Earlier Derivations Research Articles

Hierarchical three-body problem at high eccentricities = simple pendulum I: octupole

ABSTRACT The gradual evolution of the restricted hierarchical three body problem is analysed analytically, focusing on conditions of Kozai–Lidov cycles that may lead to orbital flips from prograde to retrograde motion due to the octupole (third order) term which are associated with extremely high eccentricities. We revisit the approach described by Katz, Dong and Malhotra (2011) and show that for most initial conditions, to an excellent approximation, the analytical derivation can be greatly simplified and reduces to a simple pendulum model allowing an explicit flip criterion. The resulting flip criterion is much simpler than the previous one but the latter is still needed in a small fraction of phase space. We identify a logical error in the earlier derivation but clarify why it does not affect the final results.

Transverse momentum dependent factorization for SIDIS at next-to-leading power

The semi-inclusive deep-inelastic scattering (SIDIS) is the golden process for investigating the nucleon’s transverse momentum-dependent (TMD) structure. We present the complete expression for SIDIS structure functions in the TMD factorization formalism at the next-to-leading power. All perturbative elements of the factorization theorem—coefficient functions and evolution kernels—are presented at one-loop accuracy. We found several differences with earlier derivations, which are due to accounting for nontrivial kinematics of the quark-gluon interference terms. As a side result, we present the definition and evolution of twist-three TMD fragmentation functions, including the leading-order evolution kernel. Published by the American Physical Society 2024

An N-Cyanoamide Derivative of Lithocholic Acid Co-Operates with Lysophosphatidic Acid to Promote Human Osteoblast (MG63) Differentiation.

Less-calcaemic vitamin D receptor (VDR) agonists have the potential to promote osteoblast maturation in a bone regenerative setting. The emergence of lithocholic acid (LCA) as a bona fide VDR agonist holds promise as an adjunct for arthroplasty following reports that it was less calcaemic than calcitriol (1,25D). However, LCA and some earlier derivatives, e.g., LCA acetate, had to be used at much higher concentrations than 1,25D to elicit comparable effects on osteoblasts. However, recent developments have led to the generation of far more potent LCA derivatives that even outperform the efficacy of 1,25D. These new compounds include the cyanoamide derivative, Dcha-150 (also known as AY2-79). In light of this significant development, we sought to ascertain the ability of Dcha-150 to promote human osteoblast maturation by monitoring alkaline phosphatase (ALP) and osteocalcin (OC) expression. The treatment of MG63 cells with Dcha-150 led to the production of OC. When Dcha-150 was co-administered with lysophosphatidic acid (LPA) or an LPA analogue, a synergistic increase in ALP activity occurred, with Dcha-150 showing greater potency compared to 1,25D. We also provide evidence that this synergy is likely attributed to the actions of myocardin-related transcription factor (MRTF)-serum response factor (SRF) gene transcription following LPA-receptor-induced cytoskeletal reorganisation.

Analytical Solution for Bichromatic Waves on Linearly Varying Currents

It is well-known that the bound long waves play an important role on beach morphology. The existence of the current will modify the intensity of the waves. To examine the more realistic problem where the current is non-uniform, a third-order analytical solution for bichromatic waves on currents with constant vorticity is derived using a perturbation method. Earlier derivations of theories for interactions between waves and currents have been limited to cases of bichromatic waves on depth-uniform currents and cases of monochromatic waves on linear shear currents. Unlike the derivations of monochromatic waves, the moving-frame method cannot be used in the case of bichromatic waves because there are multiple waves with different celerities, and the flow can in no way be treated as steady-state. Moreover, for shear currents where the flows are rotational, the velocity potential cannot be simply defined. For these reasons, it is difficult to carry out mathematical operations when the dynamic free surface boundary condition is applied. However, with the consideration of the wave part of the fluid motion remaining irrotational, some of the terms in the expanded boundary conditions can be ignored; thus, the derivations can be further processed. As a result, the third-order explicit expressions for the stream function, the velocity potential, and the surface elevation can be solved. The nonlinear dispersion relation is also derived to account for interacting wave components with different frequencies and amplitudes which can be used to solved for wavenumbers of both wave trains. The obtained solutions are verified by reducing to those of previous results for monochromatic waves and uniform currents. Furthermore, the influence of constant vorticity on the wave kinematics is illustrated. A comparison between following/opposing currents is also carried out. Finally, the effects of the shear current on the strength of the bound long waves are also illustrated.

