Continuous Family Research Articles

Charting the conformal manifold of holographic CFT$_2$'s

We construct new continuous families of AdS_3× S^3× T^4AdS3×S3×T4 and AdS_3× S^3× S^3× S^1AdS3×S3×S3×S1 solutions in heterotic and type II supergravities. These families are found in three-dimensional consistent truncations and controlled by 17 parameters, which include TsT \betaβ deformations and encompass several supersymmetric sub-families. The different uplifts are constructed in a unified fashion by means of Exceptional Field Theory (ExFT). This allows the computation of the Kaluza-Klein spectra around the deformations, to test the stability of the solutions, and to interpret them holographically and as worldsheet models. To achieve this, we describe how the half-maximal S(8,8)S(8,8) ExFT can be embedded into E_{8(8)}E8(8) ExFT.

On The Modeling of Biomedical Data Sets with a New Generalized Exponentiated Exponential Distribution

Introduction: Many experts in the field of distribution theory have focused on extending probability distributions utilizing extended families of continuous distributions to improve the modeling adaptability of the conventional probability distributions. Methods: This research employed a continuous family of probability distributions as introduced in the literature using the T-X methodology. Through this, some of statistical and mathematical properties of the model were derived and studied Results: This study had introduced a brand-new, five-parameter generalized exponentiated exponential distribution, which is a continuous probability distribution. With the aid of the quantile function, moments, moment generating function, survival function, hazard function, mean, and median, among other mathematical and statistical aspects, the new distribution's shape was deduced and researched. It was also possible to derive the probability density function for the minimum and maximum order statistics for this distribution. The method of maximum likelihood estimate was used to produce a conventional estimation of the unknown parameters. A simulation study was carried out to assess the efficiency and consistency of the estimation method used. To evaluate the fit and adaptability of the new model, it was applied to four real-world datasets in the field of medicine. Conclusion: The analysis's findings demonstrated that the new model performs better than its counterparts and offers a better fit than the Topp-Leone exponentiated exponential, Topp-Leone Kumaraswamy exponential, exponentiated exponential, and exponential distributions.

A note on the approximate controllability of damped second-order differential inclusions with state-dependent delay

In this paper, we use Bohnenblust–Karlin's fixed point theorem and the theory of strongly continuous cosine families of bounded linear operators to study the approximate controllability of damped second-order differential inclusions with state-dependent delay in Banach spaces. In particular, we obtain a new set of sufficient conditions for the approximate controllability of damped second-order differential inclusions with state-dependent delay under the assumption that the corresponding linear system is approximately controllable. An example is provided to illustrate our main results.

Iterative site percolation on triangular lattice

The site percolation on the triangular lattice stands out as one of the few exactly solved statistical systems. By initially configuring critical percolation clusters of this model and randomly reassigning the color of each percolation cluster, we obtain coarse-grained configurations by merging adjacent clusters that share the same color. It is shown that the process can be infinitely iterated in the infinite-lattice limit, leading to an iterative site percolation model. We conjecture from the self-matching argument that percolation clusters remain fractal for any finite generation, which can even take any positive real number by a generalized process. Extensive simulations are performed, and, from the generation-dependent fractal dimension, a continuous family of previously unknown universalities is revealed. Published by the American Physical Society 2024

Opinions of Patients, Families and Healthcare Professionals on Family Involvement in the Care of Patients Hospitalized in a Moroccan University Hospital: A Cross-Sectional Observational Survey.

Opinion surveys on family participation in care in non-Western countries are rare. This study aims to assess the opinions of patients, families, and healthcare professionals regarding family involvement in care to identify their preferences and the associated factors. A cross-sectional survey was conducted over eight months involving 717 participants, using structured questionnaires at the Acute Assessment Unit of a university hospital in Morocco. Comparative analyses examined the association between participant characteristics and the preferences of care categories. Poisson regression was applied to determine factors associated with participant preferences. Attitudes toward family participation in care were positive, with an average score of 3.62 ± 0.43 on a 4-point Likert scale. Healthcare professionals were more favorable towards family participation, with an average of 10.6 ± 2.44 types of care, compared to 7.17 ± 1.96 for families and 5.71 ± 2.16 for patients. Participants' opinions converged on a set of simple and less technical care tasks. Factors significantly associated with patient preferences in the final adjustment model (p < 0.05) included frailty, loss of autonomy, length of stay, and regular and continuous (day and night) family presence. This study highlights the strong support of health professionals, patients, and families for family participation in care. Understanding these preferences and related factors is essential to maximize family participation and develop a model of Patient And Family Centered Care adapted to the Moroccan context.

