Melting of xenon monolayers - computer simulations

The results of Monte Carlo simulations of xenon monolayers deposited on graphite are presented. Systems of various surface densities and in a wide range of temperatures are investigated. The results are compared to the experimental data and to the previous results for nitrogen. The results of simulations are in good agreement with the experimental ones and confirm that melting in two dimensions is vacancy-driven. Typical real-space configurations of Xe atoms and calculated specific heat results are shown.     

On the Distribution of Long-Term Time Averages on Symbolic Space

The pressure was studied in a rather abstract theory as an important notion of the thermodynamic formalism. The present paper gives a more concrete account in the case of symbolic spaces, including subshifts of finite type. We relate the pressure of an interaction function to its long-term time averages through the Hausdorff and packing dimensions of the subsets on which has prescribed long-term time-average values. Functions with values in ^d are considered. For those depending only on finitely many symbols, we get complete results, unifying and completing many partial results.     

Morgan-Scott剖分上样条空间S_8~4(Δ_(ms))的维数

Ｍｏｒｇｅｎ－Ｓｃｏｔ剖分上样条空间的维数依赖于剖分的几何性质，本文证明了Ｄｉｅｎｅｒ１９９０年提出的猜想对ｒ＝４是不正确的，需要修正．     

Zero and finite temperature phase diagram of the spinless fermion model in infinite dimensions

The phase diagram of the model of spinless fermions with repulsive nearest neighbour interaction is calculated analytically on a hypercubic lattice in infinite dimensions (d → ∞). In spite of its simplicity the model displays a rich phase diagram depending on the doping δ, the interaction U and the temperature T. The system can be in the homogeneous phase (HOM), the nonsegregated AB charge density wave (AB-CDW), the AB phase separation region (PS-AB/HOM; coexistence of AB-CDW and HOM), the incommensurate phase (IP) or the IP phase separation region (PS-AB/IP; coexistence of AB-CDW and IP). We identify three important values of the interaction U_IPL = 0.572 < U_IPH = 1.914 < U_IP/PS = 4.212 which distinguish four intervals of U. These imply four different types of phase diagrams. In all the three phase diagrams with U below U_IP/PS the IP appears. We propose a new general ansatz for the order parameter of this phase. A competition between the IP, the PS-AB/IP and the PS-AB/HOM is found. The relevance of our findings for the phase scenario of the Hubbard model is shown.     

The Effect of Space Dimensions on a Generalized Hydrogen-Atom Specific Heat in the Generalized Boltzmann-Gibbs Statistics

In this article, the effect of the space dimensions on the generalized hydrogen-atom specific heat in the generalized Boltzmann-Gibbs statistics is studied. The temperature dependence of the specific heat for a few different values of q and for different low space dimensions using Tsallis statistics is numerically calculated. The results indicate that for a fixed value of q, as the space dimension increases the temperature range where the specific heat has a nonzero value, decreases, while the general behavior of the specific heat does not show any change. Also, there exits a q-independent quantity related to two specific temperatures of the system which is almost linearly dependent on the space dimensions.     

Stability and uniqueness of periodic orbits produced during homoclinic bifurcation

Under a generic assumption, the existence and the uniqueness of the periodic orbit generating from a homoclinic bifurcation are shown, and the dimensions of its stable and unstable manifolds are given. In the case of a 3-dimensional system, our result revises the stability criterion given in [4,5].Supported by the National Natural Science Foundation of China.     

On Some L-extensions of Dimensions of Topological Spaces

The concepts of covering dimension,small inductive dimension and large inductive dimension for topological spaces are extended to L-topological spaces using the quasi-coincidence relation.Besides getting some characterizations,it is also seen that all these characterizations are good in the sense of Lowen.     

Higher Secant Varieties of ℙ n × ℙ1 Embedded in Bi-Degree (a,b)

In this article, we compute the dimension of all the higher secant varieties to the Segre–Veronese embedding of ? ⁿ × ?¹ via the section of the sheaf 𝒪(a, b) for any n, a, b ∈ ?⁺. We relate this result to the Grassmann Defectivity of Veronese varieties and we classify all the Grassmann (1, s ? 1)-defective Veronese varieties.     

ScOFi: Schematic assisted optimum fingerprinting for Wi-Fi indoor localization using peer hand-shake

Received signal strength fingerprints based on Wi-Fi spectrum have been widely adopted in the recent years for indoor localization purposes due to cost-effectiveness and availability. However, until the peer hand-shake (PHS), existing work had not constrained the schematic dimension of the target area, which could dramatically reduce the localization error. As the demand for sensors everywhere schemes for 5G networks keeps on booming, effective signal propagation characterization with in indoors is very essential for Internet of things (IoT) indoor localization and navigation applications. We review, extend the validation of the PHS technique that leverages the schematic dimensions of the target area within the total indoor environment to construct, auto-dynamically transform and update fingerprint in complex indoor environments. Extensive experimental validation has been carried out in two scenarios; Scenario 1 categorizes lobby area while Scenario 2 categorizes corridor areas. We analyze the accuracy performance using Nearest Neighbor (NN) and the KNN algorithms. Experimental results show robustness of the PHS, achieving lower average localization error in diverse indoor dimensionalities than comparisons.     

Radio Frequency Fingerprint extraction based on Multiscale Approximate Entropy

Radio Frequency (RF) fingerprinting is the technology of recognizing the transmitter using the non-linear characteristics of an intercepted RF signal. The underlying inevitable impairments of the hardware chain in transmitters are used as unique RF signatures for the distinct identification of various radios. The technique can be applied to distinguish not only between the radio of different make but also between the radios of the same make and type. In this paper, we propose a novel RF fingerprinting method, based on Multi-Scale Approximate Entropy (MSAE) which utilizes the steady-state section of the RF signal, extracted through the Higuchi Fractal Dimension (HFD) method. The MSAE feature extraction method is validated using real-world data-set for Very High Frequency (VHF) radios. The proposed method uses MSAE features which are subsequently fed to Machine Learning (ML) algorithms for classification accuracy comparison. In terms of classification accuracy, the proposed MSAE features outperforms some of the existing steady-state methods, especially at low SNR.