Narrow Results

It turns out that a parametrization of degenerate density matrices requires a parametrization of $𝔉=U(n)/(U(k_1)\times U(k_2)\times \cdots \times U(k_m))$, $n=k_1+\cdots +k_m$ where $U(k)$ denotes the set of all unitary $k\times k$-matrices with complex entries. Unfortunately, the parametrization of this quotient space is quite involved. Our solution does not rely on Lie algebra methods directly, but succeeds through the construction of suitable sections for natural projections, by using techniques from the theory of homogeneous spaces. We mention the relation to the Lie algebra background and conclude with two concrete examples.

Presented are new parameters for the calculation of L subshell ionization cross sections for proton impact using a semiempirical expression. A similar paper was published by our group in early 1993 but the fitting parameters were obtained by using only 2295 experimental L shell cross section data. Since then a large number of experimental data have become available and therefore a new fitting has been performed employing more than 5000 data points. All available data were fitted separately for L1, L2 and L3 subshells. For targets with low atomic numbers (14≤Z≤42), only coefficients for L_tot were obtained. Because of the slight Z dependence of the universal function, data were also devised into five sub-groups according to their atomic numbers and fitted separately within each group for L1, L2 and L3 subshells. To extend the energy range of validity of the new fitting function theoretical values were used in the high energy region where experimental data were lacking. Results are compared with ECPSSR predictions and discussed.

We construct the non-canonical kinetic term of a k-essence field directly from the effective equation of state function w_k(z), which describes the properties of the dark energy. Adopting the usual parametrizations of equation of state, we numerically reproduce the shape of the non-canonical kinetic term and discuss some features of the constructed form of k-essence.

We assume that universe is dominated by non-relativistic matter and tachyon field and reconstruct the potential of tachyon field directly from the effective equation of state (EOS) of dark energy. We apply the method to four known parametrizations of equation of state and discuss the general features of the resulting potentials.

In this paper, we regard dilaton in Weyl-scaled induced gravitational theory as coupled quintessence, which is called DCQ model by us. Parametrization of the dark energy model is a good method by which we can construct the scalar potential directly from the effective equation of state function ω_σ(z) describing the properties of the dark energy. Applying this method to the DCQ model, we consider four parametrizations of ω(z) and investigate the features of the constructed DCQ potentials, which possess two different evolutive behaviors called "O" mode and "E" mode. Lastly, we comprise the results of the constructed DCQ model with those of quintessence model numerically.

In this work, Friedmann–Robertson–Walker (FRW) universe filled with dark matter (DM) (perfect fluid with negligible pressure) along with dark energy (DE) in the background of Galileon gravity is considered. Four DE models with different equation of state (EoS) parametrizations have been employed namely, linear, Chevallier–Polarski–Lindler (CPL), Jassal–Bagla–Padmanabhan (JBP) and logarithmic parametrizations. From Stern, Stern+Baryonic Acoustic Oscillation (BAO) and Stern+BAO+Cosmic Microwave Background (CMB) joint data analysis, we have obtained the bounds of the arbitrary parameters ${\omega }_0$ and ${\omega }_1$ by minimizing the ${\chi }^2$ test. The best fit values and bounds of the parameters are obtained at 66%, 90% and 99% confidence levels which are shown by closed confidence contours in the figures. For the logarithmic model unbounded confidence contours are obtained and hence the model parameters could not be finitely constrained. The distance modulus $\mu$(z) against redshift $z$ has also been plotted for our predicted theoretical models for the best fit values of the parameters and compared with the observed Union2 data sample and SNe Type Ia 292 data and we have shown that our predicted theoretical models permits the observational datasets. From the data fitting it is seen that at lower redshifts $(z<0.3)$ the SNe Type Ia 292 data gives a better fit with our theoretical models compared to the Union2 data sample. So, from the data analysis, SNe Type Ia 292 data is the more favored data sample over its counterpart given the present choice of free parameters. From the study, it is also seen that the logarithmic parametrization model is less supported by the observational data. Finally, we have generated the plot for the deceleration parameter against the redshift parameter for all the theoretical models and compared the results with the work of Farooq et al., (2013).

In this paper, we have proposed a generalized parametrization for the deceleration parameter q in order to study the evolutionary history of the universe. We have shown that the proposed model can reproduce three well known q-parametrized models for some specific values of the model parameter $\alpha$. We have used the latest compilation of the Hubble parameter measurements obtained from the cosmic chronometer (CC) method (in combination with the local value of the Hubble constant $H_0$) and the Type Ia supernova (SNIa) data to place constraints on the parameters of the model for different values of $\alpha$. We have found that the resulting constraints on the deceleration parameter and the dark energy equation of state support the $\mathrm{\Lambda }$CDM model within $1\sigma$ confidence level at the present epoch.

