Continuous Family Research Articles

On a one-parameter continuous family of pairs of complementary boundary conditions

Let $C[0,\infty ]$ be the space of continuous functions on the right half-axis $\mathbb {R}^+$ with finite limits at $\infty $, and let $C[-\infty ,\infty ]$ be the space of continuous functions on the entire $\mathbb {R}$ that have finite limits at both

Superscarred quasimodes on flat surfaces with conical singularities

For any given momentum vector $\xi _0\in \mathbb {S}^1$ we construct a continuous family of quasimodes for the Laplace–Beltrami operator on a translation surface. We apply our result to rational polygonal quantum billiards and thus construct a continuous

A Literate South: Reading before Emancipation by Beth Barton Schweiger

Reviewed by: A Literate South: Reading before Emancipation by Beth Barton Schweiger Christopher N. Phillips (bio) A Literate South: Reading before Emancipation beth barton schweiger Yale University Press, 2019 258 pp. Does reading lead to liberalization? If so, what reading, or kinds of reading? As Beth Barton Schweiger argues, what she calls "the ideology of literacy," which insists on a connection between literacy and liberalization, [End Page 283] has been firmly entrenched in American culture since the middle of the nineteenth century. While it can seem obvious that a literacy-liberty correlation does not always hold historically, studies of the nineteenth-century US have long operated under the assumption that the North's higher rate of literacy was a contributing factor in the turn away from slavery, and that the South's relative lack of print publishing infrastructure enabled public opinion to support slavery. Schweiger's careful, engaging study of female readers in two families, drawing on journals and other writings at the Virginia Historical Society and in continued family possession, shows that literacy practices were a lively, continual element in the lives of rural southerners, even those whose lifestyle and infrastructure prevented them from devoting long hours to print-based activity. A Literate South might seem late for a review in EAL, focusing as it does on reading and writing practices of the 1830s through the 1850s, but as book historians such as James Raven have pointed out, the circulation of texts originating in multiple eras is a fact of reading life, and some of the reading material and much of the literacy pedagogy that the Cooley and Speer sisters experienced belonged to an earlier era. This book is very much a history of reading, following in the tradition of the micro-history exemplified by Carlo Ginzburg's The Cheese and the Worms (Johns Hopkins UP, 1992) and more recently by Allan Westphall's Books and Religious Devotion (Pennsylvania State UP, 2014). Schweiger's study does what the best of these micro-histories do, examining and contextualizing the documented experiences of a few, seemingly marginal historical figures in order to illuminate where expected patterns of reading and writing held, and especially where we may need to rethink our assumptions about literacy, culture, and the place of print in everyday life. As in the case of the ideology of literacy, Schweiger moves from fine-grained analysis to big ideas and assumptions, showing that the two scales do not always easily match and that the details of women's and girls' literacy at a given time and place may tell us much about what and how literacy was. Schweiger begins with a long introductory chapter explaining the diverse ways that print suffused the South, even at significant geographical remove from printing presses, booksellers, and newspaper offices. The Cooleys were Virginia farmers who engaged in part-time smithing and clothes-making; the Speers were North Carolina tanners whose Whig politics and middle-class values shared a similar rural space, which included [End Page 284] a print world made up primarily of periodicals, schoolbooks, hymnbooks, Bibles, and more ephemeral texts. This was not a world of many books, but Schweiger demonstrates that it was one of wide and voracious print and reading. Her canny use of Shirley Brice Heath's notion of "ways of words" allows her to detect the Cooleys' and Speers' reading not just by the titles they name but also by the phrases, cadences, and diction they use. Part I demonstrates the importance of this method by highlighting the literacy practices of the two households through writings left by Amanda and Betsy Cooley, Jennie and Ann Speer, and a few of their relatives. The chapters in this section follow the sequence of literacy textbooks that was well-established by the early nineteenth century: spellers, grammars, and rhetorics. The chapter on spellers foregrounds the experience of Jincy, an enslaved teenaged girl on the Cooley farm who Amanda recorded as studying a speller while other members of the household read, wrote, or otherwise used their leisure time. Schweiger traces a history of enslaved people's use of spellers that includes both the more familiar dimensions of prohibition and clandestine learning, and an...

