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This work is concerned with the development of a scheme to obtain boundary conditions adapted representations of derivatives (differential operators) in the orthonormal wavelet bases of Daubechies family in $$\Omega = [0, \ 1] \subset {\mathbb{R}}$$ . The scheme is employed to find approximate solution of the (1+1)-D advection-diffusion-transport equation arising in the flow of contaminant fluid (water) through a porous medium (ground). Representation of derivatives adopting Dirichlet’s boundary conditions have been derived first. These representations are then used to reduce the aforesaid advection-diffusion-transport equation to a system of nonhomogeneous first order coupled ordinary differential equations. It is observed that representations of the derivatives derived here shift the non-homogeneous terms in the boundary conditions to non-homogeneous terms of the reduced ordinary differential equations. The resulting ordinary differential equations can be solved globally in time, in general, which helps to prevent the necessary analysis of time discretization such as estimate of step lengths, error etc. In case of convection dominated problems, the system of ordinary differential equations can be solved numerically with the aid of any efficient ODE solver. An estimate of $$L^2$$ -error in wavelet-Galerkin approximation of the unknown solution has been presented. A number of examples is given for numerical illustration. It is found that the scheme is efficient and user friendly.

Resolvable incomplete block designs are often used in many asymmetrical and symmetrical factorial experiments. In this article, two new methods of constructions are proposed to obtain resolvable in...

The wave generation problem for viscous fluid of finite depth due to an axisymmetric initial surface disturbance is investigated here. Introducing the wave potential function $$\phi $$ and Stoke’s stream function $$\psi $$ , the problem is formulated as an initial value problem to describe the motion in the fluid region. Laplace and Hankel transform techniques have been used in the mathematical analysis to obtain the form of the free surface in terms of a multiple infinite integral. This integral is then evaluated asymptotically by the method of steepest descent. The asymptotic form of the free surface is depicted graphically in a number of figures for different values of the viscous parameter and for different types of initial disturbances, and appropriate conclusions are made.

SummaryThe present article is concerned with the radiation of flexural gravity waves due to a thin cap submerged in the ice-covered ocean. The problem is reduced to a system of hypersingular integral equations using the boundary perturbation method. The first-order approximation has only been considered. The effects of the rigidity of the ice sheet and depth of submergence on the added mass and damping coefficient have been analysed. Two types of caps (for example, concave upwards and concave downwards) have been considered for the numerical results. The effect of the concavity on added mass and damping coefficient has also been studied. The present study should be helpful to understand the nature of waves generated by a heaving submerged body in an ice-covered ocean.

The effect of a thin viscoelastic mud layer on the wave propagation through mangrove forests has been analyzed within the framework of linear theory. The trunks of mangrove trees are assumed to be ...

The problem of oblique scattering of surface waves by a thick partially immersed rectangular barrier or a thick submerged rectangular barrier extending infinitely downwards in deep water is studied here to obtain the reflection and transmission coefficients semi-analytically. Use of Havelock’s expansion of water wave potential function reduces each problem to an integral equation of first kind on the horizontal component of velocity across the gap above or below the barrier. Multi-term Galerkin approximations involving polynomials as basis functions multiplied by appropriate weight functions are used to solve these equations numerically. Evaluated numerical results for the reflection coefficients are plotted graphically for both the barriers. The study reveals that the reflection coefficient depends significantly on the thickness of the barrier. The accuracy of the numerical results is checked by using energy identity and by obtaining results available in the literature as special cases.

The problem of scattering of a normally incident surface wave train by an obstacle in the form of a thick rectangular vertical bottom-standing barrier submerged in finite-depth water with a free surface is extended here with an ice cover modelled as a thin uniform elastic plate. The problem is reduced to a set of singular integral equations of the first kind. The Galerkin approximation in terms of simple polynomials multiplied by appropriate weight functions whose form is dictated by the behavior of the fluid velocity near the barrier edges is used for solving the integral equations. The reflection and transmission coefficients are obtained numerically, and they are depicted graphically against the wavenumber for various ice cover parameters. It is observed that the barrier thickness plays a significant role in modelling of efficient breakwaters.

