Constant Term Research Articles

A study of entrepreneurial management performance assessment method based on multivariate statistical analysis

Abstract This paper uses multivariate statistical analysis to explore the ordinary least squares regression algorithm, principal component regression algorithm, and partial least squares regression algorithm. Then, an index system for entrepreneurial management performance assessment was constructed with public innovation space, resource collocation and entrepreneurial performance indicators, and an entrepreneurial management performance mediation model was established with this. Finally, the quartiles of entrepreneurial performance's principal components were derived by studying the relationship between entrepreneurial performance assessment and each input. The results show that the first principal component Z 1 of entrepreneurial performance is significant at all quartiles, while the second principal component Z 2 is significant only at the 0.6 quartiles, and the constant terms are significant at the 0.6, 0.7, and 0.8 quartiles. Multivariate statistical analysis is employed in this paper to provide a reference for entrepreneurship management and to assess entrepreneurial performance more accurately.

Diagnostic accuracy of virtual non-contrast CT for aortic valve stenosis severity evaluation

BackgroundComputed tomography aortic valve calcium (AVC) score has accepted value for diagnosing and predicting outcomes in aortic stenosis (AS). Multi-energy CT (MECT) allows virtual non-contrast (VNC) reconstructions from contrast scans. We aim to compare the VNC-AVC score to the true non-contrast (TNC)-AVC score for assessing AS severity. MethodsWe prospectively included patients undergoing a MECT for transcatheter aortic valve replacement (TAVR) planning. TNC-AVC was acquired before contrast, and VNC-AVC was derived from a retrospectively gated contrast-enhanced scan. The Agatston scoring method was used for quantification, and linear regression analysis to derive adjusted-VNC values. ResultsAmong 109 patients (55% female) included, 43% had concordant severe and 14% concordant moderate AS. TNC scan median dose-length product was 116 ​mGy∗cm. The median TNC-AVC was 2,107 AU (1,093–3,372), while VNC-AVC was 1,835 AU (1293-2,972) after applying the coefficient (1.46) and constant (743) terms. A strong correlation was demonstrated between methods (r ​= ​0.93; p ​< ​0.001). Using accepted thresholds (>1,300 AU for women and >2,000 AU for men), 65% (n ​= ​71) of patients had severe AS by TNC-AVC and 67% (n ​= ​73) by adjusted-VNC-AVC. After estimating thresholds for adjusted-VNC (>1,564 AU for women and >2,375 AU for men), 56% (n ​= ​61) had severe AS, demonstrating substantial agreement with TNC-AVC (κ ​= ​0.77). ConclusionsMECT-derived VNC-AVC showed a strong correlation with TNC-AVC. After adjustment, VNC-AVC demonstrated substantial agreement with TNC-AVC, potentially eliminating the requirement for an additional scan and enabling reductions in both radiation exposure and acquisition time.

Research on the Impact of Data Density on Memristor Crossbar Architectures in Neuromorphic Pattern Recognition.

Binary memristor crossbars have great potential for use in brain-inspired neuromorphic computing. The complementary crossbar array has been proposed to perform the Exclusive-NOR function for neuromorphic pattern recognition. The single crossbar obtained by shortening the Exclusive-NOR function has more advantages in terms of power consumption, area occupancy, and fault tolerance. In this paper, we present the impact of data density on the single memristor crossbar architecture for neuromorphic image recognition. The impact of data density on the single memristor architecture is mathematically derived from the reduced formula of the Exclusive-NOR function, and then verified via circuit simulation. The complementary and single crossbar architectures are tested by using ten 32 × 32 images with different data densities of 0.25, 0.5, and 0.75. The simulation results showed that the data density of images has a negative effect on the single memristor crossbar architecture while not affecting the complementary memristor crossbar architecture. The maximum output column current produced by the single memristor crossbar array decreases as data density decreases while the complementary memristor crossbar array architecture provides stable maximum output column currents. When recognizing images with data density as low as 0.25, the maximum output column currents of the single memristor crossbar architecture is reduced four-fold compared with the maximum currents from the complementary memristor crossbar architecture. This reduction causes the Winner-take-all circuit to work incorrectly and will reduce the recognition rate of the single memristor crossbar architecture. These simulation results show that the single memristor crossbar architecture has more advantages compared with the complementary crossbar architecture when the images do have not many different densities, and none of the images have very low densities. This work also indicates that the single crossbar architecture must be improved by adding a constant term to deal with images that have low data densities. These are valuable case studies for archiving the advantages of single memristor crossbar architecture in neuromorphic computing applications.

