Volume 47, Issue 3

MMI 3 -algebras are a generalization of the monadic Tarski algebras as defined by A. Monteiro and L. Iturrioz, and a particular case of the MMI n+1 -algebras defined by A. Figallo. They can also be seen as monadic three-valued Łukasiewicz algebras without a first element. By using this point of view, and the free monadic extensions, we construct the free MMI 3 -algebras on a finite number of generators, and indicate the coordinates of the generators. As a byproduct, we also obtain a construction of the free monadic Tarski algebras.

In this paper, by considering the notion of upsets, for any element x of a BL-algebra L, we construct a topology T x on L and show that L-algebras with this topology formes a semitopological BL-algebras. Then we obtain some of the topological aspects of this structure such as connectivity and compactness. Moreover, we introduced two kinds of semitopological MV -algebra by using two kinds of definition of MV -algebra and show that they are equivalent.

Skew lattices are noncommutative generalizations of lattices. The coset structure decomposition is an original approach to the study of these algebras describing the relation between its rectangular classes. In this paper, we will look at the category determined by these rectangular algebras and the morphisms between them, showing that not all skew lattices can determine such a category. Furthermore, we will present a class of examples of skew lattices in rings that are not strictly categorical, and present sufficient conditions for skew lattices of matrices in rings to constitute ^-distributive skew lattices

We study the notion of weak homomorphisms between coalgebras of different types generalizing thereby that of homomorphisms for similarly typed coalgebras. This helps extend some results known so far in the theory of Universal coalgebra over Set. We find conditions under which coalgebras of a set of types and weak homomorphisms between them form a category. Moreover, we establish an Isomorphism Theorem that extends the so-called First Isomorphism Theorem, showing thereby that this category admits a canonical factorization structure for morphisms

In this paper, we introduce the notions of microscopic and strongly microscopic sets on the plane and obtain a result analogous to Fubini Theorem.

In this paper, we study the L 2 -boundedness and L 2 -compactness of a class of h-Fourier integral operators. These operators are bounded (respectively compact) if the weight of the amplitude is bounded (respectively tends to 0).

This paper considers the asymptotic properties for the spectrum of a positive integer power l of the Laplace-Beltrami operator acting on an n-dimensional torus T. If N(λ) is the number of eigenvalues counted with multiplicity, smaller than a real positive number, we establish a Weyl-type asymptotic formula for the spectral problem of the polyharmonic operators on T, that is, as λ → +∞ N (λ) ~ ω n (VolT)λ n/21 /2(π) n where ω n is the volume of the unit ball in ℝ n and Vol T is the area of T, which gives the information of the area of the torus based on the spectrum of the polyharmonic operators.

This work deals with the Feigenbaum’s functional equation in the broad sense where ϕ 2 is the 2-fold iteration of ϕ f(x) is a strictly increasing continuous function on r0; 1s and satisfies f(0)=0; f(x) <x; x Ɛ (0, 1]). Using constructive method, we discuss the existence of single-valley-extended continuous solutions of the above equation.

In this paper, we introduce some new double sequence spaces with respect to an Orlicz function and define two new convergence methods related to the concepts of statistical convergence and lacunary statistical convergence for double sequences. We also present some inclusion theorems for our newly defined sequence spaces and statistical convergence methods

In this work, using the concept of I-convergence and using the concept of rough convergence, we introduced the notion of rough I-convergence and the set of rough I-limit points of a sequence and obtained two rough I-convergence criteria associated with this set. Later, we proved that this set is closed and convex. Finally, we examined the relations between the set of I-cluster points and the set of rough I-limit points of a sequence

In this article, we introduce the class of p-absolutely summable fuzzy real valued double sequence ( 2 l p ) F θ We have studied some algebraic properties like solid, symmetric, convergence free, sequence algebra. Further, we establish some relation with the class of p-Cesàro summable double sequences and some other important inclusion results.

We study the approximation properties of linear combinations of the so-called Phillips operators, which can be considered as genuine Szász-Mirakjan-Durrmeyer operators. As main result, we prove a direct estimate for the rate of approximation of bounded continuous functions f E C[0,x), measured in C|\[0,x)-norm and thus generalizing the results, proved earlier by Gupta, Agrawal, and Gairola in [3]. Our estimates rely on the recent results, obtained in the joint works of M. Heilmann and the author-[10, 11]

Let A be a unital algebra, δ be a linear mapping from A into itself and m, n be fixed integers. We call δ an (m, n)-derivable mapping at Z, if mδ(AB) + nδ(BA) = mδ(A)B + mAδ(B) + nδ(B)A for all A,B ∈ A with AB = Z. In this paper, (m, n)-derivable mappings at 0 (resp. I A ⊕ 0, I) on generalized matrix algebras are characterized. We also study (m, n)-derivable mappings at 0 on CSL algebras. We reveal the relationship between this kind of mappings with Lie derivations, Jordan derivations and derivations.

. In this paper, we discuss some important and interesting remarks on the concept of occasionally weakly compatible (owc) mappings, which is an active and interesting area of research in the present era. Also, we discuss here the lapses of several authors in quoting the definition of owc maps and provide the corrected proof by including some additional conditions on their results.

In the present paper, we extend the concept ofWeak Reciprocal Continuity for a hybrid pair of single-valued and multi-valued maps and introduce (T; f)-completeness of the space. Further, we establish some results on the existence of coincidence and fixed points for the hybrid pair of maps. Our results generalize several well known results available in the literature

In this paper, we introduce a new condition namely, ‘condition (W.C.C)’ and obtain two unique common fixed point theorems for pairs of hybrid mappings on a partial Hausdorff metric space without using any continuity and commutativity of the mappings.

The object of the present paper is to study Ф-projectively flat generalized Sasakian-space-forms, projectively locally symmetric generalized Sasakian-space-forms and projectively locally Ф-symmetric generalized Sasakian-space-forms. All the obtained results are in the form of necessary and sufficient conditions. Interesting relations between projective curvature tensor and conformal curvature tensor of a generalized Sasakian-spaceform of dimension greater than three have been established. Some of these properties are also analyzed in the light of quarter-symmetric metric connection, in addition with the Levi-Civita connection. Obtained results are supported by illustrative examples.

We directly prove that the foliation of the sphere S 2n+1 , the leaves of which are intersections of all complex linear 2-dimensional subspaces of ℂ n+1 translated by a constant vector p, defines a submersion that is horizontally conformal if and only if p=0. We generalise this result to the cases of S 4n+3 and S 15 with foliations constructed using quaternionic and octonionic structure (resp.) in an analogous way

The generalization of the n-dimensional cube, an n-dimensional chain, the exterior derivative and the integral of a differential n-form on it are introduced and investigated. The analogue of Stokes theorem for the differential space is given

This paper refers to standard models in the theory of inelastic deformations. We assume that non-linear inelastic constitutive function is of monotone type, that the growth condition holds and that the model is quasistatic. Initial, generic problem is transformed into an evolution equation in a maximal monotone field. Then we find solutions with very low regularity requirements of the forces acting on a body