Comment on ‘Persistent inputs and the standard H2-multivariable control problem’ by K. Park and J.J. Bongiorno Jr

It is necessary to welcome the publication of the paper by Park and Bongiorno Jr (Park, K. and Bongiorno Jr, J.J. (2009 Park, K and Bongiorno Jr, JJ. 2009. Persistent Inputs and the Standard H₂-multivariable Control Problem. International Journal of Control, 82: 2002–2012. [Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]), ‘Persistent Inputs and the Standard H₂-multivariable Control Problem’, International Journal of Control, 82, 2002–2012) in which the special cases in H₂-optimisation problems are considered. However, for correct orientation of readers we would like to note some publications which, in our opinion, are connected to a problem given by Park and Bongiorno Jr (2009 Park, K and Bongiorno Jr, JJ. 2009. Persistent Inputs and the Standard H₂-multivariable Control Problem. International Journal of Control, 82: 2002–2012. [Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]), but are absent there.     

The nature and components of perceived behavioural control as an element of theory of planned behaviour

Ajzen (1991 Ajzen, I., 1991. The theory of planned behaviour. Organizational Behaviour and Human Decision Processes, 50(2), 179–211. doi: 10.1016/0749-5978(91)90020-T[Crossref], [Web of Science ®] , [Google Scholar]. The theory of planned behaviour. Organizational Behaviour and Human Decision Processes, 50 (2), 179–211) suggested three constructs that determine the user's intention: attitude, subject norms and perceived behavioural control (PBC). Recently, some psychologists have argued that PBC is poorly understood. This study attempted to investigate the nature and components of PBC in research adapting theory of planned behaviour (TPB) to predict the intentions of bank customers with regard to adoption of Internet banking. The findings show some difficulty in discriminating between the presumed internal and external determinants of PBC. This study identifies two determinants: (1) self-efficacy (SE) and (2) facilitating conditions. The latter is broken into three facilitation factors: (1) resources, (2) technology and (3) government support (GS). Interestingly, SE, if considered as an internal factor, exhibits a significance effect on PBC in the presence of the three external factors. This shows that the external factors have a significance effect on PBC when entered for regression analysis without SE. These are valuable findings which show that both components of one's belief in one's level of control (internal factors: SE; external factors: resources, technology and GS) are important. However, which factors have the greatest effect on PBC might be related to the type of innovation or to other factors.     

A continuous review inventory model with controllable backorder rate and investments

In this study, we investigate a continuous review inventory model to reduce lead time, yield variability and setup cost simultaneously through capital investments. We assume that the backorder rate is depending on the length of the lead time through the amount of shortages. We also assume that lead time demand's distribution is not known but its first and second moments are known. We apply minimax distribution free procedure to minimise the expected total annual cost. By using logarithmic investment function we describe the relationship between the reduction in lead time, yield variability and setup cost with capital investment. This function was used in many existing models. Our main aim is to determine the optimal capital investment and ordering policies that minimises the expected total annual cost. To find out the optimal solution, an algorithm is given. With the help of this algorithm, optimal capital investment and ordering policies are wrought out. Numerical examples are given to elucidate the model. Our proposed model greatly differs from the model existing in the literature (the model by Lin and Hou (2005 Lin, LC and Hou, KL. 2005. An Inventory System with Investment to Reduce Yield Variability and Setup Cost. Journal of the Operational Research Society, 56: 67–74. [Taylor &; Francis Online], [Web of Science ®] , [Google Scholar])) viz: (1) In the above model, yield variability and setup cost were reduced through capital investment. In our model we reduce yield variability setup cost and also the lead time, which plays a vital role in any business. By reducing lead time we can improve the service level to the customer so as to increase the competitive edge in business. (2) In the model (the model by Lin and Hou (2005 Lin, LC and Hou, KL. 2005. An Inventory System with Investment to Reduce Yield Variability and Setup Cost. Journal of the Operational Research Society, 56: 67–74. [Taylor &; Francis Online], [Web of Science ®] , [Google Scholar])), it was assumed that lead time demand follows normal distribution. But in our model we take the distribution of lead time demand as distribution free. That is, it can follow any distribution which is more general. (3) In the above model (the model by Lin and Hou (2005 Lin, LC and Hou, KL. 2005. An Inventory System with Investment to Reduce Yield Variability and Setup Cost. Journal of the Operational Research Society, 56: 67–74. [Taylor &; Francis Online], [Web of Science ®] , [Google Scholar])), shortages are completely backlogged. But we consider partial backlogging and take the backlogging rate as 0 ≤ B ≤ 1. If we set backlogging rate B = 1 we get the above model. That is, the above model is particular case of our model. (4) We also assume that the backorder rate depends on the length of the lead time through the amount of shortages. If the lead time is longer then shortage accumulation is higher. The patience of customers will result in failure in business since some customers may turn to some other supplier. Hence, the backorder rate will be reduced. This assumption is very realistic.     

