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Presents a systematic method, employing a Painleve analysis for obtaining static and traveling wave solutions to a semi-linear parabolic equation arising in smectic liquid crystals. Generalization of the nonlinear quadratic Fisher equation or cubic Nagumo equation; Painleve property in partial differential equations.

This paper develops a theory for anaphase in cells. After a brief description of microtubules, the mitotic spindle and the centrosome, a mathematical model for anaphase is introduced and developed in the context of the cell cytoplasm and liquid crystalline structures. Prophase, prometaphase and metaphase are then briefly described in order to focus on anaphase, which is the main study of this paper. The entities involved are modelled in terms of liquid crystal defects and microtubules are represented as defect flux lines. The mathematical techniques employed make extensive use of energy considerations based on the work that was developed by Dafermos (1970) from the classical Frank-Oseen nematic liquid crystal energy (Frank, 1958; Oseen, 1933). With regard to liquid crystal theory we introduce the concept of regions of influence for defects which it is believed have important implications beyond the subject of this paper. The results of this paper align with observed biochemical phenomena and are explored in application to HeLa cells and Caenorhabditis elegans. This unified approach offers the possibility of gaining insight into various consequences of mitotic abnormalities which may result in Down syndrome, Hodgkin lymphoma, breast, prostate and various other types of cancer., Competing Interests: Declaration of competing interest The authors declared no competing interests., (Copyright © 2024 The Author(s). Published by Elsevier Inc. All rights reserved.)

Valvular heart diseases (such as stenosis and regurgitation) are recognized as a rapidly growing cause of global deaths and major contributors to disability. The most effective treatment for these pathologies is the replacement of the natural valve with a prosthetic one. Our work considers an innovative design for prosthetic aortic valves that combines the reliability and durability of artificial valves with the flexibility of tissue valves. It consists of a rigid support and three polymer leaflets which can be cut from an extruded flat sheet, and is referred to hereafter as the Wheatley aortic valve (WAV). As a first step towards the understanding of the mechanical behavior of the WAV, we report here on the implementation of a numerical model built with the ICFD multi-physics solver of the LS-DYNA software. The model is calibrated and validated using data from a basic pulsatile-flow experiment in a water-filled straight tube. Sensitivity to model parameters (contact parameters, mesh size, etc.) and to design parameters (height, material constants) is studied. The numerical data allow us to describe the leaflet motion and the liquid flow in great detail, and to investigate the possible failure modes in cases of unfavorable operational conditions (in particular, if the leaflet height is inadequate). In future work the numerical model developed here will be used to assess the thrombogenic properties of the valve under physiological conditions., (© 2023 John Wiley & Sons Ltd.)

This note considers the mathematical model published in the Journal of Biomechanical Engineering by McKee et al. [McKee, S., Cuminato, J. A., Stewart, I. W., and Wheatley, D. J., 2021, "A Mathematical Representation of the Wheatley Heart Valve," ASME J. Biomech. Eng., 143(8), p. 081006]. The model presented there suffers from the fact that there is a line discontinuity in the first derivative producing what appears to be a kink in each of the leaflets. This note is concerned with regularizing the shape of the valve while holding to Wheatley's essential idea [Wheatley, D. J., 2016, "Heart Valve," U.S. Patent No. 9,259,313, UK Patent No. 2,982,340 (2017), European Patent No. 2,979,666 (2017)]., (Copyright © 2023 by ASME.)

We perform the first global fit to inclusive B→X_{s}γ measurements using a model-independent treatment of the nonperturbative b-quark distribution function, with next-to-next-to-leading logarithmic resummation and O(α_{s}^{2}) fixed-order contributions. The normalization of the B→X_{s}γ decay rate, given by |C_{7}^{incl}V_{tb}V_{ts}^{*}|^{2}, is sensitive to physics beyond the standard model (SM). We determine |C_{7}^{incl}V_{tb}V_{ts}^{*}|=(14.77±0.51_{fit}±0.59_{theory}±0.08_{param})×10^{-3}, in good agreement with the SM prediction, and the b-quark mass m_{b}^{1S}=(4.750±0.027_{fit}±0.033_{theory}±0.003_{param})  GeV. Our results suggest that the uncertainties in the extracted B→X_{s}γ rate have been underestimated by up to a factor of 2, leaving more room for beyond-SM contributions.