Asymptotic lifting for completely positive maps

Let A and B be C⁎-algebras with A separable, let I be an ideal in B, and let ψ:A→B/I be a completely positive contractive linear map. We show that there is a continuous family Θt:A→B, for t∈[1,∞), of lifts of ψ that are asymptotically linear, asymptotically completely positive and asymptotically contractive. If ψ is of order zero, then Θt can be chosen to have this property asymptotically. If A and B carry continuous actions of a second countable locally compact group G such that I is G-invariant and ψ is equivariant, we show that the family Θt can be chosen to be asymptotically equivariant. If a linear completely positive lift for ψ exists, we can arrange that Θt is linear and completely positive for all t∈[1,∞). In the equivariant setting, if A, B and ψ are unital, we show that asymptotically linear unital lifts are only guaranteed to exist if G is amenable. This leads to a new characterization of amenability in terms of the existence of asymptotically equivariant unital sections for quotient maps.

Constraints on symmetry-preserving gapped phases from coupling constant anomalies

We characterize constraints on the possible IR phases of quantum field theories from coupling constant anomalies. We give conditions for when a coupling constant anomaly cannot be matched by a continuous family of symmetry preserving gapped phases: the theory must then be gapless or exhibit spontaneous symmetry breaking or a phase transition. We demonstrate examples of coupling constant anomalies which can be matched by a family of symmetry preserving gapped phases without a phase transition and comment on the interpretation of our results for the spontaneous breaking of “(−1)-form global symmetries.” Published by the American Physical Society 2024

Extreme Superposition: High-Order Fundamental Rogue Waves in the Far-Field Regime

This Memoir concerns fundamental rogue-wave solutions of the focusing nonlinear Schrödinger equation in the limit that the order of the rogue wave is large and the independent variables ( x , t ) (x,t) are proportional to the order (the far-field limit). We first formulate a Riemann-Hilbert representation of these solutions that allows the order to vary continuously rather than by integer increments. The intermediate solutions in this continuous family include also soliton solutions for zero boundary conditions spectrally encoded by a single complex-conjugate pair of poles of arbitrary order, as well as other solutions having nonzero boundary conditions matching those of the rogue waves albeit with far slower decay as x → ± ∞ x\to \pm \infty . The large-order far-field asymptotic behavior of the solution depends on which of three disjoint regions C \mathcal {C} (the “channels”), S \mathcal {S} (the “shelves”), and E \mathcal {E} (the “exterior domain”) contains the rescaled variables. On the region C \mathcal {C} , the amplitude is small and the solution is highly oscillatory, while on the region S \mathcal {S} , the solution is approximated by a modulated plane wave with a highly oscillatory correction term. The asymptotic behavior on these two domains is the same for all continuous orders. Assuming that the order belongs to the discrete sequence characteristic of rogue-wave solutions, the asymptotic behavior of the solution on the region E \mathcal {E} resembles that on S \mathcal {S} but without the oscillatory correction term. Solutions of other continuous orders behave quite differently on E \mathcal {E} .

On the approximate controllability of second-order stochastic differential systems with hemivariational inequalities with damping

In this article, we investigate the approximate controllability of damping second-order stochastic differential systems with hemivariational inequalities. First, we show the existence of a mild solution to the suggested second-order differential system with the notions of generalized Clarke's subdifferential type. Next, by adopting the fixed point technique of condensing multi-valued maps, the conditions for generalized Clarke's subdifferential and the strongly continuous cosine family is employed for the existence of a mild solution. Furthermore, the approximate controllability results for the given system are proven. In the end, an illustration is presented to highlight our primary findings.

A New Family of Distributions with an Application to Exponentially Distribution

This paper introduces a new continuous distribution family called the Alpha logarithm family, which is a new modelling strategy for fitting data subject to univariate continuous distributions. This is achieved by introducing an additional parameter for greater flexibility using a single-parameter Natural logarithm transformation which can enhance some of the modeling capabilities of some Parental Continuous Distributions: This technique was applied to the exponential distribution to obtain a new two-parameter distribution, and the changes that occurred in the exponential distribution were observed. The general properties and functions of the new distribution were also derived and studied, and the estimators of the two parameters were derived. The efficiency of the estimators is verified through the simulation study. The new distribution is also applied to two sets of real data to prove the benefit of the new transformation, and we show that the proposed model is better than the asymptotic distributions with which it was compared on the selected data.

