Volume 60, Issue 1

We introduce the definition of pseudoorthoalgebras and discuss some relationships between orthomodular lattices and pseudoorthoalgebras. Then we study the conditions that a pseudoeffect algebra is isomorphic to an “internal direct product” of ideals generated by orthogonal principal elements. At last, we give some characterizations of central elements in pseudoeffect algebras.

Having an MV-algebra, we can restrict its binary operation addition only to the pairs of orthogonal elements. The resulting structure is known as an effect algebra, precisely distributive lattice effect algebra. Basic algebras were introduced as a generalization of MV-algebras. Hence, there is a natural question what an effect-like algebra can be reached by the above mentioned construction if an MV-algebra is replaced by a basic algebra. This is answered in the paper and properties of these effect-like algebras are studied.

In this paper we discuss some relations between (pre-)Coxeter algebras and its related topics, and obtain some equivalent conditions.

In this paper we define the notion of relative subalgebra of an MV-algebra A. A particular case of this notion is the notion of interval subalgebra of A; this has been already studied in the literature. Applying these notions, two new categories denoted as r and int are introduced. In both cases the objects are MV-algebras, but the homomorphisms are defined by means of relative subalgebras or by interval subalgebras, respectively. The relations occurring between these categories and the category of all MV-algebras with usual homomorphisms are investigated. The main results of the paper deal with one-generated free MV-algebras in the variety generated by the finite chains S i, i ⩽ p (p varying over the set of all positive integers) and their relations to certain relative subalgebras of the cyclic free MV-algebra.

Some extension theorems for l-group-valued M-measures are proved.

In this paper, we introduce a new class W(a, b, c, γ, β) which consists of analytic and univalent functions with negative coefficients in the unit disc defined by Hohlov operator, we obtain distortion theorem using fractional calculus techniques for this class. Also coefficient inequalities and some results for this class are obtained.

This paper deals with the optimal control of a coefficient in the modification of Navier-Stokes equations. Namely, the motion of the viscous incompressible fluid for a small gradient of velocity is described by Navier-Stokes equations where the coefficient of the kinematic viscosity ν is the positive constant (ν 0). For a greater gradient of velocity the coefficient of kinematic viscosity is a positive function of the gradient of velocity, that is ν (|∇u|). In our case ν (|∇u|) = ν 0 + ν 1 a (|∇u|) where ν 0, ν 1 ∈ ℝ+. The function a is positive and monotone and it is taken as a control variable. The existence of a solution of the optimal control problem is proved. Further, the approximation of the control problem by the finite-dimensional control problem is performed. The proof of the existence of a solution of that aproximate problem has been brought into light. Finally, the connection between the solution of the control problem and the solution of the approximate control problem is established.

We consider the space of ultradifferentiable functions with compact supports and the space of polynomials on . Description of the polynomials algebra as a locally convex direct sum is given. Derivation in and automorphisms of this algebra are considered.

One of the couple of translatable radii of an operator in the direction of another operator introduced in earlier work [PAUL, K.: Translatable radii of an operator in the direction of another operator, Scientae Mathematicae 2 (1999), 119–122] is studied in details. A necessary and sufficient condition for a unit vector f to be a stationary vector of the generalized eigenvalue problem Tf = λAf is obtained. Finally a theorem of Williams ([WILLIAMS, J. P.: Finite operators, Proc. Amer. Math. Soc. 26 (1970), 129–136]) is generalized to obtain a translatable radius of an operator in the direction of another operator.

The geometry of slant submanifolds of a nearly trans-Sasakian manifold is studied when the tensor field Q is parallel. It is proved that Q is not parallel on the submanifold unless it is anti-invariant and thus the result of [CABRERIZO, J. L.—CARRIAZO, A.—FERNANDEZ, L. M.—FERNANDEZ, M.: Slant submanifolds in Sasakian manifolds, Glasg. Math. J. 42 (2000), 125–138] and [GUPTA, R. S.—KHURSHEED HAIDER, S. M.—SHARFUDIN, A.: Slant submanifolds of a trans-Sasakian manifold, Bull. Math. Soc. Sci. Math. Roumanie (N.S.) 47 (2004), 45–57] are generalized.