Logarithmic Expansion Research Articles

On Qi’s Normalized Remainder of Maclaurin Power Series Expansion of Logarithm of Secant Function

In the study, the authors introduce Qi’s normalized remainder of the Maclaurin power series expansion of the function lnsecx=−lncosx; in view of a monotonicity rule for the ratio of two Maclaurin power series and by virtue of the logarithmic convexity of the function (2x−1)ζ(x) on (1,∞), they prove the logarithmic convexity of Qi’s normalized remainder; with the aid of a monotonicity rule for the ratio of two Maclaurin power series, the authors present the monotonic property of the ratio between two Qi’s normalized remainders.

Supersymmetric Expansion Algorithm and Complete Analytical Solution for the Hulthén and Anharmonic Potentials

Abstract An algorithm for providing analytical solutions to Schrödinger’s equation with non-exactly solvable potentials is elaborated. It represents a symbiosis between the logarithmic expansion method and the techniques of the supersymmetric quantum mechanics as extended toward non shape invariant potentials. The complete solution to a given Hamiltonian H0 is obtained from the nodeless states of the Hamiltonian H0 and of a set of supersymmetric partners H1, H2, …, Hr. The nodeless states (dubbed “edge” states) are unique and in general can be ground or excited states. They are solved using the logarithmic expansion which yields an infinite system of coupled first order hierarchical differential equations, converted later into algebraic equations with recurrence relations which can be solved order by order. We formulate the aforementioned scheme, termed to as “Supersymmetric Expansion Algorithm” step by step and apply it to obtain for the first time the complete analytical solutions of the three dimensional Hulthén–, and the one-dimensional anharmonic oscillator potentials.

Light quark mediated Higgs boson production in association with a jet at the next-to-next-to-leading order and beyond

We study the light quark effect on the Higgs boson production in association with a jet at the LHC in the intermediate transverse momentum region between the quark and the Higgs boson mass scales. Though the effect is suppressed by the small Yukawa coupling, it is enhanced by large logarithms of the quark mass ratio to the Higgs boson mass or transverse momentum. Following a remarkable success of the logarithmic expansion [40] for the prediction of the next-to-next-to-leading bottom quark contribution to the total cross section of the Higgs boson production we extend the analysis to its kinematical distributions. A new factorization formula is derived for the light quark mediated gg → Hg amplitudes and the differential cross section of the process is computed in the logarithmic approximation, which is used for an estimate of the bottom quark effect at the next-to-next-to-leading order.

Logarithmic Expansion, Entropy, and Dimension for Set-Valued Maps

Logarithmic Expansion, Entropy, and Dimension for Set-Valued Maps

Tensions with the flat ΛCDM model from high-redshift cosmography

ABSTRACT The longstanding search for the cosmological model that best describes the Universe has been made more intriguing since the recent discovery of the Hubble constant, H0, tension observed between the value of H0 from the Cosmic Microwave Background and from type Ia supernovae (SNe Ia). Hence, the commonly trusted flat Λ cold dark matter (ΛCDM) model is under investigation. In this scenario, cosmography is a very powerful technique to investigate the evolution of the Universe without any cosmological assumption, thus revealing tensions between observational data and predictions from cosmological models in a completely model-independent way. We here employ a robust cosmographic technique based on an orthogonal logarithmic polynomial expansion of the luminosity distance to fit quasars (QSOs) alone and QSOs combined with Gamma-Ray Bursts (GRBs), SNe Ia, and Baryon Acoustic Oscillations. To apply QSOs and GRBs as probes we use, respectively, the Risaliti–Lusso relation between ultraviolet and X-ray luminosities and the ‘Dainotti GRB 3D relation’ among the rest-frame end time of the X-ray plateau emission, its corresponding luminosity, and the peak prompt luminosity. We also correct QSOs and GRBs for selection biases and redshift evolution and we employ both the traditional Gaussian likelihood and the newly discovered best-fitting likelihoods for each probe investigated. This comprehensive analysis reveals a strong tension ($\gt 4 \, \sigma$) between our data sets and the flat ΛCDM model proving the power of both the cosmographic approach and high-redshift sources, such as QSOs and GRBs, which can probe the Universe at early epochs.