Approximation of nilpotent orbits for simple Lie groups

We propose a systematic and topological study of limits \(\lim_{\nu\to 0^+}G_\mathbb{R}\cdot(\nu x)\) of continuous families of adjoint orbits for a non-compact simple real Lie group \(G_\mathbb{R}\). This limit is always a finite union of nilpotent orbits. We describe explicitly these nilpotent orbits in terms of Richardson orbits in the case of hyperbolic semisimple elements. We also show that one can approximate minimal nilpotent orbits or even nilpotent orbits by elliptic semisimple orbits. The special cases of \(\mathrm{SL}_n(\mathbb{R})\) and \(\mathrm{SU}(p,q)\) are computed in detail.

Hukuhara differentiability of continuous sine and cosine families of linear set-valued functions

Hukuhara differentiability of continuous sine and cosine families of linear set-valued functions

One parameter family of rationally extended isospectral potentials

We start from a given one dimensional rationally extended shape invariant potential associated with Xm exceptional orthogonal polynomials and using the idea of supersymmetry in quantum mechanics, we obtain one continuous parameter (λ) family of rationally extended strictly isospectral potentials. We illustrate this construction by considering three well known rationally extended potentials, two with pure discrete spectrum (the extended radial oscillator and the extended Scarf-I) and one with both the discrete and the continuous spectrum (the extended generalized Pöschl–Teller) and explicitly construct the corresponding one continuous parameter family of rationally extended strictly isospectral potentials. Further, in the special case of λ=0 and −1, we obtain two new exactly solvable rationally extended potentials, namely the rationally extended Pursey and the rationally extended Abraham–Moses potentials respectively. We illustrate the whole procedure by discussing in detail the particular case of the X1 rationally extended one parameter family of potentials including the corresponding Pursey and the Abraham Moses potentials.

Higher-dimensional soliton generation, stability and excitations of the [formula omitted]-symmetric nonlinear Schrödinger equations

We study a class of physically intriguing PT-symmetric generalized Scarf-II (GS-II) potentials, which can support exact solitons in one- and multi-dimensional nonlinear Schrödinger equation. In the 1D and multi-D settings, we find that a properly adjusted localization parameter may support fully real energy spectra. Also, continuous families of fundamental and higher-order solitons are produced. The fundamental states are shown to be stable, while the higher-order ones, including 1D multimodal solitons, 2D solitons, and 3D light bullets, are unstable. Further, we find that the stable solitons can always propagate, in a robust form, remaining trapped in slowly moving potential wells of the GS-II type, which opens the way for manipulations of optical solitons. Solitons may also be transformed into stable forms by means of adiabatic variation of potential parameters. Finally, an alternative type of n-dimensional PT-symmetric GS-II potentials is reported too. These results will be useful to further explore the higher-dimensional PT-symmetric solitons and to design the related physical experiments.

A Liouville Theorem for Möbius Invariant Equations

In this paper, we classify Möbius invariant differential operators of second order in two-dimensional Euclidean space, and establish a Liouville type theorem for general Möbius invariant elliptic equations. The equations are naturally associated with a continuous family of convex cones $$\Gamma _p$$ in $$\mathbb R^2$$ , with parameter $$p\in [1, 2]$$ , joining the half plane $$\Gamma _1:=\{ (\lambda _1, \lambda _2):\lambda _1+\lambda _2>0\}$$ and the first quadrant $$\Gamma _2:=\{ (\lambda _1, \lambda _2):\lambda _1, \lambda _2>0\}$$ . Chen and C. M. Li established in 1991 a Liouville type theorem corresponding to $$\Gamma _1$$ under an integrability assumption on the solution. The uniqueness result does not hold without this assumption. The Liouville type theorem we establish in this paper for $$\Gamma _p$$ , $$1<p\le 2$$ , does not require any additional assumption on the solution as for $$\Gamma _1$$ . This is reminiscent of the Liouville type theorems in dimensions $$n\ge 3$$ established by Caffarelli, Gidas and Spruck in 1989 and by A. B. Li and Y. Y. Li in 2003–2005, where no additional assumption was needed either. On the other hand, there is a striking new phenomena in dimension $$n=2$$ that $$\Gamma _p$$ for $$p=1$$ is a sharp dividing line for such uniqueness result to hold without any further assumption on the solution. In dimensions $$n\ge 3$$ , there is no such dividing line.