Starting from a hand-drawn contour plot, this note develops a set of intersecting and contiguous circles whose perimeter, upon extending appropriately to three dimensions, can be seen to be a natural mathematical representation of the Wheatley heart valve., (Copyright © 2021 by ASME.)

We examine some leading-order flow and stability properties of smectic A (SmA) liquid crystals (LCs) in two spatial dimensions by analysing a fully nonlinear continuum theory of these materials. We derive a system of equations for the dynamic variables describing the flow velocity and orientation of the material under suitable assumptions upon these quantities. This system can provide insight into the leading-order behaviour under quite general circumstances, and we provide an example of utilising this system to determine the flow induced by a constant pressure gradient applied normally to the smectic layers. We then consider the effect of oscillatory perturbations on a relaxed, stationary sample of SmA, and provide criteria under which one would expect to see the onset of instability in the form of inequalities between the material parameters and perturbative wave number. We find that instability occurs for physically realisable values of these quantities, and, in particular, that certain viscosities characterising the SmA phase can act as 'destabilising agents' such that one could, for a given sample with known parameter values, manipulate the behaviour of that sample., (© 2021 IOP Publishing Ltd.)

We discuss the static configuration of a smectic A liquid crystal subject to an edge dislocation under the assumption that the director and layer normal fields ([Formula: see text] and [Formula: see text], respectively) defining the smectic arrangement are not, in general, equivalent. After constructing the free energy for the smectic, we obtain exact solutions to the equilibrium equations which result from its minimisation at quadratic order in the variables which describe the distortion, and hence a complete description of the smectic configuration across the domain of the sample. We also examine the effect of relaxing the constraint [Formula: see text] for different values of the constants which characterise the response of the material to distortions, and compare these results with the 'classical' case considered by previous authors, in which equivalence of [Formula: see text] and [Formula: see text] is enforced.

The most precise top quark mass measurements use kinematic reconstruction methods, determining the top mass parameter of a Monte Carlo event generator m_{t}^{MC}. Because of hadronization and parton-shower dynamics, relating m_{t}^{MC} to a field theory mass is difficult. We present a calibration procedure to determine this relation using hadron level QCD predictions for observables with kinematic mass sensitivity. Fitting e^{+}e^{-} 2-jettiness calculations at next-to-leading-logarithmic and next-to-next-to-leading-logarithmic order to pythia 8.205, m_{t}^{MC} differs from the pole mass by 900 and 600 MeV, respectively, and agrees with the MSR mass within uncertainties, m_{t}^{MC}≃m_{t,1  GeV}^{MSR}.

We formulate an effective field theory description for SU(2)_{L} triplet fermionic dark matter by combining nonrelativistic dark matter with gauge bosons in the soft-collinear effective theory. For a given dark matter mass, the annihilation cross section to line photons is obtained with 5% precision by simultaneously including Sommerfeld enhancement and the resummation of electroweak Sudakov logarithms at next-to-leading logarithmic order. Using these results, we present more accurate and precise predictions for the gamma-ray line signal from annihilation, updating both existing constraints and the reach of future experiments.

An essential part of high-energy hadronic collisions is the soft hadronic activity that underlies the primary hard interaction. It includes soft radiation from the primary hard partons, secondary multiple parton interactions (MPI), and factorization-violating effects. The invariant mass spectrum of the leading jet in Z+jet and H+jet events is directly sensitive to these effects, and we use a QCD factorization theorem to predict its dependence on the jet radius R, jet p_{T}, jet rapidity, and partonic process for both the perturbative and nonperturbative components of primary soft radiation. We prove that the nonperturbative contributions involve only odd powers of R, and the linear R term is universal for quark and gluon jets. The hadronization model in Pythia8 agrees well with these properties. The perturbative soft initial state radiation (ISR) has a contribution that depends on the jet area in the same way as the underlying event, but this degeneracy is broken by dependence on the jet p_{T}. The size of this soft ISR contribution is proportional to the color state of the initial partons, yielding the same positive contribution for gg→Hg and gq→Zq, but a negative interference contribution for qq[over ¯]→Zg. Hence, measuring these dependencies allows one to separate hadronization, soft ISR, and MPI contributions in the data.