Cebir Öğretim Sürecinin Jestler Bağlamında Göstergebilimsel Olarak İncelenmesi

This research aims to examine the gestures used by teachers and students in the algebra learning-teaching process and the purpose of these signs. The participants of this case study are 25 eigth graders and their mathematics teacher. The data were collected through video recordings and clinical interviews. Deductive analysis was used to analyze the data, while synchronic and diachronic analyses were utilized to analyze the signs in terms of semiotics. Findings revealed that the teacher used a bunch of iconic, metaphoric, deictic, and beat gestures during the algebra teaching process. The meaning of the iconic gestures that resulted in the study can be listed as centering and itemization, illustration of a table, constant term, preceding element, decrease, separation, base and power, rectangle and side, length, and vertical-horizontal. On the other hand, the metaphorical gestures attribute holding, equality, moving the term from one side to the other, numbers or letters, equality, distributing and hiding. The deictic gestures imply pointing out boards with fingers, board markers or hands, and indicating students and notebooks with fingers, while the beat gestures refer to lowering the hands from top to bottom, waving the fist up and down and moving the hand back and forth. It is seen that the teacher aims to strengthen her expression and support students' mathematical understanding through the gestures she uses.

Teleparallel Robertson-Walker Geometries and Applications

In teleparallel geometries, the coframe and corresponding spin connection are the principal geometric objects and, consequently, the appropriate definition of a symmetry is that of an affine symmetry. The set of invariant coframes and their corresponding spin connections that respect the full six dimensional Lie algebra of Robertson–Walker affine symmetries are displayed and discussed. We will refer to such geometries as teleparallel Robertson–Walker (TRW) geometries, where the corresponding derived metric is of Robertson–Walker form and is characterized by the parameter k=(−1,0,1). The field equations are explicitly presented for the F(T) class of teleparallel TRW spacetimes. We are primarily interested in investigating the k≠0 TRW models. After first studying the k=0 models and, in particular, writing their governing field equations in an appropriate form, we then study their late time stability with respect to perturbations in k in both the cases of a vanishing and non-vanishing effective cosmological constant term. As an illustration, we consider both quadratic F(T) theories and power-law solutions.

Probabilistic deconstruction of a theory of gravity, part I: Flat space

We define and analyze a stochastic process in anti-de Sitter Jackiw-Teitelboim gravity, induced by the quantum dynamics of the boundary and whose random variable takes values in AdS_2AdS2. With the boundary in a thermal state and for appropriate parameters, we take the asymptotic limit of the quantum process at short time scales and flat space, and show associated classical joint distributions have the Markov property. We find that Einstein’s equations of the theory, sans the cosmological constant term, arise in the semi-classical limit of the quantum evolution of probability under the asymptotic process. In particular, in flat Jackiw-Teitelboim gravity, the area of compactified space solved for by Einstein’s equations can be identified as a probability density evolving under the Markovian process.

Analysis of some flavonoids for inhibitory mechanism against cancer target phosphatidylinositol 3-kinase (PI3K) using computational tool.

