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The proton capture cross-section of the least abundant proton-rich stable isotope of cadmium, $^{108}$Cd (abundance 0.89\%), has been measured near the Gamow window corresponding to a temperature range of 3-4 GK. The measurement of the $^{108}$Cd(p,$\gamma$)$^{109}$In reaction was carried out using the activation technique. The cross-section at the lowest energy point of 3T$_9$, E$_p$$^{lab}$= 2.28 MeV, has been reported for the first time. The astrophysical S-factor was measured in the energy range relevant to the astrophysical p-process, between E$_p$$^{cm}$= 2.29 and 6.79 MeV. The experimental results have been compared with theoretical predictions of Hauser-Feshbach statistical model calculations using TALYS-1.96. A calculated proton-optical potential was implemented to achieve better fitting, with different combinations of available nuclear level densities (NLDs) and $\gamma$-ray strength functions in TALYS-1.96. The calculations provided satisfactory agreement with the experimental results. The reaction rate was calculated using the calculated potential in TALYS-1.96 and compared with the values provided in the REACLIB database.

The image of a given orthonormal basis for a separable Hilbert space $\mathcal{H}$ under a bijective, bounded, and linear operator acting on $\mathcal{H}$ is called a Riesz basis of $\mathcal{H}$. Contrary to what happens with Riesz bases (in the usual sense) in separable Hilbert spaces, it is not true in general that the image of a matrix-valued orthonormal basis under a bounded, linear, and bijective operator on $L^2(G, \mathbb{C}^{s\times r})$ is also a basis and frame for the space $L^2(G, \mathbb{C}^{s\times r})$, where $G$ is a $\sigma$-compact and metrizable locally compact abelian (LCA) group. We give some classes of operators for the construction of matrix-valued Riesz bases from orthonormal bases of the space $L^2(G, \mathbb{C}^{s\times r})$. Motivated by a result due to Holub, we show that a bounded, linear, and bijective operator acting on $L^2(G, \mathbb{C}^{s\times r})$ which is adjointable with respect to the matrix-valued inner product is positive if and only if it maps a matrix-valued Riesz basis of the space $L^2(G, \mathbb{C}^{s\times r})$ to its dual Riesz basis.

Scenarios seeking to address the issue of electroweak symmetry breaking often have heavy colored gauge bosons coupling preferentially to the top quark. Considering the bulk Randall-Sundrum as a typical example, we consider the prospects of the first Kaluza-Klein mode ($G^{(1)}$) of the gluon being produced at the LHC in association with a $t \bar{t}$ pair. The enhanced coupling not only dictates that the dominant decay mode would be to a $t \bar{t}$ pair, but also to a very large $G^{(1)}$ width, necessitating the use of a renormalised $G^{(1)}$ propagator. This, alongwith the presence of large backgrounds (specially $t \bar{t} j j$), renders a conventional cut-based analysis ineffective, yielding only marginal significances of only around 2$\sigma$. The use of Machine Learning (ML) techniques alleviates this problem to a great extent. In particular, the use of Artificial Neural Networks helps us identify the most discriminating observables, thereby allowing a significance in excess of 4$\sigma$ for $G^{(1)}$ masses of $\sim$ 4 TeV., Comment: 35 pages, 9 figures, 5 tables

The detailed process of preparing enriched $^{108}$Cd targets on mylar and copper backing using the vacuum evaporation technique is described. These targets were employed in an experiment to measure the proton capture cross-section at energies significantly below the Coulomb barrier, for the astrophysical p-process studies. Due to the low melting point and high vapor pressure of cadmium, some adjustments were implemented in the Telemark multipocket e-beam setup. The target thickness was determined through the measurement of alpha particle energy loss from a triple alpha source and also by RBS measurements. The thickness of the $^{108}$Cd films varies between 290 to 660 $\mu$g/cm$^2$, with a non-uniformity of approximately 10$\%$. X-ray Photoelectron Spectroscopy (XPS) and X-ray Fluorescence (XRF) analyses were conducted to examine the presence of impurities and to assess surface morphology, phase, and chemical composition.

