Digital Commons Network^™

Designing System Coherence For Designated English Language Development, Raquel Gonzalez, Ph.D., Magaly Lavadenz, Ph.D., Elvira G. Armas, Ed.D., Jeimee Estrada-Miller, Britt Jung

Center on English Language Proficiency Implementation Briefs

Designing System Coherence for Designated English Language Development is the fourth and final brief in a series designed to guide state, regional, and local educational agencies in establishing equitable, high-quality comprehensive English Language Development (ELD) systems. The brief examines the organizational infrastructure, leadership, and resource alignment needed to scale and sustain high-quality designated ELD. An adapted framework of seven interconnected foundational practices guides the discussion of how educational leaders can protect instructional time, support sustained professional learning and coaching, and connect designated ELD to grade-level academic content. The brief also examines systemic coherence across three levels—state education agencies, local education …

Academic Symposium Program

The Inauguration of Joseph C. Hartman (2026)

The Academic Symposium highlights the innovations in scholarship and excellence in teaching that make WNE a place where possibilities take shape.

Academic Symposium At-A-Glance And Map

The Inauguration of Joseph C. Hartman (2026)

The Academic Symposium highlights the innovations in scholarship and teaching, student engagement, and social impact that make WNE a place where possibilities take shape.

Waste Streams From Next Generation Molten Salt Reactors: The Challenge Of Creating An Insoluble Ceramic For Chloride Salt Waste, Alevtina A. Maksimova, Jake W. Amoroso, Matthew Page, Gregory Morrison, Hans Conrad Zur Loye

Faculty Publications

Molten salt reactors (MSRs) design development is of interest to many research groups and companies. Waste management for MSRs is one of the most important issues that needs to be resolved due to its impact on environmental safety, primarily via the dissolution of radionuclides in water. Furthermore, the waste treatment strategy will have a significant influence on the operating cost of MSRs, which is why a reliable process for the immobilization, transportation, storage and disposal of MSR waste must be addressed. This work presents a new approach for the immobilization of chloride salts from molten salt reactors in stable oxyhalide …

The Jefferson-D’Hondt Method And Majorization, Stanley Chang

The Mathematics Enthusiast

This article investigates the interplay between apportionment functions and order-theoretic structures on population and allocation vectors. We define a class of functions, called apportionment maps, that respect population monotonicity, house monotonicity, and size monotonicity. A central focus is placed on the preservation or violation of majorization under these functions, with particular attention to the Jefferson method and related divisor schemes. By applying tools from convex analysis and the theory of Schur-convex functions, we characterize the extent to which fairness criteria are preserved under apportionment.

Standard Monomials For Positroid Varieties, Ayah Almousa, Shiliang Gao, Daoji Huang

Mathematics Faculty Publications

We give an explicit characterization of the standard monomials for positroid varieties with respect to the Hodge degeneration and give a Gröbner basis. Furthermore, we show that promotion and evacuation biject standard monomials of a positroid variety with those of its cyclic shifts and w₀-reflection, respectively. The connection to promotion allows us to identify standard monomials of a positroid variety with Lam's cyclic Demazure crystal. Using a recurrence on the Hilbert series, we give an inductive formula for the character of cyclic Demazure modules.

Enhancing Programming Productivity For Individuals With Adhd Through Generative Artificial Intelligence: An Inductive Analysis, Lionel Mew

School of Professional and Continuing Studies Faculty Publications

Attention-deficit/hyperactivity disorder (ADHD) significantly impacts computer programmers through challenges in sustained attention, executive functioning, and organizational skills. While traditional intervention strategies have shown varying degrees of success, the emergence of generative artificial intelligence (AI) presents novel opportunities to address ADHD-related programming challenges. This paper presents an inductive analysis synthesizing current research on ADHD's effects on programming, traditional productivity enhancement techniques, and the potential of generative AI tools. Through examination of recent literature and field studies, we propose that generative AI can serve as a transformative intervention by providing personalized cognitive support, reducing executive function demands, and enhancing code generation efficiency. …

Implementation Brief 3 Classroom Brightspots, Center On English Language Proficiency

Resources

No abstract provided.

