On the Representations of a Number as the Sum of Three Cubes and a Fourth or Fifth Power

Let R _k (n) denote the number of representations of a natural number n as the sum of three cubes and a kth power. In this paper, we show that R ₃ (n) n ^5/9+, and that R ₄ (n) n ^47/90+, where > 0 is arbitrary. This extends work of Hooley concerning sums of four cubes, to the case of sums of mixed powers. To achieve these bounds, we use a variant of the Selberg sieve method introduced by Hooley to study sums of two kth powers, and we also use various exponential sum estimates.     

Electrochemical Detection of Artemisinin Using Cobalt Sulphide/Reduced Graphene Oxide Nanocomposite

Solvothermally synthesized cobalt sulphide/reduced graphene oxide (CoS/rGO) was used to fabricate an electrochemical sensor for detection of artemisinin. Microscopic techniques were used to characterize CoS/rGO nanocomposite. The electrochemical sensor was fabricated by modifying the surface of glassy carbon electrode with CoS/rGO nanocomposite. [Fe(CN)6]^3−/4− was used as a mediator to aid oxidation of artemisinin. Differential pulse voltammetric technique was used for the detection of artemisinin. A linear range of 30–100 μM was used. Experimentally, a detection limit of 0.5 μM was obtained. Therefore, the developed sensor can be used for quality control of artemisinin.     

Driving matrix liquid crystal displays

Liquid crystal displays had a humble beginning with wrist watches in the seventies. Continued research and development in this multi-disciplinary field have resulted in displays with increased size and complexity. After three decades of growth in performance, LCDs now offer a formidable challenge to the cathode ray tubes (CRT). A major contribution to the growth of LCD technology has come from the developments in addressing techniques used for driving matrix LCDs. There are several approaches like passive matrix addressing, active matrix addressing and plasma addressing to drive a matrix display. Passive matrix LCD has a simple construction and uses the intrinsic non-linear characteristic of the LCD for driving. Departure from conventional line by line addressing of a passive matrix has resulted in improved performance of the display. Orthogonal functions have played a crucial role in the development of passive matrix addressing. Simple orthogonal functions that are useful for driving a matrix LCD are introduced. The basics of driving several rows simultaneously (multi-line addressing) are discussed by drawing analogies from multiplexing in communication. The impact of multi-line addressing techniques on the performance of the passive matrix LCDs in comparison with the conventional technique will be discussed.     

Four contemporary interpretations of the nature of science

Instrumentalism is an approach to science that treats a theory as a tool and only as a tool for computation; it dispenses with the concept of truth.Conventionalism treats a theory as true by convention if it forms a pattern of observations from which correct predictions can be made.Operationalism denies meaning to the concepts of a theory unless they can be defined operationally. It is argued in this paper that truth-value is indispensable to science, because a theory can be rejected only if an empirical consequence is false and if falsity of a conclusion entails falsity of a premise. This undermines the above positions. The fourth interpretation isinduction. Induction, by contrast, uses the notion of truth-value. What is focused on here is its reliance on the ultimacy ofobservation. The present thesis is that instrumentalism, conventionalism, and induction are different attempts to handle observations. The common problem is the gap between data and theory.All these interpretations share a philosophy of observationalism. The aim of this paper is to show that the several orthodox interpretations of science all fail to solve the problem of the data-theory gap, and to show that they all presuppose a philosophy of observation.     

On the governing equations for the compressing process and its coupling with other processes

As a continuation of a recent linear analysis by Mao et al.(Acta Mech Sin,2010,26:355),in this paper we propose a general theoretical formulation for the compressing process in complex Newtonian fluid flows,which covers gas dynamics,aeroacoustics,nonlinear thermoviscous acoustics,viscous shock layer,etc.,as its special branches.The principle on which our formulation is based is the maximally natural and dynamic Helmholtz decomposition of the Navier-Stokes equation,along with the kinematic Helmholtz decompos...     

Innovation, imitation, and problem-solving in a networked group

We implemented a problem-solving task in which groups of participants simultaneously played a simple innovation game in a complex problem space, with score feedback provided after each of a number of rounds. Each participant in a group was allowed to view and imitate the guesses of others during the game. The results showed the use of social learning strategies previously studied in other species, and demonstrated benefits of social learning and nonlinear effects of group size on strategy and performance. Rather than simply encouraging conformity, groups provided information to each individual about the distribution of useful innovations in the problem space. Imitation facilitated innovation rather than displacing it, because the former allowed good solutions to be propagated and preserved for further cumulative innovations in the group. Participants generally improved their solutions through the use of fairly conservative strategies, such as changing only a small portion of one's solution at a time, and tending to imitate solutions similar to one's own. Changes in these strategies over time had the effect of making solutions increasingly entrenched, both at individual and group levels. These results showed evidence of nonlinear dynamics in the decentralization of innovation, the emergence of group phenomena from complex interactions of individual efforts, stigmergy in the use of social information, and dynamic tradeoffs between exploration and exploitation of solutions. These results also support the idea that innovation and creativity can be recognized at the group level even when group members are generally cautious and imitative.     