A short version of the visual aesthetics of websites inventory

The present paper addresses a need for a brief assessment instrument to measure perceived visual aesthetics of websites. A short version of the Visual Aesthetics of Websites inventory (VisAWI; Moshagen and Thielsch 2010 Moshagen, M., Thielsch, M. T., 2010. Facets of visual aesthetics. International Journal of Human-Computer Studies, 68, 689–709. doi: 10.1016/j.ijhcs.2010.05.006[Crossref], [Web of Science ®] , [Google Scholar]) called VisAWI-S was developed and evaluated in three studies comprising 1673 participants in total. The results indicate that the VisAWI-S is a reliable measure that captures a single dimension of perceived visual aesthetics and provides a good approximation to the full-length version. Convergent validity was established by a strong relationship to overall appeal. Evidence for divergent validity was obtained by weaker correlations to perceived usability, pragmatic quality and quality of content as well as by absence of a significant correlation to participants’ mood. In addition to this, the VisAWI-S was found to be substantially related to the intention to revisit a website. Overall, the results indicate that the VisAWI-S may gainfully be employed to measure perceived visual aesthetics of websites when assessment times must be kept to a minimum.     

A numerical algorithm to find soft-constrained Nash equilibria in scalar LQ-games

This paper provides a numerical algorithm to calculate all soft-constrained Nash equilibria in a regular scalar indefinite linear-quadratic game. The algorithm is based on the calculation of the eigenstructure of a certain matrix. The analysis follows the lines of the approach taken by Engwerda (2003 Engwerda, JC. 2003. Solving the scalar feedback Nash algebraic Riccati equations: an eigenvector approach. IEEE Trans. Automat. Contr., 48: 847–853. [Crossref] , [Google Scholar]) to calculate the solutions of a set of scalar coupled feedback Nash algebraic Riccati equations.     

A parallel time-memory tradeoff attack on the Hill cipher

Leap et al. (2016 Leap, T., T. McDevitt, K. Novak, and N. Siermine. 2016. Further improvements to the Bauer-Millward attack on the Hill cipher. Cryptologia 40:1–16.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]) reduced the time complexity of the Bauer-Millward (2007 Bauer, C., and K. Millward. 2007. Cracking matrix encryption row by row. Cryptologia 31(1):76–83.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]) ciphertext-only attack on the Hill cipher from 𝒪(Lⁿ) to 𝒪(L^n?1), where L is the length of the alphabet, and n is the block size. This article presents an attack that reduces the complexity to 𝒪(L^n?1?s), 0?≤?s?≤?n???1. The practical limitation on the size of s is the memory available on the computer being used for the attack. Specifically, the computer must be able to hold L^s integer arrays of length N, where N is the number of blocks of ciphertext. The key idea is not to iterate over potential rows of the decryption matrix, but to iterate over randomly chosen characters in the plaintext. This attack also admits a straightforward parallel implementation on multiple processors to further decrease the run time of the attack.     

Two truck travelling salesman simulation

There are many algorithms currently available to approximate solutions to the ‘travelling salesman’ problem of finding the shortest route connecting n points in a complete tour. Conley (1988 CONLEY , W. C. , ( 1988 ), Int. J. Systems Sei. , 19 , 2115 .[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]) presents a multi–stage simulation on a rank ordered distance array to solve a one vehicle problem for n = 20. A modification of that approach is presented here to deal with sending out two delivery trucks (or one truck making two trips) to touch all n points and return. An example for n = 33 is developed. The multi–stage simulation approach is then compared with other techniques.     

