Constructions and properties of k out of n scalable secret image sharing

Recently, Wang et al. introduced a novel (2, n) scalable secret image sharing (SSIS) scheme, which can gradually reconstruct a secret image in a scalable manner in which the amount of secret information is proportional to the number of participants. However, Wang et al.’s scheme is only a simple 2-out-of-n case. In this paper, we consider (k, n)-SSIS schemes where a qualified set of participants consists of any k participants. We provide two approaches for a general construction for any k, 2 ? k ? n. For the special case k = 2, Approach 1 has the lesser shadow size than Wang et al.’s (2, n)-SSIS scheme, and Approach 2 is reduced to Wang et al.’s (2, n)-SSIS scheme. Although the authors claim that Wang et al.’s (2, n)-SSIS scheme can be easily extended to a general (k, n)-SISS scheme, actually the extension is not that easy as they claimed. For the completeness of describing the constructions and properties of a general (k, n)-SSIS scheme, both approaches are introduced in this paper.     

High-temperature measurements of the rates of the reactions CH2O + Ar → Products and CH2O + O2 → Products

The two-channel thermal decomposition of formaldehyde [CH₂O], (1a) CH₂O + Ar → HCO + H + Ar, and (1b) CH₂O + Ar → H₂ + CO + Ar, was studied in shock tube experiments in the 2258-2687 K temperature range, at an average total pressure of 1.6 atm. OH radicals, generated on shock heating trioxane-O₂-Ar mixtures, were monitored behind the reflected shock front using narrow-linewidth laser absorption. 1,3,5 trioxane [C₃H₆O₃] was used as the CH₂O precursor in the current experiments. H-atoms formed upon CH₂O and HCO decomposition rapidly react with O₂ to produce OH via H + O₂ → O + OH. The recorded OH time-histories show dominant sensitivity to the formaldehyde decomposition pathways. The second-order reaction rate coefficients were inferred by matching measured and modeled OH profiles behind the reflected shock. Two-parameter fits for k_1a and k_1b, applicable in this temperature range, are:

     

A theoretical study of the water gas shift reaction mechanism on Cu(1 1 1) model system

The water gas shift (WGS) reaction is an important reaction system and has wide applications in several processes. However, the mechanism of the reaction is still in dispute. In this paper we have investigated the reaction mechanism on the model Cu(1 1 1) system using the density functional method and slab models. We have characterized the kinetics and the thermodynamics of the four reaction pathways containing 24 elementary steps and computed the reaction potential energy surfaces. Calculations show that the formate (HCOO) intermediate mechanism (CO + OH → HCOO → CO₂ + H) and the associative mechanism (CO + OH → CO₂ + H) are kinetically unlikely because of the high formation barrier. On the other hand, the carboxyl (HOCO) intermediate mechanism (CO + OH → HOCO → CO₂ + H) and the redox mechanism (CO + O → CO₂) are demonstrated to be feasible. Our calculations also indicate that surface oxygen atoms can reduce the barriers of both water dissociation and HOCO decomposition significantly. The calculated potential energy surfaces show that the water dissociation which produces OH groups is the rate-determining step at the initial stage of the reaction or in the absence of surface oxygen atoms. With the development of the reaction or in the presence of oxygen atoms on the surface, CO + OH → HOCO and CO + O → CO₂ become the rate-limiting step for the carboxyl and redox mechanisms, respectively.     

The multiphoton ionization spectrum of jet-cooled pyrimidine in the 3p Rydberg and B1 (π,n) states

Resonance-enhanced multiphoton ionization (REMPI) has been applied to study the n → 3p Rydberg transition of pyrimidine (jet-cooled sample and mass resolved spectrum). Only the one component, the 3p_z(B₂), appears in the (2 + 1) REMPI and the active vibrations are ν_6a = 622, ν₁ = 946, and ν_9a = 1116 cm⁻¹. The symmetry of the state was determined by polarization measurements (linear, circular polarization). The first (π^∗,n) ³B₁ triplet state appears as a one-photon resonance in the three-photon ionization process.     

