Hazards pulses are undesirable short pulses caused by stray delays in digital circuits. Such pulses not only may cause errors in the circuit operation, but also consume energy, and add to the computation time. It is therefore very important to detect hazards in circuit designs. Two-valued Boolean algebra, which is commonly used for the analysis and synthesis of digital circuits, cannot detect h...

In this paper, we define what we call (non)degenerate valued and graded division algebras [Definition 3.1] and use them to give examples of division p-algebras that are not tensor product of cyclic algebras [Corollary 3.17] and examples of indecomposable division algebras of prime exponent [Theorem 5.2, Corollary 5.3 and Remark 5.5]. We give also, many results concerning subfields of these divi...

We study an extension of MV algebras, called μMV algebras, in which minimal and maximal fixed points are definable. The first result is that μMV algebras are term-wise equivalent to divisible MV∆algebras, i.e. a combination of two known extensions of MV algebras: divisible MV algebras [4] and MV∆algebras [6]. Using methods from the two known extensions we derive a number of results about μMV al...

This paper attempts to generalize universal algebras on classical sets to $L$-sets when $L$ is a GL-quantale. Some basic notions of fuzzy universal algebra on an $L$-set are introduced, such as subalgebra, quotient algebra, homomorphism, congruence, and direct product etc. The properties of them are studied. $L$-valued power algebra is also introduced and it is shown there is an onto homomorphi...

In this paper the multi-valued versions of some well-known hybrid fixed point theorems of Dhage [6, 7] in Banach algebras are proved. As an application, an existence theorem for a certain integral inclusion in Banach algebras is proved.

We prove a new criterion that guarantees self-adjointness of Toeplitz operators with unbounded operator-valued symbols. Our applies, in particular, to symbols Lipschitz continuous derivatives, which is the natural class Hamiltonian functions for classical mechanics. For this we extend Berger-Coburn estimate case vector-valued Segal-Bargmann spaces. Finally, apply our result (operator-valued) qu...

This paper is a study of solutions to nonlinear Dirac equations, in domains in Euclidean space, which are generalizations of the Clifford Laplacian as well as elliptic equations in divergence form. A Caccioppoli estimate is used to prove a global integrability theorem for the image of a solution under the Euclidean Dirac operator. Oscillation spaces for Clifford valued functions are used which ...

Let P ,X and Y be Banach spaces. Suppose that f : P ×X → Y is continuously Fréchet differentiable function depend on the point (p, x) and F : X ⇒ 2 is a set-valued mapping with closed graph. Consider the following parametric generalized equation of the form: 0 ∈ f(p, x) + F (x). (1) In the present paper, we study an extended Newton-type method for solving parametric generalized equation (1). In...

We show the existence result of viable solutions to the differential inclusion ẋ(t) ∈ G(x(t)) + F (t, x(t)) x(t) ∈ S on [0, T ], where F : [0, T ] × H → H (T > 0) is a continuous set-valued mapping, G : H → H is a Hausdorff upper semi-continuous set-valued mapping such that G(x) ⊂ ∂g(x), where g : H → R is a regular and locally Lipschitz function and S is a ball, compact subset in a separable H...

In this paper we investigate under which conditions the composition of two set-valued maps enjoys the linear openness property. To obtain our results, we use the Nadler’s fixed point theorem, and Lim’s lemma which provides an estimate for the distance between the sets of fixed points of two (set-valued) contractions. As an application, we obtain the Lipschitz property of the implicit solution m...