Coefficient Functions Research Articles

Infinite quantum signal processing

Quantum signal processing (QSP) represents a real scalar polynomial of degree d using a product of unitary matrices of size 2×2, parameterized by (d+1) real numbers called the phase factors. This innovative representation of polynomials has a wide range of applications in quantum computation. When the polynomial of interest is obtained by truncating an infinite polynomial series, a natural question is whether the phase factors have a well defined limit as the degree d→∞. While the phase factors are generally not unique, we find that there exists a consistent choice of parameterization so that the limit is well defined in the ℓ1 space. This generalization of QSP, called the infinite quantum signal processing, can be used to represent a large class of non-polynomial functions. Our analysis reveals a surprising connection between the regularity of the target function and the decay properties of the phase factors. Our analysis also inspires a very simple and efficient algorithm to approximately compute the phase factors in the ℓ1 space. The algorithm uses only double precision arithmetic operations, and provably converges when the ℓ1 norm of the Chebyshev coefficients of the target function is upper bounded by a constant that is independent of d. This is also the first numerically stable algorithm for finding phase factors with provable performance guarantees in the limit d→∞.

Method for predicting the risk of type 2 diabetes mellitus development in persons with visceral obesity and prediabetes

Aim. To create a mathematical model, which will predict the development of type 2 diabetes mellitus (DM 2) in individuals with visceral obesity and/or prediabetes. Materials and methods. Clinical and laboratory data of 330 patients were analyzed. Multivariate regression and cosinor analysis determined the most sensitive parameters influencing the development of DM 2. With the help of discriminant linear analysis, a mathematical model for predicting DM 2 was built, with confirmation of its quality by ROC analysis. Results. In the studied groups (DM 2), prediabetes and without carbohydrate metabolism disorders (n=110), statistically significant correlations were obtained: between basal body temperature (BBT) and daily energy value – DEV (r=0.5; p0.0001), circadian rhythm amplitude glycemia and waist circumference (r=-0.7; p=0.004), age and BBT (r=0.5; p0.001). In groups without carbohydrate metabolism disorders and prediabetes, multiple regression analysis identified significant factors influencing the development of DM 2: daily amplitude of BBT, daily amplitude of glycemia and bedtime (p=0.001), DEV and meal time (p=0.0001). Cosinor analysis of the daily model of glycemia and BBT established an amplitude-phase shift (p=0.028; p=0.012). Linear discriminant analysis yielded a predictive model: D=-16.845 + age х 0.044 + gender х 0.026 + amplitude of circadian rhythm of BBT х 1.424 + amplitude of circadian rhythm of glycemia х 11.155 + bedtime х 0.054 + DEV х 0.0001 + waist circumference х 0.022 + glycated hemoglobin х 1.19, where -16.845 – constant, 0.044, 0.026, 1.424, 11.155, 0.054, 0.0001, 0.022, 1.19 – coefficients of the linear discriminant function. At D0 no development of DM 2 is predicted, at D0 the development of DM 2 is in the near future. Sensitivity ratio – 92.5%, specificity – 79.1% (ROC analysis). Conclusion. The presented predictive model has a high (92.5%) sensitivity due to the combination of 2 mathematical analyses. Most of the applied parameters are modifiable, which makes it possible to apply this model at the preventive stage.

First principle calculations of structural, electronic, and optical properties of XSnO3 (X: Ca, Mg, Sr) perovskite oxides

The perovskite oxides XSnO3have garnered significant attention due to their potential applications in various fields, including electronics, photonics, and renewable energy technologies. This study presents a comprehensive theoretical investigation of the structural, electronic, and optical properties of XSnO3(X: Ca, Mg, Sr) compounds with density functional theory based on the full potential linearized augmented plane wave method. Our analysis begins with thoroughly examining the structural stability and lattice parameters of XSnO3compounds, revealing their robust perovskite crystal structures. These compounds' lattice constants, total energy, bulk modulus, and cohesive energy were determined. Subsequently, we delve into the electronic properties of XSnO3, elucidating their electronic band structures, density of states, and charge densities. The studied compounds are indirect bandgap semiconductors having band gaps in the visible range. Furthermore, our investigation extends to the optical properties of XSnO3, encompassing absorption spectra, refractive indices, energy loss function, reflectivity, extinction coefficient, and dielectric functions across a wide range of wavelengths. Overall, the excellent optical properties of these compounds make them suitable for optoelectronic applications.

