Norms of Dual Complex Vectors and Dual Complex Matrices

In this paper,we investigate some properties of dual complex numbers,dual complex vectors,and dual complex matrices.First,based on the magnitude of the dual complex number,we study the Young inequality,the Hölder inequality,and the Minkowski inequality in the setting of dual complex numbers.Second,we define the p-norm of a dual complex vector,which is a nonnegative dual number,and show some related properties.Third,we study the properties of eigenvalues of unitary matrices and unitary triangulation of arbitrary dual complex matrices.In particular,we introduce the operator norm of dual complex matrices induced by the p-norm of dual complex vectors,and give expressions of three important operator norms of dual complex matrices.

Furfural residues from straw become complex fertilizer by addition method

The additives such as phosphoric acid, calcium phosphate, calcium super phosphate, calcium over super phosphate, calcium carbonate, sodium hydrosulphite, etc. were used to produce furfural from the straw by hydrolysis with sulfuric acid. The effect of amount of the additives, the content of the added substance and the conditions of distillation on the acidity of the residues were studied. The experiment results showed that the all residues became neutral complex fertilizer, and the productivity of furfural increases under the following conditions: sulfuric acid concentration is 20% (by weight), the ratio of liquid to solid is 3∶1—4∶1 (by weight), the ratio of the additives to straw is suitable.

Dynamic analysis of a sexually transmitted disease model on complex networks

In this paper,a sexually transmitted disease model is proposed on complex networks,where contacts between humans are treated as a scale-free social network.There are three groups in our model,which are dangerous male,non-dangerous male,and female.By mathematical analysis,we obtain the basic reproduction number for the existence of endemic equilibrium and study the effects of various immunization schemes about different groups.Furthermore,numerical simulations are undertaken to verify more conclusions.

Study on High-Speed Magnitude Approximation for Complex Vectors

High-speed magnitude approximation algorithms for complex vectors are discussed intensively. The performance and the convergence speed of these approximation algorithms are analyzed. For the polygon fitting algorithms, the approximation formula under the least mean square error criterion is derived. For the iterative algorithms, a modified CORDIC (coordinate rotation digital computer) algorithm is developed. This modified CORDIC algorithm is proved to be with a maximum relative error about one half that of the original CORDIC algorithm. Finally, the effects of the finite register length on these algorithms are also concerned, which shows that 9 to 12-bit coefficients are sufficient for practical applications.

A new pseudorandom number generator based on a complex number chaotic equation

In recent years, various chaotic equation based pseudorandom number generators have been proposed. However, the chaotic equations are all defined in the real number field. In this paper, an equation is proposed and proved to be chaotic in the imaginary axis. And a pseudorandom number generator is constructed based on the chaotic equation. The alteration of the definitional domain of the chaotic equation from the real number field to the complex one provides a new approach to the construction of chaotic equations, and a new method to generate pseudorandorn number sequences accordingly. Both theoretical analysis and experimental results show that the sequences generated by the proposed pseudorandom number generator possess many good properties.

COMPLEX NUMBER MODE APPROACH FOR REDUCING VIBRATION OF STRUCTURAL FLEXIBLE REDUNDANT ROBOT MANIPULATORS

A complex number mode analysis approach is proposed for vibration reducing of structural flexible redundant manipulators by utilizing self motion. In the proposed approach, the self motion is evaluated to nullify the modal exciting force of flexural motion, and the approach can be freely used when the degree of freedom of flexural motion is much greater than the available degree of reundancy. The availability and effectiveness of the proposed approach are demonstrated through numerical simulation with a four link spatial robotic manipulator possessing an end flexible link.

Erratum to “The Riemann Hypothesis-Millennium Prize Problem” [Advances in Pure Mathematics 6 (2016) 915-920]

The original online version of this article (Durmagambetov, A.A. (2016) The Riemann Hypothesis-Millennium Prize Problem. Advances in Pure Mathematics, 6, 915-920. 10.4236/apm.2016.612069) unfortunately contains a mistake. The author wishes to correct the errors in Theorem 2 of the result part.

The Riemann Hypothesis-Millennium Prize Problem

This work is dedicated to the promotion of the results C. Muntz obtained modifying zeta functions. The properties of zeta functions are studied;these properties lead to new regularities of zeta functions. The choice of a special type of modified zeta functions allows estimating the Riemann’s zeta function and solving Riemann Problem-Millennium Prize Problem.

The Kinematics Analysis of Heald Selecting Mechanism of Rotary Electronic Dobby

In order to improve the reliability of the mechanical movement of the rotary electronic dobby, the kinematics analysis of the heald selection mechanism is carried out and the simulation is carried out with Matlab. Firstly, the operation mechanism of the heald selection mechanism is analyzed in detail. The conjugate cam is mapped. The cam profile curve is fitted with cubic spline interpolation. Secondly, based on the overall analysis method and the complex vector method, the kinematics analysis of the key components after the high pair low generation is performed, and the angular displacement and angular velocity of each component are calculated with the rotation of the active cam. Finally, the movement curve diagram is drawn with Matlab, which lays the foundation for the dynamic analysis and in-depth study of the selection mechanism in the future.

Semi-Continuity of Complex Fuzzy Functions

This paper introduces the concept of semi-continuity of complex fuzzy functions, and discusses some of their elementary properties, such as the sum of two complex fuzzy functions of type I upper (lower) semi-continuity is type I upper (lower) semi-continuous, and the opposite of complex fuzzy functions of type I upper (lower) semi-continuity is type I lower (upper) semi-continuous. Based on some assumptions on two complex fuzzy functions of type I upper (lower) semi-continuity, it is shown that their product is type I upper (lower) semi-continuous. The paper also investigates the convergence of complex fuzzy functions. In particular, sign theorem, boundedness theorem, and Cauchy's criterion for convergence are kept. In this paper the metrics introduced by Zhang Guangquan was used. This paper gives a contribution to the study of complex fuzzy functions, and extends the corresponding work of Zhang Guangquan.

On a non-abelian invariant on complex surfaces of general type Dedicated to Professor Sheng GONG on the occasion of his 75th birthday

In this paper,we give certain homotopy and diffeomorphism versions as a generalization to an earlier result due to W.S.Cheung,Bun Wong and Stephen S.T.Yau concerning a local rigidity problem of the tangent bundle over compact surfaces of general type.

Challenging the limitation:Synthesis and application of complexes with the highest carbon coordination number in plane

Subject Code:B02With the support by the National Natural Science Foundation of China and the National Basic Research Program of China,the research team led by Prof.Xia Haiping(夏海平)of Xiamen University described the first example of CCCCC pentadentate chelate with all binding atoms being carbon atoms.This result represents a new record of planar carbon coordination number for a transition metal,which was

ANALYTIC SOLUTIONS OF AN ITERATIVE EQUATION WITH FIRST ORDER DERIVATIVE

This paper is concerned with a nonlinear iterative equation with first order derivative. By construction a convergent power series solution, analytic solutions for the original equation are obtained.