Flaminio and Montagna (2008) enlarged the language of MV-algebras by a unary operation σ, called internal state or a state operator, equationally defined so as to preserve the basic properties of a state in its usual meaning. The resulting class of MV-algebras is called state MV-algebras. Jenča (2007) and Vetterlein (2008), using different approaches, represented MV-algebras through the quotien...

By applying the concept of Lukasiewicz fuzzy set to BE-algebras, notions BE-algebra and BE-filter are introduced, their properties investigated. Characterizations discussed, relationship between (resp., BE-filter) is established. The conditions for ∈-set, q-set O-set be BE-subalgebras explored. created by using BE-filter.

Milk thistle (Silybum marianum) is a native plant of Mediterranean Sea areas. Silymarin, an extract from its seeds, is used in various liver diseases for its hepatoprotective effects. It contains silymarin flavonoids (SF) such as silybin, silydianin and silychristin. Cyclosporin A (CsA) is widely used as an immunosuppressant in organ transplantations. Its other applications in many autoimmune d...

The relations M(κ, λ, µ) → B [resp. B(σ)] meaning that if A ⊂ [κ] λ with |A| = κ is µ-almost disjoint then A has property B [resp. has a σ-transversal] had been introduced and studied under GCH in [EH]. Our two main results here say the following: Assume GCH and ̺ be any regular cardinal with a supercompact [resp. 2-huge] cardinal above ̺. Then there is a ̺-closed forcing P such that, in V P , we ...

In this paper, for a complete residuated lattice L, we present the categorical properties of ?-neighborhood spaces and their relationships to neighborhood stratified L-neighborhood spaces. The main results are: (1) category is topological category; (2) can be embedded in as reflective subcategory, when L meet-continuous lattice, subcategory; (3) continuous (resp., spaces) simultaneously corefle...

Letn ≡ k−1, 0 or 1 (mod k).An R̃MP(k, ; n,m) (resp. R̃MC(k, ; n,m)) is a resolvable packing (resp. covering)withmaximum (resp. minimum) possible number m of parallel classes which are mutually distinct, each parallel class consists of (n− k + 1)/k blocks of size k and one block of size n− k (n− k+ 1)/k , and its leave (resp. excess) is a simple graph. Such designs can be used to construct certain...

(1) ‖p(T )‖ ≤M sup{|p(ζ)| : |ζ| = 1} ∀ polynomial p, and to be power bounded (notation T ∈ (PW)) if (1) holds for every polynomial of the special form p(ζ) = ζ where n is a positive integer. If T ∈ (PB) [resp., T ∈ (PW)], then there is a smallest number M which satisfies (1) [resp., (1) restricted]. This number will be called the polynomial bound of T [resp., the power bound of T ] and denoted ...

Let H and H ′ be two ample line bundles over a smooth projective surface X , and M(H) (resp. M(H )) the coarse moduli scheme of H-semistable (resp. H -semistable) sheaves of fixed type (r, c1, c2). We construct a sequence of blowing-ups which describes how M(H) differs from M(H ) not only when r = 2 but also when r is arbitrary. Means we here utilize are elementary transforms and the notion of ...

There are many structures (algebras, categories, etc) with natural gradings such that the degree 0 components are not semisimple. Particular examples include tensor algebras with non-semisimple degree 0 parts, extension algebras of standard modules of standardly stratified algebras. In this thesis we develop a generalized Koszul theory for graded algebras (categories) whose degree 0 parts may b...