Cancer has been one of the leading causes of mortality worldwide over the past few years. Some progress has been made in the development of more effective cancer therapeutics, resulting in improved survival rates. However, the desired outcome in the form of successful treatment is yet to be achieved. There is high demand for the development of innovative, inexpensive, and effective anticancer treatments using natural resources. Natural compounds have been increasingly discovered and used for cancer therapy owing to their high molecular diversity, novel biofunctionality, and minimal side effects. These compounds can be utilized as chemopreventive agents because they can efficiently inhibit cell growth, control cell cycle progression, and block several tumor-promoting signaling pathways. PI3K is an important upstream protein of the PI3K-Akt-mTOR pathway and a well-established cancer therapeutic target. This study aimed to explore the small molecules, natural flavonoids, viz. quercetin, luteolin, kaempferol, genistein, wogonin, daidzein, and flavopiridol for PI3Kγ kinase activity inhibition. In this study, the binding pose, interacting residues, molecular interactions, binding energies, and dissociation constants were investigated. Our results showed that these flavonoids bound well with PI3Kγ with adequate binding strength scores and binding energy ranging from (-8.19 to -8.97Kcal/mol). Among the explored ligands, flavopiridol showed the highest binding energy of -8.97Kcal/mol, dock score (-44.40), and dissociation constant term, of 6.58 against PI3Kγ. Based on the above results, the stability of the most promising ligand, flavopiridol, against PI3Kγ was evaluated by molecular dynamics simulations for 200ns, confirming the stable flavopiridol and PI3Kγ complex. Our study suggests that among the selected flavonoids specifically flavopiridol may act as potential inhibitors of PI3Kγ and could be a therapeutic alternative to inhibit the PI3Kγ pathway, providing new insights into rational drug discovery research for cancer therapy.

Interacting New Tsallis holographic dark energy

We constructed the evolution of a flat FRW universe filled with New Tsallis holographic dark energy (NTHDE) and matter (dust) that interact with each other via a wellknown source term. Assuming the hubble horizon IR cutoff length, extracted the governing equation for the NTHDE density parameter’s evolution and solved it numerically to find the evolution of other relevant cosmological parameters, e.g., equation of state and deceleration parameters. We then repeated same findings when the radiation component was included. According to our findings, the cosmos has a normal thermal history, with radiation, dark matter (DM) and dark energy (DE) eras occurring one after the other until dark energy eventually takes over entirely in the far future. We also found that according to the values of the parameters (δ, b12, b22), the NTHDE equation of state parameter can be either quintessence like or phantom like or very close to cosmological constant during the cosmic evolution. This fascinating feature of the scenario is achieved without the use of an explicit cosmological constant term, and it arises purely from modified cosmology through an interacting NTHDE with varying δ. Finally, the hubble parameter’s evolution is examined and contrasted with the most recent hubble parameter results.

Nonzero spatial curvature in symmetric teleparallel cosmology

We consider the symmetric teleparallel fQ-gravity in Friedmann–Lemaître–Robertson–Walker cosmology with nonzero spatial curvature. For a nonlinear fQ model there exist always the limit of General Relativity with or without the cosmological constant term. The de Sitter solution is always provided by the theory and for the specific models fAQ≃Qαα−1,fBQ≃Q+f1Qαα−1 and fCQ≃Q+f1QlnQ it was found to be the unique attractor. Consequently small deviations from STGR can solve the flatness problem and lead to a de Sitter expansion without introduce a cosmological constant term. This result is different from that given by the power-law theories for the other two scalar of the trinity of General Relativity. What makes the nonlinear symmetric teleparallel theory to stand out are the new degree of freedom provided by the connection defined in the non-coincidence frame which describes the nonzero spatial curvature.

