Topological multiplicity of the maximum eigenvalue of graph 1-Laplacian

In this paper, we reveal the connection between the independent number of a graph and the topological multiplicity of the maximal eigenvalue of the corresponding graph 1-Laplacian. The pseudo independent number of a graph is introduced, which provides a better lower estimate of the topological multiplicity of the maximum eigenvalue. The technique of our proof is based on the localization property of the eigenvector for graph 1-Laplacian, the Krasnoselski genus, and its relation to the topological join.     

On tight 6-cycle decompositions of complete 3-uniform hypergraphs

The complete 3-uniform hypergraph of order v has a vertex set V of size v and the set of all 3-element subsets of V as its edge set. A tight 6-cycle is a hypergraph with vertex set $\{a,b,c,d,e,f\}$ and edge set $\{\{a,b,c\},\{b,c,d\},\{c,d,e\},\{d,e,f\},\{e,f,a\},\{f,a,b\}\}$. We show that there exists a decomposition of the complete 3-uniform hypergraph of order v into isomorphic copies of a tight 6-cycle if and only if $v\equiv 1$, 2, 10, 20, 28, or $29(\mathrm{mod}36)$.     

Singularities and spectral asymptotics of a random nonlinear wave in a nondispersive system

In this paper, we study the propagation of high-intensity acoustic noise in free space and in waveguide systems. A mathematical model generalizing the Burgers equation is used. It describes the nonlinear wave evolution inside tubes of variable cross-section, as well as in ray tubes, if the geometric approximation for heterogeneous media is used. The generalized equation transforms to the common Burgers equation with a dissipative parameter, known as the “Reynolds–Goldberg number”. In our model, this number depends on the distance travelled by the wave. With a zero “viscous” dissipative term, the model reduces to the Riemann (or Hopf) equation. Its solution presents the field by an implicit function. The spectral form of this solution makes it possible to derive explicit expressions for both dynamic and statistical characteristics of intense waves. The use of a spectral approach allowed us to describe the high-intensity noise in media with zero and finite viscosity. Applicability conditions of these solutions are defined. Since the phase matching is fulfilled for any triplet of interacting spectral components, there is an avalanche-like increase in the number of harmonics and the formation of shocks. The relationship between these discontinuities and other singularities and the high-frequency asymptotic of intense noise is studied. The possibility is shown to enhance nonlinear effects in waveguide systems during the evolution of noise.     

Switching of heating and cooling modes using thermal radiation films

We study emissivity (ε)-dependent radiative heat transfer phenomena in remote and contact configurations. To demonstrate the emissivity-dependent radiative heating mode in a remote configuration, we fabricated miniature greenhouses covered with low (0.34)- and high-ε (0.86) polyethylene films and monitored temperatures on the floors, insides, and covers of the greenhouses during 24 h. The high-ε greenhouse yielded a 9-°C increase in floor temperature relative to the low-ε greenhouse at a one-sun solar irradiance because the high-ε film effectively trapped floor radiation. In contrast, the cover temperature remained lower in the high-ε greenhouse due to intensified radiation released from the high-ε film. This self-cooling effect was more evident when an emissive film was in physical contact with an object. While bare copper heated up to 55 °C, a high-ε film coated copper substrate was kept cooler by 4 and 2 °C compared with the bare and low-ε film coated copper samples, respectively.     

Constrained radar waveform optimization for a cooperative radar-communication system

The coexistence of radar-sensing and communication systems research has received a surge of interest in recent times to tackle the issue of spectrum inadequacy. Designing an optimized radar waveform for a coexistence scenario has been a challenging task for accomplishing the convergence of radar-sensing and communication functionalities, without degrading the performance at either end. This paper proposes a novel global optimization-based Spatial Branch and Bound (SBnB) approach to optimize the phase coefficients of a Non-Linear Frequency Modulated (NLFM) waveform in a CRCS framework. In addition, the Modified-Power Ratio Constraint-Cramér–Rao Lower Bound (M-PRC-CRLB), a local optimization-based approach is proposed to optimize the phase coefficients of an NLFM waveform. The spectral energy distribution and auto-correlation characteristics of an NLFM waveform are comprehensively investigated for various values of polynomial order (N) and at different threshold Signal-to-Noise-Ratio (SNR) values. To compare the proposed waveform design approaches (M-PRC-CRLB, SBnB) with the existing waveform design approaches namely, Minimum Estimation Error Variance (MEEV) and PRC- CRLB, a Peak-to-Side-Lobe-Ratio (PSLR), and Integrated-Side-Lobe-Ratio (ISLR) are evaluated at various polynomial orders and threshold SNR values. Furthermore, the performance of a CRCS is assessed using the radar estimation rate and communication data rate. The simulation results reveal that the proposed optimized radar waveform design approaches provide improved performance compared to the existing radar waveform design approaches in terms of radar estimation rate. Further, the proposed global optimization-based SBnB approach achieves a comparable performance of the communication data rate. In addition, the proposed approaches accomplish enhanced spectral utilization, controlled side-lobe energy levels, reduced range-domain ambiguities, and a higher information rate in a CRCS.     