Implementation Brief 4 Sea And Lea Brightspots, Center On English Language Proficiency

Resources

No abstract provided.

The Definitive Assessment Playbook: Tips And Tools For Educators Of Multilingual Learners, Margo Gottlieb

Resources

The Definitive Assessment Playbook: Tips and Tools for Educators of Multilingual Learners is a practical, evidence-based guide designed to humanize classroom assessment and elevate the agency of all assessment players. Grounded in the Science of Teaching and Learning and structured around twelve Focused Assessment Principles, the Playbook translates research into actionable practices, tools, and reflection opportunities for classroom, school, district, and community learning ecologies. Practical tips, tools, reflection templates, and inquiry frameworks support assessment players in applying these principles to build fair, balanced, learning-centered, and sustainable assessment systems for multilingual learners.

The Playbook includes five sections organized around major themes: …

The Library Papers (Vol. 2, Issue 1, September 2026), Wolf Law Library, William & Mary Law School

Library Newsletter

No abstract provided.

Cover And Contents

Turkish Journal of Mathematics

No abstract provided.

Generalized Spectral Bound For Quasi-Twisted Codes, Buket Özkaya

Turkish Journal of Mathematics

Minimum distance bounds play a central role in the analysis of algebraic codes. For cyclic and constacyclic codes, several bounds based on their zero set have been developed. However, analogous results for quasi-twisted (QT) codes are comparatively limited. In this paper, we further investigate the spectral theory of QT codes and derive a general spectral bound on their minimum distance. Our bound unifies and generalizes previously known spectral bounds for quasi-cyclic (QC) and QT codes, and contains them as special cases. We present a new proof technique and show that the bound can be formulated with respect to an arbitrary …

A Novel Iterative Algorithm For Approximating Common Fixed Points Of Generalized Α-Nonexpansive Multivalued Mappings In Kohlenbach Hyperbolic Spaces, Makbule Kaplan Özekes

Turkish Journal of Mathematics

In this paper, we propose a new iterative scheme involving three multivalued mappings in Kohlenbach hyperbolic spaces. Strong and ∆-convergence theorems are established for approximating common fixed points of nonexpansive multivalued mappings under suitable conditions. A numerical example is also presented to illustrate the efficiency and faster convergence of the proposed method. The results obtained extend and unify several related contributions in the existing literature.

On Families Of Finsler Metrics, İsmai̇l Sağlam, Ken'ichi Ohshika, Athanase Papadopoulos

Turkish Journal of Mathematics

In this paper, we answer some natural questions concerning symmetrisation and more general combinations of Finsler metrics, with a view to applications to Funk and Hilbert geometries and metrics on Teichmüller spaces. The metrics on Teichmüller space that we consider are the Thurston metric and the earthquake metric, both introduced by Thurston. The first metric has been thoroughly studied over the last couple of decades, and the second over the last few years. The Funk metric and its symmetrisation, the Hilbert metric, are classical metrics that have been investigated in the contexts of hyperbolic geometry and geometric function theory and, …

On The Monoid Of Partial Order-Preserving Transformations Of A Finite Chain Whose Domains And Ranges Are Intervals, Hayrullah Ayik, Vítor H. Fernandes, Emrah H. Korkmaz

Turkish Journal of Mathematics

In this paper, we consider the monoid PIO_n of all partial order-preserving transformations on a chain with n elements whose domains and ranges are intervals, along with its submonoid PIO_n⁻ of order-decreasing transformations. Our main aim is to give presentations for PIO_n⁻ and PIO_n. Moreover, for both monoids, we describe regular elements and determine their ranks, cardinalities and the numbers of idempotents and nilpotents.

