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 作者：E. C. Nduka 来源：[J].Int. J. Math. Educ. Sci. Technol., 1997, Vol.28 (3), pp.317-320ZBMATH
 作者：Leif Mejlbro 来源：[J].Int. J. Math. Educ. Sci. Technol., 1997, Vol.28 (3), pp.321-331ZBMATH 摘要：In this paper is considered a new and ingenious approach of solving linear differential equations $$d^nx/dt^n+ a_{n-1} (t)d^{n-1} x/dt^{n-1}+ \cdots+ a_1(t)dx/dt +a_0(t)x =f(t),\ t\in I. \tag 1$$ This new method consists in writing the equation (1) in the form $$d/dt \Biggl\{1/p_...  作者：Sergio Invernizzi 来源：[J].Int. J. Math. Educ. Sci. Technol., 1997, Vol.28 (3), pp.357-365ZBMATH 摘要：The author proves that there exist vertical plane C^1 curves such that the classical Newton mechanics based on ordinary differential equations cannot uniquely determine the future motion of a particle sliding down under the effect of gravity. He gives as example a C^1 concave...  作者：M.A. Seoud , M.Z. Youssef 来源：[J].Int. J. Math. Educ. Sci. Technol., 1997, Vol.28 (3), pp.367-371ZBMATH 摘要：A graph G=(V, E) is graceful if there is a function f:V\to \{0,1,\dots,|E|\}, such that each edge \{v,w\}\in E gets a different value for |f(v)-f(w)| from the set \{1,\dots,|E|\}. A graph G= (V,E) is harmonious, if there is an injection f:V\to\text{Z}_m such that th...  作者：G.R. Lindfield , J.E.T. Penny 来源：[J].Int. J. Math. Educ. Sci. Technol., 1997, Vol.28 (3), pp.427-436ZBMATH 摘要：The authors describe some MATLAB functions that allow computations with sparse matrices. This is not a complete description but rather a good didactic introduction to that topic.  作者：David E. Dobbs 来源：[J].Int. J. Math. Educ. Sci. Technol., 1997, Vol.28 (3), pp.447-451ZBMATH 摘要：Working within the Poincar\'e half-plane model for the hyperbolic plane, the author gives in this Classroom Note a short proof that each real number d, such that 0...  作者：Kazuaki Kitahara , Nobuyuki Kemoto , Toshiya Urabe 来源：[J].Int. J. Math. Educ. Sci. Technol., 1997, Vol.28 (3), pp.462-465ZBMATH 摘要：The authors offer a variant of {\it L. Vietoris}' argument [J. Reine Angew. Math. 186, 1-15 (1944; Zbl 0060.19108)] deriving$$f(x+y)=f(x)f(y)-g(x)g(y),$$for real valued functions f,g of a real variable from$$f(x-y)=f(x)f(y)+g(x)g(y) and then claims to show that from these ...
 作者：J\"urgen Gross , G\"otz Trenkler 来源：[J].Int. J. Math. Educ. Sci. Technol., 1997, Vol.28 (3), pp.465-468ZBMATH 摘要：Summary: In this note it is shown that the usual restricted least squares estimator is uniquely determined by two of its properties, namely, (a) it is a projection of the ordinary least squares estimator into the linear manifold generated by the restrictions, and, (b) it has smal...
 作者：A.F. Gilman 来源：[J].Int. J. Math. Educ. Sci. Technol., 1997, Vol.28 (3), pp.468-472ZBMATH 摘要：$x^3+y^3+z^3- 3xyz$ factors as $[(x^2+y^2+z^2)- (xy+xz+yz)] (x+y+z)$. The author takes $m=y-x$, $n=z-y$ and gets $x+y+z= 3x+2m+n$, and the first factor equals $m^2+mn+n^2$. So it is easy to get a solution for $x$ in parameters $m$, $n$ and a power of the prime $p$. The real quest...