Propagation of hermite-cosh-gaussian beams passing through ABCD optical system with an annular aperture

By using the expansion of the aperture function into a finte sum of complex Gaussian functions, the corresponding analytical expressions of Hermite-cosh-Gaussian beams passing through annular apertured paraxially and symmetrically optical systems written in terms of ABCD matrix were derived, and they could reduce to the cases with squared aperture. In a similar way, the corresponding analytical expres- sions of cosh-Gaussian beams through annular apertured ABCD matrix were also given. The method could save more calculation time than that by using the diffraction integral formula directly.

Some generalized limit theorems concerning delayed sums of random sequence

For a sequence of arbitrarily dependent m-valued random variables （Xn） n∈N , the generalized strong limit theorem of the delayed average is investigated. In our proof, we improved the method proposed by Liu [6] . As an application, we also studied some limit properties of delayed average for inhomogeneous Markov chains.

Mathematical Modelling of the COVID-19 Epidemic in Northern Ireland in 2020

In this study, we investigate the dynamics of the COVID-19 epidemic in Northern Ireland from 1st March 2020 up to 25th December 2020, using several copies of a Susceptible-Exposed-Infectious-Recovered (SEIR) compartmental model, and compare it to a detailed publicly available dataset. We split the data into 10 time intervals and fit the models on the consecutive intervals to the cumulative number of confirmed positive cases on each interval. Using the fitted parameter estimates, we also provide estimates of the reproduction number. We also discuss the limitations and possible extensions of the employed model.

Holomorphic Curves into ■~N(C) That Share a Set of Moving Hypersurfaces

Let F be a family of holomorphic curves of a domain D in C into a closed subset X in ■~N(C). Let Q_1(z),…, Q_(2t+1)(z) be moving hypersurfaces in ■~N(C) located in pointwise t-subgeneral position with respect to X. If each pair of curves f and g in F share the set {Q_1(z),…, Q_(2t+1)(z)}, then F is normal on D. This result greatly extend some earlier theorems related to Montel's criterion.

Reversible Properties of Monoid Crossed Products

We study the reversible properties of monoid crossed products. The new class of strongly CM-reversible rings is introduced and characterized. This class of rings is a generalization of those of strongly reversible rings, skew strongly reversible rings and strongly M-reversible rings. Some well-known results on this subject are generalized and extended.

Preparation of cluster state in large detuned cavity

An experimentally realizable physical scheme for preparing multiqubit cluster states from a large detuned atomcavity interaction is proposed. The scheme is free of any type of measurement and insensitive to the cavity decay, and the cavity field is only virtually excited so that there is no information exchanging between atom and cavity. The time required for the gate operations is very short, which is important for decoherence. We also discuss the experimental feasibility of our scheme.

Estimating the Level of Asymptomatic COVID-19 Infections in Northern Ireland in 2020

The identification and understanding of COVID-19 potential routes of transmission are fundamental to informing policies and strategies to successfully control the outbreak. Various studies highlighted asymptomatic infections as one of the silent drivers of the epidemic. An accurate estimation of the asymptomatic cases and the understanding of their contribution to the spread of the disease could enhance the effectiveness of current control strategies, mainly based on the symptom onset, to curb transmission. We investigate the dynamics of the COVID-19 epidemic in Northern Ireland during the period 1st March 25th to December 2020 to estimate the proportion of the asymptomatic infections in the country. We extended our previous model to include the stage of the asymptomatic infection, and we implement the corresponding deterministic model using a publicly available dataset. We partition the data into 11 sets over the period of study and fit the model parameters on the consecutive intervals using the cumulative number of confirmed positive cases for each interval. Moreover, we assess numerically the impacts of uncertainty in testing and we provide estimates of the reproduction numbers using the fitted parameters. We found that the proportion of asymptomatically infectious subpopulations, in Northern Ireland during the period of study, ranged between 5% and 25% of exposed individuals. Also, the estimate of the basic reproduction number, R0, is 3.3089. The lower and upper estimates for herd immunity are (0.6181, 0.7243) suggesting that around 70% of the population of Northern Ireland should acquire immunity via infection or vaccination, which is in line with estimates reported in other studies.

