Comment on: “Globally exponential synchronization in array of asymmetric coupled neural networks” [Phys. Lett. A 369 (2007) 444]

In this Letter, we indicate that the proposed sufficient condition in Letter [J.Q. Lu, W.C. Ho, M. Liu, Phys. Lett. A 369 (2007) 444] does not hold when coupling matrix G satisfies Assumption 3 in Letter [J.Q. Lu, W.C. Ho, M. Liu, Phys. Lett. A 369 (2007) 444]. Besides, there are some mistakes in deducing Theorem 1. The mistakes have been corrected and a correct version is given in this Letter.     

Comment on: “A class of bound entangled states” [Phys. Lett. A 352 (2006) 321]

We generalize the condition keeping the special states bound entangled [S.-M. Fei, X. Li-Jost, B.-Z. Sun, Phys. Lett. A 352 (2006) 321] to the general states. Taking the original 4×4$4\times 4$ states as 2×8$2\times 8$ states we show that they still can be bound entangled.     

Comment on “Deterministic six states protocol for quantum communication” [Phys. Lett. A 358 (2006) 85]

In [J.S. Shaari, M. Lucamarini, M.R.B. Wahiddin, Phys. Lett. A 358 (2006) 85] the deterministic six states protocol (6DP) for quantum communication has been developed. This protocol is based on three mutually unbiased bases and four encoding operators. Information is transmitted between the users via two qubits from different bases. Three attacks have been studied; namely intercept-resend attack (IRA), double-CNOT attack (2CNOTA) and quantum man-in-the-middle attack. In this Letter, we show that the IRA and 2CNOTA are not properly addressed. For instance, we show that the probability of detecting Eve in the control mode of the IRA is 70% instead of 50% in the previous study. Moreover, in the 2CNOTA, Eve can only obtain 50% of the data not all of it as argued earlier.     

Comment on: “Series solution to the Thomas-Fermi equation” [Phys. Lett. A 365 (2007) 111]

We discuss a recently proposed analytic solution to the Thomas-Fermi (TF) equation and show that earlier approaches provide more accurate results. In particular, we show that a simple and straightforward rational approximation to the TF equation yields the slope at origin with unprecedented accuracy, as well as remarkable values of the TF function and its first derivative for other coordinate values.     

Comment on “Piezonuclear decay of thorium” [Phys. Lett. A 373 (2009) 1956]

Subjecting a solution of ²²⁸Th to ultrasound (20 kHz, 100 W), Cardone et al. [F. Cardone, R. Mignani, A. Petrucci, Phys. Lett. A 373 (2009) 1956] claim to observe an increase in the transformation or decay rate of ²²⁸Th by a factor of 10⁴. The evidence provided seems however far from conclusive and in part contradictory to the claims made. In fact, looking at the presented data we find it cannot be taken as justification to discard the null hypothesis, namely, that the data from exposed and non-exposed samples are drawn from the same distribution. We suggest a number of additional tests that should be made in order to improve the quality of the study and test the hypothesis of so-called piezonuclear reactions.     

Comment on “Piezonuclear decay of thorium” [Phys. Lett. A 373 (2009) 1956]

Cardone et al. [F. Cardone, R. Mignani, A. Petrucci, Phys. Lett. A 373 (2009) 1956] claim that cavitation speeds up radioactive decay of ²²⁸Th dissolved in water. The experimental evidence they presented was criticized by Ericsson et al. [G. Ericsson, S. Pomp, H. Sjöstrand, E. Traneus, Phys. Lett. A 373 (2009) 3795]. This Comment focuses on a presumably-ignored trivial effect that might be responsible for the reported experimental results. It also contains suggestions for improving the quality of future investigations.     

Reply to “Comment on ‘Piezonuclear decay of thorium’ [Phys. Lett. A 373 (2009) 1956]” [Phys. Lett. A 373 (2009) 3795]

In a paper appearing in this issue of Physics Letters A, Ericsson et al. raise some critical comments on the experiment [F. Cardone, R. Mignani, A. Petrucci, Phys. Lett. A 373 (2009) 1956] we carried out by cavitating a solution of thorium-228, which evidenced its anomalous decay behaviour, thus confirming the results previously obtained by Urutskoev et al. by explosion of titanium foils in solutions. In this Letter, we reply to these comments. In our opinion, the main shortcomings of the criticism by the Swedish authors are due to their omitting of inserting our experiment in the wider research stream of piezonuclear reactions, and to the statistical analysis they used, which does not comply with the rules generally accepted for samples with small numbers. However, apart from any possible theoretical speculation, there is the basic fact that two different experiments (ours and that by Urutskoev et al.), carried out independently and by different means, highlight an analogous anomaly in the decay of thorium subjected to pressure waves. Such a convergence of results shows that it is worth to further carry on experimental investigations, in order to get either a confirmation or a disproof of the induced-pressure anomalous behaviour of radioactive nuclides even different from thorium.     

