On some applications of Ruscheweyh derivative

In this paper, we discuss a subclass V_k(β,b,δ) of analytic functions, which was introduced and discussed by Latha and Nanjunda Rao (1994) [3]. Some results such as inclusion relationship, coefficient inequality and radius of convexity for this class are proved. We also observe that this class is preserved under the Bernardi integral transform.     

The order of convexity of some general integral operators

The main object of the present paper is to discuss some extensions of certain integral operators and to obtain their order of convexity. Several other closely related results are also considered.     

Certain sufficient conditions for a subclass of analytic functions involving Hohlov operator

Making use of the Hohlov operator, the authors obtain inclusion relations between the classes of certain normalized analytic functions. Relevant connections of our work with the earlier works are pointed out.     

Permutation equivalence of cubic rotation symmetric Boolean functions

Rotation symmetric Boolean functions have been extensively studied for about 15 years because of their applications in cryptography and coding theory. Until recently little was known about the basic question of when two such functions are affine equivalent. The simplest case of quadratic rotation symmetric functions which are generated by cyclic permutations of the variables in a single monomial was only settled in 2009. For the much more complicated case of cubic rotation symmetric functions generated by a single monomial, the affine equivalence classes under permutations which preserve rotation symmetry were determined in 2011. It was conjectured then that the cubic equivalence classes are the same if all nonsingular affine transformations, not just permutations, are allowed. This conjecture is probably difficult, but here we take a step towards it by proving that the cubic affine equivalence classes found in 2011 are the same if all permutations, not just those preserving rotation symmetry, are allowed. The needed new idea uses the theory of circulant matrices.     

Some preserving subordination and superordination of analytic functions involving the Liu-Owa integral operator

In this paper, we obtain some subordination and superordination-preserving results of analytic functions involving the Liu-Owa integral operator. Sandwich-type result is also obtained.     

On the number of rotation symmetric Boolean functions

Rotation symmetric Boolean functions (RSBFs) have been used as components of different cryptosystems. This class of functions are invariant under circular translation of indices. In this paper, we investigated balanced RSBFs and 1st order correlation immune RSBFs. Based on constructive techniques, we give an accurate enumeration formula for n-variable balanced RSBFs when n is a power of a prime. Furthermore, an original and efficient method to enumerate all n-variable (n prime) 1st order correlationimmune f...     

代数免疫度最优的偶数元旋转对称布尔函数的构造

针对目前许多流密码算法无法抵抗代数攻击问题,提出了一种构造代数免疫度最优的偶数元旋转对称布尔函数的新方法。该方法在择多函数的基础上,通过巧妙选择汉明重量不一的若干轨道,并改变这些轨道上的函数值,从而构造出一类新的旋转对称布尔函数。给定布尔函数达到代数免疫度最优的一个充分条件,通过证明新构造的布尔函数满足该充分条件,从而表明该类函数代数免疫度最优,能够有效抵抗代数攻击。     

Optimization-based computation of analytic interpolants of bounded complexity

This paper provides a unifying algorithm for computing any analytic interpolant of bounded complexity. Such computation can be performed by solving an optimization problem, due to a theorem by Georgiou and Lindquist. This optimization problem is numerically solvable by a continuation method. The proposed numerical algorithm is useful, among other cases, for designing a low-degree controller for a benchmark problem in robust control. The algorithm unifies previously developed algorithms for the Carathéodory extension and the Nevanlinna–Pick interpolation to one for more general interpolation problems.     

Some functional inequalities and inclusion relationships associated with certain families of integral operators

By making use of certain familiar integral operators, the authors introduce and investigate several new subclasses of starlike, convex, close-to-convex, and quasi-convex functions. Among other results presented here, the authors establish a number of inclusion relationships associated with some of these integral operators. Some of the results established in this paper would provide extensions of those given in earlier works.     

On sign-changing solutions for a second-order integral boundary value problem

In this paper, we obtain the existence of sign-changing solutions for nonlinear second-order differential equations with integral boundary value conditions, by applying a new fixed point theorem in ordered Banach spaces, with the lattice structure derived by Liu and Sun. Our results improve on those in the literature.     

On neighborhoods of two new subclasses of multivalent functions with negative coefficients

In this paper, we introduce two new subclasses of p-valent analytic functions defined by means of fractional derivative of order δ. We obtained the various results including coefficient bounds and distortion inequalities for these function classes. Furthermore, we determine some inclusion relations for the (n,p,ε)-neighborhoods of a family of p-valent analytic functions with negative coefficients which is defined by means of a certain nonhomogeneous Cauchy-Euler differential equation.     

On the stabilization of feedforward systems with bounded control

For the global asymptotic stabilization of nonlinear—controllable in the first approximation—cascades consisting of a globally asymptotically—locally exponentially stable system driving a stable system, a Lyapunov-like design is proposed. This yields (bounded) control laws, where the control magnitude can be chosen arbitrarily large. This result provides an alternative to classical forwarding.     

On the computation of spherical Bessel functions of complex arguments

In this short paper, problems with existing algorithms for computing spherical Bessel functions of complex arguments are reported. As a remedy, a revised algorithm based on the recurrence is proposed. The upper and lower limits for the starting order that can be used in the backward recurrence to reach a desired accuracy are given. The proposed algorithm is stable and is capable of computing a wide range of arguments approaching machine accuracy.     

On the lower bounds of the second order nonlinearities of some Boolean functions

The rth order nonlinearity of a Boolean function is an important cryptographic criterion in analyzing the security of stream as well as block ciphers. It is also important in coding theory as it is related to the covering radius of the Reed-Muller code R(r,n). In this paper we deduce the lower bounds of the second order nonlinearities of the following two types of Boolean functions:

1.

with d=2^2r+2^r+1 and , where n=6r.

2.

, where x,y∈F_2^t,n=2t,n?6 and i is an integer such that 1?i<t,gcd(2^t-1,2ⁱ+1)=1.

For some λ, the functions of the first type are bent functions, whereas Boolean functions of the second type are all bent functions, i.e., they possess the maximum first order nonlinearity. It is demonstrated that in some cases our bounds are better than the previously obtained bounds.