Order Alpha Research Articles

A note on the Fr\xf6hlich dynamics in the strong coupling limit

We revise a previous result about the Fröhlich dynamics in the strong coupling limit obtained in Griesemer (Rev Math Phys 29(10):1750030, 2017). In the latter it was shown that the Fröhlich time evolution applied to the initial state varphi _0 otimes xi _alpha , where varphi _0 is the electron ground state of the Pekar energy functional and xi _alpha the associated coherent state of the phonons, can be approximated by a global phase for times small compared to alpha ^2. In the present note we prove that a similar approximation holds for t=O(alpha ^2) if one includes a nontrivial effective dynamics for the phonons that is generated by an operator proportional to alpha ^{-2} and quadratic in creation and annihilation operators. Our result implies that the electron ground state remains close to its initial state for times of order alpha ^2, while the phonon fluctuations around the coherent state xi _alpha can be described by a time-dependent Bogoliubov transformation.

Estimate on the Dimension of the Singular Set of the Supercritical Surface Quasigeostrophic Equation

We consider the SQG equation with dissipation given by a fractional Laplacian of order alpha <frac{1}{2}. We introduce a notion of suitable weak solution, which exists for every L^2 initial datum, and we prove that for such solution the singular set is contained in a compact set in spacetime of Hausdorff dimension at most frac{1}{2alpha } left( frac{1+alpha }{alpha } (1-2alpha ) + 2right) .

Surface terms in effective action of O-plane at order alpha '^2

The effective action of string theory has both bulk and boundary terms if the spacetime is an open manifold. Recently, the known classical effective action of string theory at the leading order of alpha ' and its corresponding boundary action have been reproduced by constraining the effective actions to be invariant under gauge transformations and under string duality transformations. In this paper, we use this idea to find the classical effective action of the O-plane and its corresponding boundary terms in type II superstring theories at order alpha '^2 and for NS–NS couplings. We find that these constraints fix the bulk action and its corresponding boundary terms up to one overall factor. They also produce three multiplets in the boundary action that their coefficients are independent of the bulk couplings under the string dualities.

Power corrections in a transverse-momentum cut for vector-boson production at NNLO: the qg-initiated real-virtual contribution

We consider the production of a vector boson (Z, W^pm or gamma ^*) at next-to-next-to-leading order in the strong coupling constant alpha _mathrm{S}. We impose a transverse-momentum cutoff, q_{mathrm{T}}^{mathrm{cut}}, on the vector boson produced in the qg-initiated channel. We then compute the power corrections in the cutoff, up to the second power, of the real-virtual interference contribution to the cumulative cross section at order alpha _mathrm{S}^2. Other terms with the same kinematics, originating from the subtraction method applied to the double-real contribution, have been also considered. The knowledge of such power corrections is a required ingredient in order to reduce the dependence on the transverse-momentum cutoff of the QCD cross sections at next-to-next-to-leading order, when the q_{mathrm{T}}-subtraction method is applied. In addition, the study of the dependence of the cross section on q_{mathrm{T}}^{mathrm{cut}} allows as well for an understanding of its behaviour in the small transverse-momentum limit, giving hints on the structure at all orders in alpha _mathrm{S} and on the identification of universal patterns. Our result are presented in an analytic form, using the process-independent procedure described in a previous paper for the calculation of the all-order power corrections in q_{mathrm{T}}^{mathrm{cut}}.

T-dualization of G\xf6del string cosmologies via Poisson\u2013Lie T-duality approach

Using the homogeneous Gödel spacetimes we find some new solutions for the field equations of bosonic string effective action up to first order in alpha ' including both dilaton and axion fields. We then discuss in detail the (non-)Abelian T-dualization of Gödel string cosmologies via the Poisson–Lie (PL) T-duality approach. In studying Abelian T-duality of the models we get seven dual models in such a way that they are constructed by one-, two- and three-dimensional Abelian Lie groups acting freely on the target space manifold. The results of our study show that the Abelian T-dual models are, under some of the special conditions, self-dual; moreover, by applying the usual rules of Abelian T-duality without further corrections, we are still able to obtain two-loop solutions. We also study the Abelian T-duality of Gödel string cosmologies up to alpha '-corrections by using the T-duality rules at two-loop order derived by Kaloper and Meissner. Afterwards, non-Abelian duals of the Gödel spacetimes are constructed by two- and three-dimensional non-Abelian Lie groups such as A_2, A_2 oplus A_1 and SL(2, mathbb {R}). In this way, the PL self-duality of AdS_3 times mathbb {R} space is discussed.

