Order Alpha Research Articles

A distributional approach to fractional Sobolev spaces and fractional variation: asymptotics I

We continue the study of the space BV^alpha ({mathbb {R}}^n) of functions with bounded fractional variation in {mathbb {R}}^n of order alpha in (0,1) introduced in our previous work (Comi and Stefani in J Funct Anal 277(10):3373–3435, 2019). After some technical improvements of certain results of Comi and Stefani (2019) which may be of some separated insterest, we deal with the asymptotic behavior of the fractional operators involved as alpha rightarrow 1^-. We prove that the alpha -gradient of a W^{1,p}-function converges in L^p to the gradient for all pin [1,+infty ) as alpha rightarrow 1^-. Moreover, we prove that the fractional alpha -variation converges to the standard De Giorgi’s variation both pointwise and in the Gamma -limit sense as alpha rightarrow 1^-. Finally, we prove that the fractional beta -variation converges to the fractional alpha -variation both pointwise and in the Gamma -limit sense as beta rightarrow alpha ^- for any given alpha in (0,1).

Inactivated whole-virion vaccine BBV152/Covaxin elicits robust cellular immune memory to SARS-CoV-2 and variants of concern.

BBV152 is a whole-virion inactivated vaccine based on the Asp614Gly variant. BBV152 is the first alum-imidazoquinolin-adjuvanted vaccine authorized for use in large populations. Here we characterized the magnitude, quality and persistence of cellular and humoral memory responses up to 6 months post vaccination. We report that the magnitude of vaccine-induced spike and nucleoprotein antibodies was comparable with that produced after infection. Receptor binding domain-specific antibodies declined against variants in the order of Alpha (B.1.1.7; 3-fold), Delta (B.1.617.2; 7-fold) and Beta (B.1.351; 10-fold). However, pseudovirus neutralizing antibodies declined up to 2-fold against the Delta followed by the Beta variant (1.7-fold). Vaccine-induced memory B cells were also affected by the Delta and Beta variants. The SARS-CoV-2-specific multicytokine-expressing CD4+ T cells were found in ~85% of vaccinated individuals. Only a ~1.3-fold reduction in efficacy was observed in CD4+ T cells against the Beta variant. We found that antigen-specific CD4+ T cells were present in the central memory compartment and persisted for at least up to 6 months post vaccination. Vaccine-induced CD8+ T cells were detected in ~50% of individuals. Importantly, the vaccine was capable of inducing follicular T helper cells that exhibited B-cell help potential. These findings show that inactivated vaccine BBV152 induces robust immune memory to SARS-CoV-2 and variants of concern that persists for at least 6 months after vaccination.

Jet broadening in the opacity and twist expansions

We compute the in-medium jet broadening langle p_perp ^2rangle to leading order in energy in the opacity expansion. At leading order in alpha _s the elastic energy loss gives a jet broadening that grows with ln E. The next-to-leading order in alpha _s result is a jet narrowing, due to destructive LPM interference effects, that grows with ln ^2 E. We find that in the opacity expansion the jet broadening asymptotics are – unlike for the mean energy loss – extremely sensitive to the correct treatment of the finite kinematics of the problem; integrating over all emitted gluon transverse momenta leads to a prediction of jet broadening rather than narrowing. We compare the asymptotics from the opacity expansion to a recent twist-4 derivation of langle p_perp ^2rangle and find a qualitative disagreement: the twist-4 derivation predicts a jet broadening rather than a narrowing. Comparison with current jet measurements cannot distinguish between the broadening or narrowing predictions. We comment on the origin of the difference between the opacity expansion and twist-4 results.

Effects of order alpha ^3 on the determination of the Pauli form factor F_2 of the tau -lepton

We introduce optimal observables to measure the Pauli form factor F_2 of the tau -lepton in the pair-production process mathrm{e}^- mathrm{e}^+ rightarrow tau ^-tau ^+ from the intensity distribution of the decay products. The spin-density matrix for the production process is calculated in QED up to order alpha ^3 including virtual photon-loops and soft bremsstrahlung, as well the gamma Z^0 interference. We find that the decay channel (rho ^-nu _tau )times (rho ^+ {bar{nu }}_tau ) yields the best resolution for ReF_2(s) and ImF_2(s) due to its high branching fraction. We also study the bias that is introduced in the determination of F_2, if the production spin-density matrix is taken in tree-level (one-photon exchange) approximation.