Quantum entanglement dynamics of spacetime and matter

It was known long ago that quantum theory and general relativity are in sharp conflict in their foundations. Their fundamental inconsistencies render a consistent theory of quantum gravity the most challenging problem in physics. Here we propose an information-complete quantum field theory (ICQFT), which describes elementary fermions, their gauge fields, and gravity (together, called the trinary fields) as an elementary trinity without any conceptual inconsistency of existing theories. The ICQFT unifies matter and spacetime (gravity) as information via spacetime-matter entanglement, which encodes complete physical predictions of the theory and leads to a compelling solution to the problem of time. We consider two particular forms of spacetime-matter entangled states and their physical consequences. One of them results in a universal relation between entanglement entropy and geometry (area and volume), allowing us to determine the cosmological constant term in the classical Einstein equation. Based on a quantum-information definition of dark energy, our Universe is not strictly holographic. We predict the interior quantum state of a Schwarzschild black hole to be maximally information-complete. As a concrete quantum formulation of gravity coupled with matter, the ICQFT is quantum entanglement dynamics for spacetime and matter and eliminates the conceptual obstacles of existing quantum gravity theory.

A Galerkin approach for analysing coupling effects in the piezoelectric semiconducting beams

The piezoelectric semiconductor combines the characteristics of both piezoelectric and semiconducting materials, making it highly promising for a variety of engineering applications. The present work adopts a Galerkin approach to derive a general weak form of the coupled governing equations for the analysis of piezoelectric semiconductors. The coupling effect between the strain, the electric field, and the gradients of the concentrations of holes and electrons has been considered. Piezoelectric semiconductors are often deployed in the shape of rods and beams and therefore commonly experience axial and transverse load. Thus, the Euler–Bernoulli beam theory is employed to formulate a numerical approach to analyse the coupling behaviour of such piezoelectric semiconductor beams. In order to satisfy the C1 continuity requirement of Euler–Bernoulli beam theory without introducing additional degrees of freedom, a discretisation with B-Splines is used. Non-mechanical variables, including electrical potential, holes and electrons concentrations, are decomposed into constant, linear and quadratic terms through series expansion along the thickness, which ensures compatibility with beam formulation. To validate the proposed method, an N-type piezoelectric semiconducting beam under a sinusoidal distributed load, for which an analytical solution is available, is initially examined. Subsequently, complex examples including a cantilever beam with generalised loading conditions and a beam with PN-junction are analysed to demonstrate the capabilities of the proposed method in handling more challenging scenarios.

Isotropic Durgapal IV fluid sphere in bigravity

We analyze an isotropic uncharged fluid sphere model within bigravity considering the Durgapal IV metric (M.C. Durgapal, J. Phys. A: Math. Gen. 15, 2637 (1982)). In this work, we investigate the effects of the scale parameter k on the local matter distribution. Here, we have chosen the compact star candidate SMC X-1 with observed values of mass = (1.29 ± 0.05) M⊙ and radius [Formula: see text] km, respectively, to analyze our results analytically as well as graphically. For smaller values of k, we get the stiff (or hard) equation of state (EoS). Here, we solve the modified Einstein field equations in the presence of the background metric γμν. Due to this constant curvature background, the density and pressure terms are modified by adding an extra term, which affects the EoS. For r ≪ k, the background de Sitter space–time reduces into Minkowski form, and the coupling vanishes. We discuss certain physical quantities of our obtained solution, such as density, isotropic pressure, sound speed, pressure-density gradients, compactness, and surface redshift, to claim the physical viability of our model. It is found that our model clearly satisfies all the energy conditions, the causality condition, and the dynamical equilibrium via a modified Tolman–Oppenheimer–Volkov equation. Finally, we can conclude that our proposed model is physically realistic and well behaved.

