[6] **viXra:1601.0289 [pdf]**
*submitted on 2016-01-26 11:04:20*

**Authors:** Antonio Boccuto, Xenofon Dimitriou

**Comments:** 7 Pages.

We give some Korovkin-type theorems on
convergence and estimates of rates of approximations for nets of functions, satisfying suitable axioms, whose particular cases are filter/ideal convergence, almost convergence and triangular A-statistical convergence, where A is a non-negative summability method. Furthermore, we give some comparison result between different types of convergence and applications to integral type
and discrete operators.

**Category:** Functions and Analysis

[5] **viXra:1601.0283 [pdf]**
*submitted on 2016-01-26 05:07:27*

**Authors:** Eckhard Hitzer

**Comments:** 15 Pages. Submitted to S. Bernstein and P. Cerejeiras (eds), Complex Variables and Elliptic Equations (Taylor & Francis), Special Issue entitled “Clifford analysis – theory and applications”, 26 Jan. 2016.

In this paper we use the steerable space-time Fourier transform (SFT), and relate the classical convolution of the algebra for space-time $Cl(3,1)$-valued signals over the space-time vector space $\R^{3,1}$, with the (equally steerable) Mustard convolution. A Mustard convolution can be expressed in the spectral domain as the point wise product of the SFTs of the factor functions. In full generality do we express the classical convolution of space-time signals in terms of finite linear combinations of Mustard convolutions, and vice versa the Mustard convolution of space-time signals in terms of finite linear combinations of classical convolutions.

**Category:** Functions and Analysis

[4] **viXra:1601.0189 [pdf]**
*replaced on 2016-09-26 21:24:48*

**Authors:** GuagSan Yu

**Comments:** 8 Pages.

The Newton's second law and third law has proven to be wrong, his mistake is the derivative operation the limitation resulting. Therefore new derivative the computation method desiderate the creation, this is the Inverse Derivative algorithm. The Inverse Derivative is a kind of extension of the derivative computation, it is based on the derivative calculated generated, using most of the derivative formulas to converted adjusted. In the field of physics and mechanical engineering, Inverse Derivative may be a large number of employed, to replace original derivative computation method. Will produce the enormous and profound influence.

**Category:** Functions and Analysis

[3] **viXra:1601.0165 [pdf]**
*replaced on 2016-01-23 08:13:42*

**Authors:** Eckhard Hitzer

**Comments:** 16 Pages. Submitted to special issue of Adv. in Appl. Cliff. Algs., 1 color figure.

In this paper we use the general two-sided quaternion Fourier transform (QFT), and relate the classical convolution of quaternion-valued signals over $\R^2$ with the Mustard convolution. A Mustard convolution can be expressed in the spectral domain as the point wise product of the QFTs of the factor functions. In full generality do we express the classical convolution of quaternion signals in terms of finite linear combinations of Mustard convolutions, and vice versa the Mustard convolution of quaternion signals in terms of finite linear combinations of classical convolutions.

**Category:** Functions and Analysis

[2] **viXra:1601.0129 [pdf]**
*submitted on 2016-01-12 15:46:52*

**Authors:** Wu Sheng-Ping

**Comments:** 1 Page.

I find the mistake in Cauchy's theorem of Complex variables.

**Category:** Functions and Analysis

[1] **viXra:1601.0039 [pdf]**
*replaced on 2016-09-26 21:16:25*

**Authors:** GuagSan Yu

**Comments:** 7 Pages. The Chinese

The Newton second law and the law of third have beened wrong by the proof, his mistake be caused by the localization of the derivative. Therefore new derivative the computation method desiderate the creation, this is the Inverse Derivative computation method. The inverse derivative is a kind of extension of the derivative computation, it creation been according to derivative the computation, the adoption is through regulatory and conversion the computation formula of the mostly derivative. In the physics and mechanics engineering realm, the Inverse Derivative be may adopted in largeness, to replace original derivative computation method. Will produce the enormous and profound influence.

**Category:** Functions and Analysis