On the approximate inverse Laplace transform of the transfer function with a single fractional order

The history of fractional calculus dates back to 1600s and it is almost as old as classical mathematics. Although many studies have been published on fractional-order control systems in recent years, there is still a lack of analytical solutions. The focus of this study is to obtain analytical solutions for fractional order transfer functions with a single fractional element and unity coefficient. Approximate inverse Laplace transformation, that is, time response of the basic transfer function, is obtained analytically for the fractional order transfer functions with single-fractional-element by curve fitting method. Obtained analytical equations are tabulated for some fractional orders of [Formula: see text]. Moreover, a single function depending on fractional order alpha has been introduced for the first time using a table for [Formula: see text]. By using this table, approximate inverse Laplace transform function is obtained in terms of any fractional order of [Formula: see text] for [Formula: see text]. Obtained analytic equations offer accurate results in computing inverse Laplace transforms. The accuracy of the method is supported by numerical examples in this study. Also, the study sets the basis for the higher fractional-order systems that can be decomposed into a single (simpler) fractional order systems.

Minimal gauge invariant couplings at order alpha '^3: NS\u2013NS fields

Removing the field redefinitions, the Bianchi identities and the total derivative freedoms from the general form of gauge invariant NS–NS couplings at order alpha '^3, we have found that the minimum number of independent couplings is 872. We find that there are schemes in which there is no term with structures R,,R_{mu nu },,nabla _mu H^{mu alpha beta }, nabla _mu nabla ^mu Phi . In these schemes, there are sub-schemes in which, except one term, the couplings can have no term with more than two derivatives. In the sub-scheme that we have chosen, the 872 couplings appear in 55 different structures. We fix some of the parameters in type II supersting theory by its corresponding four-point functions. The coupling which has term with more than two derivatives is constraint to be zero by the four-point functions.

Performance Evaluation of the Application of Terotechnology in the University of Benin, Nigeria, Enterprise Table Water Factory, Using Cronbach Alpha (α) Model

Terotechnology is an observational science that integrates technological and managerial skills essentially for the socio-economic development of an industry, it is employed in this paper using statistical study to apply mathematical models such as the Cronbach alpha in analyzing data for performance evaluation of a table water factory gathered from administered questionnaires in a five Likert scale in order to evaluate its practices in the factory to help boost the productivity of the University of Benin Enterprises table water factory. The goal of this study is to reduce poor maintenance practices. Primary data were collected from the factory workers and utilized in computing the Cronbach Alpha in order to evaluate internal consistency collected data. From the index of association, α ≥ 0.9 was considered excellent and the percentage of respondents that strongly agreed on the practice of terotechnology was high at 265 out of 500 respondents with 53% response with a value of Cronbach Alpha recorded at 0.9598, indicating that the questions were internally consistent. Therefore, 85% of the workforce supported the implementation and the practice of Terotechnology in the table water factory in order to improve the day to day running of the table water factory.

DELTA^m STATISTICAL CONVERGENCE OF ORDER alpha FOR DOUBLE SEQUENCES OF FUNCTIONS

In this paper, we introduce and examine the concepts of Delta^m pointwise and Delta^m uniform statistical convergence of order alpha for double sequences of real valued functions. Also we give the concept of Delta^m statistically Cauchy sequence for double sequences of real valued functions and prove that it is equivalent to Delta^m pointwise statistical convergence of order alpha for double sequences of real valued functions. Also some relations between S_alpha^ 2(Delta^m,f )-statistical convergence and strong [w_p^2]_alpha (Delta^m,f )-summability are given.

