Two-parameter Formula Research Articles

A simple model for two-proton radioactivity* *Supported in part by the National Natural Science Foundation of China (12175100, 11975132), the Construct Program of the Key Discipline in Hunan Province, the Research Foundation of Education Bureau of Hunan Province, China (21B0402, 18A237), the Natural Science Foundation of Hunan Province, China (2018JJ2321), the Innovation Group of Nuclear and Particle Physics in USC,

In this work, considering the preformation factor of the emitted two protons in parent nucleus and the effect of the parent nucleus deformation, based on the Wentzel-Kramers-Brillouin approximation and Bohr-Sommerfeld quantization condition, we improve a simple phenomenological model proposed by Bayrak [J. Phys. G: 47, 025102 (2020)] to systematically study radioactivity half-lives. This model contains two adjustable parameters and , which are related to the depth of nuclear potential and effect of deformation. The calculated results show that this model can effectively reproduce the experimental data with a corresponding root-mean-square (RMS) standard deviation of σ = 0.683. For comparison, we include the Gamow-like model (GLM) proposed by Liu et al. [Chin. Phys. C 45, 044110 (2021)], generalized liquid drop model (GLDM) proposed by Cui et al. [Phys. Rev. C 101, 014301 (2020)], effective liquid drop model (ELDM) proposed by M. Gonalves et al. [Phys. Lett. B 774, 14 (2017)], two-potential approach with Skyrme-Hartree-Fock (TPASHF) proposed by Pan et al. [Chin. Phys. C 45, 124104 (2021)], phenomenological model with a screened electrostatic barrier (SEB) propoesed by Zou et al. [Chin. Phys. C 45, 104101 (2021)], unified fission model (UFM) proposed by Xing et al. [Chin. Phys. C 45, 124105 (2021)], Coulomb and proximity potential model for deformed nuclei (CPPMDN) proposed by Santhosh [Phys. Rev. C 104, 064613 (2021)], two-parameter empirical formula proposed by Liu et al. [Chin. Phys. C 45, 024108 (2021)], and four-parameter empirical formula proposed by Sreeja et al. [Eur. Phys. J. A 55, 33 (2019)]. In addition, we use this model to predict the radioactive half-lives of some possible potential nuclei whose radioactivity are energetically allowed or observed but not yet quantified in NUBASE2020.

Two-parameter wave reflection coefficient for an impermeable breakwater armored with Accropodes

Coastal breakwaters serve a vital role in dissipating wave energy in severe ocean environments and mitigating disastrous impacts of global climate change. As one of the key metrics in evaluating performance of breakwaters, reflection coefficients are usually formulated empirically as a function of either the Iribarren number accounting for wave breaking or the relative water depth measuring wave dispersion. In this work, we conduct a scaled physical model experiment to investigate wave reflection from a horizontally composite breakwater with a steep impermeable slope armored by Accropodes. Tests with specifically designed regular wave conditions produce 400 plus measurements over a grid of Iribarren number and relative water depth to analyze their interplay in jointly determining the reflection coefficients. Empirical formulas in terms of either one or two parameters are proposed through regression analysis for performance evaluation. Error analysis indicates the two-parameter formulas outperform the one-parameter ones with significantly improved predictive skills for the studied breakwater. The two-parameter approach allows complementary influences from the Iribarren number and the relative water depth in fitting the observations and can have broad applications in studies of fluid-structure interactions involving wave reflection, overtopping, transmission, and armor stability, especially when the coastal structures are located outside the shallow-water zone.

Reference intervals and sources of variation of pressure pain threshold for quantitative sensory testing in a Japanese population