Spectral Theory of the Nazarov-Sklyanin Lax Operator

In their study of Jack polynomials, Nazarov-Sklyanin introduced a remarkable new graded linear operator ${\mathcal L} \colon F[w] \rightarrow F[w]$ where $F$ is the ring of symmetric functions and $w$ is a variable. In this paper, we (1) establish a cyclic decomposition $F[w] \cong \bigoplus_{\lambda} Z(j_{\lambda}, {\mathcal L})$ into finite-dimensional ${\mathcal L}$-cyclic subspaces in which Jack polynomials $j_{\lambda}$ may be taken as cyclic vectors and (2) prove that the restriction of ${\mathcal L}$ to each $Z(j_{\lambda}, {\mathcal L})$ has simple spectrum given by the anisotropic contents $[s]$ of the addable corners $s$ of the Young diagram of $\lambda$. Our proofs of (1) and (2) rely on the commutativity and spectral theorem for the integrable hierarchy associated to ${\mathcal L}$, both established by Nazarov-Sklyanin. Finally, we conjecture that the ${\mathcal L}$-eigenfunctions $\psi_{\lambda}^s {\in F[w]}$ {with eigenvalue $[s]$ and constant term} $\psi_{\lambda}^s|_{w=0} = j_{\lambda}$ are polynomials in the rescaled power sum basis $V_{\mu} w^l$ of $F[w]$ with integer coefficients.

Modeling two-phase flow behaviour in a shale gas reservoir with complex fracture networks and flow dynamics

In this work, a robust and pragmatic method has been developed, validated, and applied to describe two-phase flow behaviour of a multifractured horizontal well (MFHW) in a shale gas formation. As for a fracture subsystem, its permeability modulus, non-Darcy flow coefficient, and slippage factor have been defined and embedded into the governing equation, while an iterative method is applied to update the gas/water saturation in each fracture segment within discrete fracture networks. Different from the traditional treatment that a water-source/sink in the matrix is simplified by assuming it as a constant term, a skin factor on a fracture face is defined and introduced to represent the change in relative permeability in the matrix domain at each timestep, while the adsorption/desorption term is incorporated into the diffusivity equation to accurately calculate the shale gas production by taking the adsorbed gas in nanoscale porous media into account. Then, the theoretical model can be applied to accurately capture the two-phase flow behaviour in different subdomains. The accuracy of this newly developed model has been confirmed by the numerical simulation and then it is extended to field applications with excellent performance. The stress-sensitivity, non-Darcy flow, and slippage effect in a hydraulic fracture (HF) are found to be obvious during the production, while the initial gas saturation in a matrix and HFs imposes an evident influence on the production profile. As for an HF with a high gas saturation, the dewatering stage is missing and water from the matrix can be neglected during a short production time. For the matrix subsystem, a high-water saturation in the matrix near an HF can affect gas production during the entire stage since gas relative permeability in the HF remains low. In addition, the adsorption/desorption in the matrix subsystem can increase gas production but decrease water production. Compared to the observed gas/water production rates for field applications, the solutions obtained from the method in this work are found to be well matched, confirming its reliability and robustness.

Valued fields with a total residue map

When [Formula: see text] is a finite field, [J. Becker, J. Denef and L. Lipshitz, Further remarks on the elementary theory of formal power series rings, in Model Theory of Algebra and Arithmetic, Proceedings Karpacz, Poland, Lecture Notes in Mathematics, Vol. 834 (Springer, Berlin, 1979)] observed that the total residue map [Formula: see text], which picks out the constant term of the Laurent series, is definable in the language of rings with a parameter for [Formula: see text]. Driven by this observation, we study the theory [Formula: see text] of valued fields equipped with a linear form [Formula: see text] which restricts to the residue map on the valuation ring. We prove that [Formula: see text] does not admit a model companion. In addition, we show that [Formula: see text] is undecidable whenever [Formula: see text] is an infinite field. As a consequence, we get that [Formula: see text] is undecidable, where [Formula: see text] maps [Formula: see text] to its complex residue at [Formula: see text].

