Let $$G=(V, E)$$ be a graph where V and E are the vertex edge sets, respectively. For two disjoint subsets A B, we say dominates B if every of is adjacent to at least one A. partition $$\pi = \{V_1, V_2, \ldots , V_k\}$$ G called transitive k-partition $$V_i$$ $$V_j$$ for all i, j $$1\le i<j\le k$$ . The maximum integer k which above exists transitivity it denoted by Tr(G). Maximum Transitivity...

A complete set of eigenstates for the supersymmetric t-J model in one dimension is obtained by combining the Bethe-ansatz with the Spl(2,1) supersymmetry of the model.

we study different completeness definitions for two categories of lattice-valued cauchy spaces and the relations between these definitions. we also show the equivalence of a so-called completion axiom and the existence of a completion.

we investigate a class of fourth-order differential operators with eigenparameter dependent boundary conditions and transmission conditions. a self-adjoint linear operator a is defined in a suitable hilbert space h such that the eigenvalues of such a problem coincide with those of a . we discuss asymptotic behavior of its eigenvalues and completeness of its eigenfunctions. finally, we obtain th...

We present a concept of trust that integrates the truster’s goal, the trustee’s action that ensures the achievement of the truster’s goal, and the trustee’s ability and intention to do this action. This concept of trust is formalized in modal logic and is applied to the particular domain of trust in information sources. In this context trust may be derived, in particular, from the truster’s bel...

The space D(R) of test functions (infinitely differentiable functions with compact support) is an important example of a non-metrizable (LF)-space, and the domain of distributions (generalized functions). E. Bishop suggested in [1, Appendix A] and [2, Chapter 7, Notes] that the completeness of D(R) and the weak completeness of its dual space would not hold in Bishop’s constructive mathematics. ...

One of the assumptions of recursive multiple-priors utility (Epstein and Schneider, J. Econ. Theory, 113(1) (2003), 1-31) is that conditional preferences at every node satisfy an intertemporal version of the multiple-priors axioms (Gilboa and Schmeidler, J. Math. Econ., 18(2) (1989) 141-153). This note weakens this assumption: Given that conditional preferences depend only on the continuations ...

We prove a strong form of model completeness for expansions of the field of real numbers by (the real and imaginary parts of) the modular function J, by the modular forms E4 and E6 and quasimodular form E2 defined in the usual fundamental domain, and the restricted sine function and the (unrestricted) exponential function. This is done using ideas of Peterzil and Starchenko’s paper [12] on the ...