Neutron deficient nuclei from $^{74}$Se$-^{196}$Hg are thought to be produced by $\gamma$-induced reactions ($\gamma$,n), ($\gamma$,p) and ($\gamma,\alpha$) processes. The relatively high abundance of $^{113}$In odd A $p$-nuclei has inspired to study its production processes. As reaction with $\gamma$-beam is difficult to perform in the laboratory, $\gamma$-induced reaction rate is calculated from the inverse reaction data employing reciprocity theorem. Stacked foil activation method was used to measure the $^{113}$In($\alpha,\gamma$) and $^{113}$In($\alpha$, n) reactions cross-section near the astrophysical energies. Theoretical statistical model calculations were performed with different nuclear input parameters and compared with the experimental results. An appropriate $\alpha$-optical potential has been identified from the ($\alpha,\gamma$) and ($\alpha$, n) fitting, which provides the major source of uncertainty in the statistical model calculations. The other nuclear input parameters like level density, and $\gamma$-ray strength function were also constrained for theoretical calculations. $^{113}$In($\alpha,\gamma$)$^{117}$Sb and $^{117}$Sb($\alpha,\gamma$)$^{113}$In reaction rates were calculated using best-fitted input parameters.

The cross-section measurement of $^{144}$Sm(p, $\gamma$)$^{145}$Eu (T$_{1/2}=$5.93(4) days) reaction has been performed at proton energies around 2.6, 3.1, 3.7, 4.1, 4.2, 4.7, 5.1, 5.5, 5.9, 6.4, 6.8 MeV using the activation technique. These energies correspond to the Gamow window for 3, 4 GK and a partial portion for 2 GK. $^{144}$Sm has been chosen for the present study because of its significantly higher abundance compared to the other neighboring $p$-nuclides (Z $>$ 50). The astrophysical $S-$factor of this reaction has been measured for the first time at E$^{cm}_p=$ 2.57$\pm$0.13 MeV, $S-$ factor$=$2.542$\pm$1.152($\times$10$^{10}$) MeV-b. Cross-section data were compared with the previously measured experimental data from literature and the theoretical predictions obtained using Hauser-Feshbach statistical model codes TALYS 1.96 and NON-SMOKER. A satisfactory agreement between experimental data and theoretical results was observed. Molecular deposition technique was used to prepare the $^{144}$Sm targets having thickness between 100$-$350 $\mu$g/cm$^2$ on Al backing. Obtained results were utilized to predict the reaction rates for $^{144}$Sm (p, $\gamma$) and $^{145}$Eu ($\gamma$, p) reactions using TALYS 1.96 and the reciprocity theorem.

In the current study, we investigate a scalar field cosmological model with Lyra's geometry to explain the present cosmic expansion in a homogeneous and isotropic flat FRW universe. In Einstein's field equations, we presupposed a variable displacement vector as an element of Lyra's geometry. In the context of the conventional theory of gravity, we suggest a suitable parameterization of the scalar field's dark energy density in the hybrid function of redshift $z$, confirming the essential transition behavior of the universe from a decelerating era to the present accelerated scenario. We present constraints on model parameters using the most recent observational data sets from OHD, BAO/CMB, and Pantheon, taking Markov Chain Monte Carlo (MCMC) analysis into account. For the proposed model, the best estimated values of parameters for the combined dataset (OHD, BAO/CMB, and Pantheon) are $ H_0 = 71.15\pm 0.26$ km/s/Mpc, $ \Omega_{m0}=0.2625\pm 0.0024$, $ \Omega_{\phi0} = 0.676\pm0.038$, $ \alpha=-0.22\pm0.13$, $n = 0.096\pm0.079$, and $k = 0.38\pm0.32$. The model exhibits a flipping nature, and the redshift transition occurs at $z_t = 0.756^{+0.005}_{-0.015}$. The current value of the decelerated parameter for the proposed model is calculated as $q_0 = -0.625^{+0.067}_{-0.085}$ for the combined dataset. Some dynamical properties of the model like energy density ($\rho_{\phi}$), scalar field pressure ($p_{\phi}$), EoS parameter of scalar field ($\omega_{\phi}$), and effective EoS parameter ($\omega_{eff}$) are analyzed and presented. Further, we have also examined the statefinder diagnosis and jerk parameters of the derived model. The total density parameter for the derived model is found to be unity which is in nice agreement with recent standard findings., Comment: 24 pages, 12 figures