Equine glanders is an infectious and notifiable bacterial disease caused by Burkholderia mallei. The disease has been reported in South American, African and Asian countries including India. Here, we present the outcome of glanders serosurveillance carried out between January 2015 and December 2018 to know the status of equine glanders among different states in India. A total of 102,071 equid sera from 299 districts of twenty-one states and one union territory were tested for glanders. Samples were screened with Hcp1 indirect ELISA followed by confirmatory diagnosis by CFT. During this four-year surveillance, a total of 932 glanders-positive cases were detected from 120 districts of 12 states. The study also revealed increasing trend of glanders from 2016 onwards with maximum occurrence in northern India. Overall seroprevalence ranged between 0.62% (95% CI, 0.52-0.72) and 1.145% (95% CI, 1.03-1.25). Seasonal shifting from winter to summer (March to June) coincided with highest number glanders incidence with corresponding seroprevalences of 1.2% (95% CI, 1.09-1.30). The present surveillance unveils territorial ingression of glanders to six states like Jammu & Kashmir, Gujarat, Rajasthan, Madhya Pradesh, Delhi and Tamil Nadu. In addition, re-emerging cases have been reported in Maharashtra, Haryana and Punjab after a gap of 10 years. Lack of awareness, little veterinary care and unrestricted movement of equids across state borders might have led to the introduction and establishment of the infection to these states. We believe that information from this study will provide a baseline data on glanders for devising surveillance and control strategies in India. Being a zoonotic disease, the persistence of glanders poses a potential threat to occupationally exposed humans especially equine handlers and veterinarians. Therefore, targeted surveillance of human population from each glanders outbreak is also recommended.

The classical problem of water wave scattering by an infinite step in deep water with a free surface is extended here with an ice-cover modelled as a thin uniform elastic plate. The step exists between regions of finite and infinite depths and waves are incident either from the infinite or from the finite depth water region. Each problem is reduced to an integral equation involving the horizontal component of velocity across the cut above the step. The integral equation is solved numerically using the Galerkin approximation in terms of simple polynomial multiplied by an appropriate weight function whose form is dictated by the behaviour of the fluid velocity near the edge of the step. The reflection and transmission coefficients are obtained approximately and their numerical estimates are seen to satisfy the energy identity. These are also depicted graphically against thenon-dimensional frequency parameter for various ice-cover parameters in a number of figures. In the absence of ice-cover, the results for the free surface are recovered.

The problem of oblique scattering of surface water waves by a vertical wall with a gap submerged in infinitely deep water is re-investigated in this paper. It is formulated in terms of two first kind integral equations, one involving the difference of potential across the wetted part of the wall and the other involving the horizontal component of velocity across the gap. The integral equations are solved approximately using one-term Galerkin approximations involving constants multiplied by appropriate weight functions whose forms are dictated by the physics of the problem. This is in contrast with somewhat complicated but known solutions of corresponding deep water integral equations for the case of normal incidence, used earlier in the literature as one-term Galerkin approximation. Ultimately this leads to very closed (numerically) upper and lower bounds of the reflection and transmission coefficients so that their averages produce fairly accurate numerical estimates for these coefficients. Known numerical results for normal incidence and for a narrow gap obtained by other methods in the literatura are recovered, thereby confirming the correctness of the method employed here. Resumen En este artículo re-investigamos el problema de dispersión oblicua de ondas superficiales de agua por una pared vertical con una abertura sumergida en agua infinitamente profunda. Se formula en términos de dos ecuaciones integrales de primera especie, una involucrando la diferencia de potencial a través de la parte mojada de la pared y la otra involucrando la componente horizontal de la velocidad a través de la apertura. Las ecuaciones integrales son resueltas aproximadamente usando aproximaciones de Galerkin de un término involucrando constantes multiplicadas por funciones peso apropiadas, cuyas formas son dictadas por la física del problema. Esto se contrapone con lo complicado de soluciones conocidas para las correspondientes ecuaciones integrales de agua profunda para el caso de incidencia normal, usadas anteriormente en la literatura como aproximaciones de Galerkin de un término. Últimamente esto lleva a cotas superiores e inferiores muy cercanas (numéricamente) para los coeficientes de reflexión y transmisión de tal suerte que sus promedios producen estimaciones numéricas razonablemente precisas para estos coeficientes. Se recuperan resultados numéricos conocidos en la literatura para la incidencia normal y para una apertura delgada, confirmando que los métodos empleados son correctos.

A field experiment was conducted at ICAR-Research Complex for NEH Region, Umiam, Meghalaya to study the effect of organic manure along with lime on upland rice (Oryza sativa L.) in hilly region during kharif 2018 in FRBD with 3 replications and 12 treatment combinations: control, 100% inorganic, 100% FYM, 50% FYM + 50% VC (vermicompost), 50% FYM + 50% PM (poultry manure) and 50% FYM + 50% SM (pig manure), each treatment alternated with lime @ 400 kg/ha. Results support that among organic manures, 50% FYM + 50% SM resulted in highest grain yield (3.98 t/ha), and production efficiency that was at par with chemical fertilizer. Grain yields from 50% FYM + 50% SM were 9.6%, 7.2%, 1.5% and 1.2% higher over 100% FYM, 50% FYM + 50% VC, 50% FYM + 50% PM and 100% inorganic, respectively. 50% FYM + 50% SM gave highest production efficiency (29.4 kg/ ha/day) of 1% and 1.3% higher over 100% inorganic and 50% FYM + 50% PM, respectively. The application of organic manure 50% FYM + 50% SM was found to be the best treatment as it improved the soil physical, chemical and biological properties as well and reduced nutrient losses. Therefore, substantial amount of NPK fertilizers and also fertilizer cost can be saved by application of farm available organic manures.

