New β-delayed proton decays in the rare-earth region near the proton drip line

The β-delayed proton precursors 125Nd, 128Pm, 129Sm, 137Gd and 139Dy near the proton drip line were produced by the irradiation of 92Mo, 96Ru and 106Cd with an 36Ar beam, and conclusively identified for the first time by using proton-gamma coincidence in combination with a He-jet tape transport system. Their half-lives were determined to be 0.60(15)s,1.0(3)s,0.55(10)s,2.2(2)s and 0.6(2)s, respectively. The measured energy spectra of β-delayed protons and estimated proton branching ratios to the final states in "daughter" nuclei for the precursors 125Nd, 129Sm, 137Gd and 139Dy, as well as the previously reported ones for the precursors 135Gd and 121Ce, were fitted by a statistical model calculation. The ground-state spins and parities of 121Ce, 125Nd, 129Sm, 135Gd, 137Gd and 139Dy were then assigned as 5/2±,5/2±,1/2±(or 3/2+),5/2+,7/2± and 7/2, respectively. The consistency between the experimental spin-parity assignment and the predicted Nilsson diagrams indirectly indicates that the ground states of 121Ce, 125Nd, 129Sm, 135Gd, 137Gd and 139Dy are highly deformed with β2～0.3.     

β-delayed proton decays of 81Zr and 85Mo

β-delayed proton decays of Tz=1/2 series nuclei 81Zr and 85Mo have been studied in detail by using p-γ coincidence measurement. The β-delayed proton spectra populating the first excited states of the daughter nuclei have been obtained. Half-life of 81Zr has been measured to be 5.3 s±0.5 s and that of 85Mo 3.2 s±0.2 s. By using statistical model calculations and systematic analyses, spins and parities for the ground states of 81Zr and 85Mo have been tentatively assigned to be 3/2- and 1/2-, respectively. Mass excess of 81Zr is -58.3 MeV±0.2 MeV and that of 85Mo -59.1 MeV±0.4 MeV. Combining the measured half-lives with the calculated partial ones yields the branches of β-delayed proton decay for 81Zr and 85Mo of (1.2±0.2)×10-3 and (1.4±0.2)×10-3, respectively.     

Effects of Cone Angles on Nonlinear Vibration Responses of Functionally Graded Shells北大核心CSCD

The nonlinear vibration responses of functionally graded materials (FGMs) shells with different cone angles under external loads were studied. Firstly, the Voigt model was employed to describe the physical properties along the thickness direction of FGMs conical shells. Then, the motion equations were derived based on the 1st-order shear deformation theory, the von Kármán geometric nonlinearity and Hamilton’s principle. Next, the Galerkin method was applied to discretize the motion equations and the governing equations were simplified into a 1DOF nonlinear vibration differential equation under Volmir’s assumption. Finally, the nonlinear motion equations were solved with the harmonic balance method and the Runge-Kutta method, and the amplitude frequency response characteristic curves of the FGMs conical shells were obtained. The effects of different material distribution functions and different ceramic volume fraction exponents on the amplitude frequency response curves of conical shells were discussed. The bifurcation diagrams of conical shells with different cone angles, as well as time process diagrams and phase diagrams for different excitation amplitudes, were described. The motion characteristics were characterized by Poincaré maps. The results show that, the FGMs conical shells present the nonlinear characteristics of hardening springs. The chaotic motions of the FGMs conical shells are restrained and not prone to motion instability with the increase of the cone angle. The FGMs conical shell present a process from the periodic motion to the multi-periodic motion and then to chaos with the increase of the excitation amplitude. © 2022 Editorial Office of Applied Mathematics and Mechanics. All rights reserved.     

Weyl and Lidski? Inequalities for General Hyperbolic Polynomials

The roots of hyperbolic polynomials satisfy the linear inequalities that were previously established for the eigenvalues of Hermitian matrices, after a conjecture by A. Horn. Among them are the so-called Weyl and Lidskiǐ inequalities. An elementary proof of the latter for hyperbolic polynomials is given. This proof follows an idea from H. Weinberger and is free from representation theory and Schubert calculus arguments, as well as from hyperbolic partial differential equations theory.     

