A Restricted SIR Model with Vaccination Effect for the Epidemic Outbreaks Concerning COVID-19

This paper presents a restricted SIRmathematicalmodel to analyze the evolution of a contagious infectious disease outbreak(COVID-19)using available data.The new model focuses on two main concepts:first,it can present multiple waves of the disease,and second,it analyzes how far an infection can be eradicated with the help of vaccination.The stability analysis of the equilibrium points for the suggested model is initially investigated by identifying the matching equilibrium points and examining their stability.The basic reproduction number is calculated,and the positivity of the solutions is established.Numerical simulations are performed to determine if it is multipeak and evaluate vaccination’s effects.In addition,the proposed model is compared to the literature already published and the effectiveness of vaccination has been recorded.

Model and algorithm of optimizing alternate traffic restriction scheme in urban traffic network

An optimization model and its solution algorithm for alternate traffic restriction(ATR) schemes were introduced in terms of both the restriction districts and the proportion of restricted automobiles. A bi-level programming model was proposed to model the ATR scheme optimization problem by aiming at consumer surplus maximization and overload flow minimization at the upper-level model. At the lower-level model, elastic demand, mode choice and multi-class user equilibrium assignment were synthetically optimized. A genetic algorithm involving prolonging codes was constructed, demonstrating high computing efficiency in that it dynamically includes newly-appearing overload links in the codes so as to reduce the subsequent searching range. Moreover,practical processing approaches were suggested, which may improve the operability of the model-based solutions.

Surface structures of equilibrium restricted curvature model on two fractal substrates

With the aim to probe the effects of the microscopic details of fractal substrates on the scaling of discrete growth models, the surface structures of the equilibrium restricted curvature （ERC） model on Sierpinski arrowhead and crab sub- strates are analyzed by means of Monte Carlo simulations. These two fractal substrates have the same fractal dimension dr, but possess different dynamic exponents of random walk Zrw. The results show that the surface structure of the ERC model on fractal substrates are related to not only the fractal dimension df, but also to the microscopic structures of the substrates expressed by the dynamic exponent of random walk Zrw- The ERC model growing on the two substrates follows the well-known Family-Vicsek scaling law and satisfies the scaling relations 2a ~ df ~ z ~ 2Zrw. In addition, the values of the scaline exponents are in ~ood a^reement with the analytical orediction of the fractional Mullins-Herring equation.

Gas-Fluid and Fluid-Solid Phase Instability for Restricted Primitive Model

By considering the fluctuation of grand potential f~ around equilibrium with respect to small one-particle density fluctuations δpα（r→）, the phase instability of restricted primitive model （RPM） of ionic systems is investigated. We use the integral equation theory to calculate the direct correlation functions in the reference hypernetted chain approximation and obtain the spinodai line of RPM. Our anaiysis explicitly indicates that the gas-fluid phase instability is induced by k = 0 fluctuation mode, while the fluid-solid phase instability is related to k ≠ 0 fluctuation modes. The spinodai line is qualitatively consistent with the result of computer simulations by others.

Synthesis and Crystal Structure of N-[1-(2-Methyl-1-methylcarbamoyl-propylcarbamoyl)-2,3-diphenyl-cyclopropyl]-benzamide

N-[1-（2-Methyl-1-methylcarbamoyl-propylcarbamoyl）-2,3-diphenyl-cyclopropyl]-ben- zamide, C29H31N3O3, has been synthesized and characterized by IR, ^1H NMR, ^13C NMR and singlecrystal X-ray diffraction. The crystal is of orthorhombic, space group P212121 with a = 11.0855（11）, b = 18.7756（19）, c = 24.434（2）A, V = 5085.5（9）A^3, Z = 8, Mr = 469.57, Dc = 1.227 g/cm^3, λ = 0.71070 A,μ（MoKα） = 0.080 mm^-1, F（000） = 2000, the final R = 0.0579 and wR = 0.1111 for 4569 observed reflections with I 〉 2σ（I）. The N-H and oxygen atom are involved in intermolecular hydrogen bonds which link the molecules into a one-dimensional chain.

Theoretical Investigation of Ru(II) Complexes as Photosensitizer for Photodynamic Therapy

This work was undertaken to see how Ru II complexes can be suitable for photodynamic therapy through theoretical prediction. For that, four Ru II complexes, α-RuCl2(Azpy)2, , and were used in unrestricted state by providing with no more energy than 2.68 eV. The unrestricted state allows the complex molecule to display each of its electrons in one orbital. All the calculations such as optimization, frequency and TD-DFT calculations were performed at WB97XD/Lanl2dz level. It resulted from this investigation that Ru II complexes are active for both mechanisms suitable for photodynamic therapy in presence or absence of 3O2. Moreover, this reaction was assumed to take place only with Guanine DNA base as demonstrated in literature. Therefore, Guanine is admitted as the base most reacting with ruthenium complexes for photodynamic therapy. This work confirms our prediction regarding metallic complexes that are assumed to be photosensitized in condition that an electron must be isolated to favor the excitation. Nevertheless, Ru II complexes are found suitable for superficial therapy while Ru III must be active for deep therapy.

Restricted Cohomology of Restricted Lie Superalgebras

Suppose the ground field F is an algebraically closed field characteristic of p>2.In this paper,we investigate the restricted cohomology theory of restricted Lie superalgebras.Algebraic interpretations of low dimensional restricted cohomology of restricted Lie superalgebra are given.We show that there is a family of restricted model filiform Lie superalgebra Lλp,p structures parameterized by elementsλ∈Fp.We explicitly describe both the 1-dimensional ordinary and restricted cohomology superspaces of Lλp,p with coefficients in the 1-dimensional trivial module and show that these superspaces are equal.We also describe the 2-dimensional ordinary and restricted cohomology superspaces of Lλp,p with coefficients in the 1-dimensional trivial module and show that these superspaces are unequal.

On Equalities for BLUEs under Misspecified Gauss-Markov Models

This paper studies relationships between the best linear unbiased estimators （BLUEs） of an estimable parametric functions Kβunder the Gauss-Markov model {y, Xβ, σ^2]E} and its misspecified model {y, X0β,σ^2∑0}. In addition, relationships between BLUEs under a restricted Gauss Markov model and its misspecified model are also investigated.

Fiducial generalized p-values for testing zero-variance components in linear mixed-effects models

Linear mixed-effects models are widely used in analysis of longitudinal data. However, testing for zero-variance components of random effects has not been well-resolved in statistical literature, although some likelihood-based procedures have been proposed and studied. In this article, we propose a generalized p-value based method in coupling with fiducial inference to tackle this problem. The proposed method is also applied to test linearity of the nonparametric functions in additive models. We provide theoretical justifications and develop an implementation algorithm for the proposed method. We evaluate its finite-sample performance and compare it with that of the restricted likelihood ratio test via simulation experiments. We illustrate the proposed approach using an application from a nutritional study.

Asymptotic properties of Lasso in high-dimensional partially linear models

We study the properties of the Lasso in the high-dimensional partially linear model where the number of variables in the linear part can be greater than the sample size.We use truncated series expansion based on polynomial splines to approximate the nonparametric component in this model.Under a sparsity assumption on the regression coefficients of the linear component and some regularity conditions,we derive the oracle inequalities for the prediction risk and the estimation error.We also provide sufficient conditions under which the Lasso estimator is selection consistent for the variables in the linear part of the model.In addition,we derive the rate of convergence of the estimator of the nonparametric function.We conduct simulation studies to evaluate the finite sample performance of variable selection and nonparametric function estimation.