Cancellation Of Terms Research Articles

Global regularity criteria for the 2D Magneto-micropolar Equations with Partial Dissipation

The magneto-micropolar equations model the motion of electrically conducting micropolar fluids in the presence of a magnetic field.These equations have been the focus of numerous analytical, experimental, and numerical investigations.One fundamental problem concerning these equations is whether their classical solutions are globally regular for all time or if they develop finite time singularities.The global regularity problem can be particularly challenging when there is only partial dissipation. In this paper, we study the 2D incompressible magneto-micropolar equations with partial dissipation prove two new regularity results. The first result addresses a weak solution, and the second result establishes global regularity criteria. As a consequence, we can single out one special partial dissipation case and establish the global regularity if (∂y u1, ∂y u2) ∈ L∞ [0, T ], R2. The proofs of our main results rely on anisotropic Sobolev-type inequalities and the appropriate combination and cancellation of terms.

On the resilience of the gravitational variational principle under renormalization

A well-defined variational principle for gravitational actions typically requires to cancel boundary terms produced by the variation of the bulk action with a suitable set of boundary counterterms. This can be achieved by carefully balancing the coefficients multiplying the bulk operators with those multiplying the boundary ones. A typical example of this construction is the Gibbons-Hawking-York boundary action that needs to be added to the Einstein-Hilbert one in order to have a well-defined metric variation for General Relativity with Dirichlet boundary conditions. Quantum fluctuations of matter fields lead to a renormalization of these coefficients which may or may not preserve this balance. Indeed, already at the level of General Relativity, the resilience of the matching between bulk and boundary constants is far from obvious and it is anyway incomplete given that matter generically induces quadratic curvature operators. We investigate here the resilience of the matching of higher-order couplings upon renormalization by a non-minimally coupled scalar field and show that a problem is present. Even though we do not completely solve the latter, we show that it can be greatly ameliorated by a wise splitting between dynamical and topological contributions. Doing so, we find that the bulk-boundary matching is preserved up to a universal term (present for any Weyl invariant matter field content), whose nature and possible cancellation we shall discuss in the end.

Extended quasiparticle Padé approximation for non-Fermi liquids

The extended quasiparticle picture is adapted to non-Fermi systems by suggesting a Padé approximation which interpolates between the known small scattering-rate expansion and the deviation from the Fermi energy. The first two energy-weighted sum rules are shown to be fulfilled independent of the interpolating function for any selfenergy. For various models of one-dimensional Fermions scattering with impurities the quality of the Padé approximation for the spectral function is demonstrated and the reduced density matrix or momentum distribution is reproduced not possessing a jump at the Fermi energy. Though the two-fold expansion is necessary to realize the spectral function and reduced density, the extended quasiparticle approximation itself is sufficient for the description of transport properties due to cancellation of divergent terms under integration. The T-matrix approximation leads to the delay time as the time two particles spend in a correlated state. This contributes to the reduced density matrix and to an additional part in the conductivity which is presented at zero and finite temperatures. Besides a localization at certain impurity concentrations, the conductivity shows a maximum at small temperatures interpreted as onset of superconducting behaviour triggered by impurities. The Tan contact reveals the same universal behaviour as known from electron–electron scattering.Graphic abstract

Recombination mechanism for D0-meson production and [formula omitted] production asymmetry in the LHCb p+20Ne fixed-target experiment

We discuss production of neutral D mesons in proton-proton collisions at the LHC (fixed target mode) in the framework of the BJM recombination model. We present rapidity and transverse momentum distributions of D mesons and compare the recombination contribution to the dominant gluon-gluon fusion mechanism. Both the direct production, as dictated by the matrix element, and fragmentation of the associated c or c¯ are included. The latter mechanism generates D mesons with smaller rapidities than those produced directly. We calculate the D0+D‾0 meson distributions relevant for fixed target p+4He collisions at s = 86.6 GeV as well as for p+20Ne collisions at s = 69 GeV. The recombination component is consistent with the LHCb data and in addition results in production asymmetry. The asymmetries in D0−D0‾ production as a function of rapidity and transverse momentum are shown and the cancellation of terms for direct production and associated c/c¯ fragmentation is discussed.

Can FMR1 CGG repeat lengths predict the outcome in ICSI cycles?