F-LACUNARY STATISTICAL CONVERGENCE AND STRONG f-LACUNARY SUMMABILITY OF ORDER α OF DOUBLE SEQUENCES

The main object of this article is to introduce the concepts of f-lacunary statistical convergence of order alpha and strong f-lacunary summability of order alpha of double sequences and give some inclusion relations between these concepts.

Transversity and heavy quark production on hadron colliders

The azimuthal asymmetry of heavy quarks production on double polarized proton–proton and proton–antiproton colliders are studied in this work at next-to-leading order in alpha _s, with some details included. The purpose is to see whether the effect of extracted transversity distribution functions can be seen on present and near future colliders. All analytic one-loop hard coefficients are given. Numerical results for the asymmetry on proton–(anti)proton colliders are presented.

Technology Party

Next month, the MACH 2020 show will open its doors. In the second of our major previews, we have more show news. Exhibitors are listed by alpha order (UK agents, where relevant, in brackets), with their technology areas highlighted by various technology hashtags

Saturation rates of filtered back projection approximations

This paper concerns the approximation of bivariate functions by using the well-known filtered back projection (FBP) formula from computerized tomography. We prove error estimates and convergence rates for the FBP approximation of target functions from Sobolev spaces mathrm H^alpha ({mathbb {R}}^2) of fractional order alpha >0, where we bound the FBP approximation error, which is incurred by the application of a low-pass filter, with respect to the weaker norms of the rougher Sobolev spaces mathrm H^sigma ({mathbb {R}}^2), for {0 le sigma le alpha }. In particular, we generalize our previous results to non band-limited filter functions and show that the decay rate of the error saturates at fractional order depending on smoothness properties of the filter’s window function at the origin. The theoretical results are supported by numerical simulations.

On the Starting Blocks

We are just a couple of months away from the UK’s premier manufacturing technology show, MACH. The exhibitors are beginning to reveal their wares, so we kick off our MACH previews in earnest this issue, having set the scene in January ( https://is.gd/gipabu ). Exhibitors are listed by alpha order (UK agents, where relevant, in brackets), with their technology areas highlighted by various hashtags

Regularity of solutions to anisotropic nonlocal equations

We study harmonic functions associated to systems of stochastic differential equations of the form dX_t^i=A_{i1}(X_{t-})dZ_t^1+cdots +A_{id}(X_{t-})dZ_t^d, iin {1,dots ,d}, where Z_t^j are independent one-dimensional symmetric stable processes of order alpha _jin (0,2), jin {1,dots ,d}. In this article we prove Hölder regularity of bounded harmonic functions with respect to solutions to such systems.

A variation on strongly ideal lacunary ward continuity

The main purpose of this paper is to introduce the concept of strongly ideal lacunary quasi-Cauchyness of order (alpha,beta) of sequences of real numbers. Strongly ideal lacunary ward continuity of order (alpha,beta) is also investigated. Interesting results are obtained.

Fractional-Order Phase Shifters with Constant Magnitude Frequency Responses

This contribution presents and experimentally analyzes the idea how to reach the constant magnitude as well as the phase response in the fractional-order (FO) phase when shifting two-ports. The straightforward method employing the automatic gain control circuit (AGC) in a cascade after so-called constant phase block approximating FO integrator or differentiator is studied. The variable gain amplifier utilized in AGC and simple RC-based FO constant phase elements (approximating capacitors with order alpha = 1/4 and alpha = 1/2 as an example) connected in the feedback of operational amplifier-based integrator are established in the experimental setup. The operation indicated in three decades (between 100 Hz and 100 kHz) is evaluated. The known solutions of the standard FO phase shifting circuits are discussed and generally compared with the features obtained in this paper, together with the supposed effects of AGC on their performances.