Fourier transform infrared emission spectra of MnH and MnD

Fourier transform infrared emission spectra of MnH and MnD were observed in the ground X⁷Σ⁺ electronic state. The vibration-rotation bands from v = 1 → 0 to v = 3 → 2 for MnH and from v = 1 → 0 to v = 4 → 3 for MnD were recorded at an instrumental resolution of 0.0085 cm⁻¹. Spectroscopic constants were determined for each vibrational level and equilibrium constants were found from a Dunham-type fit. The equilibrium vibrational constant (ω_e) for MnH was found to be 1546.84518(65) cm⁻¹, the equilibrium rotational constant (B_e) is 5.6856789(103) cm⁻¹ and the eqilibrium bond distance (r_e) was determined to be 1.7308601(47) Å.     

Observation of nonstationary effects in saturation spectroscopy

We have studied the nonstationary effects in saturated absorption spectroscopy of the ⁸⁷Rb D₂ line. Varying the size of the σ⁺ polarized pump laser beam, we observed saturated absorption spectra for the σ^± polarized probe beam. For equal polarizations of the pump and probe beams, we found that the resonance signal for the F_g = 1 → F_e = 2 line, and the crossover lines between F_g = 1 → F_e = 2 and F_g = 1 → F_e = 1 (and 0) lines increased to a greater extent than the others. This observation can be understood from the calculated time evolution of the populations of the ground-state sublevels by means of a rate equation model. We also compared experimental data for other conditions with the calculated results. We found good agreement between the calculated results and the data.     

The bΣ(b0) → XΣ(X10,X21) and aΔ(a2) → X21 transitions of AsBr

Emission spectra of the b¹Σ⁺(b0⁺) → X³Σ⁻(X₁0⁺,X₂1) and a¹Δ(a2) → X₂1 transitions of AsBr have been measured in the near-infrared spectral region with a Fourier-transform spectrometer. The arsenic bromide radicals were generated in fast-flow systems by reaction of arsenic vapor (As_x) with bromine and were excited by microwave-discharged oxygen. The most prominent features in the spectrum are the Δv = +1,0,−1, and −2 band sequences of the b¹Σ⁺(b0⁺) → X³Σ⁻(X₁0⁺) transition in the range 11 700-12 700 cm⁻¹. With lower intensities, the Δv = 0 and −1 sequences of the b¹Σ⁺(b0⁺) → X³Σ⁻(X₂1) sub-system show up in the same range. Further to the red, between 6000 and 6700 cm⁻¹, the Δv = 0, +1, and −1 sequences of the hitherto unknown a¹Δ(a2) → X₂1 transition are observed. Analyses of medium- and high-resolution spectra have yielded improved molecular constants for the X₁0⁺, X₂1, and b0⁺ states and first values of the electronic energy and the vibrational constants of the a2 state.     

Second order gauge theory

A gauge theory of second order in the derivatives of the auxiliary field is constructed following Utiyama’s program. A novel field strength G = ∂F + fAF arises besides the one of the first order treatment, F = ∂A − ∂A + fAA. The associated conserved current is obtained. It has a new feature: topological terms are determined from local invariance requirements. Podolsky Generalized Eletrodynamics is derived as a particular case in which the Lagrangian of the gauge field is L_P ∝ G². In this application the photon mass is estimated. The SU (N) infrared regime is analysed by means of Alekseev-Arbuzov-Baikov’s Lagrangian.     

Study of S ion-assisted sulfurization of n-GaAs (1 0 0) surface

The chemical structure and site location of sulfur atoms on n-GaAs (1 0 0) surface treated by bombardment of S⁺ ions over their energy range from 10 to 100 eV have been studied by X-ray photoelectron spectroscopy and low energy electron diffraction. The formation of Ga-S and As-S species on the S⁺ ion bombarded n-GaAs surface is observed. An apparent donor doping effect is observed for the n-GaAs by the 100 eV S⁺ ion bombardment. It is found that the S⁺ ions with higher energy are more effective in the formation of Ga-S species, which assists the n-GaAs (1 0 0) surface in reconstruction into an ordered (1 × 1) structure upon subsequent annealing. The treatment is further extended to repair Ar⁺ ion damaged n-GaAs (1 0 0) surface. It is found that after a n-GaAs (1 0 0) sample is damaged by 150 eV Ar⁺ ion bombardment, and followed by 50 eV S⁺ ion treatment and subsequent annealing process, finally an (1 × 1) ordering GaAs (1 0 0) surface with low surface states is obtained.     

