Narrow Results

We prove that the uniform recurrence of morphic sequences is decidable. For this we show that the number of derived sequences of uniformly recurrent morphic sequences is bounded. As a corollary we obtain that uniformly recurrent morphic sequences are primitive substitutive sequences.

Dendric words are infinite words that are defined in terms of extension graphs. These are bipartite graphs that describe the left and right extensions of factors. Dendric words are such that all their extension graphs are trees. They are also called tree words. This class of words includes classical families of words such as Sturmian words, codings of interval exchanges, or else, Arnoux–Rauzy words. We investigate here the properties of substitutive dendric words and prove some rigidity properties, that is, algebraic properties on the set of substitutions that fix a dendric word. We also prove that aperiodic minimal dendric subshifts (generated by dendric words) cannot have rational topological eigenvalues, and thus, cannot be generated by constant length substitutions.

This paper starts by setting the ground for a lambda calculus notation that strongly mirrors the two fundamental operations of term construction, namely abstraction and application. In particular, we single out those parts of a term, called items in the paper, that are added during abstraction and application. This item notation proves to be a powerful device for the representation of basic substitution steps, giving rise to different versions of β-reduction including local and global β-reduction. In other words substitution, thanks to the new notation, can be easily formalised as an object language notion rather than remaining a meta language one. Such formalisation will have advantages with respect to various areas including functional application and the partial unfolding of definitions. Moreover our substitution is, we believe, the most general to date. This is shown by the fact that our framework can accommodate most of the known reduction strategies, which range from local to global. Finally, we show how the calculus of substitution of Abadi et al., can be embedded into our calculus. We show moreover that many of the rules of Abadi et al. are easily derivable in our calculus.

A series of samples of Y_1-xPr_xBa₂Cu₃O_y (YPrBCO) with 0.05 ≤ x ≤ 0.6 was synthesized and characterized by DC magnetization, X-ray diffraction (XRD), and Rietveld refinement. It is found that besides Pr substitution for Y, a part of Pr substituted for Ba in YBa₂Cu₃O_y (YBCO), and the amount of Pr in the Y and Ba positions, respectively, is estimated by the refinement with the help of bond valence sum (BVS) calculation. By comparing the correlation of structural changes such as Ba-O(4) and Cu(1, 2)-O(4) bond lengths and superconductivity between our system with the reference system where Pr just replaces Y, structural evidences are found to explain Pr substitution for Ba suppresses T_c more strongly than that for Y.

Nanocrystalline spinel Zn–Cu–Cr ferrites with Gd substitution were prepared by a rheological phase reaction method. By means of the Fourier transform infrared (FTIR) spectra, Raman spectra, and X-ray diffraction (XRD), the cubic spinel structure of samples had been confirmed. The magnetic parameters such as saturation magnetization, remanent magnetization and coercivity can be tailored by controlling the content of substituting Gd ions.

The effect of a small amount of Sb doping (5%) on the formation of the high temperature superconducting phase has been investigated on the Bi_1.5Pb_0.5Sr₂Ca₂Cu₃O_y compound. It is observed that at 860°C the T_c zero value depends on the sintering time. It first increases to a maximum value of 96 K and then decreases to a stable lowest value of 88 K. The samples have been characterized by X-ray diffraction (XRD), four probe electrical resistance and current density measurements. The XRD revealed the presence of two phases: an orthorhombic high-T_c 2223 phases with lattice constants a = 5.395 Å, b = 5.508 Å, c = 37.0422 Å and another tetragonal low-T_c 2212 phase with lattice constants a = b = 5.419 Å, c = 30.832 Å.

