Addendum to: “Hamilton-laceable bi-powers of locally finite bipartite graphs” [Discrete Math. 345 (2022) 112777]

In this addendum we give a short and easy negative answer to the two questions raised in the original article.     

VIBRATIONAL SPECTRA AND NORMAL COORDINATE ANALYSIS OF 1,2-BIS(2-FORMYLGLYCINEBENZENESULFENYL) ETHANE Pd(II) DICHLORIDE COMPLEX

The normal coordinate analysis of the title complex, 1,2-bis(2-formylglycinebenzenesulfenyl) ethane Pd(II) dichloride has been carried out by using the Urey-Bradley force field. According to the molecular structure determined by x-ray crystallographic analysis, 182 internal coordinates were established and 112 theoretical vibration frequencies agree well with the observed values with the average difference of 2.53 cm^?1 and the maximum deviation of 16.0 cm^?1.     

Quantitative study of the temperature dependence of normal LWIR apparent emissivity

In a previous work, a method of measurement of apparent emissivity in situ was implemented. This approach has the decisive advantage of being suitable for any commercial infrared systems. It was tested successfully to characterize the normal LWIR apparent emissivity of an aluminium nitride plate in the temperature range [40–550 °C]. Apparent emissivity exhibits a tight temperature dependence. By using the classical model of apparent emissivity and taking into account the spectral emissivity of aluminium nitride ceramic and the spectral response of the IR sensor, we modelled our apparent emissivity measurement with 5% of accuracy and with dispersion better than 1% within the overall temperature range. The effect on the apparent emissivity of both the detection window and the temperature dependence of the spectral emissivity are highlighted.     

异方差回归模型近邻型估计的相合性

本文研究异方差回归模型Ｙｉ＾（ｎ）＝ｇ（ｘｉ＾（ｎ））＋εｉ＾（ｎ）,ｉ＝１,…,ｎ,其中ｇ是右实函数,ｘｉ＾（ｎ）是非随机设计点列,εｉ＾（ｎ）是随机误差,文中定义了一类ｇ（ｘ）的近邻型估计ｇｎ（ｘ）＝（ｎ）∑（ｉ＝１）Ｗｍ（ｘ）Ｙｉ＾（ｎ）,得到了ｒ阶平均相全和渐近正态性,特别,在（∞）∑（ｎ＝１）（ｎ）∑（ｉ＝１）Ｅ／εｉ＾（ｎ）／＾ｓ／（ｎｉ）＾ｓ／ｒ〈∞,ｍａｘＥ（１≤ｉ≤ｎ）／εｉ（＾     

HPLC-determination of nifedipine in plasma on normal phase

Summary For the determination of nifedipine in plasma a sensitive and selective method is required. The use of on-line pre-column enrichment, followed by reversed phase separation and UV-detection at 350 nm proved to be too susceptible. Therefore, detection was carried out after a post-column on-line reduction and photoreaction step using a fluorescence detector. Although this method proved to be extremely sensitive (limit of detection 0.1 ng/ml plasma) and selective, a number of problems cropped up caused by the reduction agent which finally prevented the procedure being used in routine analysis. As a consequence, the following method was developed. After liquid-liquid extraction of nifedipine a 1/3 of the extract was chromatographed on a normal phase (diOH) system and detected at 235 nm, because detection at 350 nm was not sensitive enough. This method has a limit of detection of 1 ng nifedipine/ml plasma and the calibration curve is linear up to 320 ng/ml. The recovery lies around 82% and the standard deviation for the range 6–320 ng/ml is less than 5%. So far about 2000 plasma samples have been analysed by this method.     

Homoclinic Bifurcations in Symmetric Unfoldings of a Singularity with Three-fold Zero Eigenvalue

In this paper we study the singularity at the origin with three-fold zero eigenvalue forsymmetric vector fields with nilpotent linear part and 3-jet C^∞-equivalent to y δ/δx zδ/δy ax^2yδ/δz with a≠0. We first obtain several subfamilies of the symmetric versal unfoldings of this singularityby using the normal form and blow-up methods under some conditions, and derive the local and global bifurcation behavior, then prove analytically the existence of the Sil‘nikov homoclinic bifurcation for some subfamilies of the symmetric versal unfoldings of this singularity, by using the generalized Mel‘nikov methods of a homoclinic orbit to a hyperbolic or non-hyperbolic equilibrium in a highdimensional space.     

Existence of positive solutions of nonlinear fractional differential equations

Existence of positive solutions for the nonlinear fractional differential equation D^su(x)=f(x,u(x)), 0<s<1, has been studied (S. Zhang, J. Math. Anal. Appl. 252 (2000) 804-812), where D^s denotes Riemann-Liouville fractional derivative. In the present work we study existence of positive solutions in case of the nonlinear fractional differential equation:

L(D)u=f(x,u),u(0)=0,0<x<1,     

Nonlinear Rayleigh–Taylor instability of two superposed magnetic fluids under parallel rotation and a normal magnetic field

The Rayleigh–Taylor instability (RTI) of a ferrofluid has been the subject of recent research, because of its implications on the stability of stellar and planetary interiors. This paper analyzes the effects of rotation and magnetic field on nonlinear RTI of two superposed ferrofluids. It is considered that the system is subjected to uniform parallel rotation and normal magnetic field. Surface tension acts at the interface. The method of multiple scales is utilized to obtain the solutions and dispersion relations are obtained for the nonlinear problem of RTI of magnetic fluids. Finally the stability of the problem is discussed.     

A geometric characterisation of resonance in Hopf bifurcation from relative equilibria

We give a new characterisation of resonance in Hopf bifurcation from relative equilibria in systems with compact symmetry group. This characterisation provides a full geometric explanation of the resonance phenomenon. In addition, we develop techniques based on normal form theory to give a complete solution to the associated bifurcation problem.     

Amphoteric refraction exhibited by anisotropic crystals

Amphoteric refraction of light ray at the interface between isotropic materials and anisotropic materials is analyzed. Depending on the incident angle, the refractive light ray can either refract positively or negatively. This amphoteric refraction phenomenon can be quite prevalent when the difference of the two principal refractive indices is large. The reflectance under various incident angles has also been calculated, and an experimental demonstration with a calcite crystal in air is presented.