Towards XUV lasers with charge transfer pumping

Detailed studies of charge exchange pumping of ions in femtosecond laser-produced plasmas colliding with a pulsed gas jet are presented. Strong selective excitation of XUV ionic transitions in the reaction C⁴⁺ + H → C³⁺ + H⁺ is observed. Dependences of line intensities on various experimental parameters are reported which are in good agreement with the theory of charge transfer processes. Analyses of experimental data provide evidence that an efficient charge exchange pumping is realized at densities of reagents well in excess of 10¹⁶ cm⁻³, which is essential for the realization of XUV lasers. In preliminary investigations of the reaction C⁶⁺ + H → C⁵⁺ (n = 3, 4) + H⁺ a strong increase of line intensities at 13.5 and 18.2 nm is reported. Analysis of lasing in Na-like ions with an example for Chlorine promises even more efficient pumping as compared with the before analyzed hydrogen like ions.     

Rotational and vibrational temperatures of electronically excited BiN radicals in a chemiluminescent flame

Rotational and vibrational temperatures of electronically excited BiN radicals in a low-pressure Bi_x+N/N₂*/N₂+Ar chemiluminescent flame have been deduced from high-resolution Fourier-transform emission spectra. Bands of three electronic transitions, a³Σ⁺(a₁1)→X¹Σ⁺(X0⁺), b⁵Σ⁺(b₁0⁺)→X¹Σ⁺(X0⁺), and b⁵Σ⁺(b₁0⁺)→a ³Σ⁺(a₁1), were analysed to determine the optical temperatures in the a³Σ⁺(a₁1) and b⁵Σ⁺(b₁0⁺) states. The rotational temperatures characterising the rotational populations in the a₁1, v=0 and 1 states were determined from the a₁→X, 0-2, 0-3, 0-4, 1-1, and 1-2 bands. The b₁→X, 0-8 and 0-11 bands, and the b₁→a₁, 0-0 bands served to determine the rotational temperature of the radicals in the b₁0⁺, v=0 state. The temperatures derived from the various bands and transitions were well consistent and the mean rotational temperature was determined to be 353±18 K, which is close to the translational temperature of the gas.Vibrational temperatures of the radicals in the a₁1 and b₁0⁺ states were derived from band intensities of the a₁→X and from the b₁→X as well as b₁→a₁ systems, respectively. The Franck-Condon factors needed were calculated with RKR potentials deduced from literature values of the rotational and vibrational constants in the three states involved. The a₁1 vibrational temperature (336±21 K) was close to the rotational temperature, while the b₁0⁺ vibrational temperature (438±36 K) differed, likely due to the previously observed perturbation of the b₁0⁺ state.     

Probabilistically perfect quantum cloning and unambiguous state discrimination

We consider the N → M probabilistically perfect quantum cloning machine that perfectly produces M faithful copies from N identical input states, where the input states are selected, with prior probabilities η₁and η₂ = 1 − η₁, from a given set of the two linearly independent states |ψ₁〉^⊗ N = (cosθ|0〉 + sinθ|1〉)^⊗ N and |ψ₂〉^⊗ N = (sinθ|0〉 + cosθ|1〉)^⊗ N (θ∈(0,π/2)). We derive the optimal distribution of the success probabilities. When M approaches infinite, the probabilistically perfect quantum cloning can be regarded as a kind of the unambiguous state discrimination, and theoretically provides the upper bound of the unambiguous state discrimination. By using the optimal distribution of the success probabilities of the optimal asymmetric 1 → M probabilistically perfect quantum cloning, we can derive the maximum average success probability of the unambiguous discrimination of two nonorthogonal quantum states |ψ₁〉and|ψ₂〉. As an example, we give the explicit transformation of the optimal symmetric 1 → M probabilistically perfect quantum cloning to copy the two input states |ψ₁〉 and |ψ₂〉.     

Three-photon resonance enhanced excitation spectrum of atomic thallium

We present first measurements on the resonance enhanced three-photon excitation in thallium, using a Nd:YAG laser pumped dye laser in conjunction with a thermionic diode ion detector. The even-parity 6s²ns²S_1/2 (15 ? n ? 31) and nd ²D_5/2 (13 ? n ? 42) Rydberg states have been observed. The measured level energies reveal a dynamic shift from the photoabsorption values, which is decreasing with increasing n, while the asymmetry in the line profile is observed to be increasing with increasing n. In addition, an autoionising level (sp²⁴P_3/2) adjacent to the ionization threshold has been observed and quantitatively analyzed using the Fano’s photoionization cross-section relation for an isolated autoionising resonance.     

