Parts Formula Research Articles

Neutrino effective potential and damping in a fermion and scalar background in the resonance region

We consider the propagation of a neutrino or an antineutrino in a medium composed of fermions $f$ and scalars $\phi$ interacting via a Yukawa-type coupling of the form $\bar f\nu\phi$, for neutrino energies at which the processes like $\nu + \phi \leftrightarrow f$ or $\nu + \bar f \leftrightarrow \bar\phi$, and the corresponding ones for the antineutrino, are kinematically accessible. The relevant energy values are around $|m^2_\phi - m^2_f|/2m_\phi$ or $|m^2_\phi - m^2_f|/2m_f$, where $m_\phi$ and $m_f$ are the masses of $\phi$ and $f$, respectively. We refer to either one of these regions as a resonance energy range. Near these points, the one-loop formula for the neutrino self-energy has a singularity. From a technical point of view, that feature is indicative that the self-energy acquires an imaginary part, which is associated with damping effects and cannot be neglected, while the integral formula for the real part must be evaluated using the principal value of the integral. We carry out the calculations explicitly for some cases that allow us to give analytic results. Writing the dispersion relation in the form $\omega = \kappa + V_{\text{eff}} - i\gamma/2$, we give the explicit formula for $V_{\text{eff}}$ and $\gamma$ for the cases considered. When the neutrino energy is either much larger or much smaller than the resonance energy, $V_{\text{eff}}$ reduces to the effective potential that has been already determined in the literature in the high or low momentum regime, respectively. The virtue of the formula we give for $V_{\text{eff}}$ is that it is valid also in the \emph{resonance energy range}, which is outside the two limits mentioned. As a guide to possible applications we give the relevant formulas for $V_{\text{eff}}$ and $\gamma$, and consider the solution to the oscillation equations including the damping term, in a simple two-generation case.

Stature estimation of Malaysians using post-mortem computed tomography images of the spine

Background Stature estimation is important in medical investigations to identify victims and is most accurate using anatomical methods utilizing the entire skeleton. However, in cases of mass fatalities, it has been calculated using regression analysis formulas of different body parts. Radiology especially post-mortem computed tomography (PMCT) is increasingly being used in victim identification as it is non- invasive and allows for multi planar reconstruction. Methods This study aims to generate stature estimation formulae using regression analysis of the vertebral column incorporating population that form the Malaysian ancestry i.e. Malay, Chinese and Indian using PMCT. This was a retrospective study involving 115 subjects who had a PMCT. Subjects consisted of Malaysian males and females (92 males and 23 females) aged 18–70 years. Cervical length (CL), thoracic length (TL), lumbar length and the whole spine length (WSL) incorporating cervical, thoracic and lumbar length were compared against cadaveric length. Results Whole spine length had the highest correlation coefficient of 0.570 and showed highest correlation with cadaveric length among female subjects compared to males. Whole spine length amongst the Malay was the highest followed by the Chinese and Indian ethnic groups (r = 0.671, 0.629, 0.402). Conclusion Our study concluded that the use of WSL from PMCT images can be used for body height estimation amongst Malaysians. This study has also successfully generated population-specific database for Malaysian experts to perform stature estimation using measurements of the vertebral column.

Weighted Generalized Fractional Integration by Parts and the Euler–Lagrange Equation

Integration by parts plays a crucial role in mathematical analysis, e.g., during the proof of necessary optimality conditions in the calculus of variations and optimal control. Motivated by this fact, we construct a new, right-weighted generalized fractional derivative in the Riemann–Liouville sense with its associated integral for the recently introduced weighted generalized fractional derivative with Mittag–Leffler kernel. We rewrite these operators equivalently in effective series, proving some interesting properties relating to the left and the right fractional operators. These results permit us to obtain the corresponding integration by parts formula. With the new general formula, we obtain an appropriate weighted Euler–Lagrange equation for dynamic optimization, extending those existing in the literature. We end with the application of an optimization variational problem to the quantum mechanics framework.