Higher-order power corrections in a transverse-momentum cut for colour-singlet production at NLO

We consider the production of a colourless system at next-to-leading order in the strong coupling constant alpha _{{displaystyle } {scriptstyle } {scriptscriptstyle } {scriptscriptstyle } mathrm{S}}. We impose a transverse-momentum cutoff, q_{{displaystyle } {scriptstyle } {scriptscriptstyle } {scriptscriptstyle } mathrm{T}}^{{displaystyle } {scriptstyle } {scriptscriptstyle } {scriptscriptstyle } mathrm{cut}}, on the colourless final state and we compute the power corrections for the inclusive cross section in the cutoff, up to the fourth power. The study of the dependence of the cross section on q_{{displaystyle } {scriptstyle } {scriptscriptstyle } {scriptscriptstyle } mathrm{T}}^{{displaystyle } {scriptstyle } {scriptscriptstyle } {scriptscriptstyle } mathrm{cut}} allows for an understanding of its behaviour at the boundaries of the phase space, giving hints on the structure at all orders in alpha _{{displaystyle } {scriptstyle } {scriptscriptstyle } {scriptscriptstyle } mathrm{S}} and on the identification of universal patterns. The knowledge of such power corrections is also a required ingredient in order to reduce the dependence on the transverse-momentum cutoff of the QCD cross sections at higher orders, when the q_{mathrm{T}}-subtraction method is applied. We present analytic results for both Drell–Yan vector boson and Higgs boson production in gluon fusion and we illustrate a process-independent procedure for the calculation of the all-order power corrections in the cutoff. In order to show the impact of the power-correction terms, we present selected numerical results and discuss how the residual dependence on q_{{displaystyle } {scriptstyle } {scriptscriptstyle } {scriptscriptstyle } mathrm{T}}^{{displaystyle } {scriptstyle } {scriptscriptstyle } {scriptscriptstyle } mathrm{cut}} affects the total cross section for Drell–Yan Z production and Higgs boson production via gluon fusion at the LHC.

Effective action of bosonic string theory at order alpha '^2

Recently, it has been shown that the gauge invariance requires the minimum number of independent couplings for B-field, metric and dilaton at order alpha '^2 to be 60. In this paper we fix the corresponding 60 parameters in string theory by requiring the couplings to be invariant under the global T-duality transformations. The Riemann cubed terms are exactly the same as the couplings that have been found by the S-matrix calculations.

Discovery of 33mer in chromosome 21 \u2013 the largest alpha satellite higher order repeat unit among all human somatic chromosomes

The centromere is important for segregation of chromosomes during cell division in eukaryotes. Its destabilization results in chromosomal missegregation, aneuploidy, hallmarks of cancers and birth defects. In primate genomes centromeres contain tandem repeats of ~171 bp alpha satellite DNA, commonly organized into higher order repeats (HORs). In spite of crucial importance, satellites have been understudied because of gaps in sequencing - genomic “black holes”. Bioinformatical studies of genomic sequences open possibilities to revolutionize understanding of repetitive DNA datasets. Here, using robust (Global Repeat Map) algorithm we identified in hg38 sequence of human chromosome 21 complete ensemble of alpha satellite HORs with six long repeat units (≥20 mers), five of them novel. Novel 33mer HOR has the longest HOR unit identified so far among all somatic chromosomes and novel 23mer reverse HOR is distant far from the centromere. Also, we discovered that for hg38 assembly the 33mer sequences in chromosomes 21, 13, 14, and 22 are 100% identical but nearby gaps are present; that seems to require an additional more precise sequencing. Chromosome 21 is of significant interest for deciphering the molecular base of Down syndrome and of aneuploidies in general. Since the chromosome identifier probes are largely based on the detection of higher order alpha satellite repeats, distinctions between alpha satellite HORs in chromosomes 21 and 13 here identified might lead to a unique chromosome 21 probe in molecular cytogenetics, which would find utility in diagnostics. It is expected that its complete sequence analysis will have profound implications for understanding pathogenesis of diseases and development of new therapeutic approaches.