Quantitative sensory testing (QST) is useful when analysing musculoskeletal pain disorders. A handheld algometer is most commonly used for pressure pain threshold (PPT) tests. However, reference intervals for PPTs are not elucidated. We assessed reference intervals of PPTs for QST in 158 healthy adult Japanese with no history of musculoskeletal or neurological problems. A handheld algometer was used to record PPT at five different assessment sites on the body: lumbar paravertebral muscle, musculus gluteus maximus, quadriceps, tibialis anterior muscle, and anterior talofibular ligament. Multiple regression analysis was performed to explore sources of variation of PPT according to sex, age, body mass index, UCLA Activity Level Rating, and Tegner Activity Score. Reference intervals were determined parametrically by Gaussian transformation of PPT values using the two-parameter Box-Cox formula. Results of multiple regression analysis revealed that age was significantly associated with PPT of lumbar paravertebral muscle and musculus gluteus maximus. In females, body mass index showed significant positive correlation with PPT of anterior talofibular ligament, and UCLA Activity Level Rating also showed significant positive association with tibialis anterior muscle and anterior talofibular ligament. Site-specific reference intervals of PPTs for Japanese are of practical relevance in fields of pain research using a handheld algometer.

Painlevé I and exact WKB: Stokes phenomenon for two-parameter transseries

For more than a century, the Painlevé I equation has played an important role in both physics and mathematics. Its two-parameter family of solutions was studied in many different ways, yet still leads to new surprises and discoveries. Two popular tools in these studies are the theory of isomonodromic deformation that uses the exact WKB method, and the asymptotic description of transcendents in terms of two-parameter transseries. Combining methods from both schools of thought, we follow work by Takei and collaborators to formulate complete, two-parameter connection formulae for solutions when they cross arbitrary Stokes lines in the complex plane. These formulae allow us to study Stokes phenomenon for the full two-parameter family of transseries solutions. In particular, we recover the exact expressions for the Stokes data that were recently found by Baldino, Schwick, Schiappa and Vega and compare our connection formulae to theirs. We also explain several ambiguities in relating transseries parameter choices to actual Painlevé transcendents, study the monodromy of formal solutions, and provide high-precision numerical tests of our results.

Linking Thermal Conductivity and Self-Diffusion Coefficient with a Simple Dimensionless Calorimetric Parameter for Saturated Liquids

Thermal conductivity and self-diffusion coefficients for saturated liquids were linked with a simple dimensionless calorimetric parameter (DCP) in this work. Similar to the DCP approach with the viscosity proposed in our previous research study, it was found that by scaling the thermal conductivity and self-diffusion coefficient, linear relations of these two transport properties with the DCP could be exhibited. On this basis, two-parameter formulas for calculating the thermal conductivity and self-diffusion coefficient through the DCP were put forward. Meanwhile, the slope and intercept of the linear formula for thermal conductivity were found to be one-dimensionally related, while the slopes of the self-diffusion coefficient equations fell in the narrow interval of −1.64 ± 0.21, revealing a quasi-universality for various nonassociation fluids. The new DCP-based model for calculating thermal conductivity was evaluated and validated with the experimental data of 21 pure fluids representing different molecular structures. The average absolute deviation and the maximum absolute deviation between the linked thermal conductivities and the literature data were within 5.04 and 8.30%, respectively. This work provided novel methods for calculating the thermal conductivity and self-diffusion coefficient of saturated liquids.

Empirical modeling of the percent depth dose for megavoltage photon beams.

This study presents an empirical method to model the high-energy photon beam percent depth dose (PDD) curve by using the home-generated buildup function and tail function (buildup-tail function) in radiation therapy. The modeling parameters n and μ of buildup-tail function can be used to characterize the Collimator Scatter Factor (Sc) either in a square field or in the different individual upper jaw and lower jaw setting separately for individual monitor unit check. The PDD curves for four high-energy photon beams were modeled by the buildup and tail function in this study. The buildup function was a quadratic function in the form of [Formula: see text] with the main parameter of d (depth in water) and n, while the tail function was in the form of e-μd and was composed by an exponential function with the main parameter of d and μ. The PDD was the product of buildup and tail function, PDD = [Formula: see text]. The PDD of four-photon energies was characterized by the buildup-tail function by adjusting the parameters n and μ. The Sc of 6 MV and 10 MV can then be expressed simply by the modeling parameters n and μ. The main parameters n increases in buildup-tail function when photon energy increased. The physical meaning of the parameter n expresses the beam hardening of photon energy in PDD. The fitting results of parameters n in the buildup function are 0.17, 0.208, 0.495, 1.2 of four-photon energies, 4 MV, 6 MV, 10 MV, 18 MV, respectively. The parameter μ can be treated as attenuation coefficient in tail function and decreases when photon energy increased. The fitting results of parameters μ in the tail function are 0.065, 0.0515, 0.0458, 0.0422 of four-photon energies, 4 MV, 6 MV, 10 MV, 18 MV, respectively. The values of n and μ obtained from the fitted buildup-tail function were applied into an analytical formula of Sc = nE(S)0.63μE to get the collimator to scatter factor Sc for 6 and 10 MV photon beam, while nE, μE, S denotes n, μ at photon energy E of field size S, respectively. The calculated Sc were compared with the measured data and showed agreement at different field sizes to within ±1.5%. We proposed a model incorporating a two-parameter formula which can improve the fitting accuracy to be better than 1.5% maximum error for describing the PDD in different photon energies used in clinical setting. This model can be used to parameterize the Sc factors for some clinical requirements. The modeling parameters n and μ can be used to predict the Sc in either square field or individual jaws opening asymmetrically for treatment monitor unit double-check in dose calculation. The technique developed in this study can also be used for systematic or random errors in the QA program, thus improves the clinical dose computation accuracy for patient treatment.