Jet substructure has emerged as a critical tool for LHC searches, but studies so far have relied heavily on shower Monte Carlo simulations, which formally approximate QCD at the leading-log level. We demonstrate that systematic higher-order QCD computations of jet substructure can be carried out by boosting global event shapes by a large momentum Q and accounting for effects due to finite jet size, initial-state radiation (ISR), and the underlying event (UE) as 1/Q corrections. In particular, we compute the 2-subjettiness substructure distribution for boosted Z→qq[over ¯] events at the LHC at next-to-next-to-next-to-leading-log order. The calculation is greatly simplified by recycling known results for the thrust distribution in e(+)e(-) collisions. The 2-subjettiness distribution quickly saturates, becoming Q independent for Q > or approximately equal to 400 GeV. Crucially, the effects of jet contamination from ISR/UE can be subtracted out analytically at large Q without knowing their detailed form. Amusingly, the Q=∞ and Q=0 distributions are related by a scaling by e up to next-to-leading-log order.

At the LHC and Tevatron strong initial-state radiation (ISR) plays an important role. It can significantly affect the partonic luminosity available to the hard interaction or contaminate a signal with additional jets and soft radiation. An ideal process to study ISR is isolated Drell-Yan production, pp → Xℓ+ ℓ- without central jets, where the jet veto is provided by the hadronic event shape beam thrust τB. Most hadron collider event shapes are designed to study central jets. In contrast, requiring τ B << 1 provides an inclusive veto of central jets and measures the spectrum of ISR. For τ B << 1 we carry out a resummation of α s(n)ln(m)τ B corrections at next-to-next-to-leading-logarithmic order. This is the first resummation at this order for a hadron-hadron collider event shape. Measurements of τ B at the Tevatron and LHC can provide crucial tests of our understanding of ISR and of τ B's utility as a central jet veto.

Jet vetoes are essential in many analyses at the LHC and Tevatron. Typical signals have a specific number of hard jets or leptons, while backgrounds have additional jets. Vetoing undesired jets efficiently discriminates signal and background. For a sample with ≥N jets, the veto to give N energetic jets defines an "exclusive" N-jet cross section. This strongly restricts the phase space and causes large double logarithms in perturbation theory that must be summed. Jet vetoes are typically implemented using jet algorithms, yielding complicated phase-space restrictions, and reliance on leading-log parton-shower Monte Carlo simulations. We introduce a global event shape "N jettiness" τN, which is defined for events with N signal jets. Requiring τN≪1 constrains radiation between the signal jets and provides a theoretically well-controlled jet veto. N jettiness yields a factorization formula with inclusive jet and beam functions.

A dynamic theory for compressible smectic C (SmC) liquid crystals is postulated following previous work by Leslie et al (1991 Mol. Cryst. Liq. Cryst. 198 443-54), Nakagawa (1996 J. Phys. Soc. Japan 65 100-6; 2004 J. Non-Newtonian Fluid Mech. 119 123-9) and de Gennes and Prost (1993 The Physics of Liquid Crystals 2nd edn (Oxford: Oxford University Press)). This theory is then implemented with a constructed bulk elastic energy and asymmetric stress tensor to describe a system of planar layered SmC liquid crystals undergoing various modes of undulation. We show that previous work on smectic A (SmA) liquid crystals by de Gennes and Prost (1993 The Physics of Liquid Crystals 2nd edn (Oxford: Oxford University Press)) can be expanded for SmC and consolidated. Novel and confirming estimates for SmC material parameter values are produced by considering the dependence of the system on these parameters.

A novel continuum model is proposed to describe the deformations of a planar lipid bilayer suspended across a circular pore. The model is derived within a new theoretical framework for smectic A liquid crystals in which the usual director n, which defines the average orientation of the molecules, is not constrained to be normal to the layers. The free energy is defined by considering the elastic splay of the director, the bending and compression of the lipid bilayer, the cost of tilting the director with respect to the layer normal, the surface tension, and the weak anchoring of the director. Variational methods are used to derive the equilibrium equations and boundary conditions. The resulting boundary value problem is then solved numerically to compute the fully nonlinear displacement of the layers and tilt of the lipid molecules. A parametric study shows that an increase in surface tension produces a decrease in the deformation of the lipid bilayers while an opposite effect is obtained when increasing the anchoring strength.