The relationship between the frame bounds of frames (Gabor) for the space $L^2(\mathbb{R})$ with several generators from the Weyl-Heisenberg group and the scalars linked to the sum of frames is examined in this paper. We give sufficient conditions for the finite sum of frames of the space $L^2(\mathbb{R})$ from the Weyl-Heisenberg group, with explicit frame bounds, in terms of frame bounds and scalars involved in the finite sum of frames, to be a frame for $L^2(\mathbb{R})$. It is shown that if a series of square roots of upper frame bounds of countably infinite frames from the Weyl-Heisenberg group is convergent and some lower frame bound majorizes the sum of all other frame bounds, then the infinite sum of frames for $L^2(\mathbb{R})$ space turns out to be a frame for the space $L^2(\mathbb{R})$. We show that the sum of frames from the Weyl-Heisenberg group and its dual frame always constitutes a frame. We provide sufficient conditions for the sum of images of frames under bounded linear operators acting on $L^2(\mathbb{R})$ in terms of lower bounds of their Hilbert adjoint operator to be a frame. The finite sum of frames where frames are perturbed by bounded sequences of scalars is also discussed. As an application of the results, we show that the frame bounds of sums of frames can increase the rate of approximation in the frame algorithm. Our results are true for all types of frames.

The present research paper is an investigation of dark energy nature of logarithmic $f(R, T)$-gravity cosmology in a flat FLRW space-time universe. We have derived modified Einstein's field equations for the function $f(R, T)=R-16\pi G\alpha\ln(T)$ where $R$ is the Ricci scalar curvature, $T$ is the trace of the stress energy momentum tensor and $\alpha$ is a model parameter. We have solved field equations in the form of two fluid scenario as perfect-fluid and dark-fluid, where dark fluid term is derived in the form of perfect fluid source. We have made an observational constraints on the cosmological parameters $\Omega_{(m)}, \omega^{(de)}$ and $H_{0}$ using $\chi^{2}$ test with observational datasets like Pantheon sample of SNe Ia and $H(z)$. With these constraints we have discussed our model with deceleration parameter $q$, energy parameters $\Omega_{(m)}, \Omega_{(de)}$, EoS parameter $\omega^{(de)}$ etc. Also, we have done Om diagnostic analysis. The derived $f(R, T)$ model shows a quintessence dark energy model $\omega^{(de)}>-1$ and late-time universe approaches to $\Lambda$CDM model., Comment: 16 pages, 8 figures

In this work, we analyze Gabor frames for the Weyl--Heisenberg group and wavelet frames for the extended affine group. Firstly, we give necessary and sufficient conditions for the existence of nonstationary frames of translates. Using these conditions, we give the existence of Gabor frames from the Weyl--Heisenberg group and wavelet frames for the extended affine group. We present a representation of functions in the closure of the linear span of a Gabor frame sequence in terms of the Fourier transform of window functions. We show that the canonical dual of frames of translates has the same structure. An approximation of inverse of the frame operator of nonstationary frames of translates is presented. It is shown that a nonstationary frame of translates is a Riesz basis if it is linearly independent and satisfies approximation of the inverse frame operator. Finally, we give equivalent conditions for a nonstationary sequence of translates to be linearly independent.

G\v avruta studied atomic systems in terms of frames for range of operators (that is, for subspaces), namely $K$-frames, where the lower frame condition is controlled by the Hilbert-adjoint of a bounded linear operator $K$. For a locally compact abelian group G and a positive integer $n$, we study frames of matrix-valued Gabor systems in the matrix-valued Lebesgue space $L^2(G, \mathbb{C}^{n\times n})$ , where a bounded linear operator $\Theta$ on $L^2(G, \mathbb{C}^{n\times n})$ controls not only lower but also the upper frame condition. We term such frames matrix-valued $(\Theta, \Theta^*)$-Gabor frames. Firstly, we discuss frame preserving mapping in terms of hyponormal operators. Secondly, we give necessary and sufficient conditions for the existence of matrix-valued $(\Theta, \Theta^*)$- Gabor frames in terms of hyponormal operators. It is shown that if $\Theta$ is adjointable hyponormal operator, then $L^2(G, \mathbb{C}^{n\times n})$ admits a $\lambda$-tight $(\Theta, \Theta^*)$-Gabor frame for every positive real number $\lambda$. A characterization of matrix-valued $(\Theta, \Theta^*)$-Gabor frames is given. Finally, we show that matrix-valued $(\Theta, \Theta^*)$-Gabor frames are stable under small perturbation of window functions. Several examples are given to support our study.

The LiF target preparation on self-supporting Ag backing (LiF/Ag) is discussed in a detailed manner using vacuum evaporation process. The target thickness is measured using the energy loss of three line alpha source. 183.74 {\mu}g/cm 2 thickness of LiF is achieved through the evaporation process. Good uniformity of targets is observed. Non-uniformity in targets is found within 6 %. The XPS analysis confirms the presence of both the F and Li atoms on sample surface.

