Construction of one-gray weight codes and two-Gray weight codes over ℤ<Subscript>4</Subscript> + <Emphasis Type="Italic">u</Emphasis>ℤ<Subscript>4</Subscript>

This paper firstly gives some necessary conditions on one-Gray weight linear codes. And then we use these results to construct several classes of one-Gray weight linear codes over ?₄+u?₄(u ² = u) with type \({16^{{k_1}}}{8^{{k_2}}}{8^{{k_3}}}{4^{{k_4}}}{4^{{k_5}}}{4^{{k_6}}}{2^{{k_7}}}{2^{{k_8}}}\) based on a distance-preserving Gray map from (?₄ + u?₄) ⁿ to ? ₄ ²ⁿ . Secondly, the authors use the similar approach to do works on two-Gray (projective) weight linear codes. Finally, some examples are given to illustrate the construction methods.     

CLT of wavelet estimator in semiparametric model with correlated errors

This paper considers the semiparametric regression model j/j= Xif3+g（U）+Vi（1 < i < n）, where（x_i,t_i） are known design points,/3 is an unknown slope parameter,g（·） is an unknown function, the correlated errors Vi=∑_j=-∞^∞c_je_i-jwith∑_j=-∞^∞|c_j|<∞,and e_i negatively associated random variables.Under appropriate conditions,the authors study the asymptotic normality for wavelet estimators ofβand g（·）.A simulation study is undertaken to investigate finite sample behavior of the estimators.     

A class of constacyclic codes over ring <Emphasis Type="Italic">R</Emphasis> + <Emphasis Type="Italic">vR</Emphasis>

By constructing a Gray map, a class of constacyclic codes over ring R = R+vR is studied. Using cyclic codes and negacyclic codes of length p ^s over ring R, the structure of (1?2v)-constacyclic codes and dual codes of length p ^s over ring R are given, the Gray images of (1 ? 2v)-constacyclic codes in a particular case are also studied. It is shown that linear codes of length p ^s over ring R are (1?2v)-constacyclic codes if and only if their Gray images are distance-invariant cyclic codes of length 2p ^s over ring R.     

Some semi-bent functions with polynomial trace form

This paper is devoted to the study of semi-bent functions with several parameters flexible on the finite field F2n.Boolean functions defined on F2n of the form f（r）ab（x） =Trn1（axr（2m-1））＋Tr41（bx（2n-1）/5） and the form g（rs）abcd（x）=Trn1（axr（2m-1））＋Tr41（bx（2n-1）/5）＋Trn1（cx（2m-1）1/2＋1）＋Trn1（dx（2m-1）s＋1） where n = 2m,m = 2（mod 4）,a,c ∈ F2n,and b ∈ F（16）,d ∈ F2,are investigated in constructing new classes of semi-bent functions.Some characteristic sums such as Kloosterman sums and Weil sums are employed to determine whether the above functions are semi-bent or not.     

The determination on weight hierarchies of <Emphasis Type="Italic">q</Emphasis>-ary linear codes of dimension 5 in class IV

The weight hierarchy of a linear [n; k; q] code C over GF(q) is the sequence (d ₁, d ₂, ···, d _k ) where d _r is the smallest support of any r-dimensional subcode of C. “Determining all possible weight hierarchies of general linear codes” is a basic theoretical issue and has important scientific significance in communication system. However, it is impossible for q-ary linear codes of dimension k when q and k are slightly larger, then a reasonable formulation of the problem is modified as: “Determine almost all weight hierarchies of general q-ary linear codes of dimension k”. In this paper, based on the finite projective geometry method, the authors study q-ary linear codes of dimension 5 in class IV, and find new necessary conditions of their weight hierarchies, and classify their weight hierarchies into 6 subclasses. The authors also develop and improve the method of the subspace set, thus determine almost all weight hierarchies of 5-dimensional linear codes in class IV. It opens the way to determine the weight hierarchies of the rest two of 5-dimensional codes (classes III and VI), and break through the difficulties. Furthermore, the new necessary conditions show that original necessary conditions of the weight hierarchies of k-dimensional codes were not enough (not most tight nor best), so, it is important to excogitate further new necessary conditions for attacking and solving the k-dimensional problem.     