The fractional variation and the precise representative of BV^{alpha ,p} functions

We continue the study of the fractional variation following the distributional approach developed in the previous works Bruè et al. (2021), Comi and Stefani (2019), Comi and Stefani (2019). We provide a general analysis of the distributional space BV^{alpha ,p}({mathbb {R}}^n) of L^p functions, with pin [1,+infty ], possessing finite fractional variation of order alpha in (0,1). Our two main results deal with the absolute continuity property of the fractional variation with respect to the Hausdorff measure and the existence of the precise representative of a BV^{alpha ,p} function.

Upper and lower estimates for the separation of solutions to fractional differential equations

Given a fractional differential equation of order alpha in (0,1] with Caputo derivatives, we investigate in a quantitative sense how the associated solutions depend on their respective initial conditions. Specifically, we look at two solutions x_1 and x_2, say, of the same differential equation, both of which are assumed to be defined on a common interval [0, T], and provide upper and lower bounds for the difference x_1(t) - x_2(t) for all t in [0,T] that are stronger than the bounds previously described in the literature.

Second Hankel Determinant of Logarithmic Coefficients of Convex and Starlike Functions of Order Alpha

In the present paper, we found sharp bounds of the second Hankel determinant of logarithmic coefficients of starlike and convex functions of order alpha .

Starlikeness of New General Differential Operators Associated with q-Bessel Functions

Owning to the importance and great interest of differential operators, two generalized differential operators, which may be symmetric or assymetric, are newly introduced in the present paper. Motivated by the familiar Jackson’s second and third Bessel functions, we derive necessary and sufficient conditions for which the new generalized operators belong to the class of q-starlike functions of order alpha. Several corollaries and consequences of the main results are also pointed out.

Effective action of string theory at order alpha ' in the presence of boundary

Recently, using the assumption that the string theory effective action at the critical dimension is background independent, the classical on-shell effective action of the bosonic string theory at order alpha ' in a spacetime manifold without boundary has been reproduced, up to an overall parameter, by imposing the O(1, 1) symmetry when the background has a circle. In the presence of the boundary, we consider a background which has boundary and a circle such that the unit normal vector of the boundary is independent of the circle. Then the O(1, 1) symmetry can fix the bulk action without using the lowest order equation of motion. Moreover, the above constraints and the constraint from the principle of the least action in the presence of boundary can fix the boundary action, up to five boundary parameters. In the least action principle, we assume that not only the values of the massless fields but also the values of their first derivatives are arbitrary on the boundary. We have also observed that the cosmological reduction of the leading order action in the presence of the Hawking–Gibbons boundary term, produces zero cosmological boundary action. Imposing this as another constraint on the boundary couplings at order alpha ', we find the boundary action up to two parameters. For a specific value for these two parameters, the gravity couplings in the boundary become the Chern–Simons gravity plus another term which has the Laplacian of the extrinsic curvature.

A quantum strategy to compute the jet quenching parameter hat{q}

Jet quenching, the modification of the properties of a QCD jet when the parton cascade takes place inside a medium, is an intrinsically quantum process, where color coherence effects play an essential role. Despite a very significant progress in the last years, the simulation of a full quantum medium induced cascade remains inaccessible to classical Monte Carlo parton showers. In this situation, alternative formulations are worth being tried and the fast developments in quantum computing provide a very promising direction. The goal of this paper is to introduce a strategy to quantum simulate single particle momentum broadening, the simplest building block of jet quenching. Momentum broadening is the modification of the quark or gluon transverse momentum due interactions with the underlying medium, modeled as a QCD background field. At the lowest order in alpha _s that we consider here, momentum broadening does not involve parton splittings and particle number is conserved, greatly simplifying the quantum algorithmic implementation. This quantity is, however, very relevant for the phenomenology of RHIC, LHC or the future EIC.