In this article, the problem of obtaining efficient block designs with unequal block sizes for incomplete factorial treatment structure with two factors excluding one treatment combination for esti...

This paper is concerned with obtaining approximate numerical solution of a classical integral equation of some special type arising in the problem of cruciform crack. This integral equation has been solved earlier by various methods in the literature. Here, approximation in terms of Daubechies scale function is employed. The numerical results for stress intensity factor obtained by this method for a specific forcing term are compared to those obtained by various methods available in the literature, and the present method appears to be quite accurate.

A two-dimensional Cauchy Poisson problem for water with a porous bottom generated by an axisymmetric initial surface disturbance is investigated here. The problem is formulated as an initial value problem for the velocity potential describing the motion in the fluid. The Laplace and Hankel transform techniques have been used in the mathematical analysis to obtain the form of the free surface in terms of a multiple infinite integral. This integral is then evaluated asymptotically by the method of stationary phase. The asymptotic form of the free surface is depicted graphically in a number of figures for different values of the porosity parameter and for different types of initial disturbances.

A study of obliquely incident water wave scattering by two, three and four unequal partially immersed vertical barriers in water of uniform finite depth has been carried out in this paper employing Havelock’s expansion of water wave potential. A formulation involving integral equations in terms of either horizontal component of velocities across the gap below each barrier or difference of potentials across each barrier are obtained using the Havelock’s inversion formulae. A multi-term Galerkin approximation technique with Chebychev’s polynomials (multiplied by appropriate weights) as basis functions is adapted to solve these integral equations and to compute the reflection and transmission coefficients numerically. The numerical results are depicted graphically against the wavenumber in several figures for various arrangements of the vertical barriers. From these figures zeros of reflection coefficient are observed when the vertical barriers are immersed upto equal depths below the mean free surface. However, this observation is not true always for non-identical vertical barriers. For two non-identical partially immersed barriers reflection coefficient never vanishes whereas for three non-identical partially immersed barriers reflection coefficient vanishes at discrete frequencies if the two outer barriers have equal lengths of submergence. For four partially immersed barriers arranged symmetrically about a vertical line, zeros of reflection coefficient are always observed. The known results of a single barrier are recovered as special cases so as to establish the correctness of the present method.

Latin hypercube designs are widely used in designing computer experiments. In recent years, nested orthogonal Latin hypercube designs have been proposed in the literature. In this article, two general methods of constructing nested orthogonal Latin hypercube designs have been developed. The methods give many new nested orthogonal Latin hypercube designs with fewer number of runs as compared to existing nested orthogonal Latin hypercube designs.

In this paper, the problem of obtaining efficient block designs for incomplete factorial treatment structure with two factors excluding one treatment combination for estimation of dual versus singl...

The classical problems of surface water waves produced by small oscillations of a thin vertical plate partially immersed as well as submerged in deep water are reinvestigated here. Each problem is reduced to an integral equation involving horizontal component of velocity across the vertical line outside the plate. The integral equations are solved numerically using Galerkin approximation in terms of simple polynomials multiplied by an appropriate weight function whose form is dictated by the behaviour of the fluid velocity near the edge(s) of the plate. Fairly accurate numerical estimates for the amplitude of the radiated wave at infinity due to rolling and also for swaying of the pate in each case are obtained and these are depicted graphically against the wave number for various cases.

Problems of water wave propagation over an infinite step in the presence of a thin vertical barrier of four different geometrical configurations are investigated in this paper. For each configuration of the barrier, the problem is reduced to solving an integral equation or a coupled integral equation of first kind involving horizontal component of velocity below or above the barrier and above the step. The integral equations are solved employing Galerkin approximation in terms of simple polynomials multiplied by appropriate weight functions whose forms are dictated by the edge conditions at the corner of the step and at the submerged end(s) of the barrier. The reflection and transmission coefficients are then computed and depicted graphically against the wave number.

In this article, we present differential transform method for solving a first kind hypersingular integral equation in which the kernel is containing a strong singular part and a regular part. Also some simple examples with exact solutions are considered to establish the validity and applicability of the proposed mechanism. Numerical outcomes reveal that our proposed technique works well and has good accuracy.