Study on the Strength Performance of Recycled Aggregate Concrete with Different Ages under Direct Shearing.

In order to study the mechanical properties of recycled aggregate concrete (RAC) at different ages, 264 standard cubes were designed to test its direct shear strength and cube compressive strength while considering the parameters of age and recycled aggregate replacement ratio. The failure pattern and load–displacement curve of specimens at direct shearing were obtained; the direct shear strength and residual shear strength were extracted from the load–displacement curves. Experimental results indicate that the influence of the replacement ratio for the front and side cracks of RAC is insignificant, with the former being straight and the latter relatively convoluted. At the age of three days, the damaged interface between aggregate and mortar is almost completely responsible for concrete failure; in addition to the damage of coarse aggregates, aggregate failure is also an important factor in concrete failure at other ages. The load–displacement curve of RAC at direct shearing can be divided into elasticity, elastoplasticity, plasticity, and stabilization stages. The brittleness of concrete decreases with its age, which is reflected in the gradual shortening of the elastoplastic stage. At 28 days of age, the peak direct shear force increases with the replacement ratio, while the trend is opposite at ages of 3 days, 7 days, and 14 days, respectively. The residual strength of RAC decreases inversely to the replacement ratio, with the rate of decline growing over time. A two-parameter RAC direct shear strength calculation formula was established based on the analysis of age and replacement rate to peak shear force of RAC. The relationship between cube compressive strength and direct shear strength of recycled concrete at various ages was investigated.

945 Fetal biometry using hadlock versus INTERGROWTH-21st in an urban zambian population

Numerous growth curves and formulas have been developed to calculate estimated fetal weight (EFW) from prenatal ultrasound (US). The four-parameter Hadlock formula (head circumference (HC), biparietal diameter, abdominal circumference (AC), and femur length) remains the most commonly used in the United States. The two-parameter INTERGROWTH-21st formula (HC and AC) was created to provide a more comprehensive international standard using fetal growth data from multiple countries. We sought to evaluate whether EFW calculated by Hadlock or INTERGROWTH-21st at 32 weeks better predicts birthweight (BW) in an urban Zambian population. The Zambian Preterm Birth Prevention Study (ZAPPS) is an ongoing prospective cohort of pregnant women enrolled at a tertiary hospital. We included women with singleton pregnancies who underwent a dating US at < 24 weeks and fetal biometry at 32 weeks. Estimated due date was calculated by US at the enrollment visit for each patient using Hadlock and INTERGROWTH-21st. EFW at 32 weeks was calculated by Hadlock and INTERGROWTH-21st formulas using the corresponding gestational age by each formula respectively. Data were analyzed using chi-square, t-test, and linear regression as appropriate. 1450 women were enrolled in the first phase of ZAPPS from 2015 to 2017. 32-week US (mean 32.1 ± 0.7 weeks) was available for 749 women. The mean EFW was 1895 ± 194g by Hadlock and 1788 ± 203g by INTERGROWTH-21st. Birthweight was available for 708 maternal-infant pairs (49%); mean birthweight was 3056 ± 487g. In an unadjusted linear regression model, EFW at 32 weeks by Hadlock and INTERGROWTH-21st were comparable predictors of birthweight. For both models, p <0.001, and adjusted R2 was 0.11 (Figure 1). A Bland-Altman plot (Figure 2) demonstrates that EFW by Hadlock is on average 107g higher (SD 74, 95% limits of agreement 107 ± 148g). Hadlock and INTERGROWTH-21st formulas are similar predictors of birthweight in an urban Zambian cohort. This suggests that INTERGROWTH-21st offers an acceptable two-parameter alternative to calculate fetal biometry.View Large Image Figure ViewerDownload Hi-res image Download (PPT)

