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A Theory of Fundamental Strata for Twisted Formal Connections
Get PDFLet be a complex reductive group. A fundamental stratum for is a triple where is a point in the Bruhat-Tits building of , is a nonnegative real number called depth of the stratum, and is a semistable functional on the Moy-Prasad filtration of \fg associated to at level . Fundamental strata were first introduced to classify admissible representations of a -adic reductive group. More recently, Bremer and Sage have shown that fundamental strata play an important role in the geometric Langlands program and developed a theory of fundamental strata for -connections. In this dissertation, we generalize Bremer and Sage\u27s result and develop a theory of fundamental strata for twisted -connection. We show that every twisted -connection contains a fundamental stratum, and every fundamental stratum contained in a twisted -connection has the same depth, which we now called the slope. We also give characterizations and properties of slope. Lastly, we construct examples of a twisted formal Frenkel-Gross connection for classical groups
A new error analysis for finite element methods for elliptic Neumann boundary control problems with pointwise control constraints
Get PDFWe present a new error analysis for finite element methods for a linear-quadratic elliptic optimal control problem with Neumann boundary control and pointwise control constraints. It can be applied to standard finite element methods when the coefficients in the elliptic operator are smooth and also to multiscale finite element methods when the coefficients are rough
Quasi-brittle fracture: The blended approach
No full textA field theory is presented for predicting damage and fracture in quasi-brittle materials. The approach taken here is new and blends a nonlocal constitutive law with a two-point phase field. In this formulation, the material displacement field is uniquely determined by the initial boundary value problem. The theory naturally satisfies energy balance, with positive energy dissipation rate in accordance with the laws of thermodynamics. Notably, these properties are not imposed but follow directly from the constitutive law and evolution equation when multiplying the equation of motion by the velocity and integrating by parts. In addition to elastic constants, the model requires at most three key material parameters: the strain at the onset of nonlinearity, the ultimate tensile strength, and the fracture toughness. The approach simplifies parameter identification while ensuring representation of material behavior. The approach seamlessly handles fracture evolution across loading regimes, from quasi-static to dynamic, accommodating both fast crack propagation and quasi-brittle failure under monotonic and cyclic loading. Numerical simulations show quantitative and qualitative agreement with experiments, including three-point bending tests on concrete. The model successfully captures the cyclic load–deflection response of crack mouth opening displacement, the structural size-effect related to ultimate load and specimen size, fracture originating from corner singularities in L-shaped domains, and bifurcating fast cracks
The explicit hypergeometric-modularity method I
No full textThe theories of hypergeometric functions and modular forms are highly intertwined. For example, particular values of truncated hypergeometric functions and hypergeometric character sums are often congruent or equal to Fourier coefficients of modular forms. In this series of papers, we develop and explore an explicit “Hypergeometric-Modularity” method for associating a modular form to a given hypergeometric datum. In particular, for certain length three and four hypergeometric data we give an explicit method for finding a modular form f such that the corresponding hypergeometric Galois representation has a subrepresentation isomorphic to the Deligne representation of f. Our method utilizes Ramanujan\u27s theory of elliptic functions to alternative bases, commutative formal group laws, and supercongruences. As a byproduct, we give a collection of eta quotients with multiplicative coefficients constructed from hypergeometric functions. In the second paper, we discuss a number of applications, including explicit connections between hypergeometric values and periods of these explicit eta quotients as well as evaluation formulae for certain special L-values
On 2-superirreducible polynomials over finite fields
Get PDFWe investigate k-superirreducible polynomials, by which we mean irreducible polynomials that remain irreducible under any polynomial substitution of positive degree at most k. Let F be a finite field of characteristic p. We show that no 2-superirreducible polynomials exist in F[t] when p=2 and that no such polynomials of odd degree exist when p is odd. We address the remaining case in which p is odd and the polynomials have even degree by giving an explicit formula for the number of monic 2-superirreducible polynomials having even degree d. This formula is analogous to that given by Gauss for the number of monic irreducible polynomials of given degree over a finite field. We discuss the associated asymptotic behaviour when either the degree of the polynomial or the size of the finite field tends to infinity
Nodal finite element approximation of peridynamics
Get PDFThis work considers the nodal finite element approximation of peridynamics, in which the nodal displacements satisfy the peridynamics equation at each mesh node. For the nonlinear bond-based peridynamics model, it is shown that, under the suitable assumptions on an exact solution, the discretized solution associated with the central-in-time and nodal finite element discretization converges to a solution in the L2 norm at the rate C1Δt+C2h2/ϵ2. Here, Δt, h, and ϵ are time step size, mesh size, and the size of the horizon or nonlocal length scale, respectively. Constants C1 and C2 are independent of h and Δt and depend on norms of the solution and nonlocal length scale. Several numerical examples involving pre-crack, void, and notch are considered, and the efficacy of the proposed nodal finite element discretization is analyzed
CONVERGENCE OF THE PLANEWAVE APPROXIMATIONS FOR QUANTUM INCOMMENSURATE SYSTEMS