Lump Solutions,Interaction Solutions and Breather Solutions of Generalized (3+1)-Dimensional KdV Equations北大核心CSCD

Based on the bilinear form of the generalized (3+1)-dimensional KdV equation, the lump solution, the interaction solution and the breather solution of the equation were obtained. The obtained lump solutions were proved to be rationally localized in all directions of the space, then the “fusion” and “fission” phenomena were observed during the interaction between the lump soliton wave and the one-stripe soliton. Finally, the breather solution of the equation was obtained. © 2023 Editorial Office of Applied Mathematics and Mechanics. All rights reserved.     

A New Criterion on k-Normal Elements over Finite Fields

The notion of normal elements for finite fields extension was generalized as k-normal elements by Huczynska et al.(2013). Several methods to construct k-normal elements were presented by Alizadah et al.(2016) and Huczynska et al.(2013), and the criteria on k-normal elements were given by Alizadah et al.(2016) and Antonio et al.(2018). In the paper by Huczynska, S., Mullen, G., Panario, D. and Thomson, D.(2013), the number of k-normal elements for a fixed finite field extension was calculated and...     

Closed Strong Spacelike Curves,Fenchel Theorem and Plateau Problem in the 3-Dimensional Minkowski Space

The authors generalize the Fenchel theorem for strong spacelike closed curves of index 1 in the 3-dimensional Minkowski space, showing that the total curvature must be less than or equal to 2π. Here the strong spacelike condition means that the tangent vector and the curvature vector span a spacelike 2-plane at each point of the curve γ under consideration. The assumption of index 1 is equivalent to saying that γ winds around some timelike axis with winding number 1. This reversed Fenchel-type inequality is proved by constructing a ruled spacelike surface with the given curve as boundary and applying the Gauss-Bonnet formula. As a by-product, this shows the existence of a maximal surface with γ as the boundary.     

The structure and magnetic properties of Fe- N thin films

200 nm Fe-N thin films deposited on glass substrates by RF sputtering were vacuum annealed at 250-350℃ under 12000 A/m magnetic field. Heat treatment was effective in improving the soft magnetic properties of the Fe-N film. When the nitrogen content was in the range of 5-7 at. %,the thin films consisted of α′ + α" after heat treatment and had excellent soft magnetic properties of 4πMs = 2.4 T, Hc ＜ 80 A/m, μr = 1500 under 2-10 MHz. The properties of the films meet the needs of a write head material used in the dual element GMR/inductive heads. The fromation mechanism and lattice constants of the α′ phase in Fe-N thin film are different from Jack's results obtained from γ→α′transformation in bulk samples. The linear relationship between a, c and Ca'N for thin film was obtained asc = 2. 866+ 1.559Ca'N,a = 2.866 + 0.181Ca'N.``     

ON FUNDAMENTAL SOLUTIONS FOR MULTIVARIATE SINGULAR INTERPOLATION

The objective of this paper is to give a constructive approach to the solution of the fundamental functions for cardinal interpolation from a shift-invariant space generated by the (multi-)integer translates of some compactly supported function whose polynomial symbol has a non-empty zero set.This problem was first introduced by Chut,Diamond,and Raphael,where explicit solutions were given for various zero sets.Later,de Boor,Hollig,and Riemenschneider gave an existence proof for zero sets which are more general.In this pa-per,we give an integral representation of the fundamental solutions that can be made explicit in some cases and we will also give a growth condition of such fundamental solutions.The four-directional box splines will be used as an illustrative example.     

