Curves in R^d intersecting every hyperplane at most d+1 times

By a curve in R^d we mean a continuous map gamma:I -> R^d, where I is a closed interval. We call a curve gamma in R^d at most k crossing if it intersects every hyperplane at most k times (counted with multiplicity). The at most d crossing curves in R^d are often called convex curves and they form an important class; a primary example is the moment curve {(t,t^2,...,t^d):t\in[0,1]}. They are also closely related to Chebyshev systems, which is a notion of considerable importance, e.g., in approximation theory. We prove that for every d there is M=M(d) such that every at most d+1 crossing curve in R^d can be subdivided into at most M convex curves. As a consequence, based on the work of Elias, Roldan, Safernova, and the second author, we obtain an essentially tight lower bound for a geometric Ramsey-type problem in R^d concerning order-type homogeneous sequences of points, investigated in several previous papers.Comment: Corrected proof of Lemma 3.

Track Layouts of Graphs

A \emph{$(k,t)$-track layout} of a graph $G$ consists of a (proper) vertex $t$-colouring of $G$, a total order of each vertex colour class, and a (non-proper) edge $k$-colouring such that between each pair of colour classes no two monochromatic edges cross. This structure has recently arisen in the study of three-dimensional graph drawings. This paper presents the beginnings of a theory of track layouts. First we determine the maximum number of edges in a $(k,t)$-track layout, and show how to colour the edges given fixed linear orderings of the vertex colour classes. We then describe methods for the manipulation of track layouts. For example, we show how to decrease the number of edge colours in a track layout at the expense of increasing the number of tracks, and vice versa. We then study the relationship between track layouts and other models of graph layout, namely stack and queue layouts, and geometric thickness. One of our principle results is that the queue-number and track-number of a graph are tied, in the sense that one is bounded by a function of the other. As corollaries we prove that acyclic chromatic number is bounded by both queue-number and stack-number. Finally we consider track layouts of planar graphs. While it is an open problem whether planar graphs have bounded track-number, we prove bounds on the track-number of outerplanar graphs, and give the best known lower bound on the track-number of planar graphs.Comment: The paper is submitted for publication. Preliminary draft appeared as Technical Report TR-2003-07, School of Computer Science, Carleton University, Ottawa, Canad

Development of Financial Intermediation and the Dynamics of Rural-Urban Inequality: China, 1978-98

housing, transportation, planning, coordination, reform, equity, justice, inequality, central banks, China

Effect of hydroalcoholic Zingiber extract on creatinine and blood urea nitrogen (BUN) of mice.

چکیده: زمینه و هدف: اکثر جمعیت جهان به خصوص در کشورهای در حال توسعه، برای احتیاجات اساسی بهداشتی خود از داروهای گیاهی استفاده می کنند. زنجبیل (Zingiber officinale Roscoe) یک چاشنی غذایی می باشد که از دو هزار سال پیش به عنوان دارو در طب چینی، پزشکی سنتی ایران و طب اسلامی استفاده شده است. از آنجایی که افزایش اوره سرم و سطوح کرآتینین در آزمایش های کلینیکی بیانگر نارسایی کلیوی می باشد، این مطالعه با هدف بررسی تأثیر عصاره هیدروالکلی زنجبیل بر نیتروژن اوره خون و کرآتینین به منظور ارزیابی عملکرد کلیه انجام شد. روش بررسی: در یک مطالعه تجربی عصاره هیدروالکلی زنجبیل به صورت یک روز در میان در یک دوره 20 روزه با دوزهای 10، 20 و 40 میلی گرم بر کیلوگرم در 48 ساعت به صورت داخل صفاقی به موشهای نر آزمایشگاهی تزریق شد. سپس خونگیری با استفاده از روش پانکسیون سینوس چشمی انجام و میزان نیتروژن اوره خون (BUN) و کراتینین اندازه گیری شد. داده ها با استفاده از آزمون های آنالیز واریانس یک طرفه و کروسکال والیس تجزیه و تحلیل شد. یافته ها: میانگین غلظت BUN در گروه کنترل 89/3±68/37 و در گروههای دریافت کننده 10، 20 و 40 میلی گرم بر کیلوگرم در 48 ساعت زنجبیل به ترتیب 38/11±54/21 (05/0