Let G be a plane graph and T an even subset of its vertices. It has been conjectured that if all T -cuts of G have the same parity and the size of every T -cut is at least k, then G contains k edge-disjoint T -joins. The case k = 3 is equivalent to the Four Color Theorem, and the cases k = 4, which was conjectured by Seymour, and k = 5 were proved by Guenin. We settle the next open case k = 6.

Diffuse normolipemic plane xanthoma is a rare disorder often seen as a para-neoplastic manifestation accompanied with gammopathies and hematologic disorders. In this report, a 44-year-old man is presented who was referred to us due to developing erythematous papules on the hands and yellow patches on different parts of the body. Based on cell blood count, peripheral blood smear and positive ant...

The Penrose limit is generalized to show that, any leading order solution of the low-energy field equations in any one of the five string theories has a plane wave solution as a limit. This limiting procedure takes into account all the massless fields that may arise and commutes with the T-duality so that any dual solution has again a plane wave limit. The scaling rules used in the limit are un...

Let G be a 3-connected planar graph and let U ⊆ V (G). It is shown that G contains a K2,t minor such that t is large and each vertex of degree 2 in K2,t corresponds to some vertex of U if and only if there is no small face cover of U . This result cannot be extended to 2-connected planar graphs.

background: in general, measurements of solar ultraviolet (uv) radiation are related to horizontal surfaces. while the hu­mans walking and standing outdoors expose to the natural solar uv radiation, their eyes, cheeks, extremities, trunks, or many other anatomical sites are close to vertical plane and random orient to different directions. in this study, we character­ized the diurnal variations...

We consider two families of plane partitions: totally symmetric self-complementary plane partitions (TSSCPPs) and cyclically symmetric transpose complement plane partitions (CSTCPPs). If T (n) and C(n) are the numbers of such plane partitions in a 2n× 2n× 2n box, then ord2(T (n)) = ord2(C(n)) for all n ≥ 1. We also discuss various consequences, along with other results on ord2(T (n)). 2000 Math...

In this paper we provide a novel linear algorithm t o est imate the direction of translation and the normal t o the scene plane, given a stereo pair with known correspondences between the corners in the images. Planar parallax which arises naturally in planar scenes( and can also be defined with respect t o virtual planes), is exploited t o achieve this. Based o n the parallax vectors and the h...

introduction: the purpose of this study was to evaluate vertical facial and dental changes after orthodontic treatment with extraction of first four premolars, and to find whether long facial height could influence the treatment result. methods: fifty-six orthodontic patients with the minimum age of 15, whose treatment plan involved extracting four first premolars, participated in the study. th...

let ? be an open connected subset of the complex plane c and let t be a bounded linear operator on a hilbert space h. for ? in ? let e the orthogonal projection onto the null-space of t-?i . we discuss the necessary and sufficient conditions for the map ?? to b e continuous on ?. a generalized gram- schmidt process is also given.