‎Let $X=left(‎ ‎begin{array}{llll}‎ ‎ x_1 & ldots & x_{n-1}& x_n\‎ ‎ x_2& ldots & x_n & x_{n+1}‎ ‎end{array}right)$ be the Hankel matrix of size $2times n$ and let $G$ be a closed graph on the vertex set $[n].$ We study the binomial ideal $I_Gsubset K[x_1,ldots,x_{n+1}]$ which is generated by all the $2$-minors of $X$ which correspond to the edges of $G.$ We show that $I_G$ is Cohen-Macaula...

A universal Gröbner basis of an ideal is the union of all its reduced Gröbner bases. It is contained in the Graver basis, the set of all primitive elements. Obtaining an explicit description of either of these sets, or even a sharp degree bound for their elements, is a nontrivial task. In their ’95 paper, Graham, Diaconis and Sturmfels give a nice combinatorial description of the Graver basis f...

‎let $x=left(‎ ‎begin{array}{llll}‎ ‎ x_1 & ldots & x_{n-1}& x_n‎ ‎ x_2& ldots & x_n & x_{n+1}‎ ‎end{array}right)$ be the hankel matrix of size $2times n$ and let $g$ be a closed graph on the vertex set $[n].$ we study the binomial ideal $i_gsubset k[x_1,ldots,x_{n+1}]$ which is generated by all the $2$-minors of $x$ which correspond to the edges of $g.$ we show that...

The scroll wraps of a scroll compressor play a very important role in the compressor’s efficiency due to their impact on leakage and leakage irreversibilities. In this work, a short summary of the scroll compressor geometry is presented. Using the geometry of the scroll wraps, an optimal scroll wrap geometry is derived for a given set of constraints on compressor displacement, scroll wrap thick...

Mound formation in the cellular slime mould Dictyostelium results from the chemotactic aggregation of competent cells. Periodic cAMP signals propagate as multiarmed spiral waves and coordinate the movement of the cells. In the late aggregate stage the cells differentiate into prespore and several prestalk cell types. Prestalk cells sort out chemotactically to form the tip, which then controls a...

Improvement of compressor efficiency using the alternative refrigerant is demanded strongly to reduce CO2 emission, which causes the global warming. Especially the compressor using in frozen temperature level has long lifetime, and the correspondence to above-mentioned is one of the most important subjects. The scroll compressor is the promising structure to solve this problem. A technical poin...

A well-known conjecture asserts that smooth threefolds X ⊂ P5 are quadratically normal with the only exception of the Palatini scroll. As a corollary of a more general statement we obtain the following result, which is related to the previous conjecture: If X ⊂ P5 is not quadratically normal, then its triple curve is reducible.

Here we give upper bounds for the degrees of generators of the homogeneous ideal of a suitable unreduced scheme Z ⊂ P n. Here we take as Z a disjoint union of fat points or of multiple structures on linear subspaces or we take as Zred a subscheme of a smooth curve or a scroll. The actors in this paper are unreduced subschemes (or ”fattening”) of P n with connected components which are fattening...

The efficiency of the scroll compressor which employs the axial and the radial sealing techniques is competitive with that of the other rotary and the reciprocating compressors. The bearing load and the torque are smooth so that quiet operation is realized. 'l'herefore the machine is suitable particularly for air conditioning application. The authors have studied the scroll compressor which uti...