Smarandache函数在两数列上的下界估计

设S(n)是Smarandache函数,其中n是一正整数.讨论Smarandache函数S(n)在数列F((2k),1)=F(n,1)=n2n+1(n=2k)与数列G(2n,1)=(2n)2n+1上的下界估计.基于初等方法证明了:当偶数n≥6时,有S(F((2k),1))=S(F(n,1))≥6×2n+1;当n≥4时,有S(G(2n,1))≥6×2n+1.     

Study of nucleon-nucleon and alphanucleon elastic scattering by the Manning-Rosen potential

Although often used in molecular dynamics, in this work the Manning–Rosen potential is parameterized to compute the scattering phase shifts for the nucleon–nucleon and the alpha-nucleon systems by exploiting the standard phase function method. We obtain excellent agreement in phase shifts with the more sophisticated calculations up to partial waves ${\ell }=2.$     

Engineering nanostructures of CuO-based photocatalysts for water treatment: Current progress and future challenges

Nowadays, increasing extortions regarding environmental problems and energy scarcity have stuck the development and endurance of human society. The issue of inorganic and organic pollutants that exist in water from agricultural, domestic, and industrial activities has directed the development of advanced technologies to address the challenges of water scarcity efficiently. To solve this major issue, various scientists and researchers are looking for novel and effective technologies that can efficiently remove pollutants from wastewater. Nanoscale metal oxide materials have been proposed due to their distinctive size, physical and chemical properties along with promising applications. Cupric Oxide (CuO) is one of the most commonly used benchmark photocatalysts in photodegradation owing to the fact that they are cost-effective, non-toxic, and more efficient in absorption across a significant fraction of solar spectrum. In this review, we have summarized synthetic strategies of CuO fabrication, modification methods with applications for water treatment purposes. Moreover, an elaborative discussion on feasible strategies includes; binary and ternary heterojunction formation, Z-scheme based photocatalytic system, incorporation of rare earth/transition metal ions as dopants, and carbonaceous materials serving as a support system. The mechanistic insight inferring photo-induced charge separation and transfer, the functional reactive radical species involved in a photocatalytic reaction, have been successfully featured and examined. Finally, a conclusive remark regarding current studies and unresolved challenges related to CuO are put forth for future perspectives.     

Lossy mode resonance-based uniform core tapered fiber optic sensor for sensitivity enhancement

A lossy mode resonance (LMR)-supported fiber optic sensor in which a uniform fiber core is placed among two identical tapered regions, is investigated numerically. Indium tin oxide (ITO) and aluminum-doped zinc oxide (AZO) are considered as LMR active materials used to excite several lossy modes and gold and silver are used as surface plasmon resonance (SPR) active materials. In this probe design, a central uniform core coated with ITO/AZO is the active sensing region, whereas tapered regions are meant for bringing the incident angle close to the critical angle. The sensitivity of the present fiber optic bio-sensor is evaluated for first two LMRs utilizing both ITO and AZO separately, along with its variation with the taper ratio (TR). For ITO, the maximum sensitivity values are observed to be 18.425 μm RIU⁻¹ (refractive index unit) and 0.825 μm RIU⁻¹, corresponding to the first and second LMRs, respectively, at a TR of 1.6 and for AZO, equivalent values are 0.79 μm RIU⁻¹ and 0.35 μm RIU⁻¹, respectively, at a TR of 2.0. The results illustrate that the first LMR is more sensitive than the second LMR and the ITO-coated probe possesses greater sensitivity than the AZO-coated probe for both LMRs. Similarly, for the fiber optic SPR sensor, the maximum value of sensitivity is 5.6425 μm RIU⁻¹, in the case of gold and 5.0615 μm RIU⁻¹ in the case of silver, at a TR of 1.6. Hence, the result shows that the sensor with the present fiber optic probe design has around a 3-fold enhancement in sensitivity compared with conventional SPR sensors. This study will have applications in many sensing schemes where the requirement of large sensitivity is vital.     

Numerical approach for the evolution of spin-boson systems and its application to the Buck–Sukumar model

We study the evolution properties of spin-boson systems by a systematic numerical iteration approach, which performs well in the whole coupling regime. This approach evaluates a set of coefficients in the formal expression of the time-dependent Schr?dinger equation by expanding the initial state in Fock space. This set of coefficients is unique for the spin-boson Hamiltonian studied, allowing one to calculate the time evolution from different initial states. To complement our numerical calculations, we apply the method to the Buck–Sukumar model. We find that when the ground-state energy of the model is unbounded and no ground state exists in a certain parameter space, the time evolution of the physical quantities is naturally unstable.     

Single top partner production in the tZ channel at eγ collision in the littlest Higgs model with T-parity

Introducing the top partner is a common way to cancel the largest quadratically divergent contribution to the Higgs mass induced by the top quark. In this work, we study single top partner production in the tZ channel at eγ collision in the littlest Higgs model with T-parity(LHT). Since it is well known that polarized beams can enhance the cross section, we analyze the signal via polarized electron beams,and photon beams. we have selected two decay modes for comparison, based on the leptonic or the hadronic decays of the W and Z from the top partner. We then construct a detailed detector simulation, and choose a set of cuts to enhance signal significance. For mode A(B), the capacity for exclusion in this process at s~(1/2)=3TeV is comparable to the current experimental limits with L=1000(500) fb~(-1). If the integrated luminosity can be increased to 3000 fb~(-1), the top partner mass+mTcan be excluded up to 1350(1440) GeV at 2σ level. We also considered the initial state radiation effect, and find that this effect reduces the excluding ability of the eγ collision on the the top partner mass by approximately 10 GeV. Moreover, the ability to exclude the LHT parameter space at eγ collision complements the existing research.     

Mixed Fano-SP resonant absorption of THz electromagnetic waves in a photonic resonator contacting with a metal film

In terahertz frequency region, we have investigated theoretically the correlation between spectra of a free photonic structure and that deposited on a metal for several models of metal. It was found that for quasi-normal incidence of p-polarized electromagnetic field the presence of metal generates narrow spectral wells in the middle of reflection windows existing in a free photonic crystal. Quite another manifestation of metal-resonator inter-influence takes place at incident angles exceeding the Brewster angle when reflection spikes coincide with modes of photonic crystal resonator and they are absent throughout the stopband areas. The effects are strongly depended on polarization, number of periods and angle of incidence.     

Theory of particle transport phenomena during fatigue and time-dependent fracture of materials based on mesoscale dynamics and their practical applications

In this work, the mesoscale mechanics of metals, which links their microscopic physics and macroscopic mechanics, was established. For practical applications, the laws for quantitatively predicting life of cycle and time-dependent fracture behavior such as fatigue, hydrogen embrittlement, and high-temperature creep were derived using particle transport phenomena theories such as dislocation group dynamics, hydrogen diffusion, and vacancy diffusion. Furthermore, these concepts were also applied for estimating the degree of viscoelastic deterioration of blood vessel walls, which is dominated by a time-dependent mechanism, and for the diagnosis of aneurysm accompanied by the viscoelastic deterioration of the blood vessel wall. In these theories, new mechanical indexes were derived as dominant factors for predicting the life of fatigue crack growth and the time-dependent fracture of notched specimens of materials such as hydrogen embrittlement and high-temperature creep. Furthermore, as an example of a practical application, these theories were applied to estimate the degree of viscoelastic deterioration and chaotic motions of blood vessel walls, which are closely related to blood vessel diseases such as atherosclerosis and aneurysm. Moreover, new indexes to diagnose them were also proposed for clinical applications.