Spin wave resonance frequency in bilayer ferromagnetic films with the biquadratic exchange interaction

The dependences of spin wave resonance(SWR)frequency on the surface anisotropy field,interface exchange coupling,symmetry,biquadratic exchange(BQE)interaction,film thickness,and the external magnetic field in bilayer ferromagnetic films are theoretically analyzed by employing the linear spin wave approximation and Green’s function method.A remarkable increase of SWR frequency,except for energetically lower two modes,can be obtained in our model that takes the BQE interaction into account.Again,the effect of the external magnetic field on SWR frequency can be increased by increasing the biquadratic to interlayer exchange ratio.It has been identified that the BQE interaction is of utmost importance in improving the SWR frequency of the bilayer ferromagnetic films.In addition,for bilayer ferromagnetic films,the frequency gap between the energetically highest mode and lowest mode is found to increase by increasing the biquadratic to interlayer exchange ratio and film thickness and destroying the symmetry of the system.These results can be used to improve the understanding of magnetic properties in bilayer ferromagnetic films and thus may have prominent implications for future magnetic devices.

Solitary excitations in one-dimensional ferromagnetic spin chains with biquadratic exchange interaction

By using the traveling wave method, the solutions of the elliptic function wave and the solitary wave are obtained in a ferromagnetic spin chain with a biquadratic exchange interaction, a single ion anisotropic interaction and an anisotropic nearest neighbour interaction. The effects of the biquadratic exchange interaction and the single ion anisotropic interaction on the properties （width, peak and stability） of the soliton are investigated. It is also found that the effects vary with the strengths of these interactions.

Anisotropic Biquadratic Finite Element with Some Natural Superconvergence Results

The paper studies the convergence and the superconvergence of the biquadratic finite element for Poisson＇ problem on anisotropic meshes. By detailed analysis, it shows that the biquadratic finite element is anisotropically superconvergent at four Gauss points in the element. Key words：

DOCCII-based electronically tunable current-mode biquadratic filters

A complete state variable current-mode biquadratic filter built by duo-output CCII (DOCCII) with variable current gain is presented. All the coefficients of the filter can be independently tuned through the variable current gain factors of the DOCCII. Based on the principles upon which the general biquadratic filter was constructed, a universal electronically tunable current-mode filter is proposed which implements the low-pass, high-pass, band-pass, band-suppress and all-pass second order transfer functions simultaneously. The PSPICE simulations of frequency responses of second-order filter of are also given.

Novel Plus Type DVCC-Based Current-Mode Biquadratic Circuit

This paper presents a novel current-mode biquadratic circuit employing only plus type DVCCs(differential voltage current conveyors).The circuit enables LP(low-pass),BP(band-pass),HP(high-pass),BS(band-stop)and AP(all-pass)responses by the selection and addition of the input and output currents without any component matching constraints.Moreover the circuit parametersω0 and Q can be set orthogonally adjusting the circuit components.A design example is given together with simulation results by PSPICE.

A DVCC-Based Mixed-Mode Biquadratic Circuit

This paper introduces a mixed-mode biquadratic circuit employing DVCCs （differential voltage current conveyors） and grounded passive components. The biquadratic circuit can perform mixed-mode operation selecting the input and output terminals. And the circuit enables LP （low-pass）, BP （band-pass）, HP （high-pass）, BS （band-stop） and AP （all-pass） transfer functions by suitably choosing the input terminals. The circuit parameters o30 and Q can be tuned orthogonally through adjusting the passive components. The biquadratic circuit enjoys very low sensitivities with respect to the circuit components. The achievement example is given together with simulation results by PSPICE.

Biquadratic tensors,biquadratic decompositions,and norms of biquadratic tensors

Biquadratic tensors play a central role in many areas of science.Examples include elastic tensor and Eshelby tensor in solid mechanics,and Riemannian curvature tensor in relativity theory.The singular values and spectral norm of a general third order tensor are the square roots of the M-eigenvalues and spectral norm of a biquadratic tensor,respectively.The tensor product operation is closed for biquadratic tensors.All of these motivate us to study biquadratic tensors,biquadratic decomposition,and norms of biquadratic tensors.We show that the spectral norm and nuclear norm for a biquadratic tensor may be computed by using its biquadratic structure.Then,either the number of variables is reduced,or the feasible region can be reduced.We show constructively that for a biquadratic tensor,a biquadratic rank-one decomposition always exists,and show that the biquadratic rank of a biquadratic tensor is preserved under an independent biquadratic Tucker decomposition.We present a lower bound and an upper bound of the nuclear norm of a biquadratic tensor.Finally,we define invertible biquadratic tensors,and present a lower bound for the product of the nuclear norms of an invertible biquadratic tensor and its inverse,and a lower bound for the product of the nuclear norm of an invertible biquadratic tensor,and the spectral norm of its inverse.

EIGENVALUE EXTRAPOLATION FORBIQUADRATIC FINITE ELEMENT APPROXIMATION IN RECTANGULAR DOMAIN

In this paper, we consider the model eigenvalue problem with the biquadratic finite element. We have obtained the following extrapolation estimate of the

Local connectivity of Julia sets for a family of biquadratic polynomials

The local connectivity of Julia sets for the family of biquadratic polynomials f_c(z)= (z^2-2c^2)z^2 with a parameter c is discussed.It is proved that for any parameter c,the boundary of the immediately attracting domain of f_c is a Jordan curve.