Classical and quantum gravitational scattering with Generalized Wilson Lines

The all-order structure of scattering amplitudes is greatly simplified by the use of Wilson line operators, describing eikonal emissions from straight lines extending to infinity. A generalization at subleading powers in the eikonal expansion, known as Generalized Wilson Line (GWL), has been proposed some time ago, and has been applied both in QCD phenomenology and in the high energy limits of gravitational amplitudes. In this paper we revisit the construction of the scalar gravitational GWL starting from first principles in the worldline formalism. We identify the correct Hamiltonian that leads to a simple correspondence between the soft expansion and the weak field expansion. This allows us to isolate the terms in the GWL that are relevant in the classical limit. In doing so we devote special care to the regularization of UV divergences that were not discussed in an earlier derivation. We also clarify the relation with a parallel body of work that recently investigated the classical limit of scattering amplitudes in gravity in the worldline formalism.

An Optimal Derivative Free Family of Chebyshev–Halley’s Method for Multiple Zeros

In this manuscript, we introduce the higher-order optimal derivative-free family of Chebyshev–Halley’s iterative technique to solve the nonlinear equation having the multiple roots. The designed scheme makes use of the weight function and one parameter α to achieve the fourth-order of convergence. Initially, the convergence analysis is performed for particular values of multiple roots. Afterward, it concludes in general. Moreover, the effectiveness of the presented methods are certified on some applications of nonlinear equations and compared with the earlier derivative and derivative-free schemes. The obtained results depict better performance than the existing methods.

Explaining the Routh–Hurwitz Criterion: A Tutorial Presentation [Focus on Education

Routh's treatise [1] was a landmark in the analysis of the stability of dynamic systems and became a core foundation of control theory. The remarkable simplicity of the result was in stark contrast to the challenge of the proof. Many researchers devoted much effort to extend the result to singular cases, with some of the earlier techniques shown to be inadequate [2]. Together with the extensions to singular cases, shorter proofs were also proposed. The proof of [3] is noteworthy, which followed the root locus arguments of [4]. A key feature of the proof is a continuity argument used in an earlier derivation [5]. In [6], the more conventional approach using Cauchy?s principle of the argument is followed. A relatively simple proof is proposed, considering the extension to complex polynomials and singular cases.

Fokker–Planck Equations for Time-Delayed Systems via Markovian Embedding

For stochastic systems with discrete time delay, the Fokker-Planck equation (FPE) of the one-time probability density function (PDF) does not provide a complete, self-contained probabilistic description. It explicitly involves the two-time PDF, and represents, in fact, only the first member of an infinite hierarchy. We here introduce a new approach to obtain a Fokker-Planck description by using a Markovian embedding technique and a subsequent limiting procedure. On this way, we find a closed, complete FPE in an infinite-dimensional space, from which one can derive a hierarchy of FPEs. While the first member is the well-known FPE for the one-time PDF, we obtain, as second member, a new representation of the equation for the two-time PDF. From a conceptual point of view, our approach is simpler than earlier derivations and it yields interesting insight into both, the physical meaning, and the mathematical structure of delayed processes. We further propose an approximation for the two-time PDF, which is a central quantity in the description of these non-Markovian systems as it directly gives the correlation between the present and the delayed state. Application to a prototypical bistable system reveals that this approximation captures the non-trivial effects induced by the delay remarkably well, despite its surprisingly simple form. Moreover, it outperforms earlier approaches for the one-time PDF in the regime of large delays.

Direct Derivation of the Comma 3-Vertex in the Full String Basis

The interacting comma 3-vertex for the bosonic open string in the full string basis is derived using the half string overlap relations directly. Thus avoiding the coherent states technique employed in earlier derivations. The resulting form of the interacting 3-vertex turns out to be precisely the desired expression obtained in terms of the full string oscillator modes. This derivation establishes that the comma 3-vertex and Witten's 3-vertex are identical and therefore are interchangeable.

Black holes in presence of cosmological constant: second order in frac{1}{D}

We have extended the results of [1] upto second subleading order in an expansion around large dimension D. Unlike the previous case, there are non-trivial metric corrections at this order. Due to our ‘background-covariant’ formalism, the dependence on Ricci and the Riemann curvature tensor of the background is manifest here. The gravity system is dual to a dynamical membrane coupled with a velocity field. The dual membrane is embedded in some smooth background geometry that also satisfies the Einstein equation in presence of cosmological constant. We explicitly computed the corrections to the equation governing the membrane-dynamics. Our results match with earlier derivations in appropriate limits. We calculated the spectrum of QNM from our membrane equations and matched them against similar results derived from gravity.

BMX-001, a novel redox-active metalloporphyrin, improves islet function and engraftment in a murine transplant model.

