摘要：
We propose a new ultra-lightweight block cipher, QTL. The 64 bits block cipher QTL supports 64 and 128 bits keys. To solve the slow diffusion of the traditional Feistel-type structures we have used a new variant of generalized Feistel network structure in design of the QTL. Traditional Feistel-type structures change only half of block messages in an iterative round, but our structure overcomes this disadvantage and changes all block messages. Thus, our structure has the fast diffusion of the Substitution Permutation Networks (SPNs) structures, which improves the security of lightweight block cipher in Feistel-type structures. Moreover, QTL algorithm has the same encryption and decryption processes, so it will occupy less area in resource-constrained applications. Furthermore, to reduce the cost of energy consumption in hardware implementation of the cipher while maintaining security, we decide not to use a key schedule. We show that QTL offers an adequate security level against classic analyses. Our hardware implementation for the 64 and the 128 bits keys modes only require 1025.52 and 1206.52 gate equivalents, respectively. QTL achieves high security and compact implementation in hardware. QTL is one of the most competitive ultra-lightweight block ciphers, which is suitable for extremely constrained devices. (C) 2016 Elsevier B.V. All rights reserved.
期刊：
International Journal of Control and Automation,2016年9(1):33-46 ISSN：2005-4297
通讯作者：
Long, Zuqiang(zuqianglong@126.com)
作者机构：
[Long, Zuqiang] Dept. of Physics and Electronics Information Science, Hengyang Normal University, Hengyang, China;[Li, Long] Dept. of Mathematics and Computational Science, Hengyang Normal University, Hengyang, China;[Xu, Yuebing] College of Electrical and Information Engineering, Hunan University, Changsha, China
通讯机构：
Dept. of Physics and Electronics Information Science, Hengyang Normal University, Hengyang, China
关键词：
Expert Rules;Flash Evaporator;Fuzzy Control;Fuzzy Systems;Phosphoric Slurry;Variable Universes of Discourse
作者机构：
[Li, Liulan] Hengyang Normal Univ, Coll Math & Stat, E Ring Rd, Hengyang 421002, Hunan, Peoples R China.;[Ponnusamy, Saminathan] Indian Stat Inst, Chennai Ctr, Soc Elect Transact & Secur, CIT Campus, Madras 600113, Tamil Nadu, India.
通讯机构：
[Li, Liulan] H;Hengyang Normal Univ, Coll Math & Stat, E Ring Rd, Hengyang 421002, Hunan, Peoples R China.
摘要：
We consider the class H
0 of sense-preserving harmonic functions
$$f = h + \bar g$$
defined in the unit disk |z| < 1 and normalized so that h(0) = 0 = h′(0) − 1 and g(0) = 0 = g′(0), where h and g are analytic in the unit disk. In the first part of the article we present two classes P
H
0(α) and G
H
0(β) of functions from H
0 and show that if f ∈ P
H
0(α) and F ∈ G
H
0(β), then the harmonic convolution is a univalent and close-to-convex harmonic function in the unit disk provided certain conditions for parameters α and β are satisfied. In the second part we study the harmonic sections (partial sums)
$${s_{n,n}}\left( f \right)\left( z \right) = {s_n}\left( h \right)\left( z \right) + \overline {{s_n}\left( g \right)\left( z \right)} ,$$
where
$$f = h + \bar g$$
∈ H
0, s
n
(h) and s
n
(g) denote the n-th partial sums of h and g, respectively. We prove, among others, that if
$$f = h + \bar g$$
∈ H
0 is a univalent harmonic convex mapping, then s
n
,n(f) is univalent and close-to-convex in the disk |z| < 1/4 for n ≥ 2, and s
n
,n(f) is also convex in the disk |z| < 1/4 for n ≥ 2 and n ≠ 3. Moreover, we show that the section s
3,3(f) of f ∈ C
H
0 is not convex in the disk |z| < 1/4 but it is convex in a smaller disk.
作者机构：
[Li, Liulan] Hengyang Normal Univ, Dept Math & Computat Sci, Hengyang 421008, Hunan, Peoples R China.;[Ponnusamy, Saminathan] MGR Knowledge City, SETS, Chennai Ctr, ISI, Madras 600113, Tamil Nadu, India.