The aim of this study was to assess relationship between CGG repeat lengths and ovarian reserve and response to controlled ovarian stimulation (COH). This prospective cohort study was carried out on patients (n = 49) who were admitted to the in vitro fertilization (IVF) clinic of the Zeynep Kamil Women's and Children's Diseases Training and Research Hospital, University of Health Sciences. Women under 40 years of age with premature ovarian insufficiency underwent genetic analysis to determine CGG repeat lengths. Ovarian reserve was assessed for each participant and participants underwent ovarian hyperstimulation and intracytoplasmic sperm injection (ICSI) cycle. Relationships between ovarian reserve, cycle outcome and CGG repeat lengths were assessed. Variables including fertility assessment including ovarian reserve tests (Follicle stimulating hormone (FSH), Luteinizing hormone (LH), Estradiol (E2), Prolactin (PRL), Thyroid stimulating hormone (TSH), Antimullerian hormone (AMH), antral follicle count (AFC) tests) and some IVF cycle characteristics were assessed in relation to number of CGG repeat numbers. None of the ovarian reserve tests and cycle characteristics was found to be correlated with CGG repeat lengths. Comparison of ovarian reserve tests and cycle characteristics revealed no difference between groups of women with CGG repeat length > 55 and CGG repeat length ≤ 55. Antimullerian hormone (AMH) was a significant predictor for cycle cancellation (AUC = 0.779, P = 0.008). AMH level > 0.035 was found to be the optimal cut off value to predict cycles reaching to embryo transfer with 71% sensitivity and 85% specificity. The rate of cycle cancellation was 71% in cases with AMH ≤ 0.035 whereas it was 20% in cases with AMH > 0.035 (p = 0.001). No difference was determined between groups with and without cycle cancellation in terms of CGG repeat lengths (55.3 vs. 53.9, p = 0.769). Among cycles reaching to embryo transfer stage, 3 (13.6%) pregnancies were achieved. Our data showed no relationship between CGG repeat lengths and ovarian reserve and response to controlled ovarian stimulation. This data also showed that no clinical difference between FMR gene mutation related POI and other etiologies.

CMB constraints on monodromy inflation at strong coupling

We carry out a thorough numerical examination of field theory monodromy inflation at strong coupling. We perform an MCMC analysis using a Gaussian likelihood, fitting multiparameter models using CMB constraints on the spectral index and the tensor to scalar ratio. We show that models with uniquely positive Wilson coefficients are ruled out. If there are coefficients that can take on both signs, there can be a cancellation of terms that flattens the potentials and allows one to satisfy current data, and forecasts with strong constraints on the tensor to scalar ratio. Models of field theory monodromy are naturally enhanced to include a mechanism for canceling off radiative corrections to vacuum energy, via vacuum energy sequestering (VES). Although they include a much larger parameter space, we find that a similar numerical examination yields no significant change in the Bayesian evidence for VES enhanced models, with naturalness considerations making them more attractive from a theoretical perspective.

Cancel Culture: An Unproductive Form of Blame

In this paper I argue that Miranda Fricker’s account of blame in “What’s the Point of Blame? A Paradigm Based Explanation” can assist in explaining why cancel culture is ultimately unproductive. In particular, the phenomenon of cancel culture possesses pathological forms of blame. There are three specific pathologies outlined by Fricker that can be observed in cancel culture. They are as follows: cancel culture does not leave room for people to learn from their mistakes, it does not express its blame in the proper ethical register, and cancel culture allows for blame to fester and spread. In the first half of my paper, I will lay out the distinct aspects of Fricker’s paper that relate to cancel culture and a definition of the term cancel culture. In the second half, I will explore the real-life cancelation of actor Lea Michele so as to validate the presence of cancel culture in our society today. Furthermore, I will expand on three of Fricker’s pathologies that are present in cancel culture and refute a counter argument people may pose who are supportive of cancel culture.

Conditions of naturalness and fine-tuning for the type-I seesaw mechanism with four-zero texture

Abstract In this paper, we search for conditions under which the mass matrix of light neutrinos mν is not a result of large cancellations for the type-I seesaw mechanism with four-zero texture. For the Yukawa matrix of neutrinos Yν and heavy Majorana mass matrix MR, these conditions are written as $(Y_{\nu })_{i2} \propto (m_{\nu })_{i2} \Rightarrow (Y_{\nu })_{i2} \propto (M_{R})_{i2}$. We call them alignment conditions because they align certain rows or columns of the three neutrino mass matrices. If these conditions do not hold, the large mixing in mν is a result of fine-tuning due to the cancellation of several terms. Then they are required from the viewpoint of naturalness. They give an explanation of the seesaw invariance of four-zero texture, and place rough restrictions on flavor structures of neutrinos. Under these conditions, Yν must have a cascade hierarchy. For MR, the 12 submatrix has a similar hierarchy to Yν and mν. However, the 23 submatrix has a waterfall hierarchy without some fine-tuning. Therefore, it is likely that Yν and MR have qualitatively different flavor structures. Furthermore, since the conditions restrict CP phases of the matrix elements, they imply the existence of a universal generalized CP symmetry in the neutrino sector.