Islet transplantation has become a well-established therapy for select patients with type 1 diabetes. Viability and engraftment can be compromised by the generation of oxidative stress encountered during isolation and culture. We evaluated whether the administration of BMX-001 (MnTnBuOE-2-PyP5+ [Mn(III) meso-tetrakis-(N-b-butoxyethylpyridinium-2-yl)porphyrin]) and its earlier derivative, BMX-010 (MnTE-2-PyP [Mn(III) meso-tetrakis-(N-methylpyridinium-2-yl)porphyrin]) could improve islet function and engraftment outcomes. Long-term culture of human islets with BMX-001, but not BMX-010, exhibited preserved in vitro viability. Murine islets isolated and cultured for 24hours with 34μmol/L BMX-001 exhibited improved insulin secretion (n=3 isolations, P<.05) in response to glucose relative to control islets. In addition, 34μmol/L BMX-001-supplemented murine islets exhibited significantly reduced apoptosis as indicated by terminal deoxynucleotidyl transferase dUTP nick end labeling, compared with nontreated control islets (P<.05). Murine syngeneic islets transplanted under the kidney capsule at a marginal dose of 150 islets revealed 58% of 34μmol/L BMX-001-treated islet recipients became euglycemic (n=11 of 19) compared with 19% of nontreated control islet recipients (n=3 of 19, P<.05). Of murine recipients receiving a marginal dose of human islets cultured with 34μmol/L BMX-001, 92% (n=12 of 13) achieved euglycemia compared with 57% of control recipients (n=8 of 14, P=.11). These results demonstrate that the administration of BMX-001 enhances in vitro viability and augments murine marginal islet mass engraftment.

Discovery of a Novel Class of Survival Motor Neuron 2 Splicing Modifiers for the Treatment of Spinal Muscular Atrophy.

Spinal muscular atrophy (SMA) is caused by mutation or deletion of the survival motor neuron 1 (SMN1) gene, resulting in low levels of functional SMN protein. We have reported recently the identification of small molecules (coumarins, iso-coumarins and pyrido-pyrimidinones) that modify the alternative splicing of SMN2, a paralogous gene to SMN1, restoring the survival motor neuron (SMN) protein level in mouse models of SMA. Herein, we report our efforts to identify a novel chemotype as one strategy to potentially circumvent safety concerns from earlier derivatives such as in vitro phototoxicity and in vitro mutagenicity associated with compounds 1 and 2 or the in vivo retinal findings observed in a long-term chronic tox study with 3 at high exposures only. Optimized representative compounds modify the alternative splicing of SMN2, increase the production of full length SMN2 mRNA, and therefore levels of full length SMN protein upon oral administration in two mouse models of SMA.

Scheme dependence and transverse momentum distribution interpretation of Collins–Soper–Sterman resummation

Following an earlier derivation by Catani, de Florian and Grazzini (2000) on the scheme dependence in the Collins–Soper–Sterman (CSS) resummation formalism in hard scattering processes, we investigate the scheme dependence of the Transverse Momentum Distributions (TMDs) and their applications. By adopting a universal C-coefficient function associated with the integrated parton distributions, the difference between various TMD schemes can be attributed to a perturbative calculable function depending on the hard momentum scale. We further apply several TMD schemes to the Drell–Yan process of lepton pair production in hadronic collisions, and find that the constrained non-perturbative form factors in different schemes are consistent with each other and with that of the standard CSS formalism.

Phase velocity effects of the wave interaction with exponentially sheared current

The nonlinear interaction between the unidirectional bichromatic wave-train and exponentially sheared current in water of an infinite depth is investigated. The model is based on the vorticity transport equation and the exact free surface conditions, without any assumptions for the existence of small physical parameters. Earlier works of the wave–current interaction were mainly restricted to either current acted on the monochromatic wave or irregular waves limited to irrotational current. Different from these previous works, no constraint is made in our model for amplitudes of the primary wave, and the current owns an exponential type profile along the vertical line. To ensure that the effect of vorticity on the phase velocity is consistent with earlier derivation, the case of a small amplitude wave traveling on the exponentially sheared current is examined firstly. Then the effect of nonlinearity on the phase velocity of primary waves in a bichromatic wave-train is considered. Accurate high-order approximations of the phase velocity are obtained under consideration of both the nonlinear wave self–self and mutual interactions. Finally, the combined effect of vorticity and nonlinearity on the phase velocity is investigated through the case of a bichromatic wave-train propagating on an exponentially sheared current. It is found that the characteristic current slope determines the effect of vorticity on the phase velocity caused by nonlinear wave self–self and mutual interactions, and the surface current strength may amplify/reduce this effect.