Fractional analytic QCD beyond leading order in the timelike region

In this paper we show that, as in the spacelike case, the inverse logarithmic expansion is applicable for all values of the argument of the analytic coupling constant. We present two different approaches, one of which is based primarily on trigonometric functions, and the latter is based on dispersion integrals. The results obtained up to the 5th order of perturbation theory, have a compact form and their acquiring is much easier than the methods that have been used before. As an example, we apply our results to study the Higgs boson decay into a bb pair.

1 H NMR-based process understanding and biochemical marker identification methodology for monitoring CHO cell culture process during commercial-scale manufacturing.

Controlling the process of CHO cell fed-batch culture is critical for biologics quality control. However, the biological complexity of cells has hampered the reliable process understanding for industrial manufacturing. In this study, a workflow was developed for the consistency monitoring and biochemical marker identification of the commercial-scale CHO cell culture process through 1 H NMR assisted with multivariate data analysis (MVDA). Firstly, a total of 63 metabolites were identified in this study object in 1 H NMR spectra of the CHO cell-free supernatants. Secondly, multivariate statistical process control (MSPC) charts were used to evaluate process consistency. According to MSPC charts, the batch-to-batch quality consistency was high, indicating the CHO cell culture process at the commercial scale was well-controlled and stable. Then, the biochemical marker identification was provided through orthogonal partial least square discriminant analysis (OPLS-DA) based S-line plots during the cell logarithmic expansion, stable growth, and decline phases. Identified biochemical markers of the three cell growth phases were as follows: L-glutamine, pyroglutamic acid, 4-hydroxyproline, choline, glucose, lactate, alanine, and proline were of the logarithmic growth phase; isoleucine, leucine, valine, acetate, and alanine were of the stable growth phase; acetate, glycine, glycerin, and gluconic acid were of the cell decline phase. Additional potential metabolic pathways that might influence the cell culture phase transitions were demonstrated. The workflow proposed in this study demonstrates that the combination of MVDA tools and 1 H NMR technology is highly appealing to the research of the biomanufacturing process, and applies well to provide guidance in future work on consistency evaluation and biochemical marker monitoring of the production of other biologics.

Fractional analytic QCD beyond leading order

Fractional analytic QCD is constructed beyond leading order using the standard inverse logarithmic expansion. It is shown that, contrary to the usual QCD coupling constant, for which this expansion can be used only for large values of its argument, in the case of analytic QCD, the inverse logarithmic expansion is applicable for all values of the argument of the analytic coupling constant. We present four different views, two of which are based primarily on Polylogarithms and generalized Euler ζ-functions, and the other two are based on dispersion integrals. The results obtained up to the 5th order of perturbation theory, have a compact form and do not contain complex special functions that were used to solve this problem earlier. As an example, we apply our results to study the polarized Bjorken sum rule, which is currently measured very accurately.

Electron-photon vertex and dynamical chiral symmetry breaking in reduced QED: An advanced study of gauge invariance

We study the effect of a refined electron-photon vertex on the dynamical breaking of chiral symmetry in reduced quantum electrodynamics. We construct an educated {\em ansatz} for this vertex which satisfies the required discrete symmetries under parity, time reversal and charge conjugation operations. Furthermore, it reproduces its asymptotic perturbative limit in the weak coupling regime and ensures the massless electron propagator is multiplicatively renormalizable in its leading logarithmic expansion. Employing this vertex {\em ansatz}, we solve the gap equation to compute dynamically generated electron mass whose dependence on the electromagnetic coupling is found to satisfy Miransky scaling law. We also investigate the gauge dependence of this dynamical mass as well as that of the critical coupling above which chiral symmetry is dynamically broken. As a litmus test of our vertex construction, both these quantities are rendered virtually gauge independent within a certain interval of values considered for the covariant gauge parameter.