In view of late-time cosmic acceleration, a dark energy cosmological model is revisited wherein Einstein’s cosmological constant is considered as a candidate of dark energy. Exact solution of Einstein field equations (EFEs) is derived in a homogeneous isotropic background in classical general relativity. The solution procedure is adopted in a model-independent way (or the cosmological parametrization). A simple parametrization of the Hubble parameter (H) as a function of cosmic time t is considered which yields an exponential type of evolution of the scale factor (a) and also shows a negative value of deceleration parameter at the present time with a signature flip from early deceleration to late acceleration. Cosmological dynamics of the model obtained have been discussed illustratively for different phases of the evolution of the universe. The evolution of different cosmological parameters is shown graphically for flat and closed cases of Friedmann–Lemaitre–Robertson–Walker (FLRW) spacetime for the presented model (open case is incompatible to the present scenario). We have also constrained our model parameters with the updated (36 points) observational Hubble dataset.

We put forward a pressure-parametric model to study the tiny deviation from cosmological constant(CC) behavior of the dark sector accelerating the expansion of the Universe. Data from cosmic microwave background (CMB) anisotropies, baryonic acoustic oscillations (BAO), Type Ia supernovae (SN Ia) observation are applied to constrict the model parameters. The constraint results show that such model suffers with $H_0$ tension as well. To realize this model more physically, we reconstruct it with the quintessence and phantom scalar fields, and find out that although the model predicts a quintessence-induced acceleration of the Universe at past and present, at some moment of the future, dark energy’s density have a disposition to increase.

In this paper, we reconstruct the late-time cosmological dynamics using a purely kinematic approach. In particular, considering a divergence-free parametrization for deceleration parameter $q$, we first derive the jerk parameter $j$ and then confront it with combination of various cosmological datasets. We use the most recent observational datasets consisting of the 1048 Pantheon Supernovae Ia data points in the redshift range $0.01<z<2.3$, the 51 data points of observational Hubble parameter (OHD) measurements in the redshift range $0.07\le z\le 2.36$, the Hubble constant $H_0$ (R19) and the CMB shift parameter measurements. We study the evolution of different cosmological quantities for the present model and compare it with the concordance $\mathrm{\Lambda }$CDM model. We find that only the combined Pantheon+OHD+R19 data shows good agreement with the $\mathrm{\Lambda }$CDM $(j=1)$ model within $1\sigma$ confidence region. We also find that our model successfully generates late time cosmic acceleration along with a decelerated expansion in the past.

The CKM matrix describing quark mixing with three generations can be parametrized by three mixing angles and one CP-violating phase. In most of the parametrizations, the CP-violating phase chosen is not a directly measurable quantity and is parametrization dependent. In this work, we propose to use experimentally measurable CP-violating quantities, α, β or γ in the unitarity triangle as the phase in the CKM matrix, and construct explicit α, β and γ parametrizations. Approximate Wolfenstein-like expressions are also suggested. Since β is most accurately measured among these three phase angles, we consider β parametrization as the best one to use.

Curves dividing the parameter plane into regions according to the presence or absence of homoclinic or heteroclinic tangle corresponding to the periodically perturbed saddle of the piecewise smooth oscillator are studied using Melnikov analysis. The analysis is not simplified by choosing the discontinuity plane at a convenient location. Separatrix of the unperturbed system is parametrized exactly in a piecewise manner. Switching times, i.e. parameter values at which the separatrix crosses the discontinuity plane, are obtained. Switching times split the Melnikov integral into various subintegrals which are evaluated either exactly using term-wise integration of the infinite series of the integrand or approximately using a finite-term series approximation of the integrand, the latter being computationally an extensive task. Integral evaluations though approximate, are purely analytical expressions in terms of special functions such as digamma and hypergeometric. Melnikov plots show that the boundary between three regions in the parameter plane differ qualitatively in case of parametric and external excitations, however; adding self-excitation to the external one does not much alter the boundary qualitatively and quantitatively.

This paper presents a study of chaos in one-dimensional cellular automata (CAs). The communication of information from one part of the system to another has been taken into consideration in this study. This communication is formalized as a binary relation over the set of cells. It is shown that this relation is an equivalence relation and all the cells form a single equivalence class when the cellular automaton (CA) is chaotic. However, the communication between two cells is sometimes blocked in some CAs by a subconfiguration which appears in between the cells during evolution. This blocking of communication by a subconfiguration has been analyzed in this paper with the help of de Bruijn graph. We identify two types of blocking — full and partial. Finally a parameter has been developed for the CAs. We show that the proposed parameter performs better than the existing parameters.

Obfuscation is a technology that secures software artifacts from reverse engineering by making its cost prohibitively high. Intermediate level obfuscator implements the defensive mechanisms inside the software, and owing to high potency and resilience, can successfully secure the sensitive software components. This paper provides an analysis and parametrization of the obfuscator, as well as a method of fine-tuning and evaluating obfuscating transformations in terms of potency, resilience and cost.