Differential expression of PLAC1 and Netrin-1 in liver metastasis of colorectal cancer and its predictive value

ObjectiveTo explore the differential expression of placental specific gene 1 (PLAC1) and neurite guidance factor 1 (netrin-1) in colorectal cancer (CRC) liver metastasis and its predictive value.MethodsParaffin specimens of primary CRC were selected, including 60 simple colorectal cancer specimens and 47 liver metastasis specimens. At the same time, 40 cases of normal colorectal mucosa were taken as the control group. The expression of PLAC1 and Netrin-1 in tissue was detected by immunohistochemistry (IHC). The correlation between PLAC1 and Netrin-1 expression and clinicopathological characteristics of patients with CRC liver metastases was analyzed. Logistic analysis was adopted to analyze the influencing factors of liver metastasis in CRC. A prediction model was established and ROC curve was used to detect the discrimination of the prediction model. The clinical value of PLAC1 and netrin-1 in predicting liver metastasis of CRC was analyzed using ROC curve. The relationship between the expression of PLAC1 and netrin-1 and the prognosis of CRC patients with liver metastasis was analyzed using Kaplan Meier survival curve.ResultsThe positive staining of PLAC1 and netrin-1 was mainly located in the cytoplasm by IHC detection. Positive expression of PLAC1 and netrin-1 in CRC tissues was markedly higher than that in normal colorectal mucosal epithelium (P < 0.05). Positive expression of PLAC1 in metastatic group was higher than that in non-metastatic group without significant difference (P > 0.05). The metastasis group had much higher positive expression of netrin-1 than the non-metastasis group (P < 0.05). The content of PLAC1 in the tissues of CRC with liver metastasis had a close relationship with differentiation degree and lymph node metastasis (P < 0.05). The expression of Netrin-1 in the tissues of CRC with liver metastasis was associated with Dukes stage, differentiation degree and lymph node metastasis (P < 0.05). Logistic regression analysis showed that Dukes stage, differentiation, lymph node metastasis, CEA, Alb and D-dimer were the independent risk factors for liver metastasis of CRC (P < 0.05). The model was constructed according to the regression coefficients and constant terms, and the discrimination of the prediction model was evaluated using ROC curve, with the AUC of 0.903 (95% CI 0.831 ~ 0.975), the sensitivity of 93.80%, the specificity of 80.00%, and the Jordan index of 0.738. The AUC of PLAC1 and netrin-1 alone and combined detection to predict liver metastasis of CRC were 0.805, 0.793 and 0.921, respectively. The survival time of patients with positive PLAC1 and netrin-1 expression were sharply shorter than that of the patients with negative expression (P < 0.05).ConclusionsThe expression of PLAC1 and netrin-1 was strongly increased in CRC with liver metastasis, which had a certain clinical value in predicting liver metastasis of CRC. Dukes stage, differentiation degree, lymph node metastasis, CEA, Alb and D-dimer were independent risk factors for liver metastasis of CRC, and the model based on these indicators had good discrimination for effectively evaluating the risk of liver metastasis in CRC.

GHOSTS AND CONGRUENCES FOR -APPROXIMATIONS OF HYPERGEOMETRIC PERIODS

AbstractWe prove general Dwork-type congruences for constant terms attached to tuples of Laurent polynomials. We apply this result to establishing arithmetic and p-adic analytic properties of functions originating from polynomial solutions modulo $p^s$ of hypergeometric and Knizhnik–Zamolodchikov (KZ) equations, solutions which come as coefficients of master polynomials and whose coefficients are integers. As an application, we show that the simplest example of a p-adic KZ connection has an invariant line subbundle while its complex analog has no nontrivial subbundles due to the irreducibility of its monodromy representation.

Dynamical System Scaling application to the design of a test facility for boron dispersion evaluation in iPWR-SMRs

Pressurizers are relevant components of Pressurized Water Reactors (PWRs) aiming at pressure control. In contrast to traditional PWRs, Small Modular Reactors (SMRs) may have surge orifices in order to promote boron mixing with primary coolant, instead of spray devices and surge lines needed to minimize reactivity transients. This paper aims to demonstrate that the parameters of a test facility under development, obtained independently by Fractional Scaling Analysis and Causative Process Related Method, when applied to average boron concentration equations, represent faithfully boron dispersion in the pressurizer of an integral Pressurized Water Reactor/Small Modular Reactor (iPWR-SMR). The demonstration is accomplished by applying a recent scaling technique known as Dynamical System Scaling (DSS), whose fractional rates are time-varying, instead of being defined by initial (constant) terms. The design of such a test facility considers one-fourth symmetry and reduced time and volume scales so as to provide cost savings. Reliable results are obtained when an important DSS parameter – the temporal displacement rate – is compared for both systems, indicating a complete similarity for them.