Decryption oracle slide attacks on T-310

T-310 is an important Cold War cipher (Schmeh 2006 Schmeh, K. 2006. The East German encryption machine T-310 and the algorithm it used. Cryptologia 30 (3):251–257.[Taylor &; Francis Online] , [Google Scholar]). It was the principal encryption algorithm used to protect various state communication lines in Eastern Germany throughout the 1980s. The cipher seems to be quite robust, and until now no researcher has proposed an attack on T-310. This article studies decryption oracle and slide attacks on T-310.     

Adaptive learning control design for robotic manipulators driven by permanent magnet synchronous motors

On the basis of the ideas recently presented in Tomei and Verrelli (Tomei, P., and Verrelli, C.M. (2010 Tomei, P and Verrelli, CM. 2010. Learning Control for Induction Motor Servo Drives with Uncertain Rotor Resistance. International Journal of Control, 83: 1515–1528. [Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]), ‘Learning Control for Induction Motor Servo Drives with Uncertain Rotor Resistance’, International Journal of Control, 83, 1515–1528) and Marino et al. (Marino, R., Tomei, P., and Verrelli, C.M. (2011 Marino, R, Tomei, P and Verrelli, CM. 2011. Robust Adaptive Learning Control for Nonlinear Systems with Extended Matching Unstructured Uncertainties. International Journal of Robust and Nonlinear Control, Early View, doi: 10.1002/rnc.1720 [Google Scholar]), ‘Robust Adaptive Learning Control for Nonlinear Systems with Extended Matching Unstructured Uncertainties’, International Journal of Robust and Nonlinear Control, Early View, doi: 10.1002/rnc.1720), we briefly show how the adaptive learning control design proposed in Liuzzo and Tomei (Liuzzo, S., and Tomei, P. (2009 Liuzzo, S and Tomei, P. 2009. Global Adaptive Learning Control of Robotic Manipulators by Output Error Feedback. International Journal of Adaptive Control and Signal Processing, 23: 97–109.  [Google Scholar]), Global Adaptive Learning Control of Robotic Manipulators by Output Error Feedback, International Journal of Adaptive Control and Signal Processing, 23, 97–109) can be extended to robotic manipulators driven by nonsalient-pole (surface) permanent magnet synchronous motors. Unstructured uncertain dynamics (that is no parameterisation is available for the uncertainties) of the rigid robot with rotational joints are considered as well as uncertainties in stator resistances of the synchronous motors are taken into account. Two solutions with clear stability proofs are presented: a global decentralised control via state feedback and a semi-global control via output feedback. Output tracking of known periodic reference signals and learning of corresponding uncertain input reference signals are achieved. Available results in the literature are thus improved since no simplification concerning negligible electrical motor dynamics is used.     

A Novel High Quality High Capacity Image Hiding Scheme Based on Image Compression and an Optical Pixel Adjustment Process

ABSTRACT

Image hiding methods embed a secret image into a host image. The resultant stego-image does not attract the interceptors that would not detect the differences between the host image and the stego-image. To exploit the great developments in the area of image compression and to improve the quality of stego-image, this paper proposes a new method to embed the secret image into the host image. Basically, the secret image is compressed and then embedded into host image. The embedding method is based on the Optimal Pixel Adjustment Process (OPAP) and genetic algorithm. In the paper we addressed the important issues to build such systems. The experimental results showed that the proposed method can improve the quality from 60% to 80% when compared with the simple Least Significant Bit (LSB) replacement methods. Adding to that, the mean square error of the stego-image is much lower compared with other methods (Chan & Cheng, 2004 Chan, C.K. and Cheng, L.M. 2004. Hiding data in images by simple LSB substitution. Pattern Recognition, 37(3): 469–474. [Crossref], [Web of Science ®] , [Google Scholar]; Chang, Hsiao, & Chan, 2003 Chang, C.C., Hsiao, J.Y. and Chan, C.S. 2003. Finding optimal least-significant-bit substitution in image hiding by dynamic programming strategy. Pattern Recognition, 36(7): 1583–1595. [Crossref], [Web of Science ®] , [Google Scholar]; Thien & Lin, 2003 Thien, C.C. and Lin, J.C. 2003. A simple and high-hiding capacity method for hiding digit-by-digit data in images based on modulus function. Pattern Recognition, 36(12): 2875–2881. [Crossref], [Web of Science ®] , [Google Scholar]; Tseng, Chan, Ho, & Chu, 208; Wang, Lin, & Lin, 2001 Wang, R.Z., Lin, C.F. and Lin, J.C. 2001. Image hiding by optimal LSB substitution and genetic algorithm. Pattern Recognition, 34(3): 671–683. [Crossref], [Web of Science ®] , [Google Scholar]). Also, the proposed technique improves capacity. In other words, we can embed a secret image with size 450?×?450 inside a hosting image with size 512?×?512.     