In this paper we consider some knowledge aspects which arise when investigating problems of optimal resource allocation with saturation. Among them we mention information state before resource allocation, utilization of lexicographical variables, space transformations, some principles used for finding solutions, finding quality form of solution on the basis of the necessary conditions of optimality, inner and outer parametrization, essential reduction of dimension of solved problems, reasons of solution non-uniqueness, utilization of continual problems for solution of analogous discrete problems.

We shall try to show the mutual interplay between software engineering and knowledge engineering. Examples of problems solved with attraction of methods discussed in this paper exist in papers [1–10] and others.

In [15] and [16] all possible torsion groups of elliptic curves E with integral j-invariant over quadratic and pure cubic number fields K are determined. Moreover, with the exception of the torsion groups of isomorphism types ℤ/2ℤ, ℤ/3ℤ and ℤ/2ℤ×ℤ/2ℤ, all elliptic curves E and all basic quadratic and pure cubic fields K such that E over K has one of these torsion groups were computed. The present paper is aimed at solving the corresponding problem for general cubic number fields K. In the general cubic case, the above groups ℤ/2ℤ, ℤ/3ℤ and ℤ/2ℤ×ℤ/2ℤ and, in addition, the groups ℤ/4ℤ, ℤ/5ℤ occur as torsion groups of infinitely many curves E with integral j-invariant over infinitely many cubic fields K. For all the other possible torsion groups, the (finitely any) elliptic curves with integral j over the (finitely many) cubic fields K are calculated here. Of course, the results obtained in [6] for pure cubic fields and in [24] for cyclic cubic fields are regained by our algorithms. However, compared with [15] and [6], a solution of the torsion group problem in the much more involved general cubic case requires some essentially new methods. In fact we shall use Gröbner basis techniques and elimination theory to settle the general case.

In this paper, we have considered a spatially flat FRW universe filled with pressureless matter and dark energy (DE). We have considered a phenomenological parametrization of the deceleration parameter $q(z)$ and from this, we have reconstructed the equation-of-state (EoS) for DE ${\omega }_{\varphi }(z)$. This divergence-free parametrization of the deceleration parameter is inspired from one of the most popular parametrization of the DE EoS given by Barboza and Alcaniz [see E. M. Barboza and J. S. Alcaniz, Phys. Lett. B666 (2008) 415]. Using the combination of datasets (Type Ia Supernova (SN Ia) + Hubble + baryonic acoustic oscillations/cosmic microwave background (BAO/CMB)), we have constrained the transition redshift $z_t$ (at which the universe switches from a decelerating to an accelerating phase) and have found the best fit value of $z_t$. We have also compared the reconstructed results of $q(z)$ and ${\omega }_{\varphi }(z)$ and have found that the results are compatible with a $\mathrm{\Lambda }$CDM universe if we consider SN Ia + Hubble data, but inclusion of BAO/CMB data makes $q(z)$ and ${\omega }_{\varphi }(z)$ incompatible with $\mathrm{\Lambda }$CDM model. The potential term for the present toy model is found to be functionally similar to a Higgs potential.

In this work, we have proposed a simple parametrization for the pressure component $p(z)$ of the dark energy model and have studied the cosmological implications of this model in the framework of $f(Q)$ modified gravity theory, aka, the symmetric teleparallel gravity theory, where Q is known as the nonmetricity scalar. By considering a particular parametric form of $p(z)$, we obtained the Hubble solution for the $f(Q)$ modified gravity model. In order to see whether this model is consistent with or challenges the $\mathrm{\Lambda }$CDM limits, we tried to put constraints on the model parameters using the recent observational datasets like Hubble data, Cosmic Chronometer data, Type Ia Supernovae (SNIa) data, baryonic acoustic oscillations (BAO) data. We have employed the ${\chi }^2$ minimization technique and have carried out the Markov Chain Monte Carlo (MCMC) analysis using emcee package. We have found that the deceleration parameter shows a smooth transition from positive to negative value in recent past which is essential for the structure formation of the Universe. It has been found that the parametric form of the dark energy pressure parameter is consistent with current cosmological scenario.

The Coulomb barrier heights are calculated by using the proximity potential with a new universal function in comparison with the results of proximity potentials Prox77, AW95, Bass73, BW91, CW76, DP and Ng80. It is found that the new results of Coulomb barrier heights are better than those of most proximity potentials. Then this proximity potential with the new universal function was used to calculate the Coulomb barrier positions and heights from light fusion systems to heavy fusion systems. The parametrized formulas are obtained for Coulomb barrier height and position, and can reproduce most of calculated barrier heights and positions within the accuracy of $\pm 1\%$.

The functional role of a neuron within a network is influenced by the geometry of its dendrites. In the present study we have used a new model of dendritic arborization to analyze how metrical and topological parameters interact to shape a certain dendritic tree. One of the specific questions addressed is how to change topological variability in a systematic way while preserving the metrical features. The second problem concerns the effect of topology on the relationship between dendritic size and the distribution of dendritic surface area with radial distance from soma. The simulation results reproduce features of dendritic architecture found in neocortical pyramidal cells and cat superior colliculus neurons.