A Semi‐Analytical Solution for Slug Test by Considering Near‐Well Formation Damage and Nonlinear Flow

AbstractThis study proposes a new analytical slug test model describing confined flow considering the effects of the formation damage and non‐Darcy flow near the wellbore. The former, primarily caused by drilling fluid invasion, introduces an extra wellbore head loss near the well screen. The latter, mainly resulting from the relatively high‐velocity flow across the gravel‐pack screen, adopts the Forchheimer equation to consider the joint effects of the laminar flow and non‐Darcy flow. The proposed model is nonlinear due to the quadratic term for non‐Darcy flow in the Forchheimer equation. The new solutions for head responses in the well and formation are derived using the Laplace transform method and integration by parts formula. Furthermore, the present solution is applied to estimate the aquifer parameters via analyzing the water level data from field slug tests conducted in the Minnelusa aquifer near Spearfish, South Dakota. We found that the present solution provides very good fit to the field data from tests in fractured aquifers, notably the data exhibits a rapid decline at late times on the normalized head vs. logarithmic time plots.

An integration by parts formula for the bilinear form of the hypersingular boundary integral operator for the transient heat equation in three spatial dimensions

While an integration by parts formula for the bilinear form of the hypersingular boundary integral operator for the transient heat equation in three spatial dimensions is available in the literature, a proof of this formula seems to be missing. Moreover, the available formula contains an integral term including the time derivative of the fundamental solution of the heat equation, whose interpretation is difficult at second glance. To fill these gaps, we provide a rigorous proof of a general version of the integration by parts formula and an alternative representation of the mentioned integral term, which is valid for a certain class of functions including the typical tensor-product discretization spaces.

Fractionally Integrated Moving Average Stable Processes With Long-Range Dependence

Long memory processes driven by L\'evy noise with finite second-order moments have been well studied in the literature. They form a very rich class of processes presenting an autocovariance function which decays like a power function. Here, we study a class of L\'evy process whose second-order moments are infinite, the so-called $\alpha$-stable processes. Based on Samorodnitsky and Taqqu (2000), we construct an isometry that allows us to define stochastic integrals concerning the linear fractional stable motion using Riemann-Liouville fractional integrals. With this construction, follows naturally an integration by parts formula. We then present a family of stationary $S\alpha S$ processes with the property of long-range dependence, using a generalized measure to investigate its dependence structure. In the end, the law of large number's result for a time's sample of the process is shown as an application of the isometry and integration by parts formula.

New Method of Sensitivity Computation Based on Markov Models with Its Application for Risk Management

Sensitivity analysis is at the core of risk management for financial engineering; to calculate the sensitivity with respect to parameters in models with probability expectation, the most traditional approach applies the finite difference method, whereafter integration by parts formula was developed based on the Brownian environment and applied in sensitivity analysis for better computational efficiency than that of finite difference. Establishing a similar version of integration by parts formula for the Markovian environment is the main focus and contribution of this paper. It is also shown by numerical simulation that our proposed methodology and approach outperform the traditional finite difference method for sensitivity computation. For empirical studies of sensitivity analysis on an NPV (net present value) model, we show the approaches of modeling, especially for parameter estimation of Markov chains given data of company loan states. Applying our newly established integration by parts formula, numerical simulation estimates the variations caused by the capital return rate and multiplier of overdue loan. Furthermore, managemental implications of these results are discussed for the effectiveness of modeling and the investment risk control.

The total variation flow in metric graphs

<abstract><p>Our aim is to study the total variation flow in metric graphs. First, we define the functions of bounded variation in metric graphs and their total variation, we also give an integration by parts formula. We prove existence and uniqueness of solutions and that the solutions reach the mean of the initial data in finite time. Moreover, we obtain explicit solutions.</p></abstract>

The principal transmission condition

<abstract><p>The paper treats pseudodifferential operators $ P = \operatorname{Op}(p(\xi)) $ with homogeneous complex symbol $ p(\xi) $ of order $ 2a > 0 $, generalizing the fractional Laplacian $ (-\Delta)^a $ but lacking its symmetries, and taken to act on the halfspace ${\mathbb R}^n_+$. The operators are seen to satisfy a principal $ \mu $-transmission condition relative to ${\mathbb R}^n_+$, but generally not the full $ \mu $-transmission condition satisfied by $ (-\Delta)^a $ and related operators (with $ \mu = a $). However, $ P $ acts well on the so-called $ \mu $-transmission spaces over ${\mathbb R}^n_+$ (defined in earlier works), and when $ P $ moreover is strongly elliptic, these spaces are the solution spaces for the homogeneous Dirichlet problem for $ P $, leading to regularity results with a factor $ x_n^\mu $ (in a limited range of Sobolev spaces). The information is then shown to be sufficient to establish an integration by parts formula over ${\mathbb R}^n_+$ for $ P $ acting on such functions. The formulation in Sobolev spaces, and the results on strongly elliptic operators going beyond certain operators with real kernels, are new. Furthermore, large solutions with nonzero Dirichlet traces are described, and a halfways Green's formula is established, as new results for these operators. Since the principal $ \mu $-transmission condition has weaker requirements than the full $ \mu $-transmission condition assumed in earlier papers, new arguments were needed, relying on work of Vishik and Eskin instead of the Boutet de Monvel theory. The results cover the case of nonsymmetric operators with real kernel that were only partially treated in a preceding paper.</p></abstract>