The diphoton q_T spectrum at N^3LL^prime \xa0+\xa0NNLO

We present a q_T-resummed calculation of diphoton production at order N^3LL^prime + NNLO. To reach the primed level of accuracy we have implemented the recently published three-loop {mathcal {O}}(alpha _s^3) virtual corrections in the qbar{q} channel and the three-loop transverse momentum dependent beam functions and combined them with the existing infrastructure of CuTe-MCFM, a code performing resummation at order N{}^3LL. While the primed predictions are parametrically not more accurate, one typically observes from lower orders and other processes that they are the dominant effect of the next order. We include in both the qbar{q} and loop-induced gg channel the hard contributions consistently together at order alpha _s^3 and find that the resummed qbar{q} channel without matching stabilizes indeed. Due to large matching corrections and large contributions and uncertainties from the gg channel, the overall improvements are small though. We furthermore study the effect of hybrid-cone photon isolation and hard-scale choice on our fully matched results to describe the ATLAS text {8} TeV data and find that the hybrid-cone isolation worsens agreement at small q_T compared to smooth-cone isolation.

Starlikeness of certain non-univalent functions

We consider three classes of functions defined using the class {mathcal {P}} of all analytic functions p(z)=1+cz+cdots on the open unit disk having positive real part and study several radius problems for these classes. The first class consists of all normalized analytic functions f with f/gin {mathcal {P}} and g/(zp)in {mathcal {P}} for some normalized analytic function g and pin {mathcal {P}}. The second class is defined by replacing the condition f/gin {mathcal {P}} by |(f/g)-1|<1 while the other class consists of normalized analytic functions f with f/(zp)in {mathcal {P}} for some pin {mathcal {P}}. We have determined radii so that the functions in these classes to belong to various subclasses of starlike functions. These subclasses includes the classes of starlike functions of order alpha , parabolic starlike functions, as well as the classes of starlike functions associated with lemniscate of Bernoulli, reverse lemniscate, sine function, a rational function, cardioid, lune, nephroid and modified sigmoid function.

O(25,\xa025) symmetry of bosonic string theory at order alpha '^2

It has been recently observed that the imposition of the O(1, 1) symmetry on the circle reduction of the classical effective action of string theory, can fix the effective action of the bosonic string theory at order alpha '^2, up to an overall factor. In this paper, we use the cosmological reduction on the action and show that, up to one-dimensional field redefinitions and total derivative terms, it can be written in the O(25, 25)-invariant form proposed by Hohm and Zwiebach.

QCD factorization of the four-lepton decay B^-rightarrow ell bar{nu }_ell ell ^{(prime )} bar{ell }^{(prime )}

Motivated by the first search for the rare charged-current B decay to four leptons, ell bar{nu }_ell ell ^{(prime )} bar{ell }^{(prime )}, we calculate the decay amplitude with factorization methods. We obtain the Brightarrow gamma ^* form factors, which depend on the invariant masses of the two lepton pairs, at leading power in an expansion in Lambda _mathrm{QCD}/m_b to next-to-leading order in alpha _s, and at mathcal {O}(alpha _s^0) at next-to-leading power. Our calculations predict branching fractions of a few times 10^{-8} in the ell ^{(prime )} bar{ell }^{(prime )} mass-squared bin up to q^2=1~GeV^2 with n_+q>3~GeV. The branching fraction rapidly drops with increasing q^2. An important further motivation for this investigation has been to explore the sensitivity of the decay rate to the inverse moment lambda _B of the leading-twist B meson light-cone distribution amplitude. We find that in the small-q^2 bin, the sensitivity to lambda _B is almost comparable to B^- rightarrow mathrm {ell }^- bar{nu }_{mathrm {ell }}gamma when lambda _B is small, but with an added uncertainty from the light-meson intermediate resonance contribution. The sensitivity degrades with larger q^2.

Fighting off field dependence in MSSM Higgs-mass corrections of order alpha _t,alpha _s and alpha _t^2

The connection between gauge and Higgs sectors makes supersymmetric extensions of the Standard Model predictive frameworks for the derivation of Higgs masses. In this paper, we study the contamination of such predictions by field-renormalization constants, in the MSSM with two-loop gaugeless corrections of mathcal {O}big (alpha _{t,b},alpha _s,,alpha _{t,b}^2big ) and full momentum dependence, and demonstrate how strict perturbative expansions allow to systematically neutralize the dependence on such unphysical objects. On the other hand, the popular procedure consisting in an iterative pole search remains explicitly dependent on field counterterms. We then analyze the magnitude of the intrinsic uncertainty that this feature implies for the iterative method, both in non-degenerate and near-degenerate regimes, and conclude that this strategy does not improve on the predictions of the more straightforward expansion. We also discuss several features related to the inclusion of the orders alpha _{t,b},alpha _s and alpha _{t,b}^2 in the so-called ‘fixed-order’ approach, such as the resummation of UV-logarithms for heavy supersymmetric spectra.

