Let N and P be smooth manifolds of dimensions n and p (n ≥ p ≥ 2) respectively. Let Ω (N, P ) denote an open subspace of J∞(N, P ) which consists of all Boardman submanifolds Σ (N, P ) of symbols J with J ≤ I. An Ω -regular map f : N → P refers to a smooth map having only singularities in Ω (N, P ) and satisfying transversality condition. We will prove what is called the homotopy principle for ...

To prove Theorem 2, we use the following two facts about the class F: 1. F is a differential ring [2]. This means that F is closed under addition, multiplication and differentiation. 2. All functions y ∈ F are entire functions of completely regular growth in the sense of Levin–Pflüger [4], with piecewise-trigonometric indicators, the notions which we recall now. Let f be a holomorphic function ...

Fluoride (F) intake is recognized to be important for dental health. Tea leaves are known F accumulators and brewed tea as well as the water used for brewing may contribute significantly to individual intake. The USDA’s Nutrient Data Laboratory determined the F content of brewed and microwaved teas using geographically matched tap water samples. Two brands of top-selling regular and one of deca...

Let K(α), 0≤α< 1, denote the class of functions g(z)= z+∑∞n=2anzn which are regular and univalently convex of order α in the unit disc U . Pursuing the problem initiated by Robinson in the present paper, among other things, we prove that if f is regular in U , f(0) = 0, and f(z)+zf ′(z) < g(z)+zg′(z) in U , then (i) f(z) < g(z) at least in |z| < r0, r0 = √ 5/3 = 0.745 . . . if f ∈ K; and (ii) f...

In this paper we define the concepts of co-medial algebra and regular algebra and we will show that for a regular co-medial algebra (A, f , g), there exist a commutative semigroup (A,+), such that the operations f , g have the linear representation on (A,+). As a consequence of above result, we have the linear representation of an n−ary medial groupoid with an regular element, which was obtaine...

Let $G$ be a group and $A$ a set. A cellular automaton (CA) $\tau$ over $A^G$ is von Neumann regular (vN-regular) if there exists a CA $\sigma$ over $A^G$ such that $\tau \sigma\tau = \tau$, and in such case, $\sigma$ is called a generalised inverse of $\tau$. In this paper, we investigate vN-regularity of various kinds of CA. First, we establish that, over any nontrivial configuration space, t...

We consider the Rosenfeld-Gröbner algorithm for computing a regular decomposition of a radical differential ideal generated by a set of ordinary differential polynomials in n indeterminates. For a set of ordinary differential polynomials F , let M(F ) be the sum of maximal orders of differential indeterminates occurring in F . We propose a modification of the Rosenfeld-Gröbner algorithm, in whi...

We consider the Rosenfeld–Gröbner algorithm for computing a regular decomposition of a radical differential ideal generated by a set of ordinary differential polynomials in n indeterminates. For a set of ordinary differential polynomials F , let M(F) be the sum of maximal orders of differential indeterminates occurring in F . We propose a modification of the Rosenfeld–Gröbner algorithm, in whic...

We consider the Rosenfeld-Gröbner algorithm for computing a regular decomposition of a radical differential ideal generated by a set of ordinary differential polynomials in n indeterminates. For a set of ordinary differential polynomials F , let M(F ) be the sum of maximal orders of differential indeterminates occurring in F . We propose a modification of the Rosenfeld-Gröbner algorithm, in whi...