Pulse oximetry values from 33,080 participants in the Apple Heart & Movement Study

Wearable devices that include pulse oximetry (SpO2) sensing afford the opportunity to capture oxygen saturation measurements from large cohorts under naturalistic conditions. We report here a cross-sectional analysis of 72 million SpO2 values collected from 33,080 individual participants in the Apple Heart and Movement Study, stratified by age, sex, body mass index (BMI), home altitude, and other demographic variables. Measurements aggregated by hour of day into 24-h SpO2 profiles exhibit similar circadian patterns for all demographic groups, being approximately sinusoidal with nadir near midnight local time, zenith near noon local time, and mean 0.8% lower saturation during overnight hours. Using SpO2 measurements averaged for each subject into mean nocturnal and daytime SpO2 values, we employ multivariate ordinary least squares regression to quantify population-level trends according to demographic factors. For the full cohort, regression coefficients obtained from models fit to daytime SpO2 are in close quantitative agreement with the corresponding values from published reference models for awake arterial oxygen saturation measured under controlled laboratory conditions. Regression models stratified by sex reveal significantly different age- and BMI-dependent SpO2 trends for females compared with males, although constant terms and regression coefficients for altitude do not differ between sexes. Incorporating categorical variables encoding self-reported race/ethnicity into the full-cohort regression models identifies small but statistically significant differences in daytime SpO2 (largest coefficient corresponding to 0.13% lower SpO2, for Hispanic study participants compared to White participants), but no significant differences between groups for nocturnal SpO2. Additional stratified analysis comparing regression models fit independently to subjects in each race/ethnicity group is suggestive of small differences in age- and sex-dependent trends, but indicates no significant difference in constant terms between any race/ethnicity groups for either daytime or nocturnal SpO2. The large diverse study population and study design employing automated background SpO2 measurements spanning the full 24-h circadian cycle enables the establishment of healthy population reference trends outside of clinical settings.

Dark energy–matter equivalence by the evolution of cosmic equation of state

We consider a model-independent approach to constrain the equivalence redshift, zeq, at which dark energy and the total matter (cold dark matter and baryonic) equate their magnitudes. To this aim, in the context of a homogeneous and isotropic universe, we first consider a generic model where the dark energy contribution is provided by an unknown function of barotropic fluids. Afterwards, we compute the deceleration and jerk parameters, evaluating at our epoch, namely z=0, and at z=zeq. Thus, by Taylor expanding around current time the Hubble rate, luminosity and angular distances, we substitute the theoretical expressions obtained from the aforementioned generic dark energy model, defining a correspondence between quantities evaluated at z=0 and z=zeq. In so doing, we directly fit these quantities by means of current data sets, involving the most recent Pantheon type Ia supernovae, baryonic acoustic oscillation and Hubble rate points. We consider two hierarchies in our fitting procedures and compare our findings in the spatially-flat universe first and including spatial curvature, later. We assess constraints on the overall equation of state of the universe and its first derivative. We compare our results with those predicted by the standard ΛCDM paradigm. Specifically, our findings are in agreement at the 2σ confidence level, assuming a constant dark energy term. However, our analysis does not rule out the possibility of a slight evolution of dark energy, indicating a small deviation from the scenario of a pure cosmological constant. In particular, the possible departures appear consistent with a phenomenological ωCDM model, rather than more complicated dark energy parameterizations.