Special Affine Stockwell Transform Theory, Uncertainty Principles and Applications

In this paper, we study the convolution structure in the special affine Fourier transform domain to combine the advantages of the well known special affine Fourier and Stockwell transforms into a novel integral transform coined as special affine Stockwell transform and investigate the associated constant Q property in the joint time frequency domain. The preliminary analysis encompasses the derivation of the fundamental properties, Rayleighs energy theorem, inversion formula and range theorem. Besides, we also derive a direct relationship between the recently introduced special affine scaled Wigner distribution and the proposed SAST. Further, we establish Heisenbergs uncertainty principle, logarithmic uncertainty principle and Nazarovs uncertainty principle associated with the proposed SAST. Towards the culmination of this paper, some potential applications with simulation are presented.Comment: arXiv admin note: text overlap with arXiv:2010.01972 by other author

Willingness to Pay for Preserving National Park Biodiversity: A Case Study

This paper employs a stated preference environmental valuation method i.e. Contingent Valuation Method to estimate the willingness to pay for the conservation of the Dachigam National Park as well as value estimates crucial to the development of the park acquisition and management policy. A contingent valuation study is conducted with 301 visitors and the data are analysed using the binary logit model. Results show that the majority of the tourists (benefitted from the use values of the park) were willing to pay (WTP) for its improvement. Respondents’ willingness to pay for the conservation of the park ranges from Rs. 110 to Rs. 140 per year with a mean of around Rs. 125 per year. With the use of the benefits transfer method, this case study is expected to provide policy-makers, corporate players, stakeholders with useful information for the conservation of biodiversity in the Indian sub-continent, as well as in other countries

Scaled Ambiguity Function Associated with Quadratic-Phase Fourier Transform

Quadratic-phase Fourier transform (QPFT) as a general integral transform has been considered into Wigner distribution (WD) and Ambiguity function (AF) to show more powerful ability for non-stationary signal processing. In this article, a new version of ambiguity function (AF) coined as scaled ambiguity function associated with the Quadratic-phase Fourier transform (QPFT) is proposed. This new version of AF is defined based on the QPFT and the fractional instantaneous auto-correlation. Firstly, we define the scaled ambiguity function associated with the QPFT (SAFQ). Then, the main properties including the conjugate-symmetry, shifting, scaling, marginal and Moyal’s formulae of SAFQ are investigated in detail, the results show that SAFQ can be viewed as the generalization of the classical AF. Finally, the newly defined SAFQ is used for the detection of linear-frequency-modulated (LFM) signals

Unveiling the Potential of Sheffer Polynomials: Exploring Approximation Features with Jakimovski–Leviatan Operators

In this article, we explore the construction of Jakimovski–Leviatan operators for Durrmeyer-type approximation using Sheffer polynomials. Constructing positive linear operators for Sheffer polynomials enables us to analyze their approximation properties, including weighted approximations and convergence rates. The application of approximation theory has earned significant attention from scholars globally, particularly in the fields of engineering and mathematics. The investigation of these approximation properties and their characteristics holds considerable importance in these disciplines

Uncertainty Principles for the Two-Sided Quaternion Windowed Quadratic-Phase Fourier Transform

A recent addition to the class of integral transforms is the quaternion quadratic-phase Fourier transform (Q-QPFT), which generalizes various signal and image processing tools. However, this transform is insufficient for addressing the quadratic-phase spectrum of non-stationary signals in the quaternion domain. To address this problem, we, in this paper, study the (two sided) quaternion windowed quadratic-phase Fourier transform (QWQPFT) and investigate the uncertainty principles associated with the QWQPFT. We first propose the definition of QWQPFT and establish its relation with quaternion Fourier transform (QFT); then, we investigate several properties of QWQPFT which includes inversion and the Plancherel theorem. Moreover, we study different kinds of uncertainty principles for QWQPFT such as Hardy’s uncertainty principle, Beurling’s uncertainty principle, Donoho–Stark’s uncertainty principle, the logarithmic uncertainty principle, the local uncertainty principle, and Pitt’s inequality