Characterization of the NIST shellfish Standard Reference Material 4358

A new shellfish Standard Reference Material 4358 was developed by the National Institute of Standards and Technology through an international interlaboratory comparison that involved twelve laboratories-participants from nine countries. The results from the participants were statistically evaluated, and the most robust certified values were based on the median of laboratories’ reported means and the uncertainties derived using the bootstrap method. Massic activity certified values were established for fourteen radionuclides, five activity ratios, and informational massic activity values for eight more radionuclides and two activity ratios.     

On the Representations of a Number as the Sum of Four Fifth Powers

It is known from Vaughan and Wooley's work on Waring's problemthat every sufficiently large natural number is the sum of atmost 17 fifth powers [13]. It is also known that at least sixfifth powers are required to be able to express every sufficientlylarge natural number as a sum of fifth powers (see, for instance,[5, Theorem 394]). The techniques of [13] allow one to showthat almost all natural numbers are the sum of nine fifth powers.A problem of related interest is to obtain an upper bound forthe number of representations of a number as a sum of a fixednumber of powers. Let R(n) denote the number of representationsof the natural number n as a sum of four fifth powers. In thispaper, we establish a non-trivial upper bound for R(n), whichis expressed in the following theorem.     

Why a Diachronic View of Base Property Exemplification is Necessary in Metaethics

In a recent issue of this journal, Jorn Sonderholm presents two main criticisms of my 2008 case for a diachronic view of base property exemplification in metaethics. This essay contends that neither of Sonderholm??s criticisms hit their mark, and that there are additional reasons to adopt a diachronic view of base property exemplification. Thus, the case for a diachronic view of base property exemplification in metaethics is stronger than previously thought.     

Zn(II) and Cu(II) unsymmetrical formamidine complexes as effective initiators for ring‐opening polymerization of cyclic esters

A series of Zn(II) and Cu(II) complexes were synthesized using unsymmetrical N,N′‐ diarylformamidine ligands, i.e. N‐(2‐methoxyphenyl)‐N′‐2,6‐dichorophenyl)‐formamidine ( L1 ), N‐(2‐methoxyphenyl)‐N′‐phenyl)‐formamidine ( L2 ), N‐(2‐methoxyphenyl)‐N′‐(2,6‐dimethylphenyl)‐formamidine ( L3 ) and N‐(2‐methoxyphenyl)‐N′‐(2,6‐diisopropylphenyl)‐formamidine ( L4 ). The complexes, [Zn₂( L1 )₂(OAc)₄] ( 1) , [Zn₂( L2 )₂(OAc)₄] ( 2 ), [Zn₂( L3 )₂(OAc)₄] ( 3 ), [Zn₂( L4 )₂(OAc)₄] ( 4 ), [Cu₂( L1 )₂(OAc)₄] ( 5 ), [Cu₂( L2 )₂(OAc)₄] ( 6 ), [Cu₂( L3 )₂(OAc)₄] ( 7 ) and [Cu₂( L4 )₂(OAc)₄] ( 8 ), were prepared via a mechanochemical method with excellent yields between 95 ‐ 98% by reacting the metal acetates and corresponding ligands. Structural studies showed that both complexes are dimeric with a paddlewheel core structure in which the separation between the two metal centres are 2.9898 (8) and 2.6653 (7) Å in complexes 3 and 7 , respectively. Complexes 1 – 8 were used in ring‐opening polymerization of ε‐caprolactone (ε‐CL) and rac‐lactide (rac‐LA). Zn(II) complexes were more active than Cu(II) complexes, with complex 1 bearing electron withdrawing chloro groups being the most active (k_app = 0.0803 h^‐1). Low molecular weight poly‐(ε‐CL) and poly‐(rac‐LA) ranging from 1720 to 6042 g mol^‐1, with broad molecular weight distribution (PDIs, 1.78 – 1.87) were obtained. Complex 2 gave reaction orders of 0.56 and 1.52 with respect to ε‐CL and rac‐LA, respectively.