Kinetic modeling and iso-conversional analysis of glass-ceramics of selenium doped with carbon nanomaterials

Abstract This study addresses a gap in understanding the impact of carbon nanomaterial doping on the crystallization kinetics of selenium glass, particularly when utilizing model-free iso-conversional methods. Previous research has explored the properties of elemental selenium; however, the role of dopants like multiwall carbon nanotubes (MWCNTs) and graphene in altering glass-to-crystal phase transitions at non-isothermal conditions has not been thoroughly analyzed. In the context of selenium glass crystallization, multiwall carbon nanotubes (MWCNTs), and graphene may alter the crystal growth kinetics significantly during glass/crystal phase transformation. Keeping in mind these facts, the present endeavor focuses on analyzing the doping effect of MWCNT and Graphene on the non-isothermal kinetic reaction mechanism of Selenium measured with differential scanning calorimetry (DSC) at different heating rates. The model-free relations such as Kissinger-Akahira-Sunose (KAS), Flynn-Wall-Ozawa (FWO), Tang, and Straink methods were applied using iso-conversional approach for determining the activation energy of amorphous to crystalline transformation as well as the Avrami index. Iso-conversional study yields adequate activation energy as a function of the conversion coefficient. We have observed the decreasing behavior of E c (α) along with the extent of crystallization of four iso-conversional methods. The kinetic triplet parameters (i.e., activation energy E α , rate constant K α , and order parameter n α ) have been calculated using the VHR method derived from the Johnson–Mehl–Avrami (JMA) rate equation. The value of ‘n’ is reduced with the rise in the value of the extent of conversion α which indicates the reduction in the growth rate of crystallization because of its saturation. This study provides novel insights into the thermal stability and kinetic mechanisms within doped selenium glass-ceramics, expanding the potential applications of chalcogenide glasses in phase-change memory and other fields.

Computational investigation of the phase stability, electronic, optical, phonon spectrum, and elastic behavior of layered perovskites Ca2XO4 (X = Zr, Hf) for optoelectronic applications.

A significant class of solid-state materials, Ruddlesden-Popper (RP) perovskites are well-known for their rich chemical compositions that make them excellent electrocatalysts. Therefore, in this work, we conduct thorough analysis of RP perovskites, specifically Ca2XO4 (X = Zr, Hf). We delve into the structural, electronic, optical, and mechanical properties presenting their insights for the first time. Our investigations reveal that Ca2XO4 (X = Zr, Hf) exhibits stable tetragonal phase structures, with energies (E0) of - 10,522.93eV and - 33,520.14eV, respectively. The calculated in terms of the ground state determines to possess distinct values such as - 4.79 eV/atom for LiScTe2 and - 3.95 eV/atom for Ca2ZrO4 and Ca2HfO4. Notably, the semiconductor characteristics of Ca2ZrO4 and Ca2HfO4 are underscored by their respective wide direct band gap of 5.02eV and 5.30eV. Then, we discuss the optical parameters encompassing the dielectric function, absorption coefficient, optical conductivity, refractive index, and energy loss function. is described as ductile, whereas is defined as brittle. Our outcomes underscore remarkable ability of these materials to absorb ultraviolet radiation from the electromagnetic spectrum, positioning them as promising candidates for optoelectronic applications. We made these calculations by employing first-principles approach rooted in density functional theory (DFT) and utilizing the Perdew-Burke-Ernzerhof-Generalized Gradient Approximation (PBE-GGA) and Tran and Blaha-modified Becke-Johnson (TB-mBJ) functional within the WEIN2K framework. In this framework, Kramers-Kronig relations are used to obtain crucial optical parameters. Mechanical behavior is assessed by employing Voigt-Reuss-Hill approximation (VRH) fulfilling the Born's criteria which emphasizes that these materials are equally appropriate for a broad range of mechanical applications.

Riemann–Hilbert method for a higher-order matrix-type nonlinear Schrödinger equation with zero boundary conditions

The objective of this research is to investigate the initial value problem of a higher-order matrix-type nonlinear Schrödinger (NLS) equation with discrete spectrum as simple and double poles (simple and second-order zeros [Formula: see text] and second- and third-order zeros under [Formula: see text] under zero boundary conditions (ZBCs). Specifically, we not only consider the analyticity, symmetries and asymptotics of the Jost function, scattering and reflection coefficients in the process of direct scattering, but also residue conditions, norming constants, RH problem and the reconstruction formula in the process of inverse scattering. There exist some differences between it and the RH method in the study of vector and scalar equations, like the order of each pole of [Formula: see text] being less than or equal to the order of the zeros of [Formula: see text] (assuming [Formula: see text] is a second- or third-order zero of [Formula: see text] under [Formula: see text]), etc.