On strong lacunary summability of order α with respect to modulus functions

This research paper focuses on defining the relationships between the sets of strongly lacunary summable and lacunary statistically convergent sequences by using different modulus functions f and g under certain conditions and different orders. Furthermore, for some special modulus functions, we establish the relations between the sets of strongly f-lacunary summable sequences and strongly f-lacunary summable sequences of order alpha.

The second Hankel determinant for starlike and convex functions of order alpha

In recent years, the study of Hankel determinants for various subclasses of normalised univalent functions given by for has produced many interesting results. The main focus of interest has been estimating the second Hankel determinant of the form . A non-sharp bound for when , consisting of convex functions of order α was found by Krishna and Ramreddy (Hankel determinant for starlike and convex functions of order alpha. Tbil Math J. 2012;5:65–76), and later improved by Thomas et al. (Univalent functions: a primer. Berlin: De Gruyter; 2018). In this paper, we give the sharp result. Moreover, we obtain sharp results for for the inverse functions when , and when , the class of starlike functions of order α. Thus, the results in this paper complete the set of problems for the second Hankel determinants of f and for the classes , , and , where and are, respectively, the classes of strongly starlike, and strongly convex functions of order β.

Enhanced diversity and rock-weathering potential of bacterial communities inhabiting potash trachyte surface beneath mosses and lichens — A case study in Nanjing, China

Mosses and lichens have been shown to play an important role in enhancing global chemical weathering of the surface rock. However, there are no studies concerning the effects of mosses and lichens on the microbial communities inhabiting rock surfaces. In this study, culture-dependent and culture-independent analyses were employed to compare the diversity, composition, and rock-weathering activity of bacterial communities inhabiting potash trachyte surfaces covered by mosses (MR) and lichens (LR) with those inhabiting surrounding bare rock surfaces (BR). Analyses of 16S rRNA gene Miseq sequencing revealed that the order of alpha (α) diversity indices, in terms of the number of unique operational taxonomic units (OTUs) and Faith's index of phylogenetic diversity, was MR > LR > BR. Moreover, α-diveristy indices were positively correlated with the content of available phosphorus (AP) in rock samples (r = 0.87–0.92), and this explained 70% of the variation in bacterial community structure. The culture-dependent analyses revealed that 100% of the culturable bacterial strains could enhance potash trachyte weathering, and the order of rock-weathering acitivity of bacterial strains was MR > LR > BR. Acidolysis was found to be the major mechanism involved in the bacteria-mediated weathering of potash trachyte. Moreover, bacterial strians related to the genera Dyella and Ralstonia showed the highest rock-weatheirng activity, and both Dyella and Ralstonia were enriched in MR. The results of this study enhance our understanding of the roles of bacteria facilitated by mosses and lichens in rock weathering, element cycling, and soil formation, and provide new insights into the interaction between non-vascular plants and the bacteria on rock surfaces.

Existence of solutions for fourth-order nonlinear boundary value problems

In this paper, we discuss the existence and approximation of solutions for a fourth-order nonlinear boundary value problem by using a quasilinearization technique. In the presence of a lower solution α and an upper solution β in the reverse order alpha geq beta , we show the existence of (extreme) solution.

Improvements on dipole shower colour

The dipole formalism provides a powerful framework from which parton showers can be constructed. In a recent paper (Forshaw et al. 2020), we proposed a dipole shower with improved colour accuracy and in this paper we show how it can be further improved. After an explicit check at {mathcal {O}}(alpha _{mathrm {s}}^{2}) we confirm that our original shower performs as it was designed to, i.e. inheriting its handling of angular-ordered radiation from a coherent branching algorithm. We also show how other dipole shower algorithms fail to achieve this. Nevertheless, there is an {mathcal {O}}(alpha _{mathrm {s}}^{2}) topology where it differs at sub-leading N_{mathrm {c}} from a coherent branching algorithm. This erroneous topology can contribute a leading logarithm to some observables and corresponds to emissions that are ordered in k_t but not angle. We propose a simple, computationally efficient way to correct this and assign colour factors in accordance with the coherence properties of QCD to all orders in alpha _{mathrm {s}}.