New Geiger-Nuttall law for two-proton radioactivity * *Supported in part by the National Natural Science Foundation of China (11205083, 11505100, 11705055), the Construct Program of the Key Discipline in Hunan Province, the Research Foundation of Education Bureau of Hunan Province, China (15A159, 18A237), the Natural Science Foundation of Hunan Province, China (2015JJ3103, 2015JJ2121, 2018JJ2321), the Innovation Group of Nuclear and

In the present work, a two-parameter empirical formula is proposed, based on the Geiger-Nuttall law, to study two-proton ( ) radioactivity. Using this formula, the calculated radioactivity half-lives are in good agreement with the experimental data as well as with calculated results obtained by Goncalves et al. [Phys. Lett. B 774, 14 (2017)] using the effective liquid drop model (ELDM), Sreeja et al. [Eur. Phys. J. A 55, 33 (2019)] using a four-parameter empirical formula, and Cui et al. [Phys. Rev. C 101: 014301 (2020)] using a generalized liquid drop model (GLDM). In addition, this two-parameter empirical formula is extended to predict the half-lives of 22 possible radioactivity candidates with radioactivity released energy , obtained from the latest evaluated atomic mass table AME2016. The predicted results are highly consistent with those obtained using other theoretical models such as the ELDM, GLDM and four-parameter empirical formula.

Description of Superdeformed Bands of the Isotones $$\boldsymbol{N=113}$$ for Nuclear Mass Region $$\boldsymbol{A\sim 190}$$

Electric quadrupole $$\gamma$$ -ray transition energies $$E_{\gamma}$$ , rotational frequencies $$\hbar\omega$$ and dynamic $$J^{(2)}$$ and kinematic $$J^{(1)}$$ moments of inertia have been calculated for yrast and excited superdeformed (SD) bands in Hg, Tl, Pb isotonic ( $$N=113$$ ) nuclei by using two-parameter power-law formula. The model parameters and the bandhead spins were determined using a $$\chi^{2}$$ fit by random minimization via Monte Carlo simulation technique with a uniform distribution of random numbers. The calculated results of $$E_{\gamma}$$ agreed with the experimental data published in National Nuclear Data Center (nndc) very well, and present assigned spins of the studied superdeformed rotational bands (SDRB’s) are consistent with the spins suggested by other previous formulae. The majority of the studied SD bands displayed the same large, smooth increase in $$J^{(2)}$$ by increasing $$\hbar\omega$$ . A saturation of $$J^{(2)}$$ at higher values of $$\hbar\omega$$ was observed for the two bands (1, 2) in $${}^{195}$$ Pb due to the Pauli blocking of the quasineutron alignment in the presence of quasiproton alignment. The studied SD bands exhibited staggering in their transition energies. Five pairs of signature partner SDRBs exhibited an $$\Delta I=1$$ staggering effect in their transition energies, namely $${}^{193}$$ Hg (SD1, SD2), $${}^{193}$$ Hg (SD3, SD4), $${}^{194}$$ Tl (SD1, SD2), $${}^{195}$$ Pb (SD1, SD2), and $${}^{195}$$ Pb (SD3, SD4). To investigate this $$\Delta I=1$$ staggering, we extracted the difference between the average transition $$I+2\to I$$ and $$I\to I-2$$ energies in one band and the transition $$I+1\to I-1$$ energies in the signature partner. Also, a $$\Delta I=2$$ staggering exists in three SD bands of odd–odd $${}^{194}$$ Tl. This $$\Delta I=2$$ staggering effect was determined by calculating the energy difference between two consecutive $$\gamma$$ -ray transitions as a function of rotational frequency after subtracting a smooth reference expressed in the notation of Cederwall.