Viscosity of aqueous ammonium nitrate–organic particles: equilibrium partitioning may be a reasonable assumption for most tropospheric conditions

Abstract. The viscosity of aerosol particles determines the critical mixing time of gas–particle partitioning of volatile compounds in the atmosphere. The partitioning of the semi-volatile ammonium nitrate (NH4NO3) might alter the viscosity of highly viscous secondary organic aerosol particles during their lifetimes. In contrast to the viscosity of organic particles, data on the viscosity of internally mixed inorganic–organic aerosol particles are scarce. We determined the viscosity of an aqueous ternary inorganic–organic system consisting of NH4NO3 and a proxy compound for a highly viscous organic, sucrose. Three techniques were applied to cover the atmospherically relevant humidity range: viscometry, fluorescence recovery after photobleaching, and the poke-flow technique. We show that the viscosity of NH4NO3–sucrose–H2O with an organic to inorganic dry mass ratio of 4:1 is 4 orders of magnitude lower than the viscosity of the aqueous sucrose under low-humidity conditions (30 % relative humidity (RH), 293 K). By comparing viscosity predictions of mixing rules with those of the Aerosol Inorganic–Organic Mixtures Functional groups Activity Coefficients Viscosity (AIOMFAC-VISC) model, we found that a mixing rule based on mole fractions performs similarly when data from corresponding binary aqueous subsystems are available. Applying this mixing rule, we estimated the characteristic internal mixing time of aerosol particles, indicating significantly faster mixing for inorganic–organic mixtures compared to electrolyte-free particles, especially at lower RH. Hence, the assumption in global atmospheric chemistry models of quasi-instantaneous equilibrium gas–particle partitioning is reasonable for internally mixed single-phase particles containing dissolved electrolytes (but not necessarily for phase-separated particles), for most conditions in the planetary boundary layer. Further data are needed to see whether this assumption holds for the entire troposphere at midlatitudes and at RH > 35 %.

Coefficient Shape Alignment in Multiple Functional Linear Regression

In multivariate functional data analysis, different functional covariates often exhibit homogeneity. The covariates with pronounced homogeneity can be analyzed jointly within the same group, offering a parsimonious approach to modeling multivariate functional data. In this article, a novel grouped multiple functional regression model with a new regularization approach termed “coefficient shape alignment” is developed to tackle functional covariates homogeneity. The modeling procedure includes two steps: first aggregate covariates into disjoint groups using the new regularization approach; then the grouped multiple functional regression model is established based on the detected grouping structure. In this grouped model, the coefficient functions of covariates in the same group share the same shape, invariant to scaling. The new regularization approach works by penalizing coefficient shape discrepancy. We establish the conditions under which the true grouping structure can be accurately identified and derive the asymptotic properties of the model estimates. Extensive simulation studies are conducted to assess the finite-sample performance of the proposed methods. The practical applicability of the model is demonstrated through real data analysis in the context of sugar quality evaluation. This work offers a novel framework for analyzing the homogeneity of functional covariates and constructing parsimonious models for multivariate functional data. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.

Enhanced Linear and Nonlinear Optical Characteristics of Cerium (Ce) Doped ZnO Film

ZnO and Ce-doped ZnO films with different doping concentrations (2, 4, and 6 wt%) were produced via SILAR technique, and the influence of the Ce amount on the structural, morphological, linear and nonlinear optical properties were examined in detail. Structural analyses conducted using X-ray diffraction (XRD) and Raman spectroscopy revealed the formation of hexagonal wurtzite pristine ZnO and Ce-doped ZnO nanostructures. The CeO2 phase was observed for only Ce6:ZnO samples by the XRD and Raman analyses. The morphological analyses were performed with a Scanning Electron Microscope (SEM), and it was found that the grain size decreased with Ce doping. The band gap energies decreased from 3.18eV to 2.67eV with increasing dopant (Ce) amount and increasing Urbach energy (EU). The dislocation density values (XRD) were calculated as 1.68x , 2.22x , 4.52x , and 8.65x nm-2 for ZnO, Ce2:ZnO, Ce4:ZnO, and Ce6:ZnO, respectively, which is consistent with the increasing Urbach energy. The optical characteristics such as excitation and absorption coefficient, refractive index, dielectric constant, optical conductivity, the volume (VELF) and surface (SELF) energy loss functions were estimated. The third- order nonlinear susceptibility, and the nonlinear refractive index were calculated using Miller's generalized rule with linear refractive index and Wemple-DiDomenico (W-D) model. The χ(3) and n2 values increased with Ce influence compared to undoped ZnO film. Various methods have been used to obtain Ce:ZnO films, but the low-cost SILAR method has not been reported before, and the films produced via this method showed suitable behaviours for optoelectronic devices and nonlinear applications.