Get PDFIncommensurate structures come from stacking the single layers of low dimensional materials on top of one another with misalignment such as a twist in orientation. While these structures are of significant physical interest, they pose many theoretical challenges due to the loss of periodicity. This paper studies the physical observables of continuum Schrodinger operators for incommensurate systems. We characterize the density of states and local density of states in real and reciprocal spaces, and develop novel numerical methods to approximate them. In particular, we (i) justify the thermodynamic limit of the density of states and local density of states via the operator kernel characterization; and (ii) propose efficient numerical schemes based on plane wave approximation and the trapezoidal rule in reciprocal space. We present both rigorous analysis and numerical simulations to support the reliability and efficiency of our numerical algorithms
The holomorphic discrete series contribution to the generalized Whittaker Plancherel formula II. Non-tube type groups
Get PDFFor every simple Hermitian Lie group G, we consider a certain maximal parabolic subgroup whose unipotent radical N is either abelian (if G is of tube type) or two-step nilpotent (if G is of non-tube type). By the generalized Whittaker Plancherel formula we mean the Plancherel decomposition of L2(G/N,ω), the space of square-integrable sections of the homogeneous vector bundle over G/N associated with an irreducible unitary representation ω of N. Assuming that the central character of ω is contained in a certain cone, we construct embeddings of all holomorphic discrete series representations of G into L2(G/N,ω) and show that the multiplicities are equal to the dimensions of the lowest K-types. The construction is in terms of a kernel function which can be explicitly defined using certain projections inside a complexification of G. This kernel function carries all information about the holomorphic discrete series embedding, the lowest K-type as functions on G/N, as well as the associated Whittaker vectors
EFFECTS OF SEASONALITY ON THE EXPERIENCES OF EMPLOYEES IN MINOR LEAGUE SPORTS
Get PDFThe temporal rhythms of sport organizations, driven by recurring cycles of in-season and off-season activity, create a unique organizational context that shapes decision-making, leadership behavior, and the experiences of employees. While seasonality is widely recognized in operational planning and revenue forecasting, its implications for organizational behavior in sport management remain underexplored. This three-paper dissertation examines seasonality as a temporal force influencing sport organizations at conceptual, strategic, and affective levels.
The first paper develops a sport-specific taxonomy of seasonality by synthesizing literature from econometrics, tourism, and organizational theory. It distinguishes between natural, internally institutionalized, and externally institutionalized seasonal influences, offering a conceptual model to understand how cyclical patterns impact sport organizations’ planning, staffing, and resource allocation. This paper provides the theoretical foundation for empirical exploration in the subsequent studies.
The second paper applies contingency theory to investigate how minor league sport executives adapt their leadership styles and decision-making processes across seasonal phases. The findings illustrate how cyclical transitions in temporal context necessitate parallel shifts in executive cognition, stakeholder relationships, and managerial priorities. The third paper utilizes Affective Events Theory (AET) to examine how the seasonality of emotionally intense work events contributes to employee burnout. The study repositions burnout as a cyclical, time-sensitive construct rather than a static outcome, and identifies organizational support and role autonomy as key mitigating factors.
The research aims to uncover how seasonal patterns shape employee affective experiences, behaviors, and organizational outcomes by applying AET and Contingency Theory lenses. These three studies offer a comprehensive perspective on how time and seasonality shape the internal dynamics of sport organizations. The dissertation contributes to sport management by advancing a temporally grounded framework for understanding leadership, strategic behavior, and employee well-being, while providing practical insights for sport executives, human resource professionals, and organizational planners
Autism and Down Syndrome: An Examination of the Baby and Infant Screen for Autism Traits in Toddlers with Down syndrome
Get PDFCurrent research suggests that children with Down Syndrome (DS) are at an increased risk for autism spectrum disorder (ASD) compared to the general population. Detecting ASD early in children with DS is crucial to providing access to additional treatment services and supports that may be necessary. Despite a critical need to identify ASD as early as possible, diagnoses of ASD are often delayed in individuals with DS. It can be especially difficult for clinicians to differentiate between symptoms attributed to intellectual developmental disorder (IDD), a primary feature of DS, and possible ASD symptoms. Only two research studies have evaluated the psychometric properties of ASD screening measures in individuals with DS, though neither of these studies included individuals with DS under the age of 3 years old. Therefore, this study sought to expand current literature by evaluating the factor structure of the Baby Infant Screen for Children with aUtIsm Traits (BISCUIT) in 186 toddlers diagnosed with DS as compared to 187 toddlers diagnosed with cerebral palsy (CP) aged 17 to 35 months. Additionally, the impact of diagnostic group on the frequency at which caregivers endorsed BISCUIT items, ASD symptomology, and clinician-rated communication and cognition scores on the Battelle Developmental Inventory, 2nd Edition (BDI-2) were investigated. Results indicated that a four-factor solution fit the DS sample best, while a three-factor solution fit the CP sample best. Congruence coefficients resulted in one factor (i.e., verbal communication) with good similarity between the factor loadings for the DS and CP groups. Toddlers with DS were found to demonstrate significantly less impairment than toddlers with CP across two BISCUIT composites (i.e., nonverbal communication/socialization, restricted interests/repetitive behaviors); however, toddlers with DS demonstrated significantly more impaired communication scores on the BDI-2 and their caregivers more frequently endorsed difficulties with verbal communication on individual BISCUIT items. Implications for ASD screening of children with DS, as well as recommendations for future research and clinical practices are discussed