The nonlinearity profile of a Boolean function is the sequence of its minimum Hamming distances nlr(f) to all functions of degrees at most r, for r ≥ 1. The nonlinearity profile of a vectorial function is the sequence of the minimum Hamming distances between its component functions and functions of degrees at most r, for r ≥ 1.The profile of the multiplicative inverse functions has been lower b...

and Applied Analysis 3 The rest of this paper is organized as follows. In Section 2, we give notations, definition, propositions, and lemma to be used in the proof of the main results. Delay-dependent sufficient conditions for uncertain neutral and Lur’e dynamical systems with sector-bounded nonlinearity are presented in Section 3. Numerical examples illustrated the obtained results and are giv...

This paper revisits dynamic surface control based adaptive Takagi-Sugeno (TS) fuzzy model i.e. (DSC-TS), for a problem of uncertain nonlinear dynamical systems with bounded disturbance. Dynamic surface control (DSC) methods with the combination of TS-model are used for control and approximation of uncertain nonlinear systems up to a tolerance limit. DSC has the advantage over integrator backpst...

This paper considers the local stability of systems comprising linear time-invariant operators in combination with a deadzone nonlinearity. The behaviour of systems which are not globally bounded-input boundedoutput stable is investigated, and it is shown that under certain conditions, such systems are bounded-output stable for a restricted class of inputs. A sufficient condition for this prope...

If one modifies the laws of Quantum Mechanics to allow nonlinear evolution of quantum states, this paper shows that NP-complete problems would be efficiently solvable in polynomial time with bounded probability (NP in BQP). With that (admittedly very unlikely) assumption, this is demonstrated by describing a polynomially large network of quantum gates that solves the 3SAT problem with bounded p...

This paper proposes a robust design scheme for the control of surge phenomenon appearing in a centrifugal compressor. It is known the surge instability in compressor might lead to reduce the operating efficiency and even damage the machinery while both of unstable compressor characteristics and compressor load torque are hard to exactly measure in the practical application. Based on the assumpt...

In this paper, we study Kirchhoff type problems on a bounded domain. We consider the cases that the nonlinearity is superlinear near zero but asymptotically 4-linear at infinity, and the nonlinearity is asymptotically linear near zero but 4-superlinear at infinity. By computing the relevant critical groups, we obtain nontrivial solutions via Morse theory.