modification. Applying the obtained results to diagonal Ornstein–Uhlenbeck processes with \(\alpha \)-stable noises, we show a necessary and sufficient condition for cylindrical càdlàg modification and \(V\)-cylindrical càdlàg modification in the symmetric case for \(\alpha \in (0,1)\) and give a sufficient condition in the general case for \(\alpha \in (0,2)\). Some examples illustrate the relations among the concepts of various càdlàg modifications.     

A note on De Vylder's method of estimation of IBNR claims

De Vylder's method of estimation of IBNR claims precludes consideration of independently established trends. A modification of this method is suggested by means of which an actuary would, in certain cases, combine a suspected trend with the available data to estimate IBNR claims. A numerical example is provided to demonstrate this modification.     

Stabilization of Cowell's method

This paper offers a modification of the Cowell method for the integration of orbits. The modification is characterized by the property that it will integrate unperturbed Kepler motion exactly (excluding truncation errors), thus the slight instability of the Cowell Method is avoided. Furthermore, the modification takes into account the most important secular effects of orbit motion. As an example of the applicability of the modified method to perturbed motion, the equations of motion of an artificial earth satellite are integrated. In the case of elliptic initial conditions regularization by a Levi-Civita transformation was used.Visiting Professor from Institut für Angewandte Mathematik, Eidgenössische Technische Hochschule, Zurich, Switzerland.     

Local transformations of hexahedral meshes of lower valence

The modification of conforming hexahedral meshes is difficult to perform since their structure does not allow easy local refinement or un-refinement such that the modification does not go through the boundary. In this paper we prove that the set of hex flipping transformations of Bern et al. (2002) [1] is the only possible local modification on a geometrical hex mesh of valence less than five i.e., with less than five edges per vertex. We propose a new basis of transformations that can generate sequences of local modifications on hex meshes of valence less than six. For quadrilateral meshes, we show the equivalence between modifying locally the number of quads on a mesh and the number of its internal vertices.