In this work, ${\mathrm{\text{BiFeO}}}_3$ and Eu-doped ${\mathrm{\text{BiFeO}}}_3({\mathrm{\text{Bi}}}_{0.9}{\mathrm{\text{Eu}}}_{0.1}{\mathrm{\text{FeO}}}_3)$ samples were prepared by a simple solid-phase sintering method and the structure and magnetic properties were studied. The results of X-ray diffraction show that ${\mathrm{\text{Bi}}}_{0.9}{\mathrm{\text{Eu}}}_{0.1}{\mathrm{\text{FeO}}}_3$ sample maintains the same rhombohedral R3c structure as ${\mathrm{\text{BiFeO}}}_3$ sample but with a slight lattice distortion due to the Eu substitution for Bi. Compared with ${\mathrm{\text{BiFeO}}}_3$, the ${\mathrm{\text{Bi}}}_{0.9}{\mathrm{\text{Eu}}}_{0.1}{\mathrm{\text{FeO}}}_3$ sample exhibits a larger remnant magnetization and a higher Curie–Weiss temperature. These results indicate that appropriate doping with Eu is effective in improving the magnetic properties of ${\mathrm{\text{BiFeO}}}_3$ and the solid-phase sintering method used in this study is a simple and good solid-phase sintering method to prepare ${\mathrm{\text{BiFeO}}}_3$.

This work presents an elaborate study of the effect in the structural and magnetic of ${\mathrm{\text{BiFe}}}_{1-x}{\mathrm{\text{Zn}}}_x{\mathrm{\text{O}}}_3$ ($x=0$, 0.05, 0.10, 0.15, 0.20, 0.25) multiferroic materials, synthesized via a sol-gel auto-combustion method. The synthesized materials are found to have structural distortion in the rhombohedral R3c structure as observed by X-ray diffraction (XRD). Other diffraction peaks were attributed to the second phase ${\mathrm{\text{Bi}}}_{25}{\mathrm{\text{FeO}}}_{40}$. The Mossbauer spectra (MS) of ${\mathrm{\text{BiFe}}}_{1-x}{\mathrm{\text{Zn}}}_x{\mathrm{\text{O}}}_3$ ($x=0$, 0.05, 0.10, 0.15) are fitted with a sextet and a doublet, and the presence of doublet also indicates the ${\mathrm{\text{Bi}}}_{25}{\mathrm{\text{FeO}}}_{40}$ phase. The results from XRD and MS both show that Zn-substituted BiFeO₃ suffers adverse effects on the formation of pure BiFeO₃. ${\mathrm{\text{BiFe}}}_{1-x}{\mathrm{\text{Zn}}}_x{\mathrm{\text{O}}}_3$ ($x=0.20$, 0.25) are fitted with only one paramagnetic doublet. The absence of sextet means that there is a magnetic destruction of samples on account of a thorough phase transition from a magnetic phase to a non-magnetic phase and/or successful ion substitution (iron ions were replaced with zinc ions).

The elastic properties, electronic structure, and optical properties of X ($\mathrm{\text{X}}=\mathrm{\text{B}}$, Al, Ga) atomic substitution for arsenene are calculated based on density functional theory. The results show that, at the same concentration, B-substituted arsenene shows the best structural stability, followed by Ga-substituted arsenene, with Al-substituted arsenene being the least. Arsenene and its substitution systems possess excellent mechanical stability. The substitution of X atoms leads to a reduction in the bulk modulus, shear modulus, and Young’s modulus of arsenene systems, while simultaneously increasing the Poisson’s ratio. For the substitution systems, the four parameters all gradually increase as the substitution concentration increases. The substitution of X ($\mathrm{\text{X}}=\mathrm{\text{B}}$, Al, Ga) atoms into arsenene can facilitate the transformation from an indirect to direct bandgap (except for Al and Ga substitution at a concentration of 3.13%) with a narrower bandgap for increasing substitution concentration. The B–As bond shows the strongest covalency, followed by the Ga–As bond, while the Al–As bond exhibits the strongest ionicity. Arsenene substituted with X atoms shows anisotropy of optical properties in both the xy-plane and along the z-axis direction. The static dielectric constant increases with higher substitution concentration. The imaginary part of the dielectric function shows the extent of excited electron transitions between bands. After X atom substitution, arsenene exhibits a redshift in its absorption edge, which is wider with the higher substitution concentrations. The peak reflectance and valley transmittance values of arsenene and its substitution systems are located in the ultraviolet region in both xy-plane and z-axis.