Buckling Analysis of Re-Entrant Honeycomb Structures Under General Macroscopic Stress States北大核心CSCD

Based on the negative Poisson’s ratio effect of the re-entrant honeycomb, the finite element simulation of its buckling mechanical properties was carried out, and 2 buckling modes other than those of the traditional hexagonal honeycomb structures were obtained. The beam-column theory was applied to analyze the buckling strength and mechanism of the 2 buckling modes, where the equilibrium equations including the beam end bending moments and rotation angles were established. The stability equation was built through application of the buckling critical condition, and then the analytical expression of the buckling strength was obtained. The re-entrant honeycomb specimen was printed with the additive manufacturing technology, and its buckling performance was verified by experiments. The results show that, the buckling modes vary significantly under different biaxial loading conditions; the re-entrant honeycomb would buckle under biaxial tension due to the auxetic effect, being quite different from the traditional honeycomb structure; the typical buckling bifurcation phenomenon emerges in the analysis of the buckling failure surfaces under biaxial stress states. This research provides a significant guide for the study on the failure of re-entrant honeycomb structures due to instability, and the active application of this instability to achieve special mechanical properties. © 2023 Editorial Office of Applied Mathematics and Mechanics. All rights reserved.     

Responses of SDOF Structures With SPIS-Ⅱ Dampers Under Random Seismic Excitation北大核心CSCD

A closed-form solution of responses of SDOF structures with SPIS-Ⅱ dampers under seismic excitation modeled with the Clough-Pezien spectrum was proposed, and the shock absorption performance and influential factors of this system were studied based on the proposed method. Firstly, the motion equation for the SPIS-Ⅱ damper was established, and the unified expressions of frequency domain solutions of structural responses, such as the structural displacement and the inerter force, were obtained. Secondly, based on the rational expression decomposition and the residue theorem, the quadratic orthogonal equations of the frequency response eigenvalue function and the Clough-Pezien spectrum were obtained respectively, and in turn the quadratic orthogonal equation of the structural response power spectrum was deduced. Thirdly, the concise closed-form solutions of the 0~2nd-order spectral moments of the structural responses were acquired. The proposed method and the virtual excitation method were used to analyze a case respectively, which verifies the correctness of the proposed method. Finally, the proposed method was used to analyze the effects of the inerter parameters on the seismic performances of the structure. The research shows that, the proposed method gives closed-form solutions better than those given by the virtual excitation method in terms of computation efficiency and accuracy. The damping performance will improve with the increase of µm and µξ for a constant µω and the damping performance will reach the optimum for µω=1. © 2023 Editorial Office of Applied Mathematics and Mechanics. All rights reserved.     

Fuzzy Rough Ring and Its Properties

This paper is devoted to the theories of fuzzy rough ring and its properties. The fuzzy approximation space generated by fuzzy ideals and the fuzzy rough approximation operators were proposed in the frame of fuzzy rough set model. The basic properties of fuzzy rough approximation operators were analyzed and the consistency between approximation operators and the binarv operation of ring was discussed.     

A Prediction Model for Skin Wound Suture Forces With Uncertain Material Parameters北大核心CSCD

To evaluate the forces required for the suture of skin wounds quickly and effectively, the nonlinear finite element method was used to calculate the suture forces for skin wounds with different sizes and material parameters. With the calculated results as samples, the prediction model for skin wound suture forces was constructed by means of the EBF neural network model. Given the uncertain skin material parameters influencing the reliability of numerical results, the Monte-Carlo method was used to analyze the uncertainty propagation of skin material parameters. Finally, the prediction analysis and measuring experiment of wound suture forces were carried out with pig skin specimens to verify the reliability of the method. The results showed that, the suture force increases first and then decreases according to the suture point sequence, and the peak force occurs before the center of the wound. For a 40 mm×10 mm wound, the peak suture force is about 1.7 N, and that for a 40 mm×14 mm wound is about 2.5 N. Influenced by the uncertainty of material parameters, the prediction results of suture forces fluctuate by as much as ±0.6 N. The proposed theoretical prediction model provides an effective solution to the problem of parameter uncertainty propagation for biological soft tissue materials such as skins, and makes an important mechanical reference for robotic surgical suture. © 2023 Editorial Office of Applied Mathematics and Mechanics. All rights reserved.     

