A. Carpi (1993) and A. Lepistö (1993) proved independently that smooth words are cube-free for the alphabet {1, 2}, but nothing is known on whether for the other 2-letter alphabets, smooth words are k-power-free for some suitable positive integer k. This paper establishes the derivative formula (Theorem 10) of the concatenation of two smooth words and power derivative formula of smooth words ov...

in this paper, a novel patch geodesic derivative pattern (pgdp) describing the texture map of a face through its shape data is proposed. geodesic adjusted textures are encoded into derivative patterns for similarity measurement between two 3d images with different pose and expression variations. an extensive experimental investigation is conducted using the publicly available bosphorus and bu-3...

In the sense of distributions, derivative Heaviside unit step function $H(t)$ is a generalized Dirac-$\delta$ distribution. If velocity $V(t)$ flat plate impulsive, as $V(t)=H(t)$ (i.e., it suddenly set into motion with at $t=0^+$), then its acceleration $V'(t)=\delta(t)$. The distribution has no point values. However, when forcing term an ODE (in $t$), contributes to solution. recently publish...

M. H. Al-Abbadi and M. Darus 2009 recently introduced a new generalized derivative operator μ λ1 ,λ2 , which generalizedmany well-known operators studied earlier by many different authors. In this present paper, we shall investigate a new subclass of analytic functions in the open unit disk U {z ∈ C : |z| < 1} which is defined by new generalized derivative operator. Some results on coefficient ...

Using the most general higher-derivative field redefinition for closed spacetime manifolds, we show that tree-level couplings of metric, $B$-field and dilaton at orders $\alpha'^2$ $\alpha'^3$ have been recently found by T-duality, can be written in a particular scheme terms torsional Riemann curvature ${\cal R}$ torsion tensor $H$. The order structures R}^3, H^2 {\cal R}^2$, $H^6$, only R}^4$,...

in this paper a new method is proposed for interpretation of 2d magnetic data, using multiples of the analytic signal method, in which the analytic signal of magnetic anomaly is used directly to compute the depth and the structural index of the source instead of using its higher order derivatives. this method only needs the computation of the first order derivatives of the magnetic anomaly, so ...

for every $1leq s< n$, the $s^{th}$ derivative of a polynomial $p(z)$ of degree $n$ is a polynomial $p^{(s)}(z)$ whose degree is $(n-s)$. this paper presents a result which gives generalizations of some inequalities regarding the $s^{th}$ derivative of a polynomial having zeros outside a circle. besides, our result gives interesting refinements of some well-known results.

acylisothiocyanate (1) was allowed to react with benzylidene malononitrile producing oxazine derivative (2). also, compound (1) was reacted with sodium azide followed by refluxing with sodium ethoxide affording thiazinotetrazole derivative (4). the reaction of acetylacetone with compound (1) gave pyridine derivative (5) by intramolecular cycloaddition while it was reacted with n-methyl aniline ...

The aim of this paper is to construct (p,q)-calculus on finite intervals. (pk,qk)-derivative and (pk,qk)-integral are defined some basic properties given. Also, (pk,qk)-analogue H?lder, Minkowski integral inequalities proved.

In this article, we formalize differentiability of functions on normed linear spaces. Partial derivative, mean value theorem for vector-valued functions, continuous differentiability, etc. are formalized. As it is well known, there is no exact analog of the mean value theorem for vector-valued functions. However a certain type of generalization of the mean value theorem for vectorvalued functio...