The period-doubling sequence is one of the most well-known aperiodic $0$–$1$ sequences. In this paper, a complete description of its symbolic recurrence plot is given, and formulas for asymptotic values of basic recurrence quantifiers are derived.

The themes of cancellation, internal cancellation, substitution and exchange have led to a lot of interesting research in the theory of modules over commutative and noncommutative rings. This article provides a quick and relatively self-contained introduction to the voluminous work in this area, using the notion of the stable range of rings as a unifying tool. With only a small number of exceptions, all theorems stated here are proved in full, modulo basic facts in the theory of modules and rings available in standard textbooks on ring theory.

We report on a quantum-chemical study of the electronic and optical properties of Mercury(II) complexes HgTFT (1) and its electron-withdrawing substitutent HgTFOT (2), HgTFCNT (3) [where TFT = diethynylfluorenyl, TFOT = diethynylfluorenone and TFCNT = diethynyl-(9-(dicyanomethylene)fluorene)]. Our theoretical calculations indicate that the substitution of -CO, -C(CN)₂ for -CH in HgTFT significantly decreases the bond length alternation and increases the electron affinity, which would qualify HgTFOT2 and HgTFCNT3, especially 3, as candidates for n-type electrical conductors. The vertical transition energy associated with the low-lying excited state has been examined within the time-dependent DFT formalism for mercury diethynylfluorenyl derivatives. It is found that the electron-withdrawing substitutions lead to remarkable red shift in transition energy and alter the corresponding charge transfer manner.

Several chaos-based image encryption schemes have been proposed in the last decade. Each encryption scheme has pros and cons regarding its speed, complexity, and security. This paper proposes a new chaotic map called Power-Chaotic Map (PCM). Characteristics of the proposed PCM, such as chaotic behaviour, randomness, sensitivity, and s-unimodality, are investigated. As an application of the proposed chaotic map, an image encryption scheme is proposed to encrypt greyscale and text images. The proposed three-phase image encryption scheme performs a series of substitution and permutation operations. The Pixel-Level phase utilises the PCM’s generated keystreams to perform the substitution operation of image pixels. The Row-Level phase permutates, via a proposed pseudorandom number generator, pixel locations of each row and then shuffles row locations. Finally, the Column-Level phase performs a substitution operation on pixels of each column. Performance of the proposed PCM-based image encryption scheme is investigated through histogram analysis, statistical correlation analysis, key sensitivity, encryption performance of text images, and permutation and substitution properties. Experimental results indicate that the PCM has a wider range of chaotic behaviour than well-known one-dimensional maps, meets the s-unimodality property, has high sensitivity, and generates keystreams with random-like behaviour. Furthermore, results indicate that the PCM-based image encryption scheme provides high encryption security for text images, high key sensitivity, immunity against brute-force attacks, strong statistical correlation results, strong encryption performance, and low computational complexity.

In this paper, an efficient novel dual permutation–substitution structure-based color image encryption algorithm is proposed. Initially, the Secure Hash Algorithm-512 (SHA-512) is applied to the input image to generate the initial values for the Lü system dynamically. In the first stage of permutation, inter-color-component pixel shuffling is carried out with a circular pixel-swapping mechanism. In the second stage, intra-color-component pixel shuffling is executed, based on pseudorandom positions generated by the Lü chaotic system. Pixel values are changed in the substitution stage, based on float-valued chaotic sequences generated by the Lü system. The performance of the proposed algorithm is evaluated with metrics such as key space, key sensitivity, histograms, correlation coefficients (vertical, horizontal and diagonal), information entropy, number of pixel changes rate (NPCR), unified average changing intensity (UACI), peak signal-to-noise ratio (PSNR), mean absolute error (MAE), contrast analysis, encryption time and the National Institute of Standards and Technology Special Publication 800-22 (NIST SP 800-22) statistical test. The experimental results obtained and performance assessment show that the proposed scheme has produced good results.

