Precision Measurement of the Ds∗+−Ds+D_s^{*+}- D_s^+ Mass Difference

We have measured the vector-pseudoscalar mass splitting $M(D_s^{*+})-M(D_s^+) = 144.22\pm 0.47\pm 0.37 MeV$, significantly more precise than the previous world average. We minimize the systematic errors by also measuring the vector-pseudoscalar mass difference $M(D^{*0})-M(D^0)$ using the radiative decay $D^{*0}\rightarrow D^0\gamma$, obtaining $[M(D_s^{*+})-M(D_s^+)]-[M(D^{*0})-M(D^0)] = 2.09\pm 0.47\pm 0.37 MeV$. This is then combined with our previous high-precision measurement of $M(D^{*0})-M(D^0)$, which used the decay $D^{*0}\rightarrow D^0\pi^0$. We also measure the mass difference $M(D_s^+)-M(D^+)=99.5\pm 0.6\pm 0.3$ MeV, using the $\phi\pi^+$ decay modes of the $D_s^+$ and $D^+$ mesons.Comment: 18 pages uuencoded compressed postscript (process with uudecode then gunzip). hardcopies with figures can be obtained by sending mail to: [email protected]

D-branes from M-branes

The 2-brane and 4-brane solutions of ten dimensional IIA supergravity have a dual interpretation as Dirichlet-branes, or `D-branes', of type IIA superstring theory and as `M-branes' of an $S^1$-compactified eleven dimensional supermembrane theory, or M-theory. This eleven-dimensional connection is used to determine the ten-dimensional Lorentz covariant worldvolume action for the Dirichlet super 2-brane, and its coupling to background spacetime fields. It is further used to show that the 2-brane can carry the Ramond-Ramond charge of the Dirichlet 0-brane as a topological charge, and an interpretation of the 2-brane as a 0-brane condensate is suggested. Similar results are found for the Dirichlet 4-brane via its interpretation as a double-dimensional reduction of the eleven-dimensional fivebrane. It is suggested that the latter be interpreted as a D-brane of an open eleven-dimensional supermembrane.Comment: Version to appear in Physics Letters B. Incorporates minor revisions to previous revised version. 16 p

Equitable (d,m)(d,m)-edge designs

The paper addresses design of experiments for classifying the input factors of a multi-variate function into negligible, linear and other (non-linear/interaction) factors. We give constructive procedures for completing the definition of the clustered designs proposed Morris 1991, that become defined for arbitrary number of input factors and desired clusters' multiplicity. Our work is based on a representation of subgraphs of the hyper-cube by polynomials that allows the formal verification of the designs' properties. Ability to generate these designs in a systematic manner opens new perspectives for the characterisation of the behaviour of the function's derivatives over the input space that may offer increased discrimination

Resolutions of ideals of fat points with support in a hyperplane

Our results concern minimal graded free resolutions of fat point ideals for points in a hyperplane. Suppose, for example, that I(m,d) is the ideal defining r given points of multiplicity m in the projective space P^d. Assume that the given points lie in a hyperplane P^{d-1} in P^d, and that the ground field k is algebraically closed of characteristic 0. We give an explicit minimal graded free resolution of I(m,d) in k[P^d] in terms of the minimal graded free resolutions of the ideals I(j,d-1) in k[P^{d-1}] with j < m+1. As a corollary, we give the following formula for the Poincare polynomial P_{m,d} of I(m,d) in terms of the Poincare polynomials P_{j,d-1} of I(j,d-1): P_{m,d} = (1 + XT)(\Sigma_{0<j\le m} T^{m-j}(P_{j,d-1} - 1)) + 1 + XT^m.Comment: 10 pages; to appear in Proc. Amer. Math. Soc.; some expositional changes; added a reference to paper of Geramita, Migliore and Sabourin (math.AC/0411445

Эволюция интерпретации термина "рекламное издание" в Беларуси и России

Статья посвящена установлению четкого и емкого определения термина «рекламное издание» в Беларуси и России. Проанализировано 36 нормативных, научных, практических, учебных, справочных изданий, выпущенных с 1890 по 2015 г. Описана эволюция взглядов на интерпретацию понятий «реклама», «рекламное издание» в белорусских и российских источниках. Выделены основные подходы к определению термина «рекламное издание»: использующегося в официальных и нормативных источниках, базирующегося на исследованиях А. Э. Мильчина. Установлена максимально полная дефиниция термина «рекламное издание» в нормативно-законодательной, научно-исследовательской, профессиональной, общественной среде в Беларуси и России, выявлены сходства (рекламным изданием может считаться издание, зарегистрированное в качестве специализированного для размещения (распространения) рекламы и содержащее рекламные материалы, цель которых — создание спроса на объекты рекламирования, информирование о них, форма подачи рекламных материалов — привлекающая внимание, краткая, легко запоминающаяся, расположение рекламных материалов — в зависимости от концепции издания) и отличия (сводятся к процентному объему рекламных материалов в одном выпуске издания. В Республике Беларусь содержание рекламных материалов для зарегистрированных государственных рекламных изданий может составлять 25% и более, для иных периодических изданий — 30% и более объема номера. В Российской Федерации объем рекламных материалов в зарегистрированных рекламных периодических печатных изданиях может составлять 40% и более объема одного номера. Издания, не зарегистрированные в качестве рекламных, не могут превышать указанный объем рекламных сообщений

The smallest sets of points not determined by their X-rays

Let $F$ be an $n$-point set in $\mathbb{K}^d$ with $\mathbb{K}\in\{\mathbb{R},\mathbb{Z}\}$ and $d\geq 2$. A (discrete) X-ray of $F$ in direction $s$ gives the number of points of $F$ on each line parallel to $s$. We define $\psi_{\mathbb{K}^d}(m)$ as the minimum number $n$ for which there exist $m$ directions $s_1,...,s_m$ (pairwise linearly independent and spanning $\mathbb{R}^d$) such that two $n$-point sets in $\mathbb{K}^d$ exist that have the same X-rays in these directions. The bound $\psi_{\mathbb{Z}^d}(m)\leq 2^{m-1}$ has been observed many times in the literature. In this note we show $\psi_{\mathbb{K}^d}(m)=O(m^{d+1+\varepsilon})$ for $\varepsilon>0$. For the cases $\mathbb{K}^d=\mathbb{Z}^d$ and $\mathbb{K}^d=\mathbb{R}^d$, $d>2$, this represents the first upper bound on $\psi_{\mathbb{K}^d}(m)$ that is polynomial in $m$. As a corollary we derive bounds on the sizes of solutions to both the classical and two-dimensional Prouhet-Tarry-Escott problem. Additionally, we establish lower bounds on $\psi_{\mathbb{K}^d}$ that enable us to prove a strengthened version of R\'enyi's theorem for points in $\mathbb{Z}^2$