On Generating Distributions with the Memoryless Property

The exponential and geometric distribution are well-known continuous and discrete family of distributions with the memoryless property, respectively. The memoryless property is emphasized in introductory probability and statistics textbooks even though no distribution beyond these two families of distributions has been explored in detail. By examining the relationship between these two families of distributions, we propose a general algorithm for generating distributions with the memoryless property. Then, we show that the general algorithm uniquely determines the distribution with the memoryless property given the parameter value, and non-negative support which contains zero and is closed under addition. Furthermore, we present a few nontrivial examples and their applications to demonstrate the richness of such distributions.

On Construction and Estimation of Stationary Mixture Transition Distribution Models

Mixture transition distribution (MTD) time series models build high-order dependence through a weighted combination of first-order transition densities for each one of a specified number of lags. We present a framework to construct stationary MTD models that extend beyond linear, Gaussian dynamics. We study conditions for first-order strict stationarity which allow for different constructions with either continuous or discrete families for the first-order transition densities given a prespecified family for the marginal density, and with general forms for the resulting conditional expectations. Inference and prediction are developed under the Bayesian framework with particular emphasis on flexible, structured priors for the mixture weights. Model properties are investigated both analytically and through synthetic data examples. Finally, Poisson and Lomax examples are illustrated through real data applications. Supplementary files for this article are available online.

Continuous time reversal and equality in the thermodynamic uncertainty relation

We introduce a continuous time-reversal operation which connects the time-forward and time-reversed trajectories in the steady state of an irreversible Markovian dynamics via a continuous family of stochastic dynamics. This continuous time-reversal allows us to derive a tighter version of the thermodynamic uncertainty relation (TUR) involving observables evaluated relative to their local mean value. Moreover, the family of dynamics realizing the continuous time-reversal contains an equilibrium dynamics halfway between the time-forward and time-reversed dynamics. We show that this equilibrium dynamics, together with an appropriate choice of the observable, turns the inequality in the TUR into an equality. We demonstrate our findings for the example of a particle diffusing in a tilted periodic potential.

Pulse-efficient circuit transpilation for quantum applications on cross-resonance-based hardware

We show a pulse-efficient circuit transpilation framework for noisy quantum hardware. This is achieved by scaling cross-resonance pulses and exposing each pulse as a gate to remove redundant single-qubit operations with the transpiler. Crucially, no additional calibration is needed to yield better results than a CNOT-based transpilation. This pulse-efficient circuit transpilation therefore enables a better usage of the finite coherence time without requiring knowledge of pulse-level details from the user. As demonstration, we realize a continuous family of cross-resonance-based gates for SU(4) by leveraging Cartan's decomposition. We measure the benefits of a pulse-efficient circuit transpilation with process tomography and observe up to a 50% error reduction in the fidelity of ${R}_{ZZ}(\ensuremath{\theta})$ and arbitrary SU(4) gates on IBM Quantum devices. We apply this framework for quantum applications by running circuits of the quantum approximate optimization algorithm applied to MAXCUT. For an 11-qubit nonhardware native graph, our methodology reduces the overall schedule duration by up to 52% and errors by up to 38%.

Nonsmooth modal analysis via the boundary element method for one-dimensional bar systems

A numerical scheme grounded on the Boundary Element Method expressed in the Frequency Domain is proposed to perform Nonsmooth Modal Analysis of one-dimensional bar systems. The latter aims at finding continuous families of periodic orbits of mechanical components featuring unilateral contact constraints. The proposed formulation does not assume a semi-discretization in space of the governing Partial Differential Equations, as achieved in the Finite Element Method, and so mitigates a few associated numerical difficulties, such as chattering at the contact interface, or the questionable approximation of internal resonance conditions. The nonsmooth Signorini condition stemming from the unilateral contact constraint is enforced in a weighted residual sense via the Harmonic Balance Method. Periodic responses are investigated in the form of energy-frequency backbone curves along with the associated displacement fields. It is found that for the one-bar systems, the results compare well with existing works and the proposed methodology stands as a viable option in the field of interest. The two-bar system, for which no known results are reported in the literature, exhibits very rich nonsmooth modal dynamics with entangled nonsmooth modal motions combining hardening and softening effects via the intricate interaction of various, possibly subharmonic and internally resonant, nonsmooth modes of the two bars.