Diagnostic Value of Corneal Epithelial and Stromal Thickness Distribution Profiles in Forme Fruste Keratoconus and Subclinical Keratoconus.

To assess the diagnostic values of corneal epithelial and stromal thickness distribution characteristics in forme fruste keratoconus (FFKC) and subclinical keratoconus (KC). This cross-sectional study was conducted at VISSUM Innovation and Miguel Hernandez University, Alicante, Spain. Twenty-seven eyes (27 subjects) with FFKC, 50 eyes (50 subjects) with subclinical KC with a best spectacle corrected distance visual acuity ≥20/20 (Snellen) (grade zero KC according to the Red Temática de Investigación Cooperativa en Salud classification), and 66 control eyes (66 subjects) were included. Epithelial and stromal thicknesses and epithelium/stroma (E/S) thickness ratio at center, thinnest point, 5-, and 8-mm circles obtained from the MS-39 device (CSO, Firenze, Italy) were compared among the control, FFKC, and subclinical KC groups. The FFKC group had thinner 8-mm superior-nasal epithelium and higher central E/S ratio compared with the control group (P < 0.05). In the subclinical KC group, the E/S ratios in the 5-mm temporal and superior zones were higher than those in the control group (P < 0.05). The FFKC and subclinical KC groups had thinner stroma compared with the control group (P < 0.05). A two-parameter formula correctly classified 94% of the eyes with subclinical KC and 98.5% of the normals, whereas another three-parameter model had 75% sensitivity and 94.3% specificity for discriminating FFKC from normals. This study identified different epithelial distributional and behavioral patterns in eyes with FFKC and subclinical KC. Eyes with FFKC seem to have increased central E/S ratio and asymmetric superior-nasal epithelial thinning, whereas keratometric and volumetric alterations seem to be more prominent in subclinical KC.

Study of nuclear charge radius

Based on the existing experimental data of nuclear radius, the previous formula of nuclear charge radius is verified and discussed. Comparing the formula of the single-parameter nuclear charge radius, it is proved that the formula of &lt;inline-formula&gt;&lt;tex-math id="M4"&gt;\begin{document}$Z^{1/3}$\end{document}&lt;/tex-math&gt;&lt;alternatives&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="16-20191643_M4.jpg"/&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="16-20191643_M4.png"/&gt;&lt;/alternatives&gt;&lt;/inline-formula&gt; law is better than the formula of &lt;inline-formula&gt;&lt;tex-math id="M5"&gt;\begin{document}$A^{1/3}$\end{document}&lt;/tex-math&gt;&lt;alternatives&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="16-20191643_M5.jpg"/&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="16-20191643_M5.png"/&gt;&lt;/alternatives&gt;&lt;/inline-formula&gt; law. We refitted the two-parameter formula and the three-parameter formula that have been proposed and confirmed that the two-parameter and three-parameter formula fit better than the single-parameter formula. It is shown that show that the deformation plays a key role in the nuclear charge radius. The electric quadrupole moment is an important physical quantity representing the properties of the nucleus. Its appearance indicates the deviation from spherical symmetry and also reflects the size of the nuclear deformation. The electric quadrupole moment is also one of the basic observations to understand the distribution of matter within the nucleus, to examine the nuclear model, and to observe nucleon-nuclear interactions. Taking into account the relationship between the nuclear quadrupole moment and the deformation, the electric quadrupole moment factor is added to the original three-parameter formula to obtain a new formula for the nuclear charge radius. Fitting the four-parameter formula, it is found that the theoretical value of the nuclear charge radius is in good agreement with the experimental value, the root-mean-square deviation is 0.0397 fm. Considering the relationship between the total spin and the electric quadrupole moment, the intrinsic electric quadrupole moment is obtained and brought into the formula for fitting, and the root-mean-square deviation further decreases,the root-mean-square deviation is 0.0372 fm. Finally, considering the universality of odd-even staggering, we add the &lt;inline-formula&gt;&lt;tex-math id="M6"&gt;\begin{document}$\delta$\end{document}&lt;/tex-math&gt;&lt;alternatives&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="16-20191643_M6.jpg"/&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="16-20191643_M6.png"/&gt;&lt;/alternatives&gt;&lt;/inline-formula&gt; term that can reflect the odd and even oscillation phenomenon, and the root-mean-square deviation obtained by the formula is 0.369 fm, which better reflects the relationship between the deformation and the nuclear charge radius. Compared with the formulas already proposed, the new formula can better reflect the variation trend of nuclear deformation, shell effect, odd-even staggering, etc., and the calculation accuracy is also improved, which can provide a useful reference for future experiments.