Continuous-time non-linear flatness-based predictive control: an exact feedforward linearisation setting with an induction drive example

A general flatness-based framework for non-linear continuous-time predictive control is presented. It extends the results of Fliess and Marquez (2000 Fliess, M and Marquez, R. 2000. Continuous-time Linear Predictive Control and Flatness: A Module-theoretic Setting with Examples. International Journal of Control, 73: 606–623. [Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]) to the non-linear case. The mathematical setting, which is valid for multivariable systems, is provided by the theory of flatness-based exact feedforward linearisation introduced by the authors (Hagenmeyer and Delaleau 2003b Hagenmeyer, V and Delaleau, E. 2003b. Exact Feedforward Linearization Based on Differential Flatness. International Journal of Control, 76: 537–556. [Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]). Thereby differential flatness does not only yield an easy calculation of the predicted trajectories considering the respective system constraints, but allows to use simple linear feedback parts in a two-degree-of-freedom control structure. Moreover, this formalism permits one to handle non-minimum phase systems, and furthermore to deal with parameter uncertainties and exogenous perturbations. Respective robustness analysis tools are available. Finally, an induction drive example is discussed in detail and experimental results for this fast electro-mechanical system are presented.     

Approximation error in PDE-based modelling of vehicular platoons

We study the problem of how much error is introduced in approximating the dynamics of a large vehicular platoon by using a partial differential equation, as was done in Barooah, Mehta, and Hespanha [Barooah, P., Mehta, P.G., and Hespanha, J.P. (2009 Barooah, P, Mehta, PG and Hespanha, JP. 2009. Mistuning-based Decentralised Control of Vehicular Platoons for Improved Closed Loop Stability. IEEE Transactions on Automatic Control, 54: 2100–2113. [Crossref], [Web of Science ®] , [Google Scholar]), ‘Mistuning-based Decentralised Control of Vehicular Platoons for Improved Closed Loop Stability’, IEEE Transactions on Automatic Control, 54, 2100–2113], Hao, Barooah, and Mehta [Hao, H., Barooah, P., and Mehta, P.G. (2011), ‘Stability Margin Scaling Laws of Distributed Formation Control as a Function of Network Structure’, IEEE Transactions on Automatic Control, 56, 923–929]. In particular, we examine the difference between the stability margins of the coupled-ordinary differential equations (ODE) model and its partial differential equation (PDE) approximation, which we call the approximation error. The stability margin is defined as the absolute value of the real part of the least stable pole. The PDE model has proved useful in the design of distributed control schemes (Barooah et al. 2009 Barooah, P, Mehta, PG and Hespanha, JP. 2009. Mistuning-based Decentralised Control of Vehicular Platoons for Improved Closed Loop Stability. IEEE Transactions on Automatic Control, 54: 2100–2113. [Crossref], [Web of Science ®] , [Google Scholar]; Hao et al. 2011 Hao, H, Barooah, P and Mehta, PG. 2011. Stability Margin Scaling Laws of Distributed Formation Control as a Function of Network Structure. IEEE Transactions on Automatic Control, 56: 923–929. [Crossref], [Web of Science ®] , [Google Scholar]); it provides insight into the effect of gains of local controllers on the closed-loop stability margin that is lacking in the coupled-ODE model. Here we show that the ratio of the approximation error to the stability margin is O(1/N), where N is the number of vehicles. Thus, the PDE model is an accurate approximation of the coupled-ODE model when N is large. Numerical computations are provided to corroborate the analysis.     