Sharp Second-Order Hankel Determinants Bounds for Alpha-Convex Functions Connected with Modified Sigmoid Functions

The study of the Hankel determinant generated by the Maclaurin series of holomorphic functions belonging to particular classes of normalized univalent functions is one of the most significant problems in geometric function theory. Our goal in this study is first to define a family of alpha-convex functions associated with modified sigmoid functions and then to investigate sharp bounds of initial coefficients, Fekete-Szegö inequality, and second-order Hankel determinants. Moreover, we also examine the logarithmic and inverse coefficients of functions within a defined family regarding recent issues. All of the estimations that were found are sharp.

A study of blind denoising algorithms for two-scale real images based on partial differential equations

In order to better preserve the details and texture information in the image, a dual scale real image blind denoising algorithm based on partial differential equations is studied. Input real image information, perform small-scale denoising based on differential curvature partial differential equations, and combine with a new diffusion coefficient function to distinguish the edges, flat areas, and noise of the image, allowing the algorithm to retain more subtle information such as weak edges and textures while removing noise. For the large-scale information in the input real image, a multi-stage partial differential equation is used for denoising processing. Based on the mixed denoising method of 8-neighborhood and implicit curvature, a weight function is constructed to control the proportion of the two types of equations in image denoising, effectively achieving the goal of large-scale image denoising. The experimental results show that in the MATLAB coding platform, this algorithm can eliminate different types of noise, preserve more edge and detail information of the image, and improve the registration and recognition accuracy in the image application process.

A Fixed‐Time Composite Control With Variable Exponent Coefficients for Stewart Parallel Mechanism Tracking in Task Space

ABSTRACTTo improve tracking control performance in the task space of the Stewart parallel mechanism (SPM) with uncertainties of modeling errors and external disturbances in our developed rust removal sandblasting robot for the surface roughness processing of a bridge's steel box girder, a fixed‐time composite control with variable exponent coefficients (VEC‐FxTCC) approach for multi‐input multi‐output (MIMO) nonlinear robotic systems is developed. Firstly, by devising only one regulation term with a variable exponent coefficient (VEC) function in the system's Lyapunov differential inclusion, a novel VEC fixed‐time stability theorem for the MIMO nonlinear dynamic system is proposed and proven. Secondly, based on the proposed theorem, VEC‐FxTCC is formed by designing and combining a VEC fixed‐time disturbance observer (VEC‐FxTDOB) and a VEC fixed‐time super‐twisting control (VEC‐FxTSTC), in order to achieve fast, steady, and uniformly bounded‐time convergence for SPM's end‐effector tracking, while avoiding singularity. Finally, the effectiveness of the proposed VEC‐FxTCC approach is validated through the simulations and the rust removal sandblasting robot prototype experiments.

Key Node Identification Method Based on Multilayer Neighbor Node Gravity and Information Entropy

In the field of complex network analysis, accurately identifying key nodes is crucial for understanding and controlling information propagation. Although several local centrality methods have been proposed, their accuracy may be compromised if interactions between nodes and their neighbors are not fully considered. To address this issue, this paper proposes a key node identification method based on multilayer neighbor node gravity and information entropy (MNNGE). The method works as follows: First, the relative gravity of the nodes is calculated based on their weights. Second, the direct gravity of the nodes is calculated by considering the attributes of neighboring nodes, thus capturing interactions within local triangular structures. Finally, the centrality of the nodes is obtained by aggregating the relative and direct gravity of multilayer neighbor nodes using information entropy. To validate the effectiveness of the MNNGE method, we conducted experiments on various real-world network datasets, using evaluation metrics such as the susceptible-infected-recovered (SIR) model, Kendall τ correlation coefficient, Jaccard similarity coefficient, monotonicity, and complementary cumulative distribution function. Our results demonstrate that MNNGE can identify key nodes more accurately than other methods, without requiring parameter settings, and is suitable for large-scale complex networks.

