A Fuzzy Multi-criteria Outranking Approach in Support of Business Angels’ Decision-Analysis Process for the Assessment of Companies as Investment Opportunities

In this paper, a multi-criteria method is presented for the evaluation and ranking of a selected set of companies as investment opportunities in aid of the relevant decision-analysis process of business angels. The multi-criteria methodology is based on the PROMETHEE method, which is further extended to deal with fuzzy input data in order to address the data imprecision and uncertainty of the decision process. The paper concludes by suggesting a web-based system implementation of the proposed methodology, which will significantly enhance modern business angels networks.     

Measuring the Student Group Capacity for Obtaining Geometric Information in the van Hiele Developmental Thought Process：A Fuzzy Approach

1　 IntroductionThe van Hiele level theory of geometric reasoning[1,5,9] describes the ways of studentreasoning inEuclidean geometry.The ontogeny of thiscognitive activity of mental developmentis characterised byfive hierarchical and qualitatively differe…     

A D’Alembert Formula for Flat Surfaces in the 3-Sphere

We find all the flat surfaces in the unit 3-sphere $\mathbb{S}^{3}We find all the flat surfaces in the unit 3-sphere that pass through a given regular curve of with a prescribed tangent plane distribution along this curve. The formula that solves this problem may be seen as a geometric analogue of the classical D’Alembert formula that solves the Cauchy problem for the homogeneous wave equation. We also provide several applications of this geometric D’Alembert formula, including a classification of the flat M?bius strips of  .      

A New Regularity Criterion in Terms of the Direction of the Velocity for the MHD Equations

In this paper we obtain a new regularity criterion for weak solutions to the 3D MHD equations. It is proved that if div( \fracu|u|) \mathrm{div}( \frac{u}{|u|}) belongs to L^\frac21-r( 0,T;[(X)\dot]_r( \mathbbR³) ) L^{\frac{2}{1-r}}( 0,T;\dot{X}_{r}( \mathbb{R}^{3}) ) with 0≤r≤1, then the weak solution actually is regular and unique.     

Validity of Whitham’s Equations for the Modulation of Periodic Traveling Waves in the NLS Equation

We prove that slow modulations in time and space of periodic wave trains of the NLS equation can be approximated via solutions of Whitham’s equations associated with the wave train. The error estimates are based on a suitable choice of polar coordinates, a Cauchy–Kowalevskaya-like existence and uniqueness theorem, and energy estimates.     

A New Research of the ＇Most Reasonable Region＇ for VA Objects in Value Analysis

ＡＮｅｗＲｅｓｅａｒｃｈｏｆｔｈｅ＇ＭｏｓｔＲｅａｓｏｎａｂｌｅＲｅｇｉｏｎ＇ｆｏｒＶＡＯｂｊｅｃｔｓｉｎＶａｌｕｅＡｎａｌｙｓｉｓ￥ＳｕｎＬｉａｎｚｈｉ（孙连志）（Ｆｉｓｃａｌ＆ＦｉｎａｎｃｉａｌＤｅｐａｒｔｍｅｎｔｏｆＨｅｎａｎＵｎｉｖｅｒｓｉｔ...     

On the Performance of Managers and Controllers: A Polymatrix Game Approach for the Manager–Controller–Board of Directors’ Conflict

In this article, we focus on the conflict among the manager, the controller and the board of directors of a company. We model the problem as a three-player polymatrix game. Under a set of assumptions, we identify five potential Nash equilibria. We prove that the Nash equilibrium is unique, despite its changing structure. Next, we analyze the influence of the manager’s and controller’s bonuses and penalties on the Nash equilibria. Finally, we explain how the manager and the controller may decrease or maintain their performance, when their bonuses or penalties increase.     

A criterion for the unique solvability of the dirichlet spectral problem in a cylindrical domain for a multidimensional Lavrent’ev-Bitsadze equation

We obtain a criterion for the unique solvability of the spectral problem in a cylindrical domain for a multidimensional Lavrent’ev-Bitsadze equation.     

A good foundation for number learning for five-year-olds? An evaluation of the English Early Learning ‘Numbers’ Goal in the light of research

This article sets out to evaluate the English Early Years Foundation Stage Goal for Numbers, in relation to research evidence. The Goal, which sets out to provide ‘a good foundation in mathematics’, has greater breadth of content and higher levels of difficulty than previous versions. Research suggests that the additional expectations are unachievable by the majority of rising fives, but that a more effective foundation to ensure progress and prevent later difficulties would prioritise number sense with numbers to 10, including subitising, numeral comprehension, relative number size, one more/less than and part–whole relationships.     

A. D. Alexandrov’s problem for non-positively curved spaces in the sense of Busemann

This paper is the last of a series devoted to the solution of Alexandrov’s problem for non-positively curved spaces. Here we study non-positively curved spaces in the sense of Busemann. We prove that isometries of a geodesically complete connected at infinity proper Busemann space X are characterized as follows: If a bijection f: X → X and its inverse f ⁻¹ preserve distance 1, then f is an isometry.     

Two difference schemes for the numerical solution of Maxwell’s equations as applied to extremely and super low frequency signal propagation in the Earth-ionosphere waveguide

Two explicit two-time-level difference schemes for the numerical solution of Maxwell’s equations are proposed to simulate propagation of small-amplitude extremely and super low frequency electromagnetic signals (200 Hz and lower) in the Earth-ionosphere waveguide with allowance for the tensor conductivity of the ionosphere. Both schemes rely on a new approach to time approximation, specifically, on Maxwell’s equations represented in integral form with respect to time. The spatial derivatives in both schemes are approximated to fourth-order accuracy. The first scheme uses field equations and is second-order accurate in time. The second scheme uses potential equations and is fourth-order accurate in time. Comparative test computations show that the schemes have a number of important advantages over those based on finite-difference approximations of time derivatives. Additionally, the potential scheme is shown to possess better properties than the field scheme.     

Special functions in academician A.A. Dorodnicyn’s scientific legacy: Special functions arising in the solution of boundary value problems for second-order singular ordinary differential equations by asymptotic methods

On the occasion of the centenary of Academician A.A. Dorodnicyn’s birth, his main results concerning asymptotic methods for solving second-order singular ordinary differential equations and special functions related to these equations are presented (with certain corrections and additions).     

A geometric approach to Euler’s addition formula A direct formulation of the addition law for elliptic curves given in?terms of Weierstra? quartics

Plane quartic curves given by equations of the form y ²=P(x) with polynomials P of degree 4 represent singular models of elliptic curves which are directly related to elliptic integrals in the form studied by Euler and for which he developed his famous addition formulas. For cubic curves, the well-known secant and tangent construction establishes an immediate connection of addition formulas for the corresponding elliptic integrals with the structure of an algebraic group. The situation for quartic curves is considerably more complicated due to the presence of the singularity. We present a geometric construction, similar in spirit to the secant method for cubic curves, which defines an addition law on a quartic elliptic curve given by rational functions. Furthermore, we show how this addition on the curve itself corresponds to the addition in the (generalized) Jacobian variety of the curve, and we show how any addition formula for elliptic integrals of the form ò(1/?{P(x)}) dx\int (1/\sqrt{P(x)})\,\mathrm{d}x with a quartic polynomial P can be derived directly from this addition law.