Cancer’s camouflage: Microvesicle shedding from cholesterol-rich tumor plasma membranes might blindfold first-responder immunosurveillance strategies

Intermediary metabolism of tumors is characterized, in part, by a dysregulation of the cholesterol biosynthesis pathway at its rate-controlling enzyme providing the molecular basis for tumor membranes (mitochondria, plasma membrane) to become enriched with cholesterol (Bloch, 1965; Feo et al., 1975; Brown and Goldstein, 1980; Goldstein and Brown, 1990). Cholesterol enriched tumor mitochondria manifest preferential citrate export, thereby providing a continuous supply of substrate precursor for the tumor’s dysregulated cholesterogenesis via a “truncated” Krebs/TCA cycle (Kaplan et al., 1986; Coleman et al., 1997). Proliferating tumors shed elevated amounts of plasma membrane-derived extracellular vesicles (pmEV) compared with normal tissues (van Blitterswijk et al., 1979; Black, 1980). Coordination of these metabolic phenomena in tumors supports the enhanced intercalation of cholesterol within the plasma membrane lipid bilayer’s cytoplasmic face, the promotion of outward protrusions from the plasma membrane, and the evolution of cholesterol enriched pmEV. The pmEV shed by tumors possess elevated cholesterol and concentrated cell surface antigen clusters found on the tumor cells themselves (Kim et al., 2002). Upon exfoliation, saturation of the extracellular milieu with tumor-derived pmEV could allow early onset mammalian immune surveillance mechanisms to become “blind” to an evolving cancer and lose their ability to detect and initiate strategies to destroy the cancer. However, a molecular mechanism is lacking that would help explain how cholesterol enrichment of the pmEV inner lipid bilayer might allow the tumor cell to evade the host immune system. We offer a hypothesis, endorsed by published mathematical modeling of biomembrane structure as well as by decades of in vivo data with diverse cancers, that a cholesterol enriched inner bilayer leaflet, coupled with a logarithmic expansion in surface area of shed tumor pmEV load relative to its derivative cancer cell, conspire to force exposure of otherwise unfamiliar membrane integral protein domains as antigenic epitopes to the host’s circulating immune surveillance system, allowing the tumor cells to evade destruction. We provide elementary numerical estimations comparing the amount of pmEV shed from tumor versus normal cells.

Disruption of the crypt niche promotes outgrowth of mutated colorectal tumor stem cells.

Recent data establish a logarithmic expansion of leucine rich repeat containing G protein coupled receptor 5–positive (Lgr5+) colonic epithelial stem cells (CESCs) in human colorectal cancer (CRC). Complementary studies using the murine 2-stage azoxymethane–dextran sulfate sodium (AOM-DSS) colitis-associated tumor model indicate early acquisition of Wnt pathway mutations drives CESC expansion during adenoma progression. Here, subdivision of the AOM-DSS model into in vivo and in vitro stages revealed DSS induced physical separation of CESCs from stem cell niche cells and basal lamina, a source of Wnt signals, within hours, disabling the stem cell program. While AOM delivery in vivo under non-adenoma-forming conditions yielded phenotypically normal mucosa and organoids derived thereof, niche injury ex vivo by progressive DSS dose escalation facilitated outgrowth of Wnt-independent dysplastic organoids. These organoids contained 10-fold increased Lgr5+ CESCs with gain-of-function Wnt mutations orthologous to human CRC driver mutations. We posit CRC originates by niche injury–induced outgrowth of normally suppressed mutated stem cells, consistent with models of adaptive oncogenesis.

Logarithmic expansion of many-body wave packets in random potentials

Anderson localization confines the wave function of a quantum particle in a one-dimensional random potential to a volume of the order of the localization length $\xi$. Nonlinear add-ons to the wave dynamics mimic many-body interactions on a mean field level, and result in escape from the Anderson cage and in unlimited subdiffusion of the interacting cloud. We address quantum corrections to that subdiffusion by (i) using the ultrafast unitary Floquet dynamics of discrete-time quantum walks, (ii) an interaction strength ramping to speed up the subdiffusion, and (iii) an action discretization of the nonlinear terms. We observe the saturation of the cloud expansion of $N$ particles to a volume $\sim N\xi$. We predict and observe a universal intermediate logarithmic expansion regime which connects the mean-field diffusion with the final saturation regime and is entirely controlled by particle number $N$. The temporal window of that regime grows exponentially with the localization length $\xi$.