Metal ion-molecule kinetics at combustion temperatures: The reaction of Ca with O2

The high-temperature photochemistry (HTP) technique, previously used for reactions of neutral species, has been adapted to the study of atomic metal ion-molecule reactions. Ca⁺ ions were generated by 193 nm multi-photon photolysis of calcium acetyl acetonate and its pyrolysis fragments. The relative ion concentrations were monitored by laser-induced fluorescence at 393.4 nm. Ar was used as the bath gas. The data for the Ca⁺ + O₂ + M → CaO₂⁺ + M association reaction (1) are fitted by k₁(907-1425 K) = 3.5 × 10⁻³² exp(+3161 K/T) cm⁶ molecule⁻² s⁻¹. Combining with an approximate k₁(296 K) value in the literature leads to k₁(296-1425 K) = 5.8 × 10⁻²² (T/K)^−2.9 exp(−601 K/T) cm⁶ molecule⁻² s⁻¹. Over much of the observed temperature range reaction (1) has much smaller rate coefficients than the corresponding neutral Ca association reaction. Reaction (1) is shown to behave very similarly to the O₂ association reaction with neutral K atoms, with which Ca⁺ is iso-electronic. This suggests that the initial step is ion-pair complex formation of the superoxide Ca²⁺(O₂)⁻, which is also consistent with results from density functional calculations. The k₁ values are rationalized via Troe’s unimolecular formalism, which leads to good accord with the experiments.     

Short-Range Characterization of the MeAr (Me=Zn, Cd) Ground-State Potentials from Fluorescence Spectra

First-time observed D1(¹Π)_v′=10→X0⁺(¹Σ) fluorescence in ZnAr, and A0⁺(³Π)_v′=4→X0⁺ and D1(¹Π)_v′=7,8→X0⁺ fluorescence in CdAr van der Waals (vdW) molecules were produced in a continuous supersonic molecular beam crossed with a pulsed dye-laser beam, following excitation of single vibronic levels. The dispersed fluorescence spectra displayed characteristic Condon internal diffraction (CID) patterns consisting of bound-free, reflection type, continuous spectra, and, in certain cases, bound-bound discrete features. An analysis of the A0⁺→X0⁺ and D1→X0⁺ bound-bound spectra indicates that Morse functions are adequate representations of the X0⁺ potential energy (PE) curves below their dissociation limits. In simulation of the A0⁺→X0⁺ and D1→X0⁺ bound-free spectra, the Morse, Lennard-Jones L-J(n−6), and Maitland-Smith M-S(n₀,n₁) functions were tested, and the respective M-S(11.3, 9.0) and M-S(10.6, 7.0) potentials were found to be good representations for the repulsive walls of the X0⁺ PE curves of ZnAr and CdAr, respectively, over the short range, R=2.45-4.38 Å (ZnAr) and R=2.85-4.31 Å (CdAr), of internuclear separations.     

Shape and size transformation of gold nanorods (GNRs) via oxidation process: A reverse growth mechanism

The anisotropic shape transformation of gold nanorods (GNRs) with H₂O₂ was observed in the presence of “cethyl trimethylammonium bromide” (CTAB). The adequate oxidative dissolution of GNR is provided by the following autocatalytic scheme with H₂O₂: Au⁰ → Au⁺, Au⁰ + Auⁿ⁺ → 2Au³⁺, n = 1 and 3. The shape transformation of the GNRs was investigated by UV-vis spectroscopy and transmission electron microscopy (TEM). As-synthesised GNRs exhibit transverse plasmon band (TPB) at 523 nm and longitudinal plasmon band (LPB) at 731 nm. Upon H₂O₂ oxidation, the LPB showed a systematic hypsochromic (blue) shift, while TPB stays at ca. 523 nm. In addition, a new emerging peak observed at ca. 390 nm due to Au(III)-CTAB complex formation during the oxidation. TEM analysis of as-synthesised GNRs with H₂O₂ confirmed the shape transformation to spherical particles with 10 nm size in 2 h, whereas centrifuged nanorod solution showed no changes in the aspect ratio under the same condition. Au³⁺ ions produced from oxidation, complex with excess free CTAB and approach the nanorods preferentially at the end, leading to spatially directed oxidation. This work provides some information to the crystal stability and the growth mechanism of GNRs, as both growth and shortening reactions occur preferentially at the edge of single-crystalline GNRs, all directed by Br⁻ ions.     

