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

Octonion special affine fourier transform: pitt's inequality and the uncertainty principles

The special affine Fourier transform (SAFT) is an extended version of the classical Fourier transform and incorporates various signal processing tools which include the Fourier transforms, the fractional Fourier transform, the linear canonical transform, and other related transforms. This paper aims to introduce a novel octonion special affine Fourier transform (O-SAFT) and establish several classes of uncertainty inequalities for the proposed transform. We begin by studying the norm split and energy conservation properties of the proposed (O-SAFT). Afterwards, we generalize several uncertainty relations for the (O-SAFT) which include Pitt's inequality, Heisenberg-Weyl inequality, logarithmic uncertainty inequality, Hausdorff-Young inequality, and local uncertainty inequalities. Finally, we provide an illustrative example and some possible applications of the proposed transform

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

Tanshinones Inhibit the Growth of Breast Cancer Cells through Epigenetic Modification of Aurora A Expression and Function

The objectives of this study were to evaluate the effects of tanshinones from a Chinese herb Salvia Miltiorrhiza on the growth of breast cancer cells, and to elucidate cellular and molecular mechanisms of action. Tanshinones showed the dose-dependent effect on the growth inhibition of breast cancer cells in vitro, with tanshinone I (T1) the most potent agent. T1 was also the only tanshinone to have potent activity in inhibiting the growth of the triple-negative breast cancer cell line MDA-MB231. T1 caused cell cycle arrests of both estrogen-dependent and estrogen-independent cell lines associated with alterations of cyclinD, CDK4 and cyclinB, and induced breast cancer cell apoptosis associated with upregulation of c-PARP and downregulation of survivin and Aurora A. Among these associated biomarkers, Aurora A showed the most consistent pattern with the anti-growth activity of tanshinones. Overexpression of Aurora A was also verified in breast tumors. The gene function assay showed that knockdown of Aurora A by siRNA dramatically reduced the growth-inhibition and apoptosis-induction activities of T1, suggesting Aurora A as an important functional target of T1 action. On the other hand, tanshinones had much less adverse effects on normal mammary epithelial cells. Epigenetic mechanism studies showed that overexpression of Aurora A gene in breast cancer cells was not regulated by gene promoter DNA methylation, but by histone acetylation. T1 treatment significantly reduced acetylation levels of histone H3 associated with Aurora A gene. Our results supported the potent activity of T1 in inhibiting the growth of breast cancer cells in vitro in part by downregulation of Aurora A gene function. Our previous studies also demonstrated that T1 had potent anti-angiogenesis activity and minimal side effects in vivo. Altogether, this study warrants further investigation to develop T1 as an effective and safe agent for the therapy and prevention of breast cancer

Insights on nutritional profile, nutraceutical components, pharmacological potential, and trending utilization of persimmon cultivars: A review

The commercial persimmon fruit (Diospyros kaki) is a seasonal fruit and it contains various nutrients such ascarbohydrates,vitamins, fiber, minerals, phenolic compounds (ferulic acid, p-Coumaric acid, and gallic acid) and carotenoids (β-cryptoxanthin, lycopene, β-carotene, zeaxanthin, and lutein). This current review is an effort to sum up information regarding persimmon fruit's nutrient profile, bioactive potential, pharmacological potential, and its utilization in industry. Accordingly, the bioactive components such as p-Coumaric acid, epigallocatechin gallate, proanthocyanins, flavonoids, etc. and their extraction techniques such as high hydrostatic pressure (HHP), microwave-assisted extraction, and ultrasonic-assisted extraction are also highlighted. Further this review also describe the evidence based various pharmacological application of fruit and its bioactive components which have scavenging effect on active oxygen free radicals (flavonoids), prevents oxidative stress-related illnesses (p-Coumaric), promote neural degeneration and karyopyknosis in cells (tannin), may assist with hyperlipidemia and diabetes (proanthocyanidins). Overall persimmon and its components application in multiple products in various forms in the food sector can open up new avenues for its utilization, enhancing the natural flavour and bioactive components while also improving health

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