Sampling Techniques and Error Estimation for Linear Canonical S Transform Using MRA Approach

A linear canonical S transform (LCST) is considered a generalization of the Stockwell transform (ST). It analyzes signals and has multi-angle, multi-scale, multiresolution, and temporal localization abilities. The LCST is mostly suitable to deal with chirp-like signals. It aims to possess the characteristics lacking in a classical transform. Our aim in this paper was to derive the sampling theorem for the LCST with the help of a multiresolution analysis (MRA) approach. Moreover, we discuss the truncation and aliasing errors for the proposed sampling theory. These types of sampling results, as well as methodologies for solving them, have applications in a wide range of fields where symmetry is crucial

Techno-economic and environmental assessment to mitigating climate change and building energy security: a study on willingdon island

This paper aims to solve the state's hydropower dependence, build energy security and reduce greenhouse gas emissions through a hybrid renewable energy system and its implementation in Willingdon Island. Hybrid Optimisation of Multiple Energy Resources (HOMER) is used to find the optimal solution for two grid-connected and off-grid scenarios. Of the 19 solutions, an optimal off-grid, an optimal grid-connected, a 100% variable renewable energy, and a diversified energy portfolio option are selected, analyzed, and ranked based on their techno-economic and emissions characteristics. The results suggest the combination of PV/Wind/Grid with a cost of energy of $0.044 as an optimal solution for the Island. The diversified energy solution takes the second position, having 51.4% and 38.8% solar and wind, respectively

Bounded Inverse-Slashed Pareto Model: Structural Properties and Real-Life Applications

A novel probability model with bounded support is introduced. The formulation of this new probability model is based on inverting the Slashed Pareto distribution. This new distribution has the merit of being very simple and not involving any complex mathematical function in its construction. Some interesting properties like moments, skewness and kurtosis, unimodality, L-Moments, L-skewness and L-kurtosis would be explored in detail. Various Survival properties including survival function, hazard rate function and mean residual life(MRL) like have been given. For estimating the parameters contained in the new model, methods like Method of Moments (MOM) and Maximum Likelihood Estimation (MLE) have been used

Physicochemical characterization, phytochemical analysis, and pharmacological evaluation of Sambucus wightiana

Sambucus wightiana (SW) is a 4–5-foot herbaceous stem with 5–9 leaflets and pinnatifid leaves (15–30 cm). It is used to treat stomach disorders, as an emetic for expelling poisonous substances, and as a laxative for controlling skin diseases. Phytochemical research based on ethnopharmacological knowledge is frequently regarded as an appropriate approach for discovering new agents from higher-altitude plants. Therefore, the present study focussed on identifying, collecting, and authenticating the S. wightiana and, isolating and characterizing the phytoconstituents using the DPPH method, reducing power, total flavonoid, phenolic content, anti-hyperglycemic and antioxidant capacity. Furthermore, the evaluation of antidiabetic studies of extracts/fraction and pure phytoconstituents of S. wightiana in alloxan-induced diabetic model and OGTT methods were carried out. The observed results revealed that the methanolic extract of Sambucus wightiana has significant anti-hyperglycemic and anti-oxidant activity. The methanolic extracts of S. wightiana, a dose of alloxan/SW-400 mg/Kg (111.55 ± 6.9 mg/dl) also decreased significantly the serum ALP level (p < 0.05). The methanol extracts of S. wightiana showed highly significant anti-hyperglycemic activity (p < 0.05). From the methanolic extracts, alloxan/SW-400 mg/Kg (89.55 ± 2.5 mg/dl) showed highly significant decrease in serum LDL level (p < 0.05) in extract-treated groups, not changing the body weight substantially and methanolic extract of S. wightiana at a dose of 400 mg/Kg exhibited substantial lipid, and blood glucose levels and liver enzymes lowering capacity compared to the diabetic control group. Consequently, the prevention of hyperglycaemia by various other drugs, S. wightiana could contribute to a new formulation with significant pharmacological effects