Study of the non-Hermitian PT -symmetric gϕ2(iϕ)ε theory: Analysis of all orders in ε and resummations

In a recent work the Green's functions of the $\mathcal{PT}$-symmetric scalar theory $g \phi^{2}(i\phi)^\epsilon$ were calculated at the first order of the logarithmic expansion, i.e. at first order in $\epsilon$, and it was proposed to use this expansion in powers of $\epsilon$ to implement a systematic renormalization of the theory. Using techniques that we recently developed for the analysis of an ordinary (hermitian) scalar theory, in the present work we calculate the Green's functions at $O(\epsilon^2)$, pushing also the analysis to higher orders. We find that, at each finite order in $\epsilon$, the theory is non-interacting for any dimension $d \geq 2$. We then conclude that by no means this expansion can be used for a systematic renormalization of the theory. We are then lead to consider resummations, and we start with the leading contributions. Unfortunately, the results are quite poor. Specifying to the physically relevant $i g \phi^3$ model, we show that this resummation simply gives the trivial lowest order results of the weak-coupling expansion. We successively resum subleading diagrams, but again the results are rather poor. All this casts serious doubts on the possibility of studying the theory $g \phi^{2}(i\phi)^\epsilon$ with the help of such an expansion. We finally add that the findings presented in this work were obtained by us some time ago (December 2019), and we are delighted to see that these results, that we communicated to C.M. Bender in December 2019, are confirmed in a recent preprint (e-Print:2103.07577) of C.M. Bender and collaborators.

COVID-19 PANDEMIC AND MANAGEMENT OF HYPERTENSION

Dear Editor, In December 2019, a new virus which is known as SARS-COV-2 (COVID-19) was identified. In a short period, this virus spread rapidly and caused significant morbidities and mortalities across the earth. On March 11, 2020, the World Health Organization (WHO) declared a pandemic due to the logarithmic expansion of COVID-19 cases globally.1 Various guidelines were issued, and a complete lockdown has been observed on a large scale to stop the spread of the virus. Currently, there is no specific treatment for COVID-19 is available. Throughout the year 2020, scientists struggled a lot to find the COVID-19 cure, and many vaccines are successfully developed which would be helpful in the prevention of disease. Nevertheless, the emergence of virus variants remains an issue. The epidemiological trends and clinical features of this disease have been reported in several publications.2 Due to comorbidities, COVID-19 disease can exacerbate and may result in increased severity and deadly consequences. In a study, the most common comorbidities in COVID-19 patients were reported as following; diabetes (19%), hypertension (30%), and coronary heart disease (8%). In hypertension, blood pressure elevates from the threshold level. The occurrence of hypertension is not necessarily to be associated with COVID-19 as hypertension is quite frequent in geriatric patients, and these patients are at higher risk of being infected with COVID-19.3,4 Angiotensin receptor blockers (ARBs) and angiotensin-converting enzyme (ACE) inhibitors are widely prescribed for the cure of hypertension and other cardiovascular-related diseases. On the other hand, the COVID-19 virus binds with ACE2 to gain entry into the lung cells. ACE inhibitors and ARBs escalate ACE2 that could hypothetically increase the chance of COVID-19 binding to lung cells and could headway to more damage. Conversely, in experimental studies, ACE2 showed a protective effect against lung injury. Due to the anti-inflammatory potential of ACE inhibitors and ARBs, these agents can reduce the incidence of developing myocarditis and acute respiratory distress syndrome in COVID-19 patients. There is no evidence that hypertension is linked with the COVID-19 and anti-hypertensive medicines (ACE inhibitors and ARBs) are either harmful or beneficial during the COVID-19 pandemic.5 During this unprecedented situation, the Council on Hypertension of the European Society of Cardiology released a statement that “The Council on Hypertension strongly recommends that physicians and patients should continue treatment with their usual anti-hypertensive therapy because there is no clinical or scientific evidence to suggest that treatment with ACEIs or ARBs should be discontinued because of the COVID-19 infection.” After this announcement, many other societies also recommend that patients should continue using their current hypertensive therapy and if necessary, after careful assessment, changes can be made in the hypertensive regimen.6 According to estimation, globally, 1.5 billion people can suffer from hypertension by 2025 which may contribute approximately 75% of stroke risk and 50% of heart disease risk. CVDs accounts almost 38% of deaths related to the non-communicated disease (NCDs). In Pakistan, hypertension is a chief health concern that leads to significant morbidity and mortality. Blood pressure can be control with medications and lifestyle modifications. One of the best approaches to control and improve blood pressure is team-based care consisting of doctors, pharmacists, and nurses. During COVID-19, collaborative efforts are required to improve patient’s quality of life and to reduce the healthcare burden.7,8 Keywords: COVID-19, Hypertension, Pandemic, ACE inhibitors