Gabor frames have interested many mathematicians and physicists due to their potential applications in time-frequency analysis, in particular, signal processing. A Gabor system is a collection of vectors which is obtained by applying modulation and shift operators to non-zero functions in signal spaces. In many applications, for example, signal processing related to Gabor systems, the corresponding shifts may not be uniform. That is, the set associated with shifts may not be a group under usual addition. We analyze discrete vector-valued nonuniform Gabor frames (DVNUG frames, in short) in discrete vector-valued nonuniform signal spaces, where the indexing set associated with shifts may not be a subgroup of real numbers under usual addition, but a spectrum which is based on the theory of spectral pairs. First, we give necessary and sufficient conditions for the existence of DVNUG Bessel sequences in discrete vector-valued nonuniform signal spaces in terms of Fourier transformations of the modulated window sequences. We provide a characterization of DVNUG frames in discrete vector-valued nonuniform signal spaces. It is shown that DVNUG frames are stable under small perturbation of window sequences associated with given discrete vector-valued nonuniform Gabor systems. We observed that the arithmetic mean sequences associated with window sequences of a given DVNUG frame collectively constitutes a discrete nonuniform Gabor frame. Finally, we discuss an interplay between window sequences of DVNUG systems and their corresponding coordinates.

We reassess non-standard triple gauge couplings in the light of the recent $(g-2)_\mu$ measurement at FNAL, the new lattice theory result of $(g-2)_\mu$ and the updated measurements of several $B$-decay modes. In the framework of SMEFT, three bosonic dimension-6 operators are invoked to parametrize physics beyond the Standard Model and their contributions to such low-energy observables computed. Constraints on the corresponding Wilson coefficients are then derived from fits to the current experimental bounds on the observables and compared with the most stringent ones available from the 13 TeV LHC data in the $W^+ W^-$ and $W^\pm Z$ production channels., Comment: 13 pages. Typos corrected, figures updated and a few segments expanded. Minor change in the results. Version to appear in PRD

In this article, a detailed investigation has been done for the long lived gamma activity due to neutron emitting experiments. These calculations mainly focused on the experiments used for energy calibration purposes. Calibrated energy is one of the most essential features of any accelerator facility. Several experiments have been used for this purpose. Generally, experiments having sharp curvature change in cross section of yield are used. Neutron emitting experiments are one of such. Around the globe reactions like $^7Li(p,n)$, $^{13}C(p,n)$, $^{19}F(p,n)$, $^{27}Al(p,n)$ etc. are used to calibrate energy of the beam with accelerator terminal voltage. Neutrons coming from these experiments can interact with surrounding elements. These interactions with neutrons can create long lived gamma activity which may interfere with future measurements. The present study has been done keeping in mind the new Facility for Research in Experimental Nuclear Astrophysics (FRENA) at Saha Institute of Nuclear Physics. It is a 3MV tandetron low energy high current machine.

We study the construction of Gabor frames and wavelet frames for Weyl-Heisenberg group and extended affine group by using contraction between the affine group and the Weyl-Heisenberg group due to Subag, Baruch, Birman and Mann. Firstly, we give construction of Gabor frames with several generators from a unitary irreducible representation associated to the Weyl-Heisenberg group. Wavelet frames with several generators associated with an extended affine group have been obtained. A relation between frames for Weyl-Heisenberg group and extended affine group is also discussed. Finally, we show that frames of Gabor and wavelet structure are stable under small perturbations.

A counter-example by Xiangchun Xiao, Guoping Zhao and Guorong Zhou in [J. Pseudo-Differ. Oper. Appl., (2021) 12:60] is incorrect. Further, there is no new characterization of weaving for g-frames by Xiangchun Xiao et al. in [2]. Xiangchun Xiao et al. in [2] gave a wrong interpretation about a characterization of weaving g-frames in separable Hilbert spaces which already proved by Deepshikha, Vashisht and Verma in [1].