This paper considers the onset of a shear-induced instability in a sample of smectic A liquid crystal. Unlike many previous models, the usual director n need not necessarily coincide with the local smectic layer normal a; the traditional Oseen constraint ([Formula: see text]) is not imposed when flow is present. A recent dynamic theory for smectic A (Stewart 2007 Contin. Mech. Thermodyn. 18 343-60) will be used to examine a stationary instability in a simple model when the director reorientation and smectic layer distortions are, firstly, assumed not to be coupled to the velocity and, secondly, are supposed coupled to the velocity. A critical shear rate at which the onset of the instability occurs will be identified, together with an accompanying critical director tilt angle and critical wavenumber for the associated smectic layer undulations. Despite some critical phenomena being largely unaffected by any coupling to the flow, it will be shown that the influence of some material parameters, especially the smectic layer compression constant B(0) and the coupling constant B(1), upon the critical shear rate and critical tilt angle can be greatly affected by flow.

This paper considers the dynamics of cylindrically arranged parallel layers of smectic A liquid crystal subjected to Couette flow. Governing equations are constructed using a recently developed dynamic theory for smectic A (Stewart 2007 Contin. Mech. Thermodyn. 18 343-60). These equations are solved to provide analytical solutions for the smectic layer undulations and velocity profiles. Results show the dependence of the response time of the smectic layers upon the permeation constant and the layer compression modulus. The relaxation times for the flow profiles are shown to depend upon two viscosities; estimates for these times are shown to be shorter than that for a typical approximation to the relaxation time of the smectic layer undulations.

A short-distance heavy-quark mass depends on two parameters: the renormalization scale mu and a scale R controlling the absorption of infrared fluctuations. The radius for perturbative corrections that build up the mass beyond its pointlike definition in the pole scheme is approximately 1/R. Treating R as a variable gives a renormalization-group equation. R evolution improves the stability of conversion between short-distance mass schemes, allowing us to avoid large logs and the renormalon. R evolution can also be used to study IR renormalons without using bubble chains, yielding a convergent sum rule for the coefficient of the O(Lambda(QCD)) renormalon ambiguity of the pole mass.

A precision method for determining |V(ub)| using the full range in q(2) of B --> pilnu data is presented. At large q(2) the form factor is taken from unquenched lattice QCD, at q(2) = 0 we impose a model independent constraint obtained from B --> pipi using the soft-collinear effective theory, and the shape is constrained using QCD dispersion relations. We find |V(ub)| = (3.54 +/- 0.170 +/- 0.44) x 10(-3). With 5% experimental error and 12% theory error, this is competitive with inclusive methods. Theory error is dominated by the input points, with negligible uncertainty from the dispersion relations.

Factorization based on the soft-collinear effective theory (SCET) can be used to reduce the number of hadronic parameters in an isospin analysis of B --> pi(pi) decays by one. This gives a theoretically precise method for determining the CP violating phase gamma by fitting to the B --> pi(pi) data without Cpi(0)pi(0). SCET predicts that gamma lies close to the isospin bounds. With the current world averages we find gamma = 75 degrees +/- 2 degrees(+9 degrees)(-13 degrees), where the uncertainties are theoretical, then experimental.

A theoretical investigation is made into the dynamics of pitch jumps in cholesteric liquid-crystal layers having finite strength surface-anchoring conditions. A presentation is given of general formulations which connect the dynamics of pitch jumps with the key material parameters such as the viscosity, the specific form of the anchoring potential, and the dimensionless parameter S(d)=K(22)/Wd , where K22 is the elastic modulus, W is the depth of the anchoring potential, and d is the layer thickness. To illustrate the dependence of the pitch jump dynamics upon the shape and strength of the anchoring potential, we investigate two sets of different model surface-anchoring potentials for a jump mechanism that is connected with the slipping of the director at a surface over the barrier of the anchoring potential. Two types of "narrow" well potentials that are natural extensions of the more familiar "wide" potentials are considered: one type is based upon the well-known Rapini-Papoular potential and the other upon the B potential, introduced in Belyakov, Stewart, and Osipov, JETP 99, 73 (2004). Calculations for the unwinding (winding) of the helix in the process of the jump were performed to investigate the case of infinitely strong anchoring on one surface and finite anchoring on the other, which is important in applications. The results show that an experimental investigation of the dynamics of the pitch jumps will allow one to distinguish different shapes of the finite strength anchoring potential, and will, in particular, provide a means for determining whether or not the well-known Rapini-Papoular anchoring potential is the best suited potential relevant to the dynamics of pitch jumps in cholesteric layers with finite surface-anchoring strength.