Association between air pollution in Lima and the high incidence of COVID-19: findings from a post hoc analysis.

BackgroundCoronavirus disease 2019 (COVID-19) originated in the People’s Republic of China in December 2019. Thereafter, a global logarithmic expansion of cases occurred. Some countries have a higher rate of infections despite the early implementation of quarantine. Air pollution might be related to high susceptibility to the virus and associated case fatality rates (deaths/cases*100). Lima, Peru, has the second highest incidence of COVID-19 in Latin America and also has one the highest levels of air pollution in the region.MethodsThis study investigated the association of levels of PM2.5 exposure in previous years (2010–2016) in 24 districts of Lima with cases, deaths and case fatality rates for COVID-19. Multiple linear regression was used to evaluate this association controlled by age, sex, population density and number of food markets per district. The study period was from March 6 to June 12, 2020.ResultsThere were 128,700 cases in Lima and 2382 deaths due to COVID-19. The case fatality rate was 1.93%. Previous exposure to PM2.5 (2010—2016) was associated with the number of COVID-19- cases (β = 0.07; 95% CI: 0.034–0.107) and deaths (β = 0.0014; 95% CI: 0.0006–0.0.0023) but not with the case fatality rate.ConclusionsAfter adjusting for age, sex and number of food markets, the higher rates of COVID-19 in Metropolitan Lima are attributable to the increased PM2.5 exposure in the previous years, among other reasons. Reduction in air pollution from a long-term perspective and social distancing are needed to prevent the spread of virus outbreaks.

Logarithmic expansion of field theories: higher orders and resummations

A formal expansion for the Green’s functions of a quantum field theory in a parameter delta that encodes the “distance” between the interacting and the corresponding free theory was introduced in the late 1980s (and recently reconsidered in connection with non-hermitian theories), and the first order in delta was calculated. In this paper we study the {mathcal {O}}(delta ^2) systematically, and also push the analysis to higher orders. We find that at each finite order in delta the theory is non-interacting: sensible physical results are obtained only resorting to resummations. We then perform the resummation of UV leading and subleading diagrams, getting the {mathcal {O}}(g) and {mathcal {O}}(g^2) weak-coupling results. In this manner we establish a bridge between the two expansions, provide a powerful and unique test of the logarithmic expansion, and pave the way for further studies.

