‎a $mu$-way $(v,k,t)$ $trade$ of volume $m$ consists of $mu$‎ ‎disjoint collections $t_1$‎, ‎$t_2‎, ‎dots t_{mu}$‎, ‎each of $m$‎ ‎blocks‎, ‎such that for every $t$-subset of $v$-set $v$ the number of‎ ‎blocks containing this t-subset is the same in each $t_i (1leq‎ ‎i leq mu)$‎. ‎in other words any pair of collections ${t_i,t_j}$‎, ‎$1leq i< j leq mu‎$ is a $(v,k,t)$ trade of volume $m$. in th...

‎A $mu$-way $(v,k,t)$ $trade$ of volume $m$ consists of $mu$‎ ‎disjoint collections $T_1$‎, ‎$T_2‎, ‎dots T_{mu}$‎, ‎each of $m$‎ ‎blocks‎, ‎such that for every $t$-subset of $v$-set $V$ the number of‎ ‎blocks containing this t-subset is the same in each $T_i (1leq‎ ‎i leq mu)$‎. ‎In other words any pair of collections ${T_i,T_j}$‎, ‎$1leq i< j leq mu‎$ is a $(v,k,t)$ trade of volume $m$. In th...

Presheaf models [Osius, 1975, Fourman and Scott, 1979, Moerdijk and Mac Lane, 1992] are a simple generalization of Kripke models and provide one of the most natural semantics for intuitionistic predicate logic. Although a completeness result for this semantics is known, this is usually obtained either non-constructively, by defining a canonical Kripke model, or indirectly, e.g. via categorical ...

‎for a given measure space $(x,{mathscr b},mu)$ we construct all measure spaces $(y,{mathscr c},lambda)$ in which $(x,{mathscr b},mu)$ is embeddable‎. ‎the construction is modeled on the ultrafilter construction of the stone--v{c}ech compactification of a completely regular topological space‎. ‎under certain conditions the construction simplifies‎. ‎examples are given when this simplification o...

let $k$ be a positive integer. a subset $s$ of $v(g)$ in a graph $g$ is a $k$-tuple total dominating set of $g$ if every vertex of $g$ has at least $k$ neighbors in $s$. the $k$-tuple total domination number $gamma _{times k,t}(g)$ of $g$ is the minimum cardinality of a $k$-tuple total dominating set of $g$. if$v(g)=v^{0}={v_{1}^{0},v_{2}^{0},ldots ,v_{n}^{0}}$ and $e(g)=e_{0}$, then for any in...

Using the theory of orthogonal polynomials, their associated recursion relations and differential formulas we develop a new method for evaluating integrals that include orthogonal polynomials. The method is illustrated by obtaining the following integral result that involves the Bessel function and associated Laguerre polynomial: integral(infinity)(0) x(v)e(-x/2) J(v)(mu x)L-n(2v)(x)dx = 2(v)Ga...

A  $ mu $-way  $ G $-trade ($ mu geq 2) $  consists of $ mu $ disjoint decompositions of some simple (underlying) graph $ H $ into copies of a graph $ G. $  The   number of copies of the  graph $ G $ in  each of the decompositions is the volume of the $ G $-trade and   denoted by $ s. $ In this paper, we determine all values  $ s $ for which there exists a $  mu $-way   $ K_{1,m} $-trade of  vo...

B-lymphocyte development exhibits a characteristic order of immunoglobulin gene rearrangements. Previous work has led to the hypothesis that expression of the immunoglobulin mu heavy chain induces rearrangement activity at the kappa light-chain locus. To examine this issue in more detail, we isolated five matched pairs of mu- and endogenously rearranged mu+ cell lines from the Abelson murine le...