A Finite-Difference Approximation for the Oneand Two-Dimensional Tempered Fractional Laplacian

This paper provides a finite-difference discretization for the one-and two-dimensional tempered fractional Laplacian and solves the tempered fractional Poisson equation with homogeneous Dirichlet boundary conditions.The main ideas are to,respectively,use linear and quadratic interpolations to approximate the singularity and non-singularity of the one-dimensional tempered fractional Laplacian and bilinear and biquadratic interpolations to the two-dimensional tempered fractional Laplacian.Then,we give the truncation errors and prove the convergence.Numerical experiments verify the convergence rates of the order O(h^2−2s).

Realizations of Voltage Transfer Functions Using DVCCs

Maheshwari has proposed three differential-voltage current-conveyor configurations for realizing first order all-pass filters only. This paper has exploited these configurations for realizing more complex transfer function T(s)?which yield poles and zeros of 1 -?T(s) in one of the four admissible patterns. Bilinear and biquadratic functions are dealt in detail. It is shown that only bilinear functions can be realized with all the four passive elements grounded. First order all-pass function is a special case which needs only three elements (2R, 1C) or (1R, 2C). A biquadratic function requires (2R, 2C) elements and has all the capacitor grounded. Design of second order all-pass function is given.

An Infinite Family of Number Fields with No Inert Primes

The goal of this paper is to show that there are infinitely many number fields K/Q, for which there is no inert prime p ∈ N*, i.e. ∀p ∈ N* a prime number, prime ideal of K such that where: Zk is the Dedekind domain of the integer elements of K. To prove such a result, consider for any prime p, the decomposition into a product of prime ideals of Zk, of the ideal . From this point, we use on the one hand: 1) The well- known property that says: If , then the ideal pZk decomposes into a product of prime ideals of Zk as following: . (where:;is the irreducible polynomial of θ, and, is its reduction modulo p, which leads to a product of irreducible polynomials in Fp[X]). It is clear that because if is reducible in Fp[X], then consequently p is not inert. Now, we prove the existence of such p, by proving explicit such p as follows. So we use on the other hand: 2) this property that we prove, and which is: If , is an irreducible normalized integer polynomial, whose splitting field is , then for any prime number p ∈ N: is always a reducible polynomial. 3) Consequently, and this closes our proof: let’s consider the set (whose cardinality is infinite) of monogenic biquadratic number fields: . Then each fθ(X) checks the above properties, this means that for family M, all its fields, do not admit any inert prime numbers p ∈ N. 2020-Mathematics Subject Classification (MSC2020) 11A41 - 11A51 - 11D25 - 11R04 - 11R09 - 11R11 - 11R16 - 11R32 - 11T06 - 12E05 - 12F05 -12F10 -13A05-13A15 - 13B02 - 13B05 - 13B10 - 13B25 -13F05

Multifunction Filter Employing Current Differencing Buffered Amplifier

This paper proposes a new filter biquad circuit, which utilizes three Current Differencing Buffered Amplifiers (CDBA), two capacitors and five resistors, and operates in the trans-resistance mode. This multi-input and single-output multifunction filter uses only grounded capacitors. All the employed resistors are either grounded or virtually grounded, which is an important parameter for its implementation as an integrated circuit. The circuit enjoys independent tunability of angular frequency and bandwidth. The 0.5 μm technology process parameters have been utilized to test and verify the performance characteristics of the circuit using PSPICE. The non-ideal analysis and sensitivity analysis, transient response, Monte-Carlo analysis and calculations of total harmonic distortion have also been shown.

Design and analysis of a dual mode CMOS field programmable analog array

This paper presents a novel field-programmable analog array （FPAA） architecture featuring a dual mode including discrete-time （DT） and continuous-time （CT） operation modes, along with a highly routable connection boxes （CBs） based interconnection lattice. The dual mode circuit for the FPAA is capable of achieving targeted op- timal performance in different applications. The architecture utilizes routing switches in a CB not only for the signal interconnection purpose but also for control of the electrical charge transfer required in switched-capacitor circuits. This way, the performance of the circuit in either mode shall not be hampered with adding of programmability. The proposed FPAA is designed and implemented in a 0.18 μm standard CMOS process with a 3.3 V supply voltage. The result from post-layout simulation shows that a maximum bandwidth of 265 MHz through the interconnection network is achieved. The measured results from demonstrated examples show that the maximum signal bandwidth of up to 2 MHz in CT mode is obtained with the spurious free dynamic range of 54 dB, while the signal processing precision in DT mode reaches 96.4%.

Coset Diagram for the Action of Picard Group on Q（i, √3）

In this paper coset diagrams, propounded by Higman, are used to investigate the behavior of elements as words in orbits of the action of the Picard group F = PSL（2, Z[i]） on Q（i, √3）. Graphical interpretation of amalgamation of the components of F is also given. Some elements a＋b√3/c of Q（i, √3） and their conjugates a-b√3/c a c over Q（i） have different signs in the orbits of the biquadratic field Q（i, √3） when acted upon by F. Such real quadratic irrational numbers are called ambiguous numbers. It is shown that ambiguous numbers in these coset diagrams form a unique pattern. It is proved that there are a finite number of ambiguous numbers in an orbit Fa, and they form a closed path which is the only closed path in the orbit Гa. We also devise a procedure to obtain ambiguous numbers of the form a-b√3/c, where b is a positive integer.