A popular question in recreational mathematics is the following: If we drop a spaghetti noodle and it breaks at two random places, what is the probability that we can form a triangle with the three resulting segments? See for example [2, chap.1, sec.6], [3, p.6], [4, p.31], or [7, p.30-36]. This is an elementary problem in geometric probability. Clearly the length of the noodle (or equivalently...

In general, a physical system consists of a finite or infinite number of degrees of freedom which may or may not interact. The dynamics is prescribed by a set of evolution equations which follow from varying the action with respect to the different degrees of freedom. A symmetry then corresponds to a group of transformations on the space time coordinates and/or the degrees of freedom that leave...

We present and discuss the properties and the main results of a cosmological model with a spontaneously-broken chiral symmetry. The model contains and relates dynamically, two spin-zero fields. The scalar field can provide the dynamical basis for inflation in the early universe. The pseudoscalar, Goldstone field can provide an early, small residual vacuum energy density, the absolute value of w...

Given a matroid M represented by a linear subspace L ⊂ C (equivalently by an arrangement of n hyperplanes in L), we define a graded ring R(L) which degenerates to the Stanley-Reisner ring of the broken circuit complex for any choice of ordering of the ground set. In particular, R(L) is Cohen-Macaulay, and may be used to compute the h-vector of the broken circuit complex of M . We give a geometr...

Fig. 2: Illustration of the shift distance of the water peaks between 23.5 and 39.5 °C (0.095 ppm) adjusted by Cr/PCr at 3.02 ppm as temperature independent reference. Due to the excessive intensity of water the other resonances were presented with a magnification factor of 1500. Fig. 3: Correlation between temperature and chemical shift distance of the H2O signal compared to tCho (a) and Cr/PC...

As an important algorithm, dilate algorithm can give us more connective view of a remote sensing image which has broken lines or objects. However, with the technological progress of satellite sensor, the resolution of remote sensing image has been increasing and its data quantities become very large. This would lead to the decrease of algorithm running speed or cannot obtain a result in limited...

A cytotoxic T lymphocyte (CTL) clone generated in vitro from the peripheral blood of a healthy HLA-A2-positive individual against a synthetic p53 protein-derived wild-type peptide (L9V) was shown to kill squamous carcinoma cell lines derived from two head and neck carcinomas, which expressed mutant p53 genes, in a L9V/HLA-A2 specific and restricted fashion. Thus, the normal tolerance against en...