Photoionization and Electron-Ion Recombination of n = 1 to Very High n-Values of Hydrogenic Ions

Single electron hydrogen or hydrogenic ions have analytical forms to evaluate the atomic parameters for the inverse processes of photoionization and electron-ion recombination (H I + hν↔ H II + e) where H is hydrogen. Studies of these processes have continued until the present day (i) as the computations are restricted to lower principle quantum number n and (ii) to improve the accuracy. The analytical expressions have many terms and there are numerical instabilities arising from cancellations of terms. Strategies for fast convergence of contributions were developed but precise computations are still limited to lower n. This report gives a brief review of the earlier precise methodologies for hydrogen, and presents numerical tables of photoionization cross sections (σPI), and electron-ion recombination rate coefficients (αRC) obtained from recombination cross sections (σRC) for all n values going to a very high value of 800. σPI was obtained using the precise formalism of Burgess and Seaton, and Burgess. αRC was obtained through a finite integration that converge recombination exactly as implemented in the unified method of recombination of Nahar and Pradhan. Since the total electron-ion recombination includes all levels for n = 1–∞, the total asymptotic contribution of n = 801–∞, called the top-up, is obtained through a n−3 formula. A FORTRAN program “hpxrrc.f” is provided to compute photoionization cross sections, recombination cross sections and rate coefficients for any nl. The results on hydrogen atom can be used to obtain those for any hydrogenic ion of charge z through z-scaling relations provided in the theory section. The present results are of high precision and complete for astrophysical modelings.

Casimir forces for the ideal Bose gas in anisotropic optical lattices: the effect of alternating sign upon varying dimensionality

We analyze the thermodynamic Casimir effect occurring in a gas of non-interacting bosons confined by two parallel walls with a strongly anisotropic dispersion inherited from an underlying lattice. In the direction perpendicular to the confining walls, the standard quadratic dispersion is replaced by the term |p| α with α ⩾ 2 treated as a parameter. We derive a closed, analytical expression for the Casimir force depending on the dimensionality d and the exponent α, and analyze it for thermodynamic states in which the Bose–Einstein condensate is present. For α ∈ {4, 6, 8, …} the exponent governing the decay of the Casimir force with increasing distance between the walls becomes modified and the Casimir amplitude Δ α (d) exhibits oscillations of sign as a function of d. Otherwise, we find that Δ α (d) features singularities when viewed as a function of d and α. Recovering the known previous results for the isotropic limit α = 2 turns out to occur via a cancellation of singular terms.

Modeling and Simulation of Mechanical and Electrical Transient of Variable-Speed Pumped Storage Units

In order to study the operation characteristics of large capacity variable-speed pumped storage units connected to the system, the electromechanical transient model is established. Firstly, based on the basic equations of the doubly-fed machine, the generator model represented by an equivalent voltage source is built. Secondly, on the premise of coupling term cancellation, the frequency conversion controller, frequency converter and generator connection module are normalized. Then, the generator model and variable frequency controller model are integrated to form the electromechanical transient model of the unit, which is not only the fitting of external characteristics but also retains the dynamic process of the motor flux linkage and the dynamic characteristics of the controller’s inner loop. Finally, the electromechanical transient model is simulated on the RTDS platform. The simulation results show that the model is correct and effective, which is of great significance to the study of transient problems of large-capacity doubly-fed units connected to the grid.

Current-density relation in the exclusion process with dynamic obstacles.

We investigate the totally asymmetric simple exclusion process (TASEP) in the presence of obstacles that dynamically bind and unbind from the lattice. The model is motivated by biological processes such as transcription in the presence of DNA-binding proteins. Similar models have been studied before using the mean-field approximation, but the exact relation between the particle current and density remains elusive. Here, we first show using extensive Monte Carlo simulations that the current-density relation in this model assumes a quasiparabolic form similar to that of the ordinary TASEP without obstacles. We then attempt to explain this relation using exact calculations in the limit of low and high density of particles. Our results suggest that the symmetric, quasiparabolic current-density relation arises through a nontrivial cancellation of higher-order terms, similarly as in the standard TASEP.

