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Oblique water waves are of significant importance in natural scenarios. We have offered a solution, for the scattering of oblique water waves at the interface of free water and finite submerged elastic surface of insignificant thickness, in this work. Implementing the mode matching technique with two different edge conditions – the pinned edge condition and the sliding edge condition – the answer is obtained. For a variety of physical parameters, including the submergence depth, angle of incidence, Poisson’s ratio, length, and stiffness of an elastic surface, the reflection coefficient at both edges is examined. Furthermore, an energy balance relation of the problem and convergence of the solution, which are satisfied, is presented.

In this paper, we present the scattering of plane waves through two junctions with step-down cascading discontinuities. The solutions in the form of trapped modes corresponding to discrete eigen values are also presented. We illustrate the matching of continuity of pressure and velocity at the edges, conservation of energy, convergence/error of reflection, and reflection and transmission of the incident wave that go through the wider region. We discuss the reflection and transmission amplitudes by varying dimensions of wave-guide structure against wave number. We plot the surface and contour plots along with absolute potential solutions at different frequencies where extrema of field amplitudes occur. We also derive the results of extra ordinary acoustic transmission (EAT) for existing models. We apply the Mode Matching Method (MMM) to tackle the problem. Our model would be beneficial to structure the old and new models containing cavities and junctions. However, these structure models cannot retrieve our proposed geometrical model. The results will be helpful to model the practical exhaust system in noise reduction theory.

Multidimensional achievement tests are recently gaining more importance in educational and psychological measurements. For example, multidimensional diagnostic tests can help students to determine which particular domain of knowledge they need to improve for better performance. To estimate the characteristics of candidate items (calibration) for future multidimensional achievement tests, we use optimal design theory. We generalize a previously developed exchange algorithm for optimal design computation to the multidimensional setting. We also develop an asymptotic theorem saying which item should be calibrated by examinees with extreme abilities. For several examples, we compute the optimal design numerically with the exchange algorithm. We see clear structures in these results and explain them using the asymptotic theorem. Moreover, we investigate the performance of the optimal design in a simulation study.

The solution of nonlinear mathematical models has much importance and in soliton theory its worth has increased. In the present article, we have investigated the Caudrey-Dodd-Gibbon and Pochhammer-Chree equations, to discuss the physics of these equations and to attain soliton solutions. The exp(−ϕ(ζ ))-expansion technique is used to construct solitary wave solutions. A wave transformation is applied to convert the problem into the form of an ordinary differential equation. The drawn-out novel type outcomes play an essential role in the transportation of energy. It is noted that in the study, the approach is extremely reliable and it may be extended to further mathematical models signified mostly in nonlinear differential equations.

Abstract This paper presents the diffraction of acoustic plane wave through a semi-infinite soft duct. The soft plates are enclosed symmetrically inside an infinite duct with hard boundary conditions. We fully emphasize the analysis of the behavior of the reflected field amplitude for the pentafurcated duct by applying the straightforward mode-matching technique. We also depict some graphical representations by determining the reflected field amplitude for various dimensions of the pentafurcated duct. We also present comparisons of results with the existing results of a hard pentafurcated duct problem. This research work will assist the future researchers in reducing noise effects in complicated devices and exhaust systems.

Bt-cotton germplasm, consisting of 75 genotypes was evaluated against cotton leaf curl disease (CLCuD) under high inoculum pressure in the field and using graft inoculation in glasshouse by visual symptom scoring assessments. None of the tested genotype was found disease free under both evaluation tests. Under field conditions in 2011, 3 genotypes were found resistant, 4 moderately resistant, 3 tolerant, 2 moderately susceptible and one susceptible; in 2012, 3 genotypes were tolerant, 7 moderately susceptible, 5 susceptible and 38 highly susceptible; in 2013, one was moderately susceptible and 51 were highly susceptible with varying degree of percent disease index (PDI) and severity index (SI). However, through graft evaluation in glasshouse, none of the graft inoculated plant was symptomless. All tested genotypes showed disease symptoms with SI values ranging between 5.0 and 6.0, and latent period between 12 and 14 days. Of the 75 genotypes evaluated using graft inoculation, 11 were found susceptible with SI values of 5.0 to 5.4 while remaining 64 were highly susceptible with SI values of 5.5 to 6.0. Inoculated plants of all tested genotypes exhibited severe disease symptoms within 10 days after the appearance of initial symptoms. No reduction in SI value was observed until the end of the experiment i.e., 90 days after grafting. Information generated under the present study clearly demonstrates that no sources of resistance to CLCuD are available among the tested Bt-cotton genotypes. So, a breeding programme is needed to introgress the CLCuD-resistance from other resistant sources to agronomically suitable Bt-cotton genotypes.

This article deals with the propagation of fundamental plane mode in pentafurcated waveguide structure with soft–hard boundaries. Three semi-infinite ducts are located inside an infinite waveguide. In particular, we aim to find the reflected field amplitude for the underlying problem by using the standard mode-matching approach. We also present some numerical illustrations by determining the reflected field amplitude for different dimensions of the pentafurcated waveguide structures. Such investigations are useful in the reduction of noise effects generated through variety of mechanisms.

In the title compound, C19H19ClN4S, the 2-chlorophenyl and [1,2,4]triazolo[3,4-b] [1,3,4]thiadiazole fragments (r.m.s. deviations of 0.015 and 0.017 Å, respectively) are oriented at a dihedral angle of 55.76 (6)°. The adamantane group exhibits extensive rotational disorder about the single C—C bond to the thiadiazole ring, which was modelled as occupying four orientations each with 0.25 occupancy. In the crystal, the chlorophenyl rings exhibit π–π stacking interactions with centroid–centroid distances of 3.9526 (18) Å.

The title molecule, C19H19FN4S, displays Cs molecular symmetry, in which the crystallographic mirror plane bisects the adamantan-1-yl unit while the 3-fluorophenyl triazole ring is located on the mirror plane. The F atom of the 3-fluorophenyl ring is positionally disordered [occupancy ratio 0.9:0.1]. In the crystal, π–π interactions between the triazole and phenyl rings occur [centroid–centroid distance = 3.5849 (7) Å] and weak C—H...F interactions form a ribbon propagating in [010].

In the title compound, C19H19FN4S, the planes of the 2-fluorophenyl and 1,2,4-triazolo[3,4-b][1,3,4]thiadiazole ring systems are oriented at a dihedral angle of 48.98 (6)°. In the crystal, weak C—H...S and C—H...π interactions may help to establish the packing and π–π interactions between the centroids of the benzene rings at a distance of 3.8792 (13) Å occur.

The title compound, C7H6BrNS, crystallizes with two molecules in the asymmetric unit. The dihedral angles between the aromatic ring and the thioamide fragment are 23.6 (4) and 20.5 (3)° in the two molecules. In the crystal, there are intermolecular N—H...S hydrogen-bonding interactions between the amine group and the S atoms.

In the title compound, C8H9NS, the dihedral angle between the aromatic ring and the thioamide fragment is 36.0 (2)°. There are π-stacking interactions between coplanar aryl fragments, with a centroid–centroid separation of 3.658 (2) Å. In addition, there are intermolecular hydrogen bonds between the amino group and the S atoms.

In the title compound, C7H6ClNS, the dihedral angle between the aromatic ring and the thioamide fragment is 28.1 (2)°. The structure features a π-stacking interaction between the aromatic rings with a slight offset of the rings, giving a centroid–centroid separation of 3.7942 (2) Å. There are intermolecular hydrogen-bonding interactions between the amino group and the S atoms.