Nucleosome Positioning Patterns Derived from Human Apoptotic Nucleosomes

This communication reports on the nucleosome positioning patterns (bendability matrices) for the human genome, derived from over 8 million nucleosome DNA sequences obtained from apoptotically digested lymphocytes. This digestion procedure is used here for the first time for the purpose of extraction and sequencing of the nucleosome DNA fragments. The dominant motifs suggested by the matrices of DNA bendability calculated for light and heavy isochores are significantly different. Both, however, are in full agreement with the linear description YRRRRRYYYYYR, and with earlier derivations by N-gram extensions. Thus, the choice of the nucleosome positioning patterns crucially depends on the G + C composition of the analyzed sequences.

Generalization of the van der Pauw relationship derived from electrostatics

In an earlier paper, this author, along with two others Weiss et al. (2008) [1], demonstrated that the original van der Pauw relationship could be derived from three-dimensional electrostatics, as opposed to van der Pauw’s use of conformal mapping. The earlier derivation was done for a conducting material of rectangular cross section with contacts placed at the corners. Presented here is a generalization of the previous work involving a square sample and a square array of electrodes that are not confined to the corners, since this measurement configuration could be a more convenient one. As in the previous work, the effects of non-zero sample thickness and contact size have been investigated. Buehler and Thurber derived a similar relationship using an infinite series of current images on a large and thin conducting sheet to satisfy the conditions at the boundary of the sample. The results presented here agree with theirs numerically, but analytic agreement could not be shown using any of the perused mathematical literature. By simply equating the two solutions, it appears that, as a byproduct of this work, a new mathematical relationship has been uncovered. Finally, the application of this methodology to the Hall Effect is discussed.

Exact analytical solutions to the master equation of quantum Brownian motion for a general environment

We revisit the model of a quantum Brownian oscillator linearly coupled to an environment of quantum oscillators at finite temperature. By introducing a compact and particularly well-suited formulation, we give a rather quick and direct derivation of the master equation and its solutions for general spectral functions and arbitrary temperatures. The flexibility of our approach allows for an immediate generalization to cases with an external force and with an arbitrary number of Brownian oscillators. More importantly, we point out an important mathematical subtlety concerning boundary-value problems for integro-differential equations which led to incorrect master equation coefficients and impacts on the description of nonlocal dissipation effects in all earlier derivations. Furthermore, we provide explicit, exact analytical results for the master equation coefficients and its solutions in a wide variety of cases, including ohmic, sub-ohmic and supra-ohmic environments with a finite cut-off.

CAN THE COMPOSITION OF THE SOLAR CORONA BE DERIVED FROMHINODE/EXTREME-ULTRAVIOLET IMAGING SPECTROMETER SPECTRA?

Elemental abundances appear to be the same everywhere in the photosphere, but in the solar corona they vary in different regions. Abundances in quiet Sun (closed) flux tubes are different from those in coronal hole (CH, open) magnetic field regions, and therefore abundance variations might possibly be used to determine locations of slow and fast solar wind in the corona. In active regions, abundances can change from region to region and can vary with the age of the region. In the present paper, we evaluate the feasibility of determining relative elemental abundances in the corona using spectra acquired by the Extreme-ultraviolet Imaging Spectrometer (EIS) on Hinode. As test cases, we attempt to evaluate the coronal composition above the limb in an equatorial quiet region and in a polar CH. We also determine the elemental composition of coronal regions with moderate activity on the disk and at the limb. To estimate the accuracy of the instrumental calibration and the atomic physics used in the calculations, we compare the derived composition with earlier derivations from spectra recorded by the Solar Ultraviolet Measurements of Emitted Radiation spectrometer in similar regions. We find that EIS can be used to determine relative abundance variations in the inner solar corona. The determination of absolute abundances can also be attempted after additional calibrations in space are accomplished.

Beam wander of dark hollow, flat-topped and annular beams

Benefiting from the earlier derivations for the Gaussian beam, we formulate beam wander for dark hollow (DH) and flat-topped (FT) beams, also covering the annular Gaussian (AG) beam as a special case. Via graphical illustrations, beam wander variations of these beams are analyzed and compared among themselves and to the fundamental Gaussian beam against changes in propagation length, amplitude factor, source size, wavelength of operation, inner and outer scales of turbulence. These comparisons show that in relation to the fundamental Gaussian beam, DH and FT beams will exhibit less beam wander, particularly at small primary beam source sizes, lower amplitude factors of the secondary beam and higher beam orders. Furthermore, DH and FT beams will continue to preserve this advantageous position all throughout the considered range of wavelengths, inner and outer scales of turbulence. FT beams, in particular, are observed to have the smallest beam wander values among all, up to certain source sizes.

On the derivation of the Herman–Kluk propagator

Following an earlier derivation by Miller, we give a concise derivation of the Herman–Kluk propagator that fully exploits the symplectic structure of the problem. We also show directly that the version of the thawed Gaussian semiclassical propagator obtained by Baranger and co-workers is equivalent to the linearized Herman–Kluk propagator.