Exploring photocatalytic and photovoltaic applications of chalcogenide Perovskites, ABS3 (A = Li, Na, K, Rb, Cs; B = Si, Ge, Sn): A First-Principles investigation using the HSE-06 hybrid functional

Unlike traditional semiconductors, chalcogenide perovskites offer a unique combination, merging the stability and safety of oxides with the tunability of halide semiconductors, making them particularly promising for photocatalytic and photovoltaic applications. This paper theoretically investigates the optoelectronic properties of the triclinic ABS3 (A = Li, Na, K, Rb, Cs; B = Si, Ge, Sn) perovskites using density functional theory with the HSE06 hybrid functional. The feasibility of synthesizing ABS3 materials was revealed using formation energy calculations. Band structure and density of state calculations confirm that all compounds under investigation are semiconductors exhibiting indirect bandgaps. These bandgaps increase with the ionic radius of the A-site cation, following the trend Li < Na < K < Rb < Cs. Additionally, the order of bandgap energies for the B-site elements is observed as Si > Sn > Ge. This trend emphasizes the significant influence of cation size on the electronic properties of perovskite materials. The investigated perovskites exhibit bandgaps between 1.67 and 3.55 eV, with a narrow difference (0.03–0.49 eV) between their indirect and direct gaps. We additionally compute various optical parameters (dielectric function, refractive index, extinction coefficient, optical conductivity, absorption coefficient, reflectivity, and energy loss function) across the 0–50 eV energy range. The valence and conduction band edge potentials of ABS3 perovskites were calculated to evaluate their potential applications in water splitting, carbon dioxide reduction, and photodegradation processes. The results of this study demonstrate that several ABS3 semiconductors exhibit promising characteristics that position them as efficient photocatalysts for these photocatalytic reactions. LiGeS3 and NaGeS3, in particular, are promising for solar cell applications.

Cooperative scheduling strategy for electric vehicles with Vehicle-to-Grid technology considering renewable energy generation

The randomness and intermittency of electric vehicles (EVs) charging can lead to a peak-on-peak phenomenon in the distribution network load. As the scale of EVs continues to expand, uncoordinated charging demands exacerbate the differences between peak and off-peak loads. To address this issue, this study introduces an innovative optimization method for EVs charging. First, by analyzing the charging patterns of power batteries and driver behavior, EVs charging demand is simulated and deduced using the Monte Carlo method. Subsequently, considering the constraints of EVs and the power grid, an objective function to optimize grid load is constructed based on Vehicle-to-Grid (V2G) and time-of-use pricing strategies. Finally, an Improved Backbone Particle Swarm Optimization (IBBPSO) algorithm is designed, which is further combined with a Bayesian Optimization (BO) algorithm to dynamically adjust the allocation coefficients of the objective function and the initial parameters of the IBBPSO. This approach facilitates the attainment of the optimal EVs charging and discharging scheduling strategy. Simulation results indicate that the implemented strategy effectively reduces the peak-to-valley load disparity within the power grid, flatting the adverse effects of uncoordinated EVs charging.

Electronic and optical properties of Sb2Se3 and Sb2S3: theoretical investigations

Abstract In recent developments in solar energy research, Sb2Se3 and Sb2S3 emerge as environment friendly photovoltaic absorber materials, distinguished by their narrow bandgap and high absorption coefficient. Theoretical investigations to determine the electronic structure, effective density of states, dielectric function, and absorption coefficient of Sb2Se3 and Sb2S3 crystals have been performed using first-principle methods. The results reveal band gap values of about 0.822 and 1.757 eV (PBE method), 1.114 and 1.778 eV (HSE06 method) for Sb2Se3 and Sb2S3, respectively. The valence band and conduction band edges are primarily formed by Se 4p, S 3p, and Sb 5p hybridized orbitals. The effective density of states (DOS) exhibit magnitudes on the order of 1019 cm−3. Notably, anisotropic characteristics are observed in the real and imaginary parts of the dielectric function. Furthermore, the absorption coefficient surpasses 105 cm−1 at 1 and 1.2 eV for both Sb2Se3 and Sb2S3. The result indicates that these highly efficient absorber materials are suitable in collecting solar energy.