Effect of wind-driven accretion on planetary migration

Context. Planetary migration is a key link between planet formation models and observed exoplanet statistics. So far, the theory of planetary migration has focused on the interaction of one or more planets with an inviscid or viscously evolving gaseous disk. Turbulent viscosity is thought to be the main driver of the secular evolution of the disk, and it is known to affect the migration process for intermediate- to high-mass planets. Recently, however, the topic of wind-driven accretion has experienced a renaissance because evidence is mounting that protoplanetary disks may be less turbulent than previously thought, and 3D non-ideal magnetohydrodynamic modeling of the wind-launching process is maturing. Aims. We investigate how wind-driven accretion may affect planetary migration. We aim for a qualitative exploration of the main effects and not for a quantitative prediction. Methods. We performed 2D hydrodynamic planet-disk interaction simulations with the FARGO3D code in the (r, ϕ) plane. The vertical coordinate in the disk and the launching of the wind are not treated explicitly. Instead, the torque caused by the wind onto the disk is treated using a simple two-parameter formula. The parameters are the wind mass-loss rate and the lever arm. Results. We find that the wind-driven accretion process replenishes the co-orbital region in a different way than the viscous accretion process. The former always injects mass from the outer edge of the co-orbital region, and always removes mass from the inner edge, while the latter injects or removes mass from the co-orbital region depending on the radial density gradients in the disk. As a consequence, the migration behavior can differ strongly, and can under certain conditions drive rapid type-III-like outward migration. We derive an analytic expression for the parameters under which this outward migration occurs. Conclusions. If wind-driven accretion plays a role in the secular evolution of protoplanetary disks, planetary migration studies have to include this process as well because it can strongly affect the resulting migration rate and migration direction.

New Geiger-Nuttall law for proton radioactivity

In the present work considering the contributions of the daughter nuclear charge and the orbital angular momentum taken away by the emitted proton, we propose a two-parameter formula of new Geiger-Nuttall law for proton radioactivity. A set of universal parameters of this law is obtained by fitting 44 experimental data of proton emitters in the ground state and isomeric state. The calculated results can reproduce the experimental data well. For a comparison, the calculations performed using other theoretical methods, such as UDLP proposed by Qi et al. (Phys. Rev. C 85, 011303(R) (2012)), the CPPM-Guo2013 analyzed by our previous work (Deng et al., Eur. Phys. J. A 55, 58 (2019)) and the modified Gamow-like model proposed by us (Chen et al., J. Phys. G: Nucl. Part. Phys. 96, 065107 (2019)) are also included. Meanwhile, we extend this new Geiger-Nuttall law to predict the proton radioactivity half-lives for $ 51 \leq Z \leq 91$ nuclei, whose proton radioactivity is energetically allowed or observed but not yet quantified in NUBASE2016.

Study of A = 100–150 superdeformed mass region by using two-parameterformula

Empirical formulae of rotational spectra consisting two parameters, such as single-term energy formula, E = aJb for spin J , and ab formula, were used to study the different features of superdeformed band in A = 100-150 mass region nuclei. The nuclear kinematic and dynamic moment of inertia for the ground-state rotational bands were calculated for this purpose and both showed gradual rise with rotational frequency. The study of ΔI = 2 staggering effects in the γ-ray energies, where the two sequences J = 4i; 4i + 1 and J = 4i + 2, (i = 0; 1; ...) are bifurcated, was also done. We also calculated the variation of the gamma ray energies from a smooth reference using the fourth derivative of the gamma ray energies at a given spin. The excellent agreement between the observed and calculated transition energies are in good support of the two-parameter formula.