Reply to “Comment on ‘Piezonuclear decay of thorium’ [Phys. Lett. A 373 (2009) 1956]” [Phys. Lett. A 374 (2009) 696]

In a Letter appearing in this issue of Physics Letters A, Kowalski raises some critical comments on the experiment [F. Cardone, R. Mignani, A. Petrucci, Phys. Lett. A 373 (2009) 1956] that we carried out by cavitating a solution of Thorium-228. The experiment highlighted the anomalous decay of Thorium, thus confirming the results previously obtained by Urutskoev et al. by explosion of titanium foils in solutions. In this Letter, we reply to these comments. We agree with Kowalski that critical comments are one of the key factors of the process to improve the quality of experiments and the interpretation of results. However we do hope that these comments together with the details provided in the replies will promote further and better experiments which are certainly worth performing in order to shed a brighter light on this issue, as Kowalski himself suggests in his comment.     

Comment on: “Photoionization of helium-like ions in asymptotic non-relativistic region” [Phys. Lett. A 358 (2006) 211]

The results of Mikhailov et al. [A.I. Mikhailov, A.V. Nefiodov, G. Plunien, Phys. Lett. A 358 (2006) 211] on single and double ionization of He at high energy can be obtained quite simply by combining two previous results long well known in the literature. The results of Mikhailov et al. can also be understood in a larger context, using an asymptotic Fourier transform approach, which also allows a justification of various statements assumed but not demonstrated by Mikhailov et al.     

Comment on “Propagation of flexural wave in periodic beam on elastic foundations” [Phys. Lett. A 376 (2012) 626]

In this comment, we argue that the concept of the pivotal frequency presented in Letter “Propagation of flexural wave in periodic beam on elastic foundations” is not proper and the applicability of the formula of the pivotal frequency is not valid for all conditions.     

Comment on: “Construction of bound entangled edge states with special ranks” [Phys. Lett. A 359 (2006) 603]

In a Letter by Clarisse [L. Clarisse, Phys. Lett. A 359 (2006) 603–607] the open problem of the existence of (5,5)$(5,5)$ and (6,6)$(6,6)$ PPT edge states has been solved. Here we report the existence of another large class of (5,5)$(5,5)$ entangled edge states with positive partial transposes. We also give a PPT edge state with range dimensions (6,6)$(6,6)$.     

Comment on: “Construction of bound entangled edge states with special ranks” [Phys. Lett. A 359 (2006) 603]

Recently, Clarisse [L. Clarisse, Phys. Lett. A 359 (2006) 603] and Ha [K.-C. Ha, Phys. Lett. A 361 (2007) 515] found examples of types (5,5) and (6,6) entangled states with positive partial transposes. In this Letter, we show that their examples have the Schmidt number as 2.     

Comment on: “Three-party quantum secure direct communication based on GHZ states” [Phys. Lett. A 354 (2006) 67]

The GHZ-state-based quantum secure direct communication (QSDC) protocol [X.-R. Jin, et al., Phys. Lett. A 354 (2006) 67] and its improved version [Z. Man, Y. Xia, Chin. Phys. Lett. 24 (2007) 15] are analyzed from the aspect of security. It shows that much information of the transmitted secret message will be leaked out in both protocols.     

Comment on: “Entanglement purification via controlled-controlled-NOT operations” [Phys. Lett. A 271 (2000) 44]

In this comment we show that some results presented by Feng et al. [X.-L. Feng, S.-Q. Gong, Z.-Z. Xu, Phys. Lett. A 271 (2000) 44] are incorrect.     

Comment on: “Dynamical analysis of Cohen-Grossberg neural networks with distributed delays” [Phys. Lett. A 364 (2007) 38]

It is pointed out that an unnatural assumption is made in the following Letter [Z. Mao, H. Zhao, Phys. Lett. A 364 (1) (2007) 38]. Therefore, the results of the Letter are not relevant to the real Cohen-Grossberg neural network model.     

Comment on: “A simple chaotic delay differential equation” [Phys. Lett. A 366 (2007) 397]

The purpose of this Letter is to give the reference for the model proposed in the discussion section of the above paper [J.C. Sprott, Phys. Lett. A 366 (2007) 397] and to show that chaotic behavior of this model has been studied in [A. Uçar, Int. J. Eng. Sci. 40 (2002) 251; A. Uçar, Chaos Solitons Fractals 16 (2003) 187].