Construction of one-Lee weight and two-Lee weight codes over F<Subscript><Emphasis Type="Italic">p</Emphasis></Subscript> + <Emphasis Type="Italic">v</Emphasis>F<Subscript><Emphasis Type="Italic">p</Emphasis></Subscript>

This paper is devoted to the construction of one-Lee weight codes and two-Lee weight codes over F _p + vF _p (v ² = v) with type \({p^{2{k_1}}}{p^{{k_2}}}{p^{{k_3}}}\) based on two different distance-preserving Gray maps from ((F _p + vF _p ) ⁿ , Lee weight) to (F _p ²ⁿ , Hamming weight), where p is a prime. Moreover, the authors prove that the obtained two-Lee weight codes are projective only when p = 2.     

An on-line scheduling problem of parallel machines with common maintenance time

In this paper, the authors consider an on-line scheduling problem of m (m ≥ 3) identical machines with common maintenance time interval and nonresumable availability. For the case that the length of maintenance time interval is larger than the largest processing time of jobs, the authors prove that any on-line algorithm has not a constant competitive ratio. For the case that the length of maintenance time interval is less than or equal to the largest processing time of jobs, the authors prove a lower bound of 3 on the competitive ratio. The authors give an on-line algorithm with competitive ratio $4 - \tfrac{1} {m} $ . In particular, for the case of m = 3, the authors prove the competitive ratio of the on-line algorithm is $\tfrac{{10}} {3} $ .     

The Contribution of Innovation Strategy Development and Implementation in Active Facilitation of Pharmaceutical Front End Innovation

Front end innovation (FEI) represents the first building blocks of product development, but is often regarded as a weak link in innovation literature. Various theorists emphasize that a firm??s innovation can benefit substantially by improving the front end of innovation process (Reinertsen, Res Technol Manag 42:23?C31, 1999; Stevens and Burly, Res Technol Manag 46(2):16?C25, 2003; Verworn et al., R&D Manag 38(1):1?C19, 2008) and that innovation strategies play a central role in optimization of innovation (Clark and Wheelwright, Leading product development, Free Press, New York, 1995; Cottam et al., Eur J Innov Manag 4:88?C94, 2001; Morgan and Berthon, J Manag Stud 45(8):1329?C1353, 2008). Innovation strategies are suggested in literature (e.g. Page, J Prod Innov Manag 10:273?C287, 1993; Oke, J Change Manag 2(3):272?C281, 2002; Adams et al., Int J Manag Rev 8(1):21?C47, 2006; Igartua et al., Res Technol Manag May?CJune:41?C52, 2010) as a facilitator of innovation and may therefore also be targeted at FEI support. The pharmaceutical industry has experienced a worldwide decline in the number of applications for new molecular entities to regulatory agencies since 1997. Therefore high pressures are put on pharmaceutical research and FEI to produce more valid candidates and faster for drug development. This paper explores how pharmaceutical FEI can be actively supported through the development and implementation of an innovation strategy. The empirical field and applied methodology is an action oriented longitudinal case study of a Danish pharmaceutical company. The findings and key learnings from the study are presented as propositions of how innovation strategies can be applied to actively facilitate FEI and with measurable results.     

On LCD Negacyclic Codes over Finite Fields

This paper deduces the structure of LCD negacyclic codes over the finite field Fq, where q is an odd prime power. Based on the study of q-cyclotomic cosets modulo 2 n, the authors obtain the parameters of LCD negacyclic codes of lengths n =(q+1)/2,(q~m-1)/2(q-1)and q~(t·2~τ)-1/2(q~t +1), respectively. And many optimal codes are given. Moreover, the authors research two special classes of MDS LCD negacyclic codes of length n |(q-1)/2 and n |(q+1)2, respectively.     