Band head spin determination of triaxial superdeformed bands in 163,164,165Lu through two-parameter formulae

The two-parameter formulae, i.e. the nuclear softness formula and the power index formula, have been used to obtain the band head spin (I0) of the triaxial superdeformed (SD) bands in 163Lu(1, 2, 3, 4), 164Lu(1, 2, 3) and 165Lu(1, 2, 3), in the A ∼ 160 mass region. The least squares fitting approach is used. The values of the root mean square (RMS) deviation among the computed and the measured experimental transition energies are obtained by calculating the model parameters. Whenever accurate spins are available, superb agreement is shown between the determined and the measured experimental transition energies. In comparison to the power index formula, the values of band head spin (I0) of the triaxial SD bands in 163Lu(1, 2, 3, 4), 164Lu(1, 2, 3) and 165Lu(1, 2, 3) obtained by the nuclear softness formula are closer to the experimental data. The lowest RMS deviation is also achieved by the nuclear softness formula. Hence, the nuclear softness formula works well for obtaining the band head spin (I0) for the triaxial SD bands in 163Lu(1, 2, 3, 4), 164Lu(1, 2, 3) and 165Lu(1, 2, 3) in the A ∼ 160 mass region. The dynamic moment of inertia against ħω is also studied.

A two-parameter formula of default probability term structure

A two-parameter formula of default probability term structure

Physics-based derivation of a formula for the mutual depolarization of two post-like field emitters

Recent analyses of the apex field enhancement factor (FEF) for many forms of field emitter have revealed that the depolarization effect is more persistent with respect to the separation between the emitters than originally assumed. It has been shown that, at sufficiently large separations, the fractional reduction of the FEF decays with the inverse cube power of separation, rather than exponentially. The behavior of the fractional reduction of the FEF encompassing both the range of technological interest (c being the separation and h is the height of the emitters) and large separations () has not been predicted by the existing formulas in field emission literature, for post-like emitters of any shape. In this work, we use first principles to derive a simple two-parameter formula for fractional reduction that can be useful for experimentalists for modeling and interpreting the FEFs for small clusters of emitters or arrays at separations of interest. For the structures tested, the agreement between numerical and analytical data is ∼1%.

Band head spin assignment of superdeformed bands in 133Pr using two-parameter formulae

The two-parameter formulae viz. the power index formula, the nuclear softness formula and the VMI model are adopted to accredit the band head spin [Formula: see text] of four superdeformed rotational bands in [Formula: see text]. The technique of least square fitting is used to accredit the band head spin for four superdeformed rotational bands in [Formula: see text]. The root mean deviation among the computed transition energies and well-known experimental transition energies are attained by extracting the model parameters from the two-parameter formulae. The determined transition energies are in excellent agreement with the experimental transition energies, whenever exact spins are accredited. The power index formula coincides well with the experimental data and provides minimum root mean deviation. So, the power index formula is more efficient tool than the nuclear softness formula and the VMI model. The deviation of dynamic moment of inertia [Formula: see text] against the rotational frequency is also examined.

Interpretations of Hyperbolic Growth

Abstract Hyperbolic growth describes the historical economic growth and historical growth of population, but their mechanism remains unexplained. Presented here is a brief survey of attempts to understand hyperbolic growth. Mathematical formulations are in general complicated and there is no clear advantage in using them because they do not give better description of data than the simple, two-parameter hyperbolic formula. They also do not explain the mechanism of growth. The well-known simple formula suggests a simple explanation. Two examples show how two independent investigations were on a brink of making an important and breakthrough discovery and how their potential discovery was thwarted by the established knowledge in demography and in economic research. Researchers who could have used their expertise to suggests new research directions and to advance science were constrained by doctrines, which are widely accepted by faith. Key words: Hyperbolic growth, Mechanism of growth, Population growth, Economic growth, Growth models, Growth theory, Malthusian stagnation JEL: A10, A12, C02, C12, C20, C50, Y80.