ON A NEW HALF-DISCRETE HILBERT-TYPE INEQUALITY WITH THE MULTIPLE UPPER LIMIT FUNCTION AND THE PARTIAL SUMS

<abstract> By means of the weight coefficients, the Euler-Maclaurin summation formula and Abel's summation by parts formula, a new half-discrete Hilbert-type inequality with the power function as the interval variables as well as one multiple upper limit function and one partial sums is given. As applications, the equivalent conditions of the best possible constant factor in a particular inequality related to a few parameters and some particular cases are considered. We also obtain the equivalent forms and the operator expression in the case of <italic>m</italic>=0. </abstract>

Celestial IR divergences in general most-subleading-color gluon and gravity amplitudes

Gluon amplitudes at most-subleading order in the 1/N expansion share a remarkable simplicity with graviton amplitudes: collinear divergences are completely absent in both and, as a consequence, their full IR behavior arises from soft gluon/graviton exchange among the external states. In this paper we study the effect of all-loop IR divergences of celestial most-subleading color gluon amplitudes and their similarities with the celestial gravity case. In particular, a simple celestial exponentiation formula for the dipole part can be written. We also analize how this exponentiation is modified by non-dipole contributions. Finally we also show that, in the Regge limit, the soft factor satisfies the Knizhnik-Zamolodchikov equation hinting at the possibility that, in this limit, an effective Wess-Zumino-Witten model would describe the dynamics of the infrared sector.

Convexity of the class of currents with finite relative energy

We prove the convexity of the class of currents with finite relative energy. A key ingredient is an integration by parts formula for relative non-pluripolar products which is of independent interest.

Probabilistic representation of integration by parts formulae for some stochastic volatility models with unbounded drift

In this paper, we establish a probabilistic representation as well as some integration by parts formulae for the marginal law at a given time maturity of some stochastic volatility model with unbounded drift. Relying on a perturbation technique for Markov semigroups, our formulae are based on a simple Markov chain evolving on a random time grid for which we develop a tailor-made Malliavin calculus. Among other applications, an unbiased Monte Carlo path simulation method stems from our formulas so that it can be used in order to numerically compute with optimal complexity option prices as well as their sensitivities with respect to the initial values or Greeks in finance, namely the Delta and Vega, for a large class of non-smooth European payoff. Numerical results are proposed to illustrate the efficiency of the method.

BSM master formula for \u03b5\u2032/\u03b5 in the WET basis at NLO in QCD

As an important step towards a complete next-to-leading (NLO) QCD analysis of the ratio ε′/ε within the Standard Model Effective Field Theory (SMEFT), we present for the first time the NLO master formula for the BSM part of this ratio expressed in terms of the Wilson coefficients of all contributing operators evaluated at the electroweak scale. To this end we use the common Weak Effective Theory (WET) basis (the so-called JMS basis) for which tree-level and one-loop matching to the SMEFT are already known. The relevant hadronic matrix elements of BSM operators at the electroweak scale are taken from Dual QCD approach and the SM ones from lattice QCD. It includes the renormalization group evolution and quark-flavour threshold effects at NLO in QCD from hadronic scales, at which these matrix elements have been calculated, to the electroweak scale.

