Despite significant public health investments, rural India’s sanitation challenges persist, raising questions about effective intervention strategies. This study investigates the influence of participation in social schemes on household sanitation behaviours, specifically toilet adoption and soap usage. Using panel data from the India Human Development Survey (2004–05 and 2011–12), a Linear Probability Model with Propensity Score Matching is employed to address potential selection bias. Results indicate that scheme participation increases toilet adoption by 45.5% and soap usage by 13.8%, with effects varying by socio-economic status, demographic characteristics, and local infrastructure. Particularly strong impacts are observed among historically disadvantaged communities, suggesting that social schemes can effectively reduce sanitation inequities. The spillover effect on soap usage indicates these interventions may catalyse broader hygiene behaviour changes. The findings highlight the value of social schemes in improving rural sanitation practices and offer insights for future programme design.

We study the asymptotic behaviour of the least energy solutions to the following class of nonlocal Neumann problems:

$$ \begin{align*} \begin{cases} { d(-\Delta)^{s}u+ u= \vert u\vert^{p-1}u } & \text{in } \Omega, \\ {u>0} & \text{in } \Omega, \\ { \mathcal{N}_{s}u=0 } & \text{in } \mathbb{R}^{n}\setminus \overline{\Omega}, \end{cases} \end{align*} $$

where $\Omega \subset \mathbb {R}^{n}$ is a bounded domain of class $C^{1,1}$, $1<p<({n+s})/({n-s}),\,n>\max \{1, 2s \}, 0<s<1, d>0$ and $\mathcal {N}_{s}u$ is the nonlocal Neumann derivative. We show that for small $d,$ the least energy solutions $u_d$ of the above problem achieve an $L^{\infty }$-bound independent of $d.$ Using this together with suitable $L^{r}$-estimates on $u_d,$ we show that the least energy solution $u_d$ achieves a maximum on the boundary of $\Omega $ for d sufficiently small.

In this paper, the design of a circularly polarized (CP) multiple-input–multiple-output (MIMO) antenna system is presented, utilizing a dielectric resonator (DR). This presented antenna system is subsequently integrated with a multifunctional filter, all meticulously structured on a single substrate. The multifunctional filter operates in three modes: reconfigurable band-pass and band-reject filter as well as all-pass filter. The overall structure works as a tunable filtenna. The designed filtenna is expanded into a two-port MIMO system on a unified substrate, providing strong port isolation below −28.5 dB. The overall dimension of proposed radiator is 180 × 180 × 1.6 mm3. The value of peak gain is 5.19 dBic. By switching the states of PIN diodes, the designed filtenna operates as a sensing and communicating antenna for interweave and underlay cognitive radios (CRs). The proposed antenna supports the CP waves within the working band, i.e., 3.6–4.5 GHz. The simulated results are validated by comparing them with the measured results showing less variation among them. MIMO parameters, including the envelope correlation coefficient and diversity gain, have been calculated for the proposed filtenna, representing its suitability for 5G-CR applications.