Scaled Sensitivity of Pavement–Mechanistic-Empirical Transfer Function Coefficients for Flexible and Rigid Pavements

The American Association of State Highway and Transportation Officials (AASHTO)Ware Pavement–Mechanistic-Empirical (ME) transfer functions need local calibration for reliable performance predictions. It is often not viable to calibrate all coefficients at the same time. Therefore, it is crucial to identify the most sensitive transfer function coefficients. Moreover, the sensitivity also indicates the impact of each coefficient on the performance prediction. Several studies have shown the sensitivity of the Pavement-ME design inputs, but limited research is available on the sensitivity of transfer function coefficients. Typically, the sensitivity is obtained using a normalized sensitivity index (NSI). This paper estimated the sensitivity of the Pavement-ME transfer function coefficients using scaled sensitivity coefficients (SSCs). NSI values are compared with the SSCs. Ten sections, each from flexible and rigid pavements, were used to calculate the NSI values. These are existing pavement sections from the Michigan Department of Transportation (MDOT) pavement management system (PMS) database, designed using the 1993 AASHTO design guide. Results show that SSCs provide a more reliable sensitivity on a range of independent variables rather than a point estimate, unlike NSI. NSI values showed variability among different sections and magnitudes of predicted performance. Calculation of SSCs is a forward problem and does not require any input data. A mathematical model (transfer function) is needed; therefore, SSCs can be calculated on any range of independent variables. It also shows the potential correlation between different coefficients and accuracy in estimation.

Investigating the physical properties of the binary compound CdTe under different pressures using FP-LMTO method

The structural, electronic and optical properties of Cadmium Telluride (CdTe) are investigated at different pressures using the full potential linear muffin-tin orbital FP-LMTO method based on density functional theory (DFT), within the local density approximation LDA and the generalized gradient approximation GGA approximations were used to calculate the exchange-correlation potential. The ground state properties of CdTe compound were determined for diverse phases, and the band structure and optical parameters were calculated at pressures ranging from 0 GPa to 50 GPa. Optical parameters, including real part, imaginary part of the dielectric function, reflectivity, refractive index, extinction coefficient and energy loss function, were calculated for over an energy range from 0 eV to 13.6058 eV. The results were compared with available experimental and theoretical data, showing good agreement with earlier reported result. These particularities reveal that CdTe as favorable material for optoelectronic applications, as it exhibits together important electronic and optical responses under different pressure.

There and Back Again: Mapping and Factorizing Cosmological Observables

Cosmological correlators encode invaluable information about the wave function of the primordial Universe. In this Letter we present a duality between correlators and wave function coefficients that is valid to all orders in the loop expansion and manifests itself as a Z4 symmetry. To demonstrate the power of the duality, we derive a correlator-to-correlator factorization formula for the parity-odd part of cosmological correlators that relates n-point observables to lower-point ones via a series of diagrammatic cuts. These relations serve as the first example of physically testable cutting rules as they involve observables defined for arbitrary physical kinematics. We further show how the duality allows us to translate the cosmological optical theorem for wave function coefficients into statements about cosmological correlators. Published by the American Physical Society 2024

Covariate-adjusted response-adaptive designs for semiparametric survivalmodels.

Covariate-adjusted responseadaptive (CARA) designs are effective in increasing the expected number of patients receiving superior treatment inan ongoing clinical trial, given a patient's covariate profile. There has recently been extensive research on CARA designs with parametric distributional assumptions on patient responses. However, the range of applications for such designs becomes limited in real clinical trials. Sverdlov etal. have pointed out that irrespective of a specific parametric form of the survival outcomes, their proposed CARA designs based on the exponential model provide valid statistical inference, provided the final analysis is performed using the appropriate accelerated failure time (AFT) model. In real survival trials, however, the planned primary analysis is rarely conducted using an AFT model. The proposed CARA designs are developed obviating any distributional assumptions about the survival responses, relying only on the proportional hazards assumption between the two treatment arms. To meet the multiple experimental objectives of a clinical trial, the proposed designs are developed based on an optimal allocation approach. The covariate-adjusted doubly adaptive biased coin design and the covariate-adjusted efficient-randomized adaptive design are used to randomize the patients to achieve the derived targets on expectation. These expected targets are functions of the Cox regression coefficients that are estimated sequentially with the arrival of every new patient into the trial. The merits of the proposed designs are assessed using extensive simulation studies of their operating characteristics and then have been implemented to re-design a real-life confirmatory clinical trial.