Using a Table to Make a Generalization

A generalization is a statement that is true about many instances.The following story is aboutmaking a generalization.Francie lives in Phoenix.She has a telephone in her room.She pays for all long-distance callsshe makes.One Sunday she called her cousin Meg in San Diego.As they talked,Francie forgot     

Using Table to Solve a problem

Ｗａｎｇｑｉａｎｇｔｈｏｕｇｈｔｈｅｋｎｅｗｅｖｅｒｙｔｈｉｎｇａｂｏｕｔｄｉａｇｏｎａｌｓａｎｄｐｏｌｙｇｏｎｓ.Ｂｕｔｔｈｉｓｑｕｅｓｔｉｏｎｈａｄｈｉｍｓｔｕｍｐｅｄ :Ｈｏｗｍａｎｙｄｉａｇｏｎａｌｓｄｏｅｓａ 13 ｇｏｎｈａｖｅ ?Ｈｅｒｅａｄｔｈｅｑｕｅｓｔｉｏｎｃａｒｅｆｕｌｌｙ .Ｉｔｗａｓｅａｓｙｔｏｕｎｄｅｒｓｔａｎｄ .Ｈｅｄｒｅｗａｐｉｃｔｕｒｅｏｆａ 13 ｇｉｎ .Ｈｅｓｔａｒｔｅｄｄｒａｗｉｎｇｄｉａｇｏｎａｌｓａｎｄｑｕｉｃｋｌｙｇａｖｅｕｐｔｈｉｓａｐｐｒｏａｃｈ .Ｈｅｔｈｏ…     

Conversion of a rhotrix to a ‘coupled matrix’

In this note, a method of converting a rhotrix to a special form of matrix termed a ‘coupled matrix’ is proposed. The special matrix can be used to solve various problems involving n?×?n and (n?–?1)?×?(n?–?1) matrices simultaneously.     

On Alternating Sequences Relative to a c-Matching of a Hypergraph

In[1], C.Berge has modified Theorem 1 of [2]to a theorem which is a charac-terization of maximum c-Matchings in a hypergraph (see[1], P.416, Theorem 2),and at the same time can be considered as a generalization of Berge's theorem on     

Applying Estimation Techniques to a Bar Graph

Bar graphs are convenient for showing comparisons among items．The bars may be either horizontal or vertical,and they are used to show the amounts of different items．Figure 1 is an example of a typical bar graph．The graph shows the average sales price of existing homes in the Northeast United States for three years——1970,1980,and 1997．     

Applying Estimation Techniques to a Circle Graph

Magazines and newspapers often display information using circle,bar,and line graphs．The following examples illustrate how estimation techniques can be applied to each of these graphs． Circle graphs,also called pie charts,show how a whole quantity is divided into parts．Circle     

Factorizations Orthogonal to a Subgraph in Graphs

ＦａｃｔｏｒｉｚａｔｉｏｎｓＯｒｔｈｏｇｏｎａｌｔｏａＳｕｂｇｒａｐｈｉｎＧｒａｐｈｓＬｉＧｕｏｊｕｎ（李国君）ＬｉｕＧｕｉｚｈｅｎ（刘桂真）（Ｄｅｐｔ．，ｏｆＭａｔｈ．ａｎｄＳｙｓｔｅｍｓＳｃｉｅｎｃｅ，ＳｈａｎｄｏｎｇＵｎｉｖｅｒｓｉｔｙ，Ｊｉｎ...     

Deletion–contraction to form a polymatroid

Let $M$ be a matroid with rank function $r$, and let $e\in E\left(M\right)$. The deletion–contraction polymatroid with rank function $f=r_{M?e}+r_{M/e}$ will be denoted $P_e\left(M\right)$. Notice that $P_e\left(M\right)$ is uniquely determined by $M$ and $e$. Similarly, a deletion–contraction polymatroid determines $M$, unless $e$ is a loop or co-loop. This paper will characterize all polymatroids of this deletion–contraction form by giving the set of excluded minors. Vertigan conjectured that the class of $GF\left(q\right)$-representable deletion–contraction polymatroids is well-quasi-ordered. From this attractive conjecture, both Rota’s Conjecture and the WQO Conjecture for $GF\left(q\right)$-representable matroids would follow.     

When is a centralizer near-ring isomorphic to a matrix near-ring?

Necessary conditions are found for a centralizer near-ring M_A(G) to be isomorphic to a matrix near-ring, where G is a finite group which is cyclic as an M_A(G)-module There are centralizer near-rings which are matrix near-rings. A class of such near-rings is exhibited. Examples of centralizer near-rings which are not matrix near-rings are given.     

What is a Quotient Map with Respect to a Closure Operator?

It is shown that there is no good answer to the question of the title, even if we restrict our attention to S et-based topological categories. Although very closely related, neither the natural notion of c-finality (designed in total analogy to c-initiality) nor the notion of c-quotient (modelled after the behaviour of topological quotient maps) provide universally satisfactory concepts. More dramatically, in the category T op with its natural Kuratowski closure operator k, the class of k-final maps cannot be described as the class of c-quotient maps for any closure operator c, and the class of k-quotients cannot be described as the class of c-final maps for any c. We also discuss the behaviour of c-final maps under crossing with an identity map, as in Whitehead's Theorem. In T op, this gives a new stability theorem for hereditary quotient maps.     

Existence of Positive Solutions to a Fractional-Kirchhoff System

Let Ω be a bounded smooth domain in R^N(N≥3).Assuming that 0 0 are constants,we consider the existence results for positive solutions of a class of fractional elliptic system below,■Under some assumptions of h_i(x,u,v,▽u,▽v)(i=1,2),we get a priori bounds of the positive solutions to the problem(1.1) by the blow-up methods and rescaling argument.Based on these estimates and degree theory,we establis...     

The Isometry of Riemannian Manifold to a Sphere

ＴｈｅＩｓｏｍｅｔｒｙｏｆＲｉｅｍａｎｎｉａｎＭａｎｉｆｏｌｄｔｏａＳｐｈｅｒｅＺｈａｏＰｅｉｂｉａｏ（赵培标）（Ｄｅｐｔ．ｏｆＭａｔｈ．，ＡｎｈｕｉＩｎｓｔｉｔｕｔｅｏｆＦｉｎａｎｃｅ＆Ｔｒａｄｅ，２３３０４１）Ａｂｓｔｒａｃｔ：Ｉｎｔｈｉｓｐａｐ...     

Some Results Related to a Question of Hinkkanen

In this paper, we prove several results concerning meromorphic functions f and g of hyperorder less than one such that f^（j） and g^（j） have the same zeros and poles for j=0, 1, 2. We provide some examples to show that our results are sharp.     

From a Rogers’s identity to overpartitions

In this paper, the author provides an efficient linear recurrence relation for the number of partitions of n into parts not congruent to 0, \(\pm 1\), \(\pm 8\), \(\pm 9\) and \(10 \pmod {20}\). A simple criterion for deciding whether this number is odd or even is given as a corollary of this result. Some results involving overpartitions and partitions into distinct parts have been derived in this context.