In three spatial dimensions, communication channels are free to pass over or under each other so as to cross without intersecting; in two dimensions, assuming channels of strictly positive thickness, this is not the case. It is natural, then, to ask whether one can, in a suitable, twodimensional model, cross two channels in such a way that each successfully conveys its data, in particular witho...

Let ∆ be a simplicial complex and I∆ its Stanley–Reisner ideal. It has been conjectured that, for each i and j, the graded Betti number βii+j(I∆) of I∆ is smaller than or equal to that of I∆c , where ∆ c is a combinatorial shifted complex of ∆. In the present paper the conjecture will be proved affirmatively. In particular the inequalities βii+j(I∆) ≤ βii+j(I∆lex) hold for all i and j, where ∆ ...

In origami, form follows the sequential spatial organization of folds. This requires continuous intervention and raises a natural question: Can origami arise through self-organization? We answer this affirmatively by examining the possible physical origin for the Miura-ori leaf-folding patterns that arise naturally in insect wings, leaves, and other laminae-like organelles. In particular, we po...

We consider the GI/GI/1 queue with regularly varying service requirement distribution of index −α. It is well known that, in the M/G/1 FCFS queue, the sojourn time distribution is also regularly varying, of index 1 − α, whereas in the case of LCFS or Processor Sharing, the sojourn time distribution is regularly varying of index −α. That raises the question whether there exist service discipline...

This paper answers affirmatively the open question of the existence of a polynomial size CNF encoding of pseudo-Boolean (PB) constraints such that generalized arc consistency (GAC) is maintained through unit propagation (UP). All previous encodings of PB constraints either did not allow UP to maintain GAC, or were of exponential size in the worst case. This paper presents an encoding that reali...

objective(s): iscomatrix vaccines have now been shown to induce strong antigen-specific cellular or humoral immune responses to a broad range of antigens of viral, bacterial, parasite or tumor. in the present study, we investigated the role of iscomatrix charge in induction of a th1 type of immune response and protection against leishmania major infection in balb/c mice.  materials and methods:...

UP is the class of languages accepted by polynomial-time nondeterministic Turing machines that have at most one accepting path. We show that the quadratic residue problem belongs to UP ∩ coUP. This affirmatively answers an open problem, discussed in Theory of Computational Complexity (Du and Ko, 2000), of whether the quadratic nonresidue problem is in NP. We generalize to higher powers and show...

We show that there exist genus one curves of every index over the rational numbers, answering affirmatively a question of Lang and Tate. The proof is “elementary” in the sense that it does not assume the finiteness of any Shafarevich-Tate group. On the other hand, using Kolyvagin’s construction of a rational elliptic curve whose Mordell-Weil and Shafarevich-Tate groups are both trivial, we show...

An eventual property of a matrix M ∈ C is a property that holds for all powers M, k ≥ k0, for some positive integer k0. Eventually positive and eventually nonnegative matrices have been studied extensively, and some results are known for eventually r-cyclic matrices. This paper introduces and establishs properties of eventually reducible matrices, establishs properties of the eigenstructure of ...

For a permutation ω ∈ Sn, Leclerc and Zelevinsky in Am. Math. Soc. Transl., Ser. 2 181, 85–108 (1998) introduced the concept of an ω-chamber weakly separated collection of subsets of {1,2, . . . , n} and conjectured that all inclusionwise maximal collections of this sort have the same cardinality (ω)+n+1, where (ω) is the length of ω. We answer this conjecture affirmatively and present a genera...