We investigate the phenomenological viability of real spin half, zero and one dark matter candidates, which interact predominantly with third generation heavy quarks and gluons via the twenty-eight gauge invariant higher dimensional effective operators. The corresponding Wilson coefficients are constrained one at a time from the relic density $\Omega^{\rm DM} h^2$ $\approx$ 0.1198. Their contributions to the thermal averaged annihilation cross-sections are shown to be consistent with the FermiLAT and H.E.S.S. experiments' projected upper bound on the annihilation cross-section in the $b\,\bar b$ mode. The tree-level gluon-philic and one-loop induced heavy-quark-philic DM-nucleon direct-detection cross-sections are analysed. The non-observation of any excess over expected background in the case of recoiled Xe-nucleus events for spin-independent DM-nucleus scattering in XENON-1T sets the upper limits on the eighteen Wilson coefficients. Our analysis validates the real DM candidates for the large range of accessible mass spectrum below 2 TeV for all but one interaction induced by the said operators., Comment: 42 pages, 14 figures

The direct reaction component of the $^{19}$F(p,$\alpha_{0}$) reaction at E$_{cm}$=180-600 keV is studied for the data that has become very recently available. This component has been found to be significant in the present work using the direct pickup model in framework of the DWBA formalism and indicate the strong cluster structure of $^{19}$F.

In this paper, we investigate a scalar field Brans-Dicke cosmological model in Lyra's geometry which is based on the modifications in geometrical term as well as energy term of Einstein's field equations. We have examined the validity of proposed cosmological model on observational scale by performing statistical analysis from latest $H(z)$ and SN Ia observational data. We find that the estimated values of Hubble's constant and matter energy density parameter are in agreement with their corresponding values, obtained from recent observations of WMAP and Plank collaboration. We also derived deceleration parameter, age of the universe and jerk parameter in terms of red-shift and computed its present values. The dynamics of deceleration parameter in derived model of the universe shows a signature flipping from positive to negative value and also indicates that the present universe is in accelerating phase., Comment: 9 pages, 6 Figures, Accepted for Publication in Int. J. Geom. Meth. Mod. Phys

We study the construction of nonuniform tight wavelet frames for the Lebesgue space $L^2(\mathbb{R})$, where the related translation set is not necessary a group. The main purpose of this paper is to prove the unitary extension principle (UEP) and the oblique extension principle (OEP) for construction of multi-generated nonuniform tight wavelet frames for $L^2(\mathbb{R})$. Some examples are also given to illustrate the results.

Two frames $\{\phi_{i}\}_{i \in I}$ and $\{\psi_{i}\}_{i \in I}$ for a separable Hilbert space $H$ are woven if there are positive constants $A \leq B$ such that for every subset $\sigma \subset I$, the family $\{\phi_{i}\}_{i \in \sigma} \cup \{\psi_{i}\}_{i \in \sigma^{c}}$ is a frame for $H$ with frame bounds $A, B$. Bemrose et al. introduced weaving frames in separable Hilbert spaces and observed that weaving frames has potential applications in signal processing. Motivated by this, and the recent work of Balan in the direction of application of vector-valued frames (or superframes) in signal processing, we study vector-valued weaving frames. In this paper, first we give some fundamental properties of vector-valued weaving frames. It is shown that if a family of vector-valued frames is woven, then the corresponding family of frames for atomic spaces is woven, but the converse is not true. We present a technique for the construction of vector-valued woven frames from given woven frames for atomic spaces . Necessary and sufficient conditions for vector-valued weaving Riesz sequences are given. Several numerical examples are given to illustrate the results.

Standard model (SM) spin-zero singlets are constrained through their di-Bosonic decay channels via an effective coupling induced by a vector-like quark (VLQ) loop at the LHC for $\sqrt{s}$ = 13 TeV. These spin-zero resonances are then considered as portals for scalar, vector or fermionic dark matter particle interactions with SM gauge bosons. We find that the model is validated with respect to the observations from LHC data and from cosmology, indirect and direct detection experiments for an appreciable range of scalar, vector and fermionic DM masses greater than 300 GeV and VLQ masses $\ge$ 400 GeV, corresponding to the three choice of portal masses 270 GeV, 500 GeV and 750 GeV respectively., Comment: 28 pages, 13 figures, and 2 tables

Digital media is the need of a people now a day as the alternate of paper media.As the technology grown up digital media required protection while transferring through internet or others mediums.Watermarking techniques have been developed to fulfill this requirement.This paper aims to provide a detailed survey of all watermarking techniques specially focuses on image watermarking types and its applications in today world., Comment: 4 Pages

Watermarking algorithms needs properties of robustness and perceptibility. But these properties are affected by different -2 types of attacks performed on watermarked images. The goal of performing attacks is destroy the information of watermark hidden in the watermarked image. So every Algorithms should be previously tested by developers so that it would not affected by attacks., Comment: 4 Pages