Complete noncompact G2-manifolds from asymptotically conical Calabi–Yau 3-folds

We develop a powerful new analytic method to construct complete noncompact Ricci-flat 7-manifolds, more specifically G2-manifolds, that is, Riemannian 7-manifolds (M,g) whose holonomy group is the compact exceptional Lie group G2. Our construction gives the first general analytic construction of complete noncompact Ricci-flat metrics in any odd dimension and establishes a link with the Cheeger–Fukaya–Gromov theory of collapse with bounded curvature. The construction starts with a complete noncompact asymptotically conical Calabi–Yau 3-fold B and a circle bundle M→B satisfying a necessary topological condition. Our method then produces a 1-parameter family of circle-invariant complete G2-metrics gϵ on M that collapses with bounded curvature as ϵ→0 to the original Calabi–Yau metric on the base B. The G2-metrics we construct have controlled asymptotic geometry at infinity, so-called asymptotically locally conical (ALC) metrics; these are the natural higher-dimensional analogues of the asymptotically locally flat (ALF) metrics that are well known in 4-dimensional hyper-Kähler geometry. We give two illustrations of the strength of our method. First, we use it to construct infinitely many diffeomorphism types of complete noncompact simply connected G2-manifolds; previously only a handful of such diffeomorphism types was known. Second, we use it to prove the existence of continuous families of complete noncompact G2-metrics of arbitrarily high dimension; previously only rigid or 1-parameter families of complete noncompact G2-metrics were known.

A Model of Farm Transition Planning for the U.S. Plains

Farm transition planning continues to be a significant challenge for U.S. agricultural owner/producers. Past and ongoing research points to an aging farm population with little or no planning to transition farms to succeeding farming family members, despite documented goals of continued family ownership and operation. This study developed and analyzed alternative farm asset transition strategies using a representative farm for Oklahoma. The simulations considered equity issues, family living requirements, and cash flow pre- and post-transition. Strategies analyzed considered off-farm investments and life insurance tools to even bequests between an on-farm and an off-farm heir, and also modeled splitting inheritance into an operating entity that owns machinery and other operating assets and a landholding entity that leases real estate to the on-farm heir. The simulations assumed a 20-year transition period. Results indicate that early planning is essential for success. In addition, the use of life insurance tools and/or the implementation of equitable, but unequal treatment of heirs improve the likelihood of successful farm transition between generations.

Solitary waves with intensity-dependent dispersion: variational characterization

A continuous family of singular solitary waves exists in a prototypical system with intensity-dependent dispersion. The family has a cusped soliton as the limiting lowest energy state and is formed by the solitary waves with bell-shaped heads of different lengths. We show that this family can be obtained variationally by minimization of mass at fixed energy and fixed length of the bell-shaped head. We develop a weak formulation for the singular solitary waves and prove that they are stable under perturbations which do not change the length of the bell-shaped head. Numerical simulations confirm the stability of the singular solitary waves.

Prevalence of crack cocaine use and its associated factors in patients treated in a specialized outpatient service

Abstract Background Despite the advance in studies addressing the use of crack cocaine, knowledge about the characteristics of users that seek treatment in the different modalities of care for substance use disorders is important to plan the operationalization of these services. Objective To analyze the prevalence and factors associated with the use of crack cocaine in outpatients. Method Cross-sectional study consisting in the analysis of the medical records of outpatients of a chemical dependency clinic located in the south of Brazil from 1999 to 2015. The Fisher’s exact test and the Poisson regression model were used to analyze the data. Results Medical records from 1,253 patients were analyzed, and 1,196 (95.5%) of them contained information on the use of crack cocaine. Use of this substance was reported by 47% (95% CI [44, 50]) of the outpatients. The risk group was composed of adults aged 20-39 years, with no income, who had three or more children, did not consume alcohol or marijuana, had continuous family assistance, spontaneously looked for the service, and had already been hospitalized or assisted at a therapeutic community or psychosocial center. Conclusion There is great demand for the outpatient care of crack cocaine users. It is crucial that the risk factors guide treatment planning.