Kinetic aspect of CO2 reforming of CH4 on Ni(1 1 1): A density functional theory calculation

Reaction pathways of CO₂ reforming of CH₄ on Ni(1 1 1) were investigated by using density functional theory calculation. The computed kinetic parameters agree with the available experimental data, and a new and simplified mechanism was proposed on the basis of computed energy barriers. The first step is CO₂ dissociation into surface CO and O (CO₂ → CO + O) and CH₄ sequentially dissociation into surface CH and H (CH₄ → CH₃ → CH₂ → CH). The second step is CH oxygenation into CHO (CH + O → CHO), which is more favored than its dissociation into C and hydrogen (CH → C + H). The third step is the dissociation of CHO into surface CO and H (CHO → CO + H). Finally, H₂ and CO desorb from Ni(1 1 1) and form free H₂ and CO. The rate-determining step is the CH₄ dissociative adsorption, and the key intermediate is surface adsorbed CHO. Parameters, which might modify the proposed mechanism, have been analyzed. In addition, the formation, deposition and elimination of surface carbon have been discussed accordingly.     

Quantum dynamics of hydrogen atom in complex space

We show in this paper that the electron’s quantum dynamics in hydrogen atom can be modeled exactly by quantum Hamilton-Jacobi formalism. It is found that the quantizations of energy, angular momentum, and the action variable ∫p dq are all originated from the electron’s complex motion, and that the shell structure observed in hydrogen atom is indeed originated from the structure of the complex quantum potential, from which the quantum forces acting upon the electron can be uniquely determined, the stability of atomic configuration can be justified, and the electron’s complex trajectories can be derived accordingly. Based on the derived electron’s trajectory, we can explain why the electron appears at some positions with large probability, while at some other positions with small probability. The positions with maximum probability predicted by standard quantum mechanics are found to be just the stable equilibrium points of the electron’s non-linear complex dynamics. The electron’s trajectories in hydrogen atom are discovered to be very diverse and strongly state-dependent; some of them are open and non-periodic, while some are closed and periodic. Over such a great diversity of orbits, commensurability condition ensuring the existence of closed orbit will be derived and the de Broglie’s standing wave pattern will be identified. Along the investigation of the electron’s orbits in hydrogen atom, we will also clarify why old quantum mechanics using the concept of classical orbit can correctly predict the energy quantization of hydrogen atom and meanwhile why it is not applicable to general quantum system. Finally, the internal mechanism of how the precessing, non-conical eigen-trajectories can evolve continuously to the classical, non-precessing, conical orbits as n → ∞ is explained in detail.     

Influence of Yb concentration on upconversion luminescence of Ho

Upconversion (UC) emissions at 360 ((⁵F, ³F, ⁵G)₂ → ⁵I₈), 392 (³K₇/⁵G₄ → ⁵I₈), 428 (⁵G₅ → ⁵I₈), 554 (⁵S₂/⁵F₄ → ⁵I₈), 667 (⁵F₅ → ⁵I₈) and 754 (⁵S₂/⁵F₄ → ⁵I₇) nm were obtained in 0.1 mol% Ho³⁺/x mol% Yb³⁺:Y₂O₃ (x = 2, 5, 8, 11, 15) bulk ceramics under infrared (IR) excitation at 976 nm. The intensity of the UC luminescence centered at 554 and 754 nm increased with Yb³⁺ concentration from 2 to 5 mol% and decreased from 5 to 15 mol%, while the UC luminescence centered at 392, 428 and 667 nm increased with Yb³⁺ concentration from 2 to 11 mol%, then started to reduce with Yb³⁺ concentration until 15 mol%. This comes from the competition between the energy back transfer (EBT) process [⁵S₂/⁵F₄(Ho) + ²F_7/2(Yb) → ⁵I₆(Ho) + ²F_5/2(Yb) as well as ⁵F₅(Ho) + ²F_7/2(Yb) → ⁵I₇(Ho) + ²F_5/2(Yb)] and spontaneous radiation process. The intensity of the UC luminescence centered at 360 nm always increases with Yb³⁺ concentration from 2 to 15 mol%. We believe that it may come from the cooperation of energy transfer process from Yb³⁺ ions in the ²F_5/2 state and the cross energy transfer process ⁵S₂/⁵F₄ + ⁵I₆ → (⁵F, ³F, ⁵G)₂ + ⁵I₈.