Edge crack sensitivity versus tensile local ductility of AHSS sheet steels

There is a growing interest in correlating usual tensile testing results with edge crack sensitivity testing from punched ISO16630 hole expansion ratio HER (10mm shear cut hole, 12% clearance, conical expansion tool). A new kind of tensile local ductility parameter has been developed lately based on broken sample surface of tensile specimens after testing. Reduction in area or thickness at fracture are more sensitive than conventional fracture elongation with a 50 to 80m gage length to characterize the local ductility potential of sheet steels. A representative amount (300 different sets of samples) of cold rolled sheet steels have been tested in the tensile strength range 600-1200MPa and thickness range 1-2mm with 3 replicates in the transverse and longitudinal direction with ISO 6892-1, type 2, A80 tensile samples. Correlation levels of ISO16630 HER values with conventional tensile mechanical properties such as uniform & fracture elongation, yield & tensile strength, n-& r-values or derivatives are disappointing low for the investigated AHSS grades. There is however a massive improvement in the empirical statistical correlation when using local ductility properties based on fracture area or thickness reduction measurements on broken tensile samples. Logarithmic local ductility strains correlate generally linearly with logarithmic hole expansion ratio. Logarithmic true local ductility values are proving more suitable than engineering strains for correlations. Transverse direction improves slightly the correlation quality vs. longitudinal direction. The correlation is also higher for thickness reduction in comparison to reduction of area based properties.

Generalized gravitational baryogenesis of well-known f(T,TG) and f(T,B) models

The baryogenesis presents the theoretical mechanism that describes the matter-antimatter asymmetry in the history of early universe. In this work, we investigate the gravitational baryogenesis phenomena in the frameworks of $f(T, T_G)$ (where $T$ and $T_G$ are the torsion scalar and teleparallel equivalent to the Gauss-Bonnet term respectively) and $f(T, B)$ (where $B$ denotes the boundary term between torsion and Ricci scalar) gravities. For $f(T,T_G)$-gravity, we consider two generic power law models while logarithmic and general Taylor expansion models for $f(T,B)$-gravity. We consider power law scale factor for each model and compute baryon to entropy ratio by assuming that the universe filled by perfect fluid and dark energy. We find generalized baryogenesis interaction which is proportional to $\partial_\mu f(T+T_G)$ and $\partial_\mu f(T+B)$ for both theories of gravity. We compare our results against current astrophysical data of baryon to entropy ratio, which indicates excellent consistency with observational bounds (i.e., $\frac{\eta_B}{S} = 9.42 \times 10^{-11}$).

Low-Parametrical Approximation of Solar Radiation’s Brightness Coefficient in a Gas Absorption Band

The problem of the sunlight transfer equation in the atmosphere in a gas absorption band is considered. The structure of the spectral dependence of the brightness coefficient (reflectance) of the radiation, reflected by the atmosphere–surface system is studied. The low-parametrical approximations of the reflectance as an expansion of the inverse logarithm of the reflectance by the degrees of the absorption section are constructed. The approximation are a synthesis of the Bouguer-Lambert-Beer law. The explicit algorithm for calculating the approximation parameters based on known values of reflectance is described. It is shown how the constructed approximations can be used to reduce the time of the line-by-line calculations of reflectance.

Multi-electron anisotropic quantum dots/TMDCs/CNT families under magnetic field: analytical treatment to first Brillouin zone by Fermi liquid model

Acute Coulomb interaction of the two-dimensional systems has drawn special attention due to its unusual logarithmic Green function expansion. As the number of electrons (N) increases, Pauli Exclusion principle emerges inevitably with rapidly growing electronic correlations. Quantum dot, Transition metal dichalcogenides (TMDC) and Carbon nanotube (CNT) families of 2-D anisotropic mesoscopic systems are rich habitats of electrons. Schrödinger equations of such electrons in electrical confinement and transverse magnetic field can be recast in self-adjoint Whittaker-M functions facilitating each Coulomb interaction to terminable, exact and single summed Lauricella function via Chu-Vandermonde identity. For , multipoles of Green function expansion also succumb to terminable, single-summed, analytical integrals by inserting discretised closure relations. Thus, multi-configuration Slater determinantal states are employed for strong correlation of Fermi liquid model of first Brillouin zone (FBZ) within giga-units of reciprocal lattices (mesoscopic scale). Chemical potential, addition energies of WS, GaAs and model systems of dielectric constant have set benchmark at low and high confinement potentials, as a function of magnetic field and density of electrons. Because of sharp falls in surface integrals of both Newman and Dirichlet forms of Green function, Coulomb interaction takes to (or leads to) multipole expansion of generic coordinates. Formation of composite-fermions may be anticipated. At the most, octupole is sufficient for the convergence.