Electrical Transport and Giant Magnetoresistance in (1-x)La_(0.67)Ca_(0.33)MnO_3/xCuO Composites

Samples with nominal composition of （1 - x）La0.67Ca0.33MnO3 （LCMO）/xCuO （x = 0%, 2%, 4% and 20% ） were made using a special experimental method. The temperature dependence of the resistivity （ρ） of the composites was investigated in the temperature range of 10 - 300 K and different magnetic fields of H = 0, 0.1, 0.3, 0.5, 1.0 and 3.0 T. The results showed that CuO percentage x had important effects on metal-insulator transition temperature （Tp）, zero field peak resistivity （ρmax）, and magnetoresistance （MR） properties of the composites. Tp shifted sharply towards low temperature with the increase of x in the range of x ≤4%, but was almost independent of x at high level of CuO content. Composites with x = 4 % and 20 % exhibited similar electrical transmission behavior. Compared with pure LCMO, enhanced magnetoresistance could be clearly observed even in a quite low magnetic field of 0.3 T. For x =4% and 20% samples, the MR value at 0.3 T could reach as high as - 88% and - 90%, respectively. XRD and SEM analysis showed that the substantial enhancement of MR, especially near Tp, was because of local spin disorder between contiguous LCMO ferromagnetic particles caused by the addition of CuO.

Non-Gaussian quantum states generation and robust quantum non-Gaussianity via squeezing field

Recent studies show that quantum non-Gaussian states or using non-Gaussian operations can improve entanglement distillation, quantum swapping, teleportation, and cloning. In this work, employing a strategy of non-Gaussian operations（namely subtracting and adding a single photon）, we propose a scheme to generate non-Gaussian quantum states named single-photon-added and-subtracted coherent（SPASC） superposition states by implementing Bell measurements, and then investigate the corresponding nonclassical features. By squeezed the input field, we demonstrate that robustness of nonGaussianity can be improved. Controllable phase space distribution offers the possibility to approximately generate a displaced coherent superposition states（DCSS）. The fidelity can reach up to F ≥ 0.98 and F ≥ 0.90 for size of amplitude z = 1.53 and 2.36, respectively.

Dynamic hesitant fuzzy linguistic group decision-making from a reliability perspective

A dynamic hesitant fuzzy linguistic group decisionmaking(DHFLGDM) problem is studied from the perspective of information reliability based on the theory of hesitant fuzzy linguistic term sets(HFLTSs). First, an approach is applied to transform the dynamic HFLTSs(DHFLTSs) into a set of proportional linguistic terms to eliminate the time dimension. Second, expert reliability is measured by considering both group similarity and degree of certainty, and an optimization method is employed to quantify the linguistic terms by maximizing the group similarity. Third, through computing the attribute stability as well as its reliability, a combination rule which considers both reliability and weight is proposed to aggregate the information, and then the aggregated grade values and degree of stability are used to make a selection. Finally,the application and feasibility of the proposed method are verified through a case study and method comparison.

Strongly s-Reflexive Rings Relative to a Monoid

For a monoid M and an endomorphism α of a ring R, we introduce the notion of strongly M-α-reflexive rings and study its properties. For an u.p.-monoid M and a right Ore ring R with its classical right quotient ring Q, we prove that R is strongly M-α-reflexive if and only if Q is strongly M-α-reflexive, where R is α-rigid, α is an epimorphism of R. The relationship between some special subrings of upper triangular matrix rings and strongly M-α-reflexive rings is also investigated. Several known results similar to strongly M-α-reversible rings are obtained.

Investigation of Fano resonance in compound resonant waveguide gratings for optical sensing

An optical sensor is designed to support the Fano effect based on a compound resonant waveguide grating （CRWG）. The transmission spectra of the CRWG are investigated by utilizing a theoretical method that combines the temporal coupled mode theory with the eigenmode information of the grating structure. The theoretical results, which are observed to agree closely with those acquired by rigorous coupled-wave analysis, show that the linewidth of the transmission spectrum decreases upon increasing the distance between the grating strips, and the central resonance frequency decreases as the refractive index of the analyte increases. Here, the proposed CRWG structures will find potential uses in optical sensing.

Strong dependence of upconversion luminescence on doping concentration in holmium and ytterbium co-doped Y_2O_3 phosphor

Under the excitation of 980 nm diode laser, intense green emission （5F4＋5S2–5I8） of Ho3＋ was observed in Ho3＋ and Yb3＋ co-doped cubic Y2O3. The doping concentration and laser power dependence of the upconverted emission were studied. The decay curves of 5F4＋5S2 emission of Ho3＋ under the excitation of 355 nm pulse laser were measured to investigate the energy transfer process between Ho3＋ and Yb3＋. The results indicated that two-photon process was responsible for the upconversion （UC） emission. The Ho3＋ concentration of 0.04 mol.% and the Yb3＋ concentration of 5 mol.% were determined to be the best value for the strongest Ho3＋ emission under the excitation of 980 nm light. The cross-relaxation between two neighboring Ho3＋ ions and the back energy transfer from Ho3＋ to Yb3＋ were important factors for determin- ing the optimal doping concentration. This material was a promising candidate for the application in biomedical fluorescent labels for the intense green emission upon excitation of near-infrared （NIR） light.