Optimal control of the production–inventory system with deteriorating items and tradable emission permits

Using the well-known Arrow and Karlin (1958) Arrow, K.J., and Karlin, S. (1958), ‘Production over Time with Increasing Marginal Costs’, in Studies in the Mathematical Theory of Inventory and Production, eds. K.J. Arrow and S. Karlin, Stanford: Stanford University Press, pp. 61–69. [Google Scholar] dynamic production–inventory model and the model with tradable emission permits which was presented by Dobos (2005 Dobos, I. (2005), ‘The Effects of Emission Trading on Production and Inventories in the Arrow–Karlin Model’, International Journal of Production Economics, 93–94, 301–308.[Crossref], [Web of Science ®] , [Google Scholar], 2007) Dobos I. (2007), ‘Tradable Emission Permits and Production-inventory Strategies of the Firm’, International Journal of Production Economics, 108, 329–333.[Crossref], [Web of Science ®] , [Google Scholar], we develop a model of the production–inventory system with deteriorating items and tradable emission permits. The objective of this paper is to apply the optimal control theory to solve the production–inventory problem with deteriorating items and tradable emission permits, and derive the optimal inventory level and the optimal production rate that minimise the total cost. The results are discussed with a numerical example and a sensitivity analysis of the optimal solution with respect to the parameters of the production–inventory system is carried out.     

Comment on ‘Optimal inventory replenishment policy for the EPQ model under trade credit derived without derivatives’

In this article, we complement the shortcoming of the inventory economic production quantity (EPQ) model developed by Huang and Huang (2008 Huang, YF and Huang, HF. 2008. Optimal Inventory Replenishment Policy for the EPQ Model Under Trade Credit Derived Without Derivatives. International Journal of Systems Science, 39: 539–546. [Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]), ‘Optimal Inventory Replenishment Policy for the EPQ Model Under Trade Credit Derived Without Derivatives’, International Journal of Systems Science, 39, 539–546), and propose an arithmetic–geometric inequality method to obtain the global optimal solution without taking complex differential calculus or using tedious algebraic manipulations. Finally, we provide an economical interpretation of the theoretical result so that the reader can understand the insight of the result.     

CIPHER EQUIPMENT

Abstract

In this article, a simplified version of the International Data Encryption Algorithm (IDEA) is described. This simplified version, like simplified versions of DES [8-12 Schaefer , E. 1996 . “A Simplified Data Encryption Standard Algorithm,” Cryptologia , 20 ( 1 ): 77 – 84 . Schneier , B. 1996 . Applied Cryptography, , 2nd ed . Wiley , New York , NY . Schneier , B. 1999. Crypto Guru Bruce Schneier Answers. http://slashdot.org/interviews/99/10/29/0832246.shtml last accessed February 23, 2007. Shannon , C. “Communications Theory of Secrecy Systems,” Oct. 1949 . Bell Systems Technical Journal , 28 ( 4 ): 656 – 715 . Trappe , W. and L. Washington . 2006 . Introduction to Cryptography with Coding Theory, , 2nd ed. Prentice Hall , Upper Saddle River , NJ . ] and AES [6 Musa , M. , E. Shaefer , and S. Wedig . 2003 . “A Simplified AES Algorithm and its Linear and Differential Cryptanalysis,” Cryptologia , 17 ( 2 ): 148 – 177 . [Google Scholar] 7 Phan , R. 2002 . “Mini Advanced Encryption Standard (Mini-AES): A Testbed for Cryptanalysis Students,” Cryptologia , 26 ( 4 ): 283 – 306 .[Taylor &; Francis Online] , [Google Scholar]] that have appeared in print, is intended to help students understand the algorithm by providing a version that permits examples to be worked by hand. IDEA is useful teaching tool to help students bridge the gap between DES and AES.     