This article investigates, by means of Lie point symmetries, traveling wave solutions to a dynamic equation that frequently arises in the theory of ferroelectric smectic- C liquid crystals under the influence of an electric field. The equation considered has three sinusoidal nonlinearities and possible time-dependent solutions are discussed in the context of minima and maxima of the electric energy density for these liquid crystals: solutions travel between such constant equilibrium states. Implicit solutions to an approximation of the governing dynamic equation are determined. Nondimensional control parameters that characterize changes in the availability of equilibrium states as the magnitude of the field increases are also identified.

Using chiral symmetry we investigate the leading SU(3) violation in light-cone distribution functions phi(M)(x) of the pion, kaon, and eta. It is shown that terms nonanalytic in the quark masses do not affect the shape, and only appear in the decay constants. Predictive power is retained including the leading analytic m(q) operators. With the symmetry violating corrections we derive useful model-independent relations between phi(pi),phi(eta),phiK+(,K0), and phiK(0)(,K-). Using the soft-collinear effective theory we discuss how factorization generates the subleading chiral coefficients.

A hybrid-aligned cell of the smectic A liquid material 8CB gives two stable director configurations, one of which is periodic and gives strong diffraction of light. This photonic lattice director profile arises from "frustration" caused by conflicting constraints imposed by the boundary conditions and the constant amplitude smectic density wave. A model is proposed which accords well with the experiment results, predicting correctly the dependence of the periodicity on the cell thickness and reproducing optical polarization microscopy results.

We prove that the matrix elements of four fermion operators mediating the decays B macro (0)-->D(+)pi(-) and B--->D(0)pi(-) factor into the product of a form factor describing the B-->D transition and a convolution of a short distance coefficient with the nonperturbative pion light-cone wave function. This is shown to all orders in alpha(s), with corrections suppressed by factors of 1/m(b), 1/m(c), and 1/E(pi). It is not necessary to assume that the pion state is dominated by the qq macro Fock state.

The top-quark cross section close to threshold in e(+)e(-) annihilation is computed including the summation of logarithms of the velocity at next-to-next-to-leading-logarithmic order in QCD. The remaining theoretical uncertainty in the normalization of the total cross section is at the few-percent level, an order of magnitude smaller than in previous next-to-next-to-leading order calculations. This uncertainty is smaller than the effects of a light standard-model Higgs boson.

The aim of this article is to establish some theoretical linear and nonlinear stability results for a dynamic equation that frequently appears in the smectic-C and ferroelectric smectic-C* liquid crystal literature. We consider finite planar samples confined between bounding plates as well as infinite samples. Many of the results depend on extensions of work for a nonlinear diffusion equation. Critical maximum magnitudes of applied static electric fields are determined, below which stability of a certain constant equilibrium state is ensured.

This paper derives theoretical results for determining bifurcation curves which provide bounds on anticipated "escape" regimes in a two-dimensional parameter space for an equation which is a natural extension of a commonly used second-order parametrically excited nonlinear pendulum equation. An application of these results is made for an equation which often arises in smectic liquid-crystal problems. The results for this application are more refined yet qualitatively similar to those obtained by different methods reported in the literature.

The velocity renormalization group is used to determine lnalpha contributions to QED bound state energies. The leading-order anomalous dimension for the potential gives the alpha(5)lnalpha Lamb shift. The next-to-leading-order anomalous dimension determines the alpha(6)lnalpha, alpha(7)ln (2)alpha, and alpha(8)ln (3)alpha corrections to the energy. These are used to obtain the alpha(8)ln (3)alpha Lamb shift and alpha(7)ln (2)alpha hyperfine splitting for hydrogen, muonium, and positronium, as well as the alpha(2)lnalpha and alpha(3)ln (2)alpha corrections to the ortho- and parapositronium lifetimes. This shows for the first time that these logarithms can be computed from the renormalization group.