Linearity Enhancement Techniques for Operational Transconductance Amplifier: A Survey

Background: Operational Transconductance Amplifier (OTA) plays an essential role in many analog and mixed-signal applications that encourages the researchers to contribute their work to design suitable structures of OTA for their applications with acceptable performance parameters. Methods: The linearity of an OTA is one of its key performance parameters, which affects the performance of the overall system whereas the transconductance value of OTA (Gm) contributes to decide its application area. Low transconductance OTA finds its application in biomedical and neural networks while OTA with higher transconductance is suitable for wireless communication. In any system, it is desirable to obtain a linear voltage-to-current conversion, i.e., OTA, hence various linearization techniques have been reported to linearize the OTA. Results: In the last two decades, various OTA structures have been reported with linear voltage-tocurrent conversion. Some researchers used attenuation by means of different circuit approaches to linearize the OTA or some used cancellation of nonlinearity terms by using different circuit implementation techniques. Researchers used some other methods also to linearize the OTA viz source degeneration, square root technique and mobility compensation. Conclusion: The purpose of this paper is to provide a brief survey of various popular linearization techniques reported in the past.

Superposition principle and composite solutions to coupled nonlinear Schrödinger equations

We show that the superposition principle applies to coupled nonlinear Schrödinger equations with cubic nonlinearity where exact solutions may be obtained as a linear combination of other exact solutions. This is possible due to the cancelation of cross terms in the nonlinear coupling. First, we show that a composite solution, which is a linear combination of the two components of a seed solution, is another solution to the same coupled nonlinear Schrödinger equation. Then, we show that a linear combination of two composite solutions is also a solution to the same equation. With emphasis on the case of Manakov system of two‐coupled nonlinear Schrödinger equations, the superposition is shown to be equivalent to a rotation operator in a two‐dimensional function space with components of the seed solution being its coordinates. Repeated application of the rotation operator, starting with a specific seed solution, generates a series of composite solutions, which may be represented by a generalized solution that defines a family of composite solutions. Applying the rotation operator to almost all known exact seed solutions of the Manakov system, we obtain for each seed solution the corresponding family of composite solutions. Composite solutions turn out, in general, to possess interesting features that do not exist in the seed solution. Using symmetry reductions, we show that the method applies also to systems of N‐coupled nonlinear Schrödinger equations. Specific examples for the three‐coupled nonlinear Schrödinger equation are given.

Narrowband and passband composite pulses for variable rotations

We develop a systematic approach to derive narrowband (NB) and passband (PB) composite sequences which can produce any pre-selected transition probability with any desired accuracy. The NB composite pulses are derived by successive cancellation of derivative terms in the propagator. The PB pulses are built by combining two half-$\pi$ NB pulses. Both the NB and PB pulses feature vanishing wings on both sides of the central region around the target transition probability, and the PB pulses offer also a flat (broadband) top around the target probability. The NB sequences are particularly suitable for sensing and metrology applications, while the PB sequences can be very useful for qubit control in the case of tightly spaced qubits for they ensure both selectivity (suppressed cross talk to neighbors) and robustness (suppressed laser pointing instability). Other possible applications include selective (NB), or both selective and robust (PB), control of close transitions in frequency space.

Collective transitions of two entangled atoms and the Fulling-Davies-Unruh effect

We calculate respectively, from the viewpoints of an instantaneously/locally inertial observer and a coaccelerated observer, the transition rates of the two-atom system in the symmetric/antisymmetric entangled state [$|{\ensuremath{\psi}}_{\ifmmode\pm\else\textpm\fi{}}⟩$]. The scalar fields to which the atoms are coupled are respectively assumed to be in the vacuum state and a thermal state in the instantaneously inertial frame and in the coaccelerated frame. We show that both the upward transition $|{\ensuremath{\psi}}_{\ifmmode\pm\else\textpm\fi{}}⟩\ensuremath{\rightarrow}|{e}_{A}{e}_{B}⟩$ and the downward transition $|{\ensuremath{\psi}}_{\ifmmode\pm\else\textpm\fi{}}⟩\ensuremath{\rightarrow}|{g}_{A}{g}_{B}⟩$ take place, where $|{g}_{A}{g}_{B}⟩$ and $|{e}_{A}{e}_{B}⟩$ represent two collective eigenstates of the two-atom system with both atoms in their ground state and excited state respectively, and the transition rates observed in the two frames are identical only if there exists a thermal bath at the Fulling-Davies-Unruh temperature in the coaccelerated frame. Though both the downward and upward transition rates are characterized by the Plankian factor, this factor does not show up in the average variation rate of energy of the two-atom system, as a result of the perfect cancellation of the terms in the transition rates in the instantaneously inertial frame multiplied by the Plankian factor which corresponds to the Unruh thermal bath, and the cancellation of the temperature-dependent terms in the transition rates observed in the coaccelerated frame. A comparison of the transition rates of a static two-atom system in interaction with the massless scalar field in a thermal state at an arbitrary temperature with those of a uniformly accelerated two-atom system in interaction with the vacuum massless scalar field shows that the equivalence between the thermal bath and the uniform acceleration, which is well known to be valid for the single atom case, no longer holds for the two-atom system in the symmetric/antisymmetric entangled state. The effect of atomic uniform acceleration in the transition rates of the two-atom system, and the roles of both the downward and the upward transitions in the disentanglement of the two-atom system are also discussed.