Further study strong consistency of M estimator in linear model for \tilde \rho-mixing random samples

The strong consistency of M estimators of the regression parameters in linear models for $\tilde \rho$ -mixing random errors under some mild conditions is established, which is an essential improvement over the relevant results in the literature on the moment conditions and mixing errors. Especially, Theorem of Wu (2005) is improved essentially on the moment conditions.     

THE HAMMING DISTANCES OF NEGACYCLIC CODES OF LENGTH 2^s OVER GR （2^α, m）

The Hamming distances of all negacyclic codes of length 28 over the Gaiois ring GR （2^α, m） are given. In particular, the Lee distances of all negacyclic codes over Z4 of length 2^s are obtained. The Gray images of such negacyclic codes over Z4 are also determined under the Gray map.     

Systems Thinking and Higher Education: The Vanguard Method

Reforms to the higher education sector in the UK are only increasing competitive pressures between institutions. Universities are therefore looking to gain competitive advantage over their rivals both in terms of student experience and through administrative efficiency. This paper will present an alternative view of how to transform the way that the higher education system delivers service to students in an environment where ‘student choice’ will be viewed as of paramount importance. The paper will argue that the prevailing ‘command and control’ (Seddon 2003) management logic, which can be found at work throughout both the public and private sectors, is the primary cause of inferior, expensive service. As an alternative, this paper will explore the benefits of working in a systems thinking way, whilst comparing and contrasting this with the flawed thinking which currently prevails. The Vanguard Method (Seddon 2008) is one particular form of systems thinking which has been developed for use in service organisations (Jackson et al. 2008) and which has been applied to many public sector organisations (ODPM 2005; Middleton 2010; Zokaei et al. 2010). Using a case study methodology (Yin 2009), this paper will address what has been learnt by applying the Vanguard Method in an HEI environment for the first time.     

Semi On-Line Scheduling Problem for Maximizing the Minimum Machine Completion Time on Two Uniform Machines

Ia this paper, we consider a semi on-line version on two uniform machines Mi, i = 1, 2, where the processing time of the largest job is known in advance. A speed si（s1 = 1, 1 ≤s2 = s） is associated with machine Mi. Our goal is to maximize the Cmin. We give a Cmin 2 algorithm and prove its competitive ratio is at most 2s＋1/s＋1 We also claim the Cmin 2 algorithm is tight and the gap between the competitive ratio of Cmin2 algorithm and the optimal value is not greater than 0.555. It is obvious that our result coincides with that given by He for s =1.     

Control and Stabilization of the Rosenau Equation Posed on a Periodic Domain

This paper considers the Rosenau equation with a moving control?t u + ?_t?_x~4 u + ?_xu + u?x u = a(x + ct)h(x, t), c = 0, x ∈ T = R/(2πZ), t 0.The authors prove that the Rosenau equation with a moving control is locally exact controllable in Hs(T) with s ≥ 0 and globally exponential stable in H~s(T) with s ≥ 2. The two results nontrivially extend the work of(Rosier L and Zhang B Y, 2013) from the BBM equation to the Rosenau equation.     

On algebraic immunity of trace inverse functions on finite fields of characteristic two

The trace inverse functions Tr(λx~(-1)) over the finite field F_(2~n) are a class of very important Boolean functions and are used in many stream ciphers such as SFINKS,RAKAPOSHI,the simple counter stream cipher(SCSC) presented by Si W and Ding C(2012),etc.In order to evaluate the security of those ciphers in resistance to(fast) algebraic attacks,the authors need to characterize algebraic properties of Tr(λx~(-1)).However,currently only some bounds on algebraic immunity of Tr(λx~(-1)) are given in the public literature,for example,the NGG upper bound and the Bayev lower bound,etc.This paper gives the exact value of the algebraic immunity of Tr(λx~(-1)) over F_(2~n),that is,AI(Tr(λx~(-1))) =[2n~(1/2)]- 2,where n ≥ 2,A ∈ F_(2~n) and λ≠ 0,which shows that Dalai's conjecture on the algebraic immunity of Tr(λx~(-1)) is correct.What is more,the authors demonstrate some weak properties of Tr(λx~(-1)) against fast algebraic attacks.     