Analisis Pelaksanaan Perceraian di Depan Sidang Pengadilan Agama Perspektif Ma’anil Hadis

Divorce is an emergency exit from continuous family conflict. Islam permits divorce but is hated by Allah swt for reasons prohibited by Islamic law. The reality in the community is that there is an incomplete understanding because of the disparity between the provisions of positive law and the hadith that divorce is granted even in jest or in a serious situation and without intention. The position of the court in organising the administration of marriage is very important. The purpose of this study is to examine and analyse the hadith of divorce even in jest or in seriousness and without intention whether it can be used as a basis or is no longer relevant. This research uses a qualitative descriptive approach. Data collection in this research is through literature study. Meanwhile, the data analysis is carried out by examination, classification, verification, analysis and conclusion. The result of the study is that the hadith of the fall of divorce even in jest or in a serious situation and without intention can be used as a basis and as a warning to everyone to be careful in guarding the tongue, especially the issue of divorce. If contextualised with the lives of people in Indonesia, divorce not in front of the court cannot guarantee that it can avoid negative things, especially the fate of women and children after divorce, considering that there are benefits that will be obtained if the divorce is carried out in front of a court session.

On geodesic orbit nilmanifolds

The paper is devoted to the study of geodesic orbit Riemannian metrics on nilpotent Lie groups. The main result is the construction of continuous families of pairwise non-isomorphic connected and simply connected nilpotent Lie groups, every of which admits geodesic orbit metrics. The minimum dimension of groups in the constructed families is 10.

“I Tell Them Generics, but Not the Specifics”: Exploring Tensions Underlying Familial Support for First-Generation Latinx Undergraduate Students

Families continue to play an essential role in the experiences of first-generation Latinx undergraduate students and can serve as powerful partners to support student retention and socioemotional wellbeing. This qualitative phenomenological study uses the notion of emerging adulthood to explore how first-generation Latinx undergraduate students (n = 16) conceptualize their families’ role in their college education. Specifically, this study shows that while students describe feeling supported by their families, they also experience distinct and unique tensions tied to this support, which students associate with their first-generation student status. These tensions include (1) the family’s unfamiliarity with college culture; (2) bidirectional behaviors of protection from stress and worry; and (3) continued family interactions. These findings, or tensions, are essential to understand and address. Doing so can improve the nature of familial support for first-generation Latinx undergraduate students by leading to better family—student relationships, family—institutional relationships, and student academic and non-academic outcomes.

Phase space geometry of general quantum energy transitions

The mixed density operator for coarsegrained eigenlevels of a static Hamiltonian is represented in phase space by the spectral Wigner function, which has its peak on the corresponding classical energy shell. The action of trajectory segments along the shell determine the phase of the Wigner oscillations in its interior. The classical transitions between any pair of energy shells, driven by a general external time dependent Hamiltonian, also have a smooth probability density. It is shown here that a further contribution to the transition between the corresponding pair of coarsegrained energy levels, which oscillates with either energy, or the driving time, is determined by four trajectory segments (two in the pair of energy shells and two generated by the driving Hamiltonian) that join exactly to form a closed compound orbit (CCO). In its turn, this sequence of segments belongs to the semiclassical expression of a compound unitary operator that combines four quantum evolutions: a pair generated by the static internal Hamiltonian and a pair generated by the driving Hamiltonian. The CCOs are shown to belong to continuous families, which are initially seeded at points where the classical flow generated by both Hamiltonians commute.

Massless Lifshitz field theory for arbitrary z

By using the notion of fractional derivatives, we introduce a class of massless Lifshitz scalar field theory in (1+1)-dimension with an arbitrary anisotropy index z. The Lifshitz scale invariant ground state of the theory is constructed explicitly and takes the form of Rokhsar-Kivelson (RK). We show that there is a continuous family of ground states with degeneracy parameterized by the choice of solution to the equation of motion of an auxiliary classical system. The quantum mechanical path integral establishes a 2d/1d correspondence with the equal time correlation functions of the Lifshitz scalar field theory. We study the entanglement properties of the Lifshitz theory for arbitrary z using the path integral representation. The entanglement measures are expressed in terms of certain cross ratio functions we specify, and satisfy the c-function monotonicity theorems. We also consider the holographic description of the Lifshitz theory. In order to match with the field theory result for the entanglement entropy, we propose a z-dependent radius scale for the Lifshitz background. This relation is consistent with the z-dependent scaling symmetry respected by the Lifshitz vacuum. Furthermore, the time-like entanglement entropy is determined using holography. Our result suggests that there should exist a fundamental definition of time-like entanglement other than employing analytic continuation as performed in relativistic field theory.