Super Jaulent-Miodek hierarchy and its super Hamiltonian structure,conservation laws and its self-consistent sources

A super Jaulent-Miodek hierarchy and its super Hamiltonian structures are constructed by means of a kind of Lie super algebras and super trace identity. Moreover, the self-consistent sources of the super Jaulent-Miodek hierarchy is presented based on the theory of self-consistent sources. Further- more, the infinite conservation laws of the super Jaulent-Miodek hierarchy are also obtained. It is worth noting that as even variables are boson variables, odd variables are fermi variables in the spectral problem, the commutator is different from the ordinary one.     

Markov processes and related topics

The ＂Workshop on Markov Processes and Related Topics＂ were held nine times since 2002, organized mainly by the Probability Group in the Research Center for Stochastics, Beijing Normal University. The tenth will be held in the coming August, 2014. This workshop happens almost in each year except 2003 （cancelled because of SARS）, and 2009 （cancelled because too many related conferences were held in that year）. In 2005, the ard workshop is merged into the Joint Meeting of CSPS/IMS. The research group was mainly supported by the National Natural Science Foundation of China （NSFC） in the period of 2002-2010, and by the Ministry of Education （985 project） during 2012-2014. Among the ten workshops, five of them were or will be co-organized with some universities out of Beijing.     

NECESSARY CONDITION FOR THE STRONG UNIFORM CONVERGENCE OF THE NEAREST NEIGHBOUR DENSITY ESTIMATE

Let X_1,X_2,...,X_n be iid. Sample drawn from a population with distribution F, if F have a density, denote it by f. Various methods of estimating f by x_1,X_2,...,X_n, have proposed in the literatures, for example, the kernel estimate and nearest neighhour estimate. The later was introduced by Loftsgarden and Quesenberry[1]. The method is as follows:     

Morita Context and Morita—Like Equivalence for the xst—Rings

The notion of the xst-rings was introduced by Garcfa and Marfn [5] in 1999.In this paper,we cousider Morita context,Morita-like equivalence and the exchange property for the xst-rings.The results of the first Morita theorem are generalized to the xst-rings.So we obtain an important Morita-like equivalence of the xst-rings,from which,as an immediate consequence,we deduce the main result of Xu-Shum-Turner [4] and the standard Morita equivalence,A-Mn(A),for a unital ring A.Moreover,we describe the properties of those well-known intermediate matrix rings,and show that the exchange property for a unital ring A coincides with the one for any Mn(A) as well as any intermediate matrix ring sitting between FM1(A) and FCг(A),which is an extension of a well-known result obtained by Nicholson[7].     

The Mathematical Model and Research Progress of the Boundary Layer Flashback in Premixed Combustion北大核心CSCD

Flashback is a key problem influencing the normal operation of power equipment such as gas turbines. As one of the main mechanisms that cause flashback, the boundary layer flashback has an important effect on the design and operation of gas turbine combustors and other combustion devices. Since the critical gradient model for the boundary layer flashback was put forward by Lewis et al. in 1945, the theoretical models for the boundary layer flashback, such as the Peclet number model, the Damköhler number model and the flame angle theory, were developed one after another. However, these theoretical models still need improvements. Until now, the theoretical models for the boundary layer flashback are still in continuous development and modification. The history of the boundary layer flashback was reviewed, and the background, pertinence and shortcomings of the theoretical models were elucidated in the order of the model establishment time. In addition, the development status and research progress of the theoretical models for the boundary layer flashback in recent years were summarized, especially the progress made with new methods such as numerical simulation and statistical analysis. Further, the theoretical research direction and breakthrough points of the combustion boundary layer flashback at present and in the future were put forward. © 2023 Editorial Office of Applied Mathematics and Mechanics. All rights reserved.     

All of Graphs of the Platonic Solids are Graceful

The term"graceful graph"was proposed by Professor S.W.Golomb in Southen Califor-nia University in 1972[1].A question arisen in reference [1] is answered in this article. Let G be a simple graph of γ vertices and εedges.G is graceful if there is a labelling l ofits vertices with distinct integers from the set{0,1,…,ε},so that the induced edge labellingl’defined by