This paper is dedicated to the study of two famous subsets real line, namely Lagrange spectrum L and Markov M. Our first result, Theorem 2.1, provides a rigorous estimate on smallest value t1 such that portion (−∞,t1)∩M has Hausdorff dimension 1. second 3.1, gives new upper bound set difference M∖L. In addition, we also give plot function, which hasn't appeared previously in literature our know...

We prove a Fundamental Theorem of Finite Semidistributive Lattices (FTFSDL), modelled on Birkhoff’s Distributive Lattices. Our FTFSDL is the form “A poset L finite semidistributive lattice if and only there exists set with some additional structure, such that isomorphic to admissible subsets ordered by inclusion; in this case, its structure are uniquely determined L.” The combinatorial abstract...

☞ Many of the changes in generative phonology after The Sound Pattern of English have been driven by considerations of languages different from English. In this class, we study one specific phenomenon, found in many languages but not in (any Standard variety of) English. ☞ Many developments can be seen as an interactions of considerations about representations and considerations about represent...

The notion of CD-independence is introduced as follows. A subset X of a lattice L with 0 is called CD-independent if for any x, y ∈ X , either x ≤ y or y ≤ x or x ∧ y = 0. In other words, if any two elements of X are either Comparable or Disjoint. Maximal CD-independent subsets are called CD-bases. The main result says that any two CD-bases of a finite distributive lattice L have the same numbe...

Dendritic cells (DCs) are pivotal in the development of specific T-cell responses to control pathogens, as they govern both the initiation and the polarization of adaptive immunity. To investigate the capacities of migrating DCs to respond to pathogens, we used physiologically generated lymph DCs (L-DCs). The flexible polarization of L-DCs was analysed in response to Salmonella or helminth secr...

The papers [19], [9], [1], [4], [20], [2], [18], [13], [5], [8], [14], [21], [7], [15], [12], [11], [17], [6], [10], [16], and [3] provide the terminology and notation for this paper. For simplicity we follow the rules: M is a metric space, c, g are elements of the carrier of M , F is a family of subsets of the carrier of M , A, B are subsets of the carrier of M , f is a function, n, m, p, k ar...

The objectives of this study were to determine the percentage and absolute counts of the peripheral blood lymphocyte subsets, and to examine the relationship between lymphocyte subsets and nutritional status, and total mortality in an institutionalised elderly population. Design The study had a cross-sectional and observational design. The sample of 115 permanent elderly residents was drawn fro...

A Z2Z4-additive code C ⊆ Z α 2 × Z β 4 is called cyclic if the set of coordinates can be partitioned into two subsets, the set of Z2 and the set of Z4 coordinates, such that any simultaneous cyclic shift of the coordinates of both subsets leaves invariant the code. These codes can be identified as submodules of the Z4[x]-module Z2[x]/(x − 1)×Z4[x]/(x −1). Any Z2Z4-additive cyclic code C is of t...

We compare the following three notions of uniformity for a finitely additive probability measure on the set of natural numbers: that it extend limiting relative frequency, that it be shift-invariant, and that it map every residue class mod m to 1/m. We find that these three types of uniformity can be naturally ordered. In particular, we prove that the set L of extensions of limiting relative fr...