Determination of absolute mobility and dissociation constant of lovastatin using capillary electrophoresis and empirical equation of ion mobility

作为一种可以预防动脉粥样硬化和冠心病的潜在药物洛伐他汀,其绝对淌度m0和解离常数pKa值的测定有助于其性质与应用的研究。在前期相关研究基础上,该文提出了一种基于毛细管区带电泳(CZE)和离子淌度经验公式测定洛伐他汀m0和pKa的新方法。首先,根据经验公式由实际淌度(mact)、有效淌度(meff)和m0之间的关系推导出m0的计算公式。对于一元酸HA,根据之前m0的计算公式,以氢离子的浓度为自变量,meff的倒数为因变量可得到一条直线。根据这条直线的斜率计算得到pKa。为了验证该方法的可行性和可靠性,应用该方法测定了巴比妥酸、苯甲酸、苄胺、苯酚、间甲酚等有机酸碱的m0和pKa值。同时,对于pH值低于6的缓冲体系,采用反向毛细管电泳技术,测定其pKa,并将测得的实验结果与理论参考值进行对比,发现两者具有较高的一致性,m0的标准偏差小于6.0%, pKa的标准偏差小于6.2%,且由线性回归方程的相关系数(R)可以看出测定pKa时的线性回归直线拟合度较好,说明该文建立的新方法具有较高的可靠性。最后基于这种CZE与经验公式结合的新方法,采用二甲基亚砜(DMSO)作为电渗流标记物测定了洛伐他汀的m0和pKa,得到的值分别为-1.70×10-8 m2/(V·s)和9.00。该方法适用于酸性和碱性分析物m0和pKa等理化参数的测定,在药物分析尤其是新药理化特性研究中具有重要意义。

Sensitivity of option prices via fuzzy Malliavin calculus

In this paper, we define the Malliavin derivative and the Skorohod integral for fuzzy stochastic processes for the sensitivity analysis of the option prices. The price dynamics could be modelled by equations involving uncertainties that lead to modelling with fuzzy processes in equations. We introduce a fuzzy stochastic differential equation for financial pricing models under an asset price that follows a fuzzy stochastic process. If there is no explicit solution to the equations, the sensitivity analysis, and the estimates are computationally expensive, and the result will be inaccurate due to the estimates and the derivative of the payoff function. The Malliavin calculus and the integration by parts formula in fuzzy space can be exploited to bypass the derivative of the payoff function.

Injective Rota–Baxter Operators of Weight Zero on F[x

Rota-Baxter operators present a natural generalisation of integration by parts formula for the integral operator. In 2015, Zheng, Guo, and Rosenkranz conjectured that every injective Rota-Baxter operator of weight zero on the polynomial algebra $\mathbb{R}[x]$ is a composition of the multiplication by a nonzero polynomial and a formal integration at some point. We confirm this conjecture over any field of characteristic zero. Moreover, we establish a structure of an ind-variety on the moduli space of these operators and describe an additive structure of generic modality two on it. Finally, we provide an infinitely transitive action on codimension one subsets.

Time reversal of Markov processes with jumps under a finite entropy condition

Motivated by entropic optimal transport, time reversal of Markov jump processes in Rn is investigated. Relying on an abstract integration by parts formula for the carré du champ of a Markov process recently obtained in Cattiaux et al. (2021), and using an entropic improvement strategy discovered by Föllmer (1985, 1986), we compute the semimartingale characteristics of the time reversed process for a wide class of jump processes in Rn with possibly unbounded variation sample paths and singular intensities of jump.

On the well-posedness of Banach spaces-based mixed formulations for the nearly incompressible Navier-Lamé and Stokes equations

In this paper we introduce and analyze, up to our knowledge for the first time, Banach spaces-based mixed variational formulations for nearly incompressible linear elasticity and Stokes models. Our interest in this subject is motivated by the respective need that arises from the solvability studies of nonlinear coupled problems in continuum mechanics that involve these equations. We consider pseudostress-based approaches in both cases and apply a suitable integration by parts formula for ad-hoc Sobolev spaces to derive the corresponding continuous schemes. We utilize known and new preliminary results, along with the Babuška-Brezzi theory in Banach spaces, to establish the well-posedness of the formulations for a particular range of the indexes of the Lebesgue spaces involved. Among the aforementioned new results from us, we highlight the construction of a particular operator mapping a tensor Lebesgue space into itself, and the generalization of a classical estimate in L2 for deviatoric tensors, which plays a key role in the Hilbertian analysis of linear elasticity, to arbitrary Lebesgue spaces. No discrete analysis is performed in this work.

An Integration by Parts Formula for Functionals of the Dirichlet-Ferguson Measure, and Applications

An Integration by Parts Formula for Functionals of the Dirichlet-Ferguson Measure, and Applications