On the validity of the arithmetic–geometric mean method to locate the optimal solution in a supply chain system

Cardenas-Barron [Cardenas-Barron, L.E. (2010) ‘A Simple Method to Compute Economic order Quantities: Some Observations’, Applied Mathematical Modelling, 34, 1684–1688] indicates that there are several functions in which the arithmetic–geometric mean method (AGM) does not give the minimum. This article presents another situation to reveal that the AGM inequality to locate the optimal solution may be invalid for Teng, Chen, and Goyal [Teng, J.T., Chen, J., and Goyal S.K. (2009), ‘A Comprehensive Note on: An Inventory Model under Two Levels of Trade Credit and Limited Storage Space Derived without Derivatives’, Applied Mathematical Modelling, 33, 4388–4396], Teng and Goyal [Teng, J.T., and Goyal S.K. (2009), ‘Comment on ‘Optimal Inventory Replenishment Policy for the EPQ Model under Trade Credit Derived without Derivatives’, International Journal of Systems Science, 40, 1095–1098] and Hsieh, Chang, Weng, and Dye [Hsieh, T.P., Chang, H.J., Weng, M.W., and Dye, C.Y. (2008), ‘A Simple Approach to an Integrated Single-vendor Single-buyer Inventory System with Shortage’, Production Planning and Control, 19, 601–604]. So, the main purpose of this article is to adopt the calculus approach not only to overcome shortcomings of the arithmetic–geometric mean method of Teng et al. (2009), Teng and Goyal (2009 Teng, JT, Chen, J and Goyal, SK. 2009. A Comprehensive Note on: An Inventory Model under Two Levels of Trade Credit and Limited Storage Space Derived without Derivatives. Applied Mathematical Modelling, 33: 4388–4396. [Crossref], [Web of Science ®] , [Google Scholar]) and Hsieh et al. (2008), but also to develop the complete solution procedures for them.     

Capture of shrinking targets

‘Shrinking targets’ are targets whose size diminishes with time. The task studied is a modification of Fitts' (1954 Fitts, P. M. 1954. The information capacity of the human motor system in controlling the amplitude of movement. Journal of Experimental Psychology, 67(6): 381–391. [Crossref] , [Google Scholar]) paradigm, with the difference that, as soon as the movement is started, the target size reduces at a constant rate until it finally vanishes. Very little research has been reported on this problem apart from Johnson and Hart (1987 Johnson, W. W. and Hart, S. G. Step tracking shrinking targets. Proceedings of the Human Factors Society 31st annual meeting. October1987, New York City. pp.248–252. Santa Monica, CA: HFES.  [Google Scholar]) and Hancock and Caird (1993 Hancock, P. A. and Caird, J. K. 1993. Experimental evaluation of a model of mental workload. Human Factors, 35(3): 413–429. [Crossref], [PubMed], [Web of Science ®] , [Google Scholar]). Two experiments are reported aimed at determining the parameters that affect the movement time and the probability of capturing a target when there are different amplitudes of movement, target widths and shrink rates. A multiplicative model is required to describe movement time data, which is dependent on Fitts' Index of Difficulty, the shrink rate and the product of these two variables. An alternative model describes the critical movement time, for a specified probability of target capture, in a modified form of Fitts' Law.

Statement of Relevance: Modifications of Fitts' Law have been developed for many different movement tasks. Shrinking targets occur in circumstances such as gunnery and in computer games, where a target is moving away from the person. An expression is developed for the critical time to capture the target in terms of a modified form of Fitts' Law.     

FROM THE ARCHIVES: CODETALKERS NOT WANTED

Abstract

The Hill Cipher, also known as matrix encryption, uses matrices to encipher and decipher text. Various attacks, such as those found by Jack Levine [2 Levine , J. 1961 . “Some Applications of High-Speed Computers to the Case n = 2 of Algebraic Cryptography,” Mathematics of Computation , 15 ( 75 ). [Google Scholar] 3 Levine , J. 1961 . “Some Elementary Cryptanalysis of Algebraic Cryptography,” American Mathematical Monthly , 68 ( 5 ): 411 – 418 .[Taylor &; Francis Online] , [Google Scholar] 5 Levine , J. and R. Chandler . 1989 . “The Hill Cryptographic System with Unknown Cipher Alphabet but Known Plaintext,” Cryptologia , 13 ( 1 ): 1 – 28 .[Taylor &; Francis Online] , [Google Scholar]], have been published for this system. This article reviews a few previous results and presents a powerful new attack in which the rows of the matrix can be determined independent of one another, greatly reducing the amount of time needed for decipherment.