Virtual reality (VR) offers the opportunity to create virtual worlds that could replace real experiences. This research investigates the influence of user motivation, temporal distance and experience type on the satisfaction with the VR experience, and the degree of acceptance of a VR experience as a substitute for a real experience. The results suggest that the degree of acceptance of a VR experience as a substitute for a real experience is higher for passive VR experiences compared to active VR experiences. Furthermore, the results support the assumption that users are more satisfied with passive VR experiences.

The synthesis, spectral and photophysical properties including fluorescence quenching of the following octa-substituted oxotitanium phthalocyanines are reported: 2,3,9,10,16,17,23,24-octaphenoxyphthalocyaninato titanium(IV) oxide, 2,3,9,10,16,17,23,24-[octakis(4-t-butylphenoxyphthalocyaninato)]titanium(IV) oxide, 2,3,9,10,16,17,23,24-{octakis[(4-benzyloxy)phenoxy]phthalocyaninato}titanium(IV) oxide and 2,3,9,10,16,17,23,24-octaphenylthiophthalocyaninato titanium(IV) oxide. The complexes are characterized by ¹H NMR, IR and UV-vis spectroscopies. Their photophysical properties are presented where moderate fluorescence quantum yields (0.14-0.19) and lifetimes were determined. Varied triplet quantum yields were obtained and the triplet lifetimes (40-100 μs) were short.

Firms who want to appropriate innovation often need to make decision facing the trade-off between patenting and secret. This paper explores how leading firms make trade-off between patenting and secret through the view of the interaction between leading firms and following firms who have the option of imitation or substitution, based on the evolutionary game theory. Then, a simulation model is built combining the evolutionary game model and agent-based modelling method, which allows us to implement bounded rationality and interactivities. The simulation is run with different gain parameters and the results are checked by cross-validation. It is found that leading firms are more likely to adopt patenting strategy with well developed patent protection regime. While depending on variations on patent protection effectiveness, technological characteristics, and leading firms’ investment in patent portfolio development, following firms may choose imitation strategy or substitution strategy. Considering bounded rationality, firms could choose sub-optional strategies and leads to scenarios other than evolutionary equilibrium solutions, which provide deeper insights of strategic choices of leading firms and following firms. This paper makes contributions to theory by using the perspective of multi-agent view and integrating bounded rationality in the simulation. Finally, this paper draws conclusion and puts forward some suggestions.

In this paper, we associate a primitive substitution with a family of non-integer positional number systems with respect to the same base but with different sets of digits. In this way, we generalize the classical Dumont–Thomas numeration which corresponds to one specific case. Therefore, our concept also covers beta-expansions induced by Parry numbers. But we establish links to variants of beta-expansions such as symmetric beta-expansions, too. In other words, we unify several well-known notions of non-integer representations within one general framework. A focus in our research is set on finiteness and periodicity properties. It turns out that these characteristics mainly depend on the substitution. As a consequence we are able to relate known finiteness properties that are viewed independently yet.

Site-specific single polyaniline nanowires were fabricated through electrophoresis growth with acetone wetting. After growing the nanowires, the post-process of acetone wetting of the nanowires improved morphology, topology, and electrical conductivity with coagulation and substitution in polyaniline. They showed resistance changes of 39.57 ± 11.57% and presented 2.38 × 10^-4 ± 3 × 10^-5 Ω · cm, 133.77 ± 13.82 nm thickness, and 133.17 ± 13.01 nm width in 1 μm to 5.5 μm length. The new combined growth process of electrophoresis and acetone wetting significantly improved reproducibility, reliability, and controllability in the fabrication of single polymer nanowires.

We investigate whether and how SMEs’ credit quality influences their substitution of bank credit for trade credit. Using data from the five largest European countries, we find that substitution of bank credit for trade credit decreases during the financial crisis, but it decreases significantly less for ex ante low credit quality firms. We control for pre-crisis or lagged firm characteristics including size and external finance dependence, industry effects, sample selection effects and cross-country heterogeneity. We also find that low credit quality firms increase their absolute and relative trade credit usage significantly more than high credit quality firms during the financial crisis. The effects are consistent across countries and stronger for net trade credit borrowers and financially constrained firms. The evidence highlights how credit quality influences demand-side driven substitution in SME finance.