Rational solutions to Q3δ in the Adler-Bobenko-Suris list and degenerations

We derive rational solutions in Casoratian form for the Nijhoff-Quispel-Capel (NQC) equation by using the lattice potential Korteweg-de Vries (lpKdV) equation and two Miura transformations between the lpKdV and the lattice potential modified KdV (lpmKdV) and the NQC equation. This allows us to present rational solutions for the whole Adler-Bobenko-Suris (ABS) list except Q4. The known Miura transformation for soliton solutions between the NQC equation and Q3_δ and the known degenerations for solitons from Q3_δ to Q2, Q1_δ, H3_δ, H2 and H1 in the ABS list are used. We show that the Miura transformation and degenerations are valid as well for rational solutions which are usually considered as “long-wave-limit” of solitons. All the rational solutions can be expressed in terms of {z _j} which are linear functions of (n, m).     

Untersuchung der spontanen Abscheidung von Silber an pulverförmigem Platin aus salpetersauren Lösungen

Es wurde festgestell, daβ Silberionen an mit wasserstoffgesättigten Platimpulver sich abschieden und die maximal abgeschiedence Menge im Salpeterāure-Konzentrationsbereich 5 n – 0,0001 n die der Monoshcict entsprechende Menge nicht erreicht. Die Meβergebnisse bezüglich der Konzentrationsabhängigkeit der Abscheidung scheinen formell die Langmuirsche Gleichung zu erfūllen, doch zeigen die aus dieser Gleichung berechneten T_σ - Werte eine pH-Abhāngigkeit und stimmen mit der BET-Ober-fläche nicht überein. Die spontne Abscheidung von Silber an Platinpulver kann für die Abtennung von radioaktiven Silber-Isotopen angewandt werden.     

Gamma-Radiolyse von Dimethylglyoxim

Die Strahlenresistenz von reinem und an Aktivkohle sorbiertem Dimethylglyoxim (DMG), das für die selektive Abtrennung von Palladium aus Abfallösungen der Kernbrennstoffwiederaufarbeitung geeignet ist, wurde untersucht. Die Bestrahlung erfolgte bei 20–40 °C mit einer ⁶⁰Co-γ-Bestrahlungsanlage mit Dosisleistungen von 0,6 bis 1,7 Gy/s in einem Dosisbereich von 2 kGy bis 5 MGy. Die Radiolyseprodukte wurden mit verschiedenen Methoden analysiert und die G-werte bestimmt. Es wurde gezeigt, daβ DMG bis zu Dosen von etwa 110 kGy relativ strahlenresistent ist. Bei höheren Dosen werden die reaktiven NOH-Gruppen des DMG teilweise zerstört, so daβ sie nicht mit Palladium reagieren können. In Verfahren zur Abtrennung von Palladium aus radioaktiven Abfallösungen werden diese Dosen jedoch nicht erreicht. Auf eine unzureichende Strahlenresistenz von DMG zurückzuführende Komplikationen können deshalb ausgeschlossen werden.     

Exact solutions of （3＋1）-dimensional nonlinear incompressible non-hydrostatic Boussinesq equations

The symmetries and the exact solutions of the (3+1)-dimensional nonlinear incompressible non-hydrostatic Boussinesq (INHB) equations, which describe atmospheric gravity waves, are studied in this paper. The calculation on symmetry shows that the equations are invariant under the Galilean transformations, the scaling transformations, and the space-time translations. Three types of symmetry reduction equations and similar solutions for the (3+1)-dimensional INHB equations are proposed. Traveling and non-traveling wave solutions of the INHB equations are demonstrated. The evolutions of the wind velocities in latitudinal, longitudinal, and vertical directions with space-time are demonstrated. The periodicity and the atmosphere viscosity are displayed in the (3+1)-dimensional INHB system.     

New exact solutions of a （3＋1）-dimensional Jimbo-Miwa system

By using the (G'/G)-expansion method and the variable separation method, a new family of exact solutions of the (3+1)-dimensional Jimbo-Miwa system is obtained. Based on the derived solitary wave solutions, we obtain some special localized excitations and study the interactions between two solitary waves of the system.     

Dark solitons of the Biswas–Milovic equation by the first integral method

This paper studies the Biswas–Milovic equation that is a generalized version of the familiar nonlinear Schrodinger's equation describing the propagation of solitons through optical fibers for trans-continental and trans-oceanic distances with Kerr law nonlinearity by the aid of the first integral method. The dark 1-soliton solution is retrieved by the aid of this method and a couple of other singular periodic solutions are also obtained.     

空间调制干涉光谱成像仪星上定标系统研究

经计算推导和实验,研究设计了空间调制干涉光谱仪的星上定标系统,并进行了实验室光谱测试和航天元件的多种环境测试.解决了空间调制干涉光谱仪星上定标技术的关键组件定标光源、光谱滤光片、积分球组件的技术难点.实现了全孔径、部分视场的相对光谱定标,得到了星上定标光谱和干涉图.     

Oscillating multidromion excitations in higher-dimensional nonlinear lattice with intersite and external on-site potentials using symbolic computation

We show by an extensive method of quasi-discrete multiple-scale approximation that nonlinear multi-dimensional lattice waves subjected to intersite and external on-site potentials are found to be governed by (N +1)-dimensional nonlinear Schro¨dinger (NLS) equation. In particular, the resonant mode interaction of (2+1)-dimensional NLS equation has been identified and the theory allows the inclusion of transverse effect. We apply the exponential function method to the (2+1)-dimensional NLS equation and obtain the class of soliton solutions with a purely algebraic computational method. Notably, we discuss in detail the effects of the external on-site potentials on the explicit form of the soliton solution generated recursively. Under the action of the external on-site potentials, the model presents a rich variety of oscillating multidromion patterns propagating in the system.     

A strategy for multivariate calibration based on modified single-index signal regression: Capturing explicit non-linearity and improving prediction accuracy

In this paper, a modified single-index signal regression (mSISR) method is proposed to construct a nonlinear and practical model with high-accuracy. The mSISR method defines the optimal penalty tuning parameter in P-spline signal regression (PSR) as initial tuning parameter and chooses the number of cycles based on minimizing root mean squared error of cross-validation (RMSECV). mSISR is superior to single-index signal regression (SISR) in terms of accuracy, computation time and convergency. And it can provide the character of the non-linearity between spectra and responses in a more precise manner than SISR. Two spectra data sets from basic research experiments, including plant chlorophyll nondestructive measurement and human blood glucose noninvasive measurement, are employed to illustrate the advantages of mSISR. The results indicate that the mSISR method (i) obtains the smooth and helpful regression coefficient vector, (ii) explicitly exhibits the type and amount of the non-linearity, (iii) can take advantage of nonlinear features of the signals to improve prediction performance and (iv) has distinct adaptability for the complex spectra model by comparing with other calibration methods. It is validated that mSISR is a promising nonlinear modeling strategy for multivariate calibration.