Variational discretization for parabolic optimal control problems with control constraints

This paper studies variational discretization for the optimal control problem governed by parabolic equations with control constraints.First of all,the authors derive a priori error estimates where |||u-U₍h|||_L∞（J;L²（Ω））=O（h²+k）.It is much better than a priori error estimates of standard finite element and backward Euler method where |||μ-U_h|||₍L∞（J;L²（Ω））=O（h+ k）.Secondly,the authors obtain a posteriori error estimates of residual type.Finally,the authors present some numerical algorithms for the optimal control problem and do some numerical experiments to illustrate their theoretical results.     

On-Line Scheduling on Parallel Machines to Minimize the Makespan

This paper considers two parallel machine scheduling problems,where the objectives of both problems are to minimize the makespan,and the jobs arrive over time,on two uniform machines with speeds 1 and s(s≥1),and on m identical machines,respectively.For the first problem,the authors show that the on-line LPT algorithm has a competitive ratio of(1 +5~(1/2))/2≈1.6180 and the bound is tight.Furthermore,the authors prove that the on-line LPT algorithm has the best possible competitive ratio if s≥1.8020.For the second problem,the authors present a lower bound of(15-(17)~(1/2))/8≈1.3596 on the competitive ratio of any deterministic on-line algorithm.This improves a previous result of 1.3473.     

A family of constacyclic codes over F 2 + uF 2 + vF 2 + uvF 2

This paper studies（1+u）-constacyclic codes over the ring F₂+uF₂+vF₂+uvF₂- It is proved that the image of a（1 + u）-constacyclic code of length n over F₂+uF₂+vF₂+uvF₂ under a Gray map is a distance invariant binary quasi-cyclic code of index 2 and length An.A set of generators of such constacyclic codes for an arbitrary length is determined.Some optimal binary codes are obtained directly from（1 + u）-constacyclic codes over F₂+uF₂+vF₂+uvF₂.     

Dynamic price model based on transmission delay — Petroleum price fluctuation in China

Petroleum is a kind of fundamental energy resource. Its price fluctuation transmits from upper-stream industry to the lower-stream industry as the production factors price changes. And this leads to the price changes of final consumption. Meantime, due to the cycle of industrial chain, the price changes of lower-stream industry also affect the upper-stream industry in return. This price transmission path is quite complicated. Firstly, it includes both direct and indirect paths; secondly, the transmission process is accompanied with time delay. The traditional input-output price model based on cost-push theory can efficiently solve the first problem when estimating the impact of price fluctuation on the whole price system. However, it neither reflects the dynamic characteristics of price transmission with time nor solves the second problem. To solve this problem, this paper uses the directed weighted network to describe the price transmission among industrial sectors by taking the time-dimension into account, and dynamic price transmission network model is constructed. This model not only describes transmission time delay more accurately, but also calculates the price fluctuation dynamically. On this basis, by utilizing the 2007 Chinese input-output table, this paper conducts empirical analysis on the impact of petroleum price fluctuation on other sectors. The empirical results indicate that the price fluctuation transmission mainly depends on two factors, the orice reaction period Tk and the consumption relationship with petroleum aik. 1） If t 〈 Tk, then the price change of sector k at period t △pkt = 0, the petroleum price fluctuation has not transmitted to the sector k, so the price of sector k remains unchanged. 2） If t 〉 Tk, then Apt 〉 0, and the greater aik, the higher price change rate. 3） If t →∞, it is the same with that in traditional input-output price model. So it can be clearly seen that dynamic price transmission network model is more general than the traditional model, and the traditional model is just an asymptotical special case when time approaches to infinity. Keywords Directed weighted network, input-output price model, petroleum price, transmission time delay.