通讯机构：
[Ponnusamy, Saminathan] M;MGR Knowledge City, SETS, Chennai Ctr, ISI, Madras 600113, Tamil Nadu, India.
关键词：
Convex;Harmonic convolution;Partial sum;Stable harmonic convex and close-to-convex mappings;Starlike and close-to-convex harmonic mappings;Univalent
摘要：
In this article, we consider the class SHC of normalized stable harmonic convex mappings f = h + (g) over bar in the unit disk and determine r such that every section of f is close-to-convex or convex in the disk vertical bar z vertical bar < r. Also, we show that the convolution f * f is an element of SHC whenever f is an element of SHC. In addition, we prove that the harmonic convolution f(1) * f(2) is stable harmonic close-to-convex whenever f(1) is an element of SHC and f(2) is either a slanted half-plane mapping or an asymmetric vertical strip mapping or a mapping in the family P-H(0) (alpha) which is contained in the family of harmonic close-to-convex functions in vertical bar z vertical bar < 1. (C) 2014 Elsevier Ltd. All rights reserved.
期刊：
Complex Analysis and Operator Theory,2015年9(1):183-199 ISSN：1661-8254
通讯作者：
Ponnusamy, Saminathan
作者机构：
[Li, Liulan] Hengyang Normal Univ, Dept Math & Computat Sci, Hengyang 421008, Hunan, Peoples R China.;[Ponnusamy, Saminathan] Indian Stat Inst, SETS, MGR Knowledge City, Chennai Ctr, Madras 600113, Tamil Nadu, India.;[Ponnusamy, Saminathan] Indian Stat Inst, SETS, MGR Knowledge City, Chennai Ctr, CIT Campus, Madras 600113, Tamil Nadu, India.
通讯机构：
[Ponnusamy, Saminathan] I;Indian Stat Inst, SETS, MGR Knowledge City, Chennai Ctr, CIT Campus, Madras 600113, Tamil Nadu, India.
关键词：
Harmonic;Univalent;Close-to-convex;Starlike;Convex mappings;Convex in a direction;Convolution
摘要：
Let be a fixed univalent and sense-preserving harmonic mapping which is convex in the real direction but is not starlike in the unit disk . The convolution of with other harmonic mappings, eg. half-plane mappings, is not necessarily univalent in . In this paper, under suitable restriction on the dilatation of , we show that the convolutions of with certain slanted half-plane harmonic mappings are necessarily convex in a direction. In addition, we consider a fixed harmonic mapping and with the dilatation , where denotes the class of asymmetric vertical strip mappings. We find the relationship between and such that is a sense-preserving univalent harmonic mapping and is convex in some direction. These results are a generalization of the corresponding recent result of Dorff et al.. The contents of this paper enhance the interest in univalent harmonic mappings, especially when much is not known on the harmonic convolution.
作者：
Abu Muhanna, Yusuf*;Li, Liulan;Ponnusamy, Saminathan
期刊：
Archiv der Mathematik,2014年103(6):461-471 ISSN：0003-889X
通讯作者：
Abu Muhanna, Yusuf
作者机构：
[Abu Muhanna, Yusuf] Amer Univ Sharjah, Dept Math, Sharjah 26666, U Arab Emirates.;[Li, Liulan] Hengyang Normal Univ, Dept Math & Computat Sci, Hengyang 421008, Hunan, Peoples R China.;[Ponnusamy, Saminathan] SETS, Indian Stat Inst, Chennai Ctr, Madras 600113, Tamil Nadu, India.
通讯机构：
[Abu Muhanna, Yusuf] A;Amer Univ Sharjah, Dept Math, Sharjah 26666, U Arab Emirates.
关键词：
Univalent;Convex;Starlike;Close-to-convex;Extreme points;Hayman index;Arclength;Zalcman functional;and Harmonic function
摘要：
Lawrence Zalcman's conjecture states that if is analytic and univalent in the unit disk , then for each , with equality only for the Koebe function and its rotations. This conjecture remains open although it has been verified for a few geometric subclasses of the class of univalent analytic functions. In this paper, we consider this problem for the family of normalized functions f analytic and univalent in the unit disk |z| < 1 satisfying the condition Functions satisfying this condition are known to be convex in some direction (and hence close-to-convex and univalent) in |z| < 1. A few other related basic results and remarks about the Hayman index of functions in this family are also presented.
