The problem of determining Ramsey numbers is known to be very difficult. The few known exact values and several bounds for different G1, G2 or m, n are scattered among many technical papers (see [3]). A graph G with order p is called a (G1,G2; p)-graph ((m, n; p)-graph, resp.) if G does not contain a G1 and Ḡ does not contain a G2 (Km and Kn , resp.). It is easy to see that R(G1,G2) = p0 +1 iff...

Let I be a small indexing category, G : I → Cat be a functor and BG ∈ Cat denote the Grothendieck construction on G. We define and study Quillen pairs between the category of diagrams of simplicial sets (resp. categories) indexed on BG and the category of I-diagrams over N(G) (resp. G). As an application we obtain a Quillen equivalence between the categories of presheaves of simplicial sets (re...

we develop a theory of stratified $lm$-filters which generalizes the theory of stratified $l$-filters. our stratification condition explicitly depends on a suitable mapping between the lattices $l$ and $m$. if $l$ and $m$ are identical and the mapping is the identity mapping, then we obtain the theory of stratified $l$-filters. based on the stratified $lm$-filters, a general theory of lattice-v...

the sequential $p$-convergence in a fuzzy metric space, in the sense of george and veeramani, was introduced by d. mihet as a weaker concept than convergence. here we introduce a stronger concept called $s$-convergence, and we characterize those fuzzy metric spaces in which convergent sequences are $s$-convergent. in such a case $m$ is called an $s$-fuzzy metric. if $(n_m,ast)$ is a fuzzy metri...

Let N(r,m, n) (resp. M(r,m, n)) denote the number of partitions of n whose ranks (resp. cranks) are congruent to r modulo m. Atkin and Swinnerton-Dyer gave the relations between the numbers N(r,m,mn+k) when m = 5, 7 and 0 ≤ r, k < m. Garvan gave the relations between the numbers M(r,m,mn+k) when m = 5, 7, and 11, 0 ≤ r, k < m. Here, we show that the methods of Atkin and Swinnerton-Dyer can be e...

The present paper studies fuzzy matroids in view of degree. First wegeneralize the notion of $(L,M)$-fuzzy independent structure byintroducing the degree of $M$-fuzzy family of independent $L$-fuzzysets with respect to a mapping from $L^X$ to $M$. Such kind ofdegrees is proved to satisfy some axioms similar to those satisfiedby $(L,M)$-fuzzy independent structure. ...

BACKGROUND Allergy to cat dander is a common form of allergic disease. Allergen immunotherapy has been demonstrated to be effective in decreasing allergic symptoms. OBJECTIVES To examine outcomes in allergic asthmatic patients on cat immunotherapy (CIT) compared to allergic asthmatics on traditional immunotherapy (IT) without cat sensitivity. METHODS A retrospective review identified allerg...

A one to one correspondence between regular generalized bent functions from Fn2 to Z2m , and m−tuples of Boolean bent functions is established. This correspondence maps selfdual (resp. anti-self-dual) generalized bent functions to m−tuples of self-dual (resp. anti self-dual) Boolean bent functions. An application to the classification of regular generalized bent functions under the extended aff...

We show how to do efficient moment based inference using the generalized method of moments (GMM) when data is collected by standard stratified sampling and the maintained assumption is that the aggregate shares are known.