ON HYPERSTABILITY OF THE BIADDITIVE FUNCTIONAL EQUATION

We present results on approximate solutions to the biadditive equationf（x＋y,z-w）＋f（x-y,z＋w）=2f（x,z）-2f（y,w）on a restricted domain. The proof is based on a quite recent fixed point theorem in some function spaces. Our main results state that, under some weak natural assumptions, functions satisfying the equation approximately （in some sense） must be actually solutions to it. In this way we obtain inequalities characterizing biadditive mappings and inner product spaces. Our outcomes are connected with the well known issues of Ulam stability and hyperstability.

HYPERSTABILITY OF THE GENERALIZED CAUCHY-JENSEN FUNCTIONAL EQUATION IN ULTRAMETRIC SPACES

In this article, we prove hyperstability results of the generalized Cauchy-Jensen functional equation αf(x+y/α+z)=f(x)+y(y)+αf(z)for any fixed positive integer α> 2 in ultrametric Banach spaces by using fixed point method.

THE GENERALIZED HYPERSTABILITY OF GENERAL LINEAR EQUATION IN QUASI-2-BANACH SPACE

In this paper,we study the hyperstability for the general linear equation f(ax+by)=Af(x)+Bf(y)in the setting of complete quasi-2-Banach spaces.We first extend the main fixed point result of Brzdek and Ciepliński(Acta Mathematica Scientia,2018,38 B(2):377-390)to quasi-2-Banach spaces by defining an equivalent quasi-2-Banach space.Then we use this result to generalize the main results on the hyperstability for the general linear equation in quasi-2-Banach spaces.Our results improve and generalize many results of literature.

An adaptive load torque observer using hyperstability for PMSM servo system

An adaptive load torque observer is presented to compensate the torque ripple in PMSM servo system. A simple adaptive scheme is derived using Popov ＇ s hyperstability theory. The torque ripple detected by the observer is compensated by a feed forwarding equivalent current which gives fast response. The noisy current information is exempt from the observer to avoid its deterioration to the quality of the observer. The speed measurement delay is considered by using observed speed sinee the instantaneous velocity can＇t be estimated precisely at low speed because of too few position pulses from the absolute encoder during one time interval. Simulation and experimental results demonstrate that the proposed method can improve the dynamic performance of PMSM servo system satisfyingly.

Speed Identification of Speed Sensorless Linear Induction Motor Based on MRAS

In the linear induction motor control system,the optical grating speed transducer is susceptible to strong magnetic field interference.What's more,it may reduce motor integration and raise device costs.Therefore a speed identification method to replace grating speed transducer is studied in this article.This speed identification method for linear induction motor mainly adopts Model Reference Adaptive Method(Abbreviated as MRAS)and Popov Hyperstability Theory.The research content of this paper can be divided into four parts.First,the mathematical model of the motor based on the model reference adaptive system structure is deduced.Second,the adaptive law of the estimated speed is solved by Popov hyper-stability theory,which ensures the stability of the system.Third,the simulation model of the linear induction motor speed identification control system based on model reference adaptation is built in the MATLAB environment.Finally,the simulation test and analysis are carried out.The simulation results show that the speed identification control system can track the actual speed of the linear induction motor well in the no-load operation and the load operation,and the stability of the system is guaranteed in the full speed range.

ON A FIXED POINT THEOREM IN 2-BANACH SPACES AND SOME OF ITS APPLICATIONS

The aim of this article is to prove a fixed point theorem in 2-Banach spaces and show its applications to the Ulam stability of functional equations. The obtained stability re- sults concern both some single variable equations and the most important functional equation in several variables, namely, the Cauchy equation. Moreover, a few corollaries corresponding to some known hyperstability outcomes are presented.

APPROXIMATE SOLUTION OF P-RADICAL FUNCTIONAL EQUATION IN 2-BANACH SPACES

The aim of this paper is to introduce and solve the p-radical functional equation ■We also state an analogue of the fixed point theorem [12, Theorem 1] in 2-Banach spaces and investigate stability for this equation in 2-Banach spaces.

ON APPROXIMATELY(p,q)-WRIGHT AFFINE FUNCTIONS AND INNER PRODUCT SPACES

We prove, using the fixed point approach, some results on hyperstability （in normed spaces） of the equation that defines the generalization of p-Wright affine functions and show that they yield a simple characterization of the complex inner product spaces.

Engineering a cell-penetrating hyperstable antibody scFv(Ras)-An extraordinary approach to cancer therapeutics

In the modern pharmaceutical industry,monoclonal antibodies are often used as therapeutic agents.However,they are restricted to cell surface antigens due to their inability to penetrate the outer cell membrane and maintain normal function in the reducing environment.Additionally,it can lead to cytotoxicity since it attacks cancerous cells by mimicking the human immune system.As an alternative,this study modifies the hyperstable single-chain fragment variable(scFv)antibody to eliminate cancer using its linear shape.The scFv(F8)antibody model was modified to recognize human Ras protein by altering residues in the antigen-binding site.Furthermore,a cell-penetrating peptide(CPP)was attached to the scFv(Ras)antibody model to allow entrance to the cell,creating CPP-scFv(Ras).Sodium dodecyl sulfate polyacrylamide gel electrophoresis(SDS-PAGE),western blotting,and the binding assay were performed to prove its effectiveness.As a result,CPP-scFv(Ras)was successfully engineered and bound to the antigen,HRas(G12V).