An Enumeration of Certain Projective Ternary Two‐Weight Codes

We detail the enumeration of all two‐intersection sets of the five‐dimensional projective space over the field of order 3 that are invariant under an element of order 7, which include the examples of Hill (1973) and Gulliver (1996). Up to projective equivalence, there are 6,635 such two‐intersection sets.     

Bunny hops: using multiplicities of zeroes in calculus for graphing

Students learn a lot of material in each mathematics course they take. However, they are not always able to make meaningful connections between content in successive mathematics courses. This paper reports on a technique to address a common topic in calculus I courses (intervals of increase/decrease and concave up/down) while also making use of students’ pre-existing knowledge about the behaviour of functions around zeroes based on multiplicities.     

A speciality theorem for curves in P<Superscript>5</Superscript>

Let be an integral projective curve. One defines the speciality index e(C) of C as the maximal integer t such that , where ω _C denotes the dualizing sheaf of . Extending a classical result of Halphen concerning the speciality of a space curve, in the present paper we prove that if is an integral degree d curve not contained in any surface of degree  < s, in any threefold of degree  < t, and in any fourfold of degree  < u, and if , then Moreover equality holds if and only if C is a complete intersection of hypersurfaces of degrees u, , and . We give also some partial results in the general case , .      

Counting solutions to binomial complete intersections

We study the problem of counting the total number of affine solutions of a system of n binomials in n   variables over an algebraically closed field of characteristic zero. We show that we may decide in polynomial time if that number is finite. We give a combinatorial formula for computing the total number of affine solutions (with or without multiplicity) from which we deduce that this counting problem is #P$\#P$-complete. We discuss special cases in which this formula may be computed in polynomial time; in particular, this is true for generic exponent vectors.     

Closed manifolds coming from Artinian complete intersections

We reformulate the integrality property of the Poincaré inner product in the middle dimension, for an arbitrary Poincaré -algebra, in classical terms (discriminant and local invariants). When the algebra is -connected, we show that this property is the only obstruction to realizing it by a smooth closed manifold, in dimension . We analyse the homogeneous artinian complete intersections over realized by smooth closed manifolds of dimension , and their signatures.

     

A computer model of pulse wave and input impedance in human arteries

To predict the propagation of pressure and flow pulses in arterial system and the variation of vascular input impedance, a branched and tapered tube model is studied through one-dimensional transient flow analysis. Coupling the continuity and momentum equations yields a group of quasilinear hyperbolic partial differential equations which can be solved numerically by using the method of characteristics. Several boundary conditions of the arterial system are also simplified suitably. The propagation of the pulses of the arterial system and the vascular input impedance is calculated on computer by using the dimensions and the physiological data of the arterial system. The results point out that the pressure and flow pulses of the arterial system and the vascular input impedance produced by this theoretical model is consistent quite well with the experimental results published.     

多个CCD交汇测量系统的理论研究

本文介绍了采用多个线阵ＣＣＤ 组成交汇测量系统的基本原理,导出了测量坐标的计算公式,并利用有关的误差理论对该方法的测量精度进行了详细分析。研究结果表明,多个ＣＣＤ 交汇测量系统能够得到较高的目标捕获几率,同时还能有效地提高坐标测量精度。对大靶面、高速小目标物体的精密测量具有重要意义