Stable computation of higher order Charlier moments for signal and image reconstruction

The computation of high-order discrete orthogonal moments is very complex and unstable due to fluctuations in numerical polynomial values. In this paper, we will present new algorithms for the stable computation of high-order discrete orthogonal Charlier polynomials and moments. These algorithms are based on the use of modified recurrence relations of Charlier polynomials with respect to the order n and with respect to the variable x, and on the use of the modified Gram-Schmidt orthonormalization process (GSOP). The algorithms in question allow the cancellation of terms that cause the numerical fluctuations of Charlier polynomial values during the recursive calculations. They also preserve the orthogonality property of high-order Charlier polynomials, which enables an efficient analysis of large-size bio-signals and 2D/3D images. Therefore, the simulation results prove the efficiency of the proposed algorithms when it comes to reconstructing large-size bio-signals and images.

On the Cooling-to-Space Approximation

AbstractThe cooling-to-space (CTS) approximation says that the radiative cooling of an atmospheric layer is dominated by that layer’s emission to space, while radiative exchange with layers above and below largely cancel. Though the CTS approximation has been demonstrated empirically and is thus fairly well accepted, a theoretical justification is lacking. Furthermore, the intuition behind the CTS approximation cannot be universally valid, as the CTS approximation fails in the case of pure radiative equilibrium. Motivated by this, we investigate the CTS approximation in detail. We frame the CTS approximation in terms of a novel decomposition of radiative flux divergence, which better captures the cancellation of exchange terms. We also derive validity criteria for the CTS approximation, using simple analytical theory. We apply these criteria in the context of both gray gas pure radiative equilibrium (PRE) and radiative–convective equilibrium (RCE) to understand how the CTS approximation arises and why it fails in PRE. When applied to realistic gases in RCE, these criteria predict that the CTS approximation should hold well for H2O but less so for CO2, a conclusion we verify with line-by-line radiative transfer calculations. Along the way we also discuss the well-known “τ = 1 law,” and its dependence on the choice of vertical coordinate.

Trademark cancellation in terms of commercial and administrative law: a comparison of the UAE and Jordan

This paper concerns the method of judicial review in the dismissal of a trademark, from a procedural judicial perspective. The research examines the impact procedural laws can have on substantive laws, in terms of the influence of commercial litigation and civil procedures on one hand, and administrative law procedures on the other, regarding the potential outcomes for dismissing a trademark. In the UAE's unified legal system, the civil/commercial courts review decisions to register trademarks, while in Jordan's dual legal system it is the administrative courts, which do so. This paper investigates if this difference plays any role in cancelling trademarks, and whether it has any subsequent impact on investment and commerce.

Infrared and transcendental structure of two-loop supersymmetric QCD amplitudes

Using a careful choice of infrared (IR) subtraction scheme, we demonstrate cancellation of all terms with transcendental weights 0, 1, 2 from the finite part of the full-color two-loop four-gluon mathcal{N} = 2 supersymmetric QCD amplitude, with Nf massless supersymmetric quarks. This generalizes the previously observed cancellation of weight-2 terms in the superconformal theory, where Nf = 2Nc for gauge group SU(Nc). The subtraction scheme follows naturally both from general IR factorization principles and from an integrand-level analysis of divergences in this amplitude. The divergences are written in terms of scalar triangle integrals whose expressions are known to all orders in the dimensional regulator ϵ = (4 − D)/2. We also present integrated expressions for the full-color two-loop four-point amplitudes with both matter and vectors on external legs in which lower-weight terms also cancel using an appropriate IR scheme. This provides us with values for the two-loop cusp, gluonic, and quark anomalous dimensions in mathcal{N} = 2 supersymmetric QCD, which are cross-checked between the three different amplitudes.