Intelligent resource allocation for transmission security on IRS-assisted spectrum sharing systems with OFDM

In this paper, intelligent reflecting surface (IRS) technology is employed to enhance physical layer security (PLS) for spectrum sharing communication systems with orthogonal frequency division multiplexing (OFDM). Aiming to improve the secondary users’ secrecy rates, a design problem for jointly optimizing the transmission beamforming of secondary base station (SBS), the IRS’s reflecting coefficient and the channel allocation is formulated under the constraints of the requirements of minimum data rates of primary users and the interference between users. As the scenario is highly complex, it is quite challenging to address the non-convexity of the optimization problem. Thus, a deep reinforcement learning (DRL) based approach is taken into consideration. Specifically, we use dueling double deep Q networks (D3QN) and soft Actor–Critic (SAC) to solve the discrete and continuous action space optimization problems, respectively, taking full advantage of the maximum entropy RL algorithm to explore all possible optimal paths. Finally, simulation results show that our proposed approach has a great improvement in security transmission rate compared with the scheme without IRS and OFDM, and our proposed D3QN-SAC approach is more effective than other approaches in terms of maximum security transmission rate.     

光激发四苯基卟啉钴氧化还原反应机理研究

金属卟啉在光激发条件下会呈现出重要催化特性和光学性质。四苯基卟啉亚钴(Co~Ⅱ TPP)性质稳定,难以通过强氧化剂氧化至四苯基卟啉钴(Co~ⅢTPP)。本文分别利用全波长氙灯与355nm激光脉冲诱导Co~Ⅱ TPP,探究其分子内的氧化还原过程。研究发现,Co~Ⅱ TPP的Soret带最大吸收峰随光照时长的递增出现红移,且吸收强度呈现先下降后上升的趋势,最大吸收峰位置由415nm逐渐红移至433nm,其Q带最大吸收峰位置由532nm逐渐红移至545nm。两种光源诱导Co~Ⅱ TPP均出现稳态吸光度的降低,分子内的活性中心钴离子由Co~(2+)氧化到Co~(3+)。咪唑使得Co~Ⅱ TPP受光诱导后更易出现稳态吸收峰红移。Co~Ⅱ TPP的瞬态吸收光谱有3个瞬态吸收峰,激光激发含咪唑的Co~Ⅱ TPP溶液仅在396nm出现单个瞬态吸收峰。数据表明光激发时,电子从卟啉的π成键分子轨道向具有配体特征的π~*反键分子轨道迁移,发生金属对配体的电荷迁移,生成稳定的高价态Co~Ⅲ。     

Electronic,spectra, and spin orbit interaction for FrAr van der Waals system

The potential energy curves and spectroscopic constants of the ground and many excited states of the FrAr van der Waals system have been determined using a one‐electron pseudopotential approach. The Fr⁺ core and the electron–Ar interactions are replaced by effective potentials. The Fr⁺Ar core–core interaction is incorporated using the accurate CCSD(T) potential of Hickling et al. (Phys. Chem. Chem. Phys. 2004, 6, 4233). This approach reduces the number of active electrons of the FrAr van der Waals system to only one valence electron, which permits the use of very large basis sets for the Fr and Ar atoms. Using this technique, the potential energy curves of the ground and many excited states are calculated at the self consistent field (SCF) level. In addition, the spin–orbit interaction is also considered using the semiempirical scheme for the states dissociating into Fr (7p) and Fr (8p). The FrAr system is not studied previously and its potential interactions, spectroscopic constants and dipole functions are presented here for the first time. Furthermore, we have predicted the X²Σ⁺–A²Π_1/2, X²Σ⁺–AΠ_3/2, X²Σ⁺–B²Σ_1/2⁺, X²Σ⁺–3²Π_1/2, X²Σ⁺–3²Π_3/2, and X²Σ⁺–5²Σ_1/2⁺ absorption spectra. © 2012 Wiley Periodicals, Inc.