A Likelihood-Based Multiple Change Point Algorithm for Count Data with Allowance for Over-Dispersion

Count data is almost always over-dispersed where the variance exceeds the mean. Several count data models have been proposed by researchers but the problem of over-dispersion still remains unresolved, more so in the context of change point analysis. This study develops a likelihood-based algorithm that detects and estimates multiple change points in a set of count data assumed to follow the Negative Binomial distribution. Discrete change point procedures discussed in literature work well for equi-dispersed data. The new algorithm produces reliable estimates of change points in cases of both equi-dispersed and over-dispersed count data;hence its advantage over other count data change point techniques. The Negative Binomial Multiple Change Point Algorithm was tested using simulated data for different sample sizes and varying positions of change. Changes in the distribution parameters were detected and estimated by conducting a likelihood ratio test on several partitions of data obtained through step-wise recursive binary segmentation. Critical values for the likelihood ratio test were developed and used to check for significance of the maximum likelihood estimates of the change points. The change point algorithm was found to work best for large datasets, though it also works well for small and medium-sized datasets with little to no error in the location of change points. The algorithm correctly detects changes when present and fails to detect changes when change is absent in actual sense. Power analysis of the likelihood ratio test for change was performed through Monte-Carlo simulation in the single change point setting. Sensitivity analysis of the test power showed that likelihood ratio test is the most powerful when the simulated change points are located mid-way through the sample data as opposed to when changes were located in the periphery. Further, the test is more powerful when the change was located three-quarter-way through the sample data compared to when the change point is closer (quarter-way) to the first observation.

Perfect absorption in a monolayer graphene at the near-infrared using a compound waveguide grating by robust critical coupling

We present a perfect graphene absorber with a compound waveguide grating at the near-infrared. The analytical approach is mainly based on the coupled leaky mode theory, which turns the design of the absorber to finding out the required leaky modes supported by the grating structure. Perfect absorption occurs only when the radiative loss of the leaky mode matches the intrinsic absorption loss, which is also named the critical coupling condition.Furthermore, we also demonstrate that the critical coupling of the system can be robustly controlled, and the perfect absorption wavelength can be easily tuned by adjusting the parameters of the compound waveguide grating.

Multipartite matroids and secret sharing

In a secret-sharing scheme,a secret value is distributed among a set of participants by giving each participant a share.The requirement is that only predefined subsets of participants can recover the secret from their shares.The family of the predefined authorized subsets is called the access structure.An access structure is ideal if there exists a secret-sharing scheme realizing it in which the shares have optimal length,that is,in which the shares are taken from the same domain as the secrets.Brickell and Davenport proved that ideal access structures are induced by matroids.Subsequently,ideal access structures and access structures induced by matroids have received a lot of attention.Seymour gave the first example of an access structure induced by a matroid namely the Vamos matroid,that is non-ideal.Since every matroid is multipartite and has the associated discrete polymatroid,in this paper,by dealing with the rank functions of discrete polymatroids,we obtain a sufficient condition for a multipartite access structure to be ideal.Furthermore,we give a new proof that all access structures related to bipartite and tripartite matroids coincide with the ideal ones.Our results give new contributions to the open problem,that is,which matroids induce ideal access structures.

Tunable multiple plasmon-induced transparency with side-coupled rectangle cavities

The tunable multiple plasmon-induced transparency （PIT） effect is investigated numerically in a metal-insulator-metal （MIM） waveguide with three side-coupled rectangular resonators. The system exhibits dual-mode PIT effects in the visible and near-infrared regions. By adjusting the geometrical parameters of the structure, we can manipulate not only each single PIT window, but also the double PIT windows simulta- neously. Our structures may have potential applications for optical communication, integrated optics, and optical information processing. The finite element method （FEM） illustrates our theoretical design.

Compressible Subsonic Potential Flow Past a 2D Given Sharp Angular Unbounded Domain

In this paper, we focus on the two-dimensional subsonic flow problem around an infinite long ramp. The flow is assumed to be steady, isentropic and irrotational, namely, the movement of the flow is described by a second elliptic equation. By the use of a separation variable method, Strum- Liouville theorem and scaling technique, we show that a nontriviM subsonic flow around the infinite long ramp does not exist under some certain assumptions on the potential flow with a low Mach number.