Background: Reports in the literature concerning best practice for the evaluation and management of children with visual impairments are limited, with a resulting lack of information concerning the potential for optimizing vision to enhance general development and assist with the educational needs of this population., Method: The development of a multidisciplinary approach to provide low-vision services for children with visual impairment has occurred over the past 18 years in Iowa. In that time, 1,348 children from around the state of Iowa have been evaluated through an itinerant low-vision service program, coordinated by the Iowa Braille School., Results: A low-vision clinic model--designed to provide services (primarily) for academic students--was not meeting the needs of the pediatric low-vision population in the state. After a statewide review of the program, changes were made that have resulted in low-vision services being provided to a greater and more diverse number of students. The roles of the various members of the multidisciplinary team will be reviewed. Changes in large-print orders and use by special education teachers in the state as a direct result of the low-vision services will also be discussed., Conclusion: Ongoing, comprehensive multidisciplinary low-vision services--including optometric low-vision care as a key component--are necessary to help children with visual impairments meet their educational, vocational, and avocational needs. With ongoing low-vision services, unnecessary costs such as those associated with large-print materials can be reduced, thereby creating significant savings to local, state, and federal special educational services.

The dynamics of solitary waves in ferroelectric liquid crystals is considered in the context of an overdamped double sine-Gordon model. Various possible types of single waves are studied. The dependence of wave velocity and scale on the system parameters and initial conditions is found. Sharp initial profiles lead to waves with a universal form. The parameters of the wave arising from smooth profiles are determined also by the scale of the initial conditions. Numerical calculations show good agreement with analytical results. The possibility of using such waves to improve the characteristics of liquid crystal devices is also discussed.

This paper derives theoretical results for the onset of Helfrich-Hurault-type transitions in samples of smectic-A liquid crystals arranged in concentric cylindrical layers [J. Chem. Phys. 55, 839 (1971); 59, 2068 (1973)]. A magnetic field is applied in the azimuthal direction, parallel to the layers. The governing equilibrium equation is solved in order to derive the critical magnitude H(c) of the magnetic field above which the onset of periodic smectic layer distortions is expected. The distortion solution is shown to be energetically favorable for H>H(c). Some examples of critical thresholds are given, by means of figures, for relevant physical parameters. The qualitative features of the solution at H(c) are displayed via the plot of a typical variable solution to the equilibrium equation in a particular case. The consequences of the results, especially the relationship between H(c) and the radial depth, are explored, and comparisons are drawn with known results for infinite planar aligned smectic-A samples. The results are also interpreted for the case of an electric field which follows the plane of the layers in the usual wedge geometry. Critical applied voltage magnitudes U(c) are derived for various radial sample depths and wedge angles.

Health-related monitoring of bioaerosol exposures in the workplace should ideally be carried out using size-selective personal samplers that separate the aerosol into biologically relevant size fractions and allow both quantification and identification of the microorganisms present in each fraction. As a first stage in the development of personal bioaerosol samplers a number of collection substrates were assessed for their ability to maintain the viability of the collected microorganisms, so that subsequent culturing and species identification may be carried out. The substrates were tested with bioaerosols of varying robustness, consisting of Saccharomyces cerevisiae cells, Escherichia coli cells, and Penicillium expansum spores, aerosolized under controlled environmental conditions. The survival of microorganisms on each test substrate, assessed on the basis of the culturable fractions of cells recovered, was compared with that of microorganisms collected in a reference glass cyclone sampler. These bioefficiency tests identified the substrate combinations with the potential to fulfill personal sampler design criteria. The substrates were then subjected to further development to evaluate and optimize their particle size selection characteristics. The outcome of this work is two prototype personal bioaerosol samplers in which size-selective substrates are adapted for use in existing designs of personal inhalable sampler. This offers an effective and low-cost solution to personal monitoring of bioaerosol exposures in the workplace.

Background: Reports in the literature concerning the evaluation and low vision management of visually impaired children are limited, resulting in a lack of information about the characteristics and needs of this population., Methods: A review was performed of 762 children evaluated over a 14-year period in a low vision clinic program coordinated by the Iowa Braille and Sight Saving School., Results: The age, sex, ocular condition, best corrected visual acuity, habitual near point working distance, and optical devices recommended for use by these children were analyzed., Conclusions: Ongoing, comprehensive multidisciplinary low vision services are necessary to help children with visual impairments meet their educational, vocational and avocational needs. With ongoing low vision care unnecessary costs-such as those for large print material-can be avoided, therefore creating a significant savings to local or state educational services.