On irregular Sasaki-Einstein metrics in dimension

We show that there are no irregular Sasaki-Einstein structures on rational homology 5-spheres. On the other hand, using -stability we prove the existence of continuous families of nontoric irregular Sasaki- Einstein structures on odd connected sums of . Bibliography: 30 titles.

Sustainable nurse-led care for people with dementia including mild cognitive impairment and their family in an ambulatory care setting: A scoping review.

This review aimed to determine the characteristics of a nurse-led intervention for people with dementia including mild cognitive impairment and their family in an ambulatory care setting. Enhancing the role of nurses in a multidisciplinary team of ambulatory care follow-up after a diagnosis of dementia is thought to lead to successful dementia care. This is a scoping review. MEDLINE, CINAHL, EMBASE, Cochrane, JBI, Japan Medical Abstracts Society, PsycINFO and Web of Science were searched on 14 March 2019. This scoping review was conducted using the Joanna Briggs Institute methodology, followed the PRISMA-ScR checklist and considered studies that included interventions conducted by nurses and included outcomes regarding dementia symptoms or family care burden. Eleven studies were included. Of these, all interventions were multifactorial and reported effective results. Educational interventions were most common, and the content of education included the characteristics of dementia and how to interact with patients with dementia. The roles of nurses included caregiver education, assessment, care plan creation for continuous monitoring and team building. This scoping review suggested that effective nurse-led interventions in the ambulatory care of people with dementia are continuous patient and family supports, primarily caregiver education within multidisciplinary teams.

Editors' Note: Temporal Trends and Autopsy Findings of SUDEP Based on Medicolegal Investigations in the United States

In “Temporal Trends and Autopsy Findings of SUDEP Based on Medicolegal Investigations in the United States,” Cihan et al. reviewed medical examiner reports in 3 cities in the United States and found that although there was no correlation between sudden unexplained death in epilepsy (SUDEP) and diurnal patterns or time of year, there was a reduction in the incidence of SUDEP between 2009 and 2016. There was also no difference in autopsy findings between SUDEP- and non–SUDEP-related deaths associated with epilepsy. Bleasel was encouraged by these findings, which he attributed to increased awareness of SUDEP, access to affordable medical care, and prescribing antiseizure medications. However, he emphasized the importance of continued patient and family education about the risk of SUDEP, medication compliance, and treatment of comorbidities. He also noted that other studies have shown respiratory center neuronal cellular abnormalities in patients with SUDEP. Friedman et al. agreed that this positive trend is encouraging, but that it does not obviate the need to 1) counsel patients and families about SUDEP as part of general epilepsy care or 2) continue to pursue research to explain this reduction and minimize the risk of SUDEP as much as possible. In “Temporal Trends and Autopsy Findings of SUDEP Based on Medicolegal Investigations in the United States,” Cihan et al. reviewed medical examiner reports in 3 cities in the United States and found that although there was no correlation between sudden unexplained death in epilepsy (SUDEP) and diurnal patterns or time of year, there was a reduction in the incidence of SUDEP between 2009 and 2016. There was also no difference in autopsy findings between SUDEP- and non–SUDEP-related deaths associated with epilepsy. Bleasel was encouraged by these findings, which he attributed to increased awareness of SUDEP, access to affordable medical care, and prescribing antiseizure medications. However, he emphasized the importance of continued patient and family education about the risk of SUDEP, medication compliance, and treatment of comorbidities. He also noted that other studies have shown respiratory center neuronal cellular abnormalities in patients with SUDEP. Friedman et al. agreed that this positive trend is encouraging, but that it does not obviate the need to 1) counsel patients and families about SUDEP as part of general epilepsy care or 2) continue to pursue research to explain this reduction and minimize the risk of SUDEP as much as possible.