Harmonic metrics for the Hull–Strominger system and stability

We investigate stability conditions related to the existence of solutions of the Hull–Strominger system with prescribed balanced class. We build on recent work by the authors, where the Hull–Strominger system is recasted using non-Hermitian Yang–Mills connections and holomorphic Courant algebroids. Our main development is a notion of harmonic metric for the Hull–Strominger system, motivated by an infinite-dimensional hyperKähler moment map and related to a numerical stability condition, which we expect to exist for families of solutions. We illustrate our theory with an infinite number of continuous families of examples on the Iwasawa manifold.

Mild Solutions for w-Weighted, Φ-Hilfer, Non-Instantaneous, Impulsive, w-Weighted, Fractional, Semilinear Differential Inclusions of Order μ ∈ (1, 2) in Banach Spaces

The aim of this work is to obtain novel and interesting results for mild solutions to a semilinear differential inclusion involving a w-weighted, Φ-Hilfer, fractional derivative of order μ∈(1,2) with non-instantaneous impulses in Banach spaces with infinite dimensions when the linear term is the infinitesimal generator of a strongly continuous cosine family and the nonlinear term is a multi-valued function. First, we determine the formula of the mild solution function for the considered semilinear differential inclusion. Then, we give sufficient conditions to ensure that the mild solution set is not empty or compact. The desired results are achieved by using the properties of both the w-weighted Φ-Laplace transform, w-weighted ψ-convolution and the measure of non-compactness. Since the operator, the w-weighted Φ-Hilfer, includes well-known types of fractional differential operators, our results generalize several recent results in the literature. Moreover, our results are novel because no one has previously studied these types of semilinear differential inclusions. Finally, we give an illustrative example that supports our theoretical results.

Supersymmetric Casimir energy on N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 1 conformal supergravity backgrounds

We provide a first principles derivation of the supersymmetric Casimir energy of N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 1 SCFTs in four dimensions using the supercharge algebra on general conformal supergravity backgrounds that admit Killing spinors. The superconformal Ward identities imply that there exists a continuous family of conserved R-currents on supersymmetric backgrounds, as well as a continuous family of conserved currents for each conformal Killing vector. These continuous families interpolate between the consistent and covariant R-current and energy-momentum tensor. The resulting Casimir energy, therefore, depends on two continuous parameters corresponding to the choice of conserved currents used to define the energy and R-charge. This ambiguity is in addition to any possible scheme dependence due to local terms in the effective action. As an application, we evaluate the general expression for the supersymmetric Casimir energy we obtain on a family of backgrounds with the cylinder topology ℝ × S3 and admitting a single Majorana supercharge. Our result is a direct consequence of the supersymmetry algebra, yet it resembles more known expressions for the non-supersymmetric Casimir energy on such backgrounds and differs from the supersymmetric Casimir energy obtained from the zero temperature limit of supersymmetric partition functions. We defer a thorough analysis of the relation between these results to future work.

Curved-Crease Origami for Morphing Metamaterials.

We find a closed-form expression for the Poisson's coefficient of curved-crease variants of the "Miura ori" origami tessellation. This is done by explicitly constructing a continuous one-parameter family of isometric piecewise-smooth surfaces that describes the action of folding out of a reference state. The response of the tessellations in bending is investigated as well: using a numerical convergence scheme, the effective normal curvatures under infinitesimal bending are found to occur in a ratio equal and opposite to the Poisson's coefficient. These results are the first of their kind and, by their simplicity, should provide a fruitful benchmark for the design and modeling of curved-crease origami and compliant shell mechanisms. The developed methods are used to design a curved-crease 3D morphing solid with a tunable self-locked state.

Asymptotically flat Fredholm bundles and assembly

Almost flat finitely generated projective Hilbert [Formula: see text]-module bundles were successfully used by Hanke and Schick to prove special cases of the Strong Novikov Conjecture. Dadarlat later showed that it is possible to calculate the index of a [Formula: see text]-homology class [Formula: see text] twisted with an almost flat bundle in terms of the image of [Formula: see text] under Lafforgue’s assembly map and the almost representation associated with the bundle. Mishchenko used flat infinite-dimensional bundles equipped with a Fredholm operator in order to prove special cases of the Novikov higher signature conjecture. We show how to generalize Dadarlat’s theorem to the case of an infinite-dimensional bundle equipped with a continuous family of Fredholm operators on the fibers. Along the way, we show that special cases of the Strong Novikov Conjecture can be proven if there exist sufficiently many almost flat bundles with Fredholm operator. To this end, we introduce the concept of an asymptotically flat Fredholm bundle and its associated asymptotic Fredholm representation, and prove an index theorem which relates the index of the asymptotic Fredholm bundle with the so-called asymptotic index of the associated asymptotic Fredholm representation.