On The Generalized Cesàro Sequence Spaces And Some Of Their Properties, Uğur Gönüllü, Faruk Polat, Martin Richard Weber

Turkish Journal of Mathematics

Let C_t = (c_nm)_n,m∈ℕ denote the generalized Cesàro matrix defined by c_nm = t^n−m/n for m ≤ n and t ∈ [0, 1], and c_nm = 0 otherwise. For each q ∈ [1, ∞), the associated generalized Cesàro sequence spaces ces_q^t are introduced. These spaces form Banach lattices under the coordinatewise order, equipped with a naturally defined order continuous norm. We prove that ces_q^t = ces_q⁰ for all t ∈ [0, 1) and q ∈ [1, ∞), implying that the space …

A Note On The Periodic Orbits Of Wolbachia Spread Dynamics In Mosquito Populations In Periodic Environments, Jose S. Cánovas

Turkish Journal of Mathematics

We consider the periodic model introduced by B. Zheng and J. Yu, and disprove the conjectures on the number of periodic orbits the model can have. We rebuild the conjecture to prove that for periodic sequences of maps of any period, the number of nonzero periodic trajectories is bounded by two.

Characterizations Of Bi-Riordan Arrays, Nai̇m Tuğlu, Fatma Yeşi̇l Baran

Turkish Journal of Mathematics

In this study, we introduce the concept of a bi-Riordan array. As part of this construction, we define new composition and power operations. We then establish an analogue of the well-known fundamental theorem of Riordan arrays (FTRA), which we call the fundamental theorem of bi-Riordan arrays. Next, we show that the product of two bi-Riordan matrices is again a bi-Riordan matrix. Using this product structure, we prove that the set of bi-Riordan matrices forms a monoid.

Exponential Stability For A Strongly Damped Wave Equation With Distributed Internal Delay, Manal Alotaibi, Nasser-Eddine Tatar, Waled Al-Khulaif

Turkish Journal of Mathematics

This paper investigates the exponential stability of a strongly damped wave equation subject to an internal distributed time delay. Two distinct analytical frameworks are developed: the first employs a modified energy method based on auxiliary functionals, while the second introduces a transformation that rewrites the delay term as the derivative of a convolution integral. Both approaches yield explicit decay conditions and establish exponential convergence of the energy under weaker assumptions on the damping coefficient and the delay kernel. Notably, the transformation method allows for a wider class of admissible delay weights than those permitted by classical techniques. Numerical simulations based …

Clairaut Conformal Submersions From Ricci Solitons, Murat Polat

Turkish Journal of Mathematics

In this study, we investigate Clairaut conformal submersions in the context of total manifolds that support a Ricci soliton structure. We begin by deriving the scalar curvature and Ricci tensor expressions associated with these manifolds, and we establish criteria under which the fibres can be characterized as almost Ricci solitons or Einstein manifolds. Additionally, we identify the conditions required for the base manifold to admit Ricci soliton and Einstein structures. We also determine the necessary conditions for a vector field ζ to be conformal or Killing. Moreover, we demonstrate that when the potential vector field of the Ricci soliton is …

A Delayed Siamr Prostate Cancer Model With Vertical Transmission And Treatment: Stability Analysis And Numerical Simulation, Hüseyi̇n Demir, İnci̇ Çi̇li̇ngi̇r Süngü, İbrahi̇m Keles

Turkish Journal of Mathematics

​In this paper, we propose and analyse a delayed-compartmental mathematical model of prostate cancer dynamics that incorporates vertical transmission and therapeutic intervention. The population is stratified into five compartments: susceptible (S), infected/virally activated (I), asymptomatic infectious under treatment (A), malignant untreated (M), and recovered (R). A discrete time delay τ > 0 is introduced in the force-of-infection term to model the age-dependent onset of susceptibility in middle-aged adult males. Vertical transmission of viral etiology at a rate qΛ ensures that a fraction of newborns enter the infected compartment directly, rendering the disease persistent regardless of the basic reproduction number R₀. We …

​Compact And Am-Compact Orthogonally Additive Operators, Bahri̇ Turan, Bi̇rol Altin

Turkish Journal of Mathematics

We show that compactness of orthogonally additive operators between Banach lattices is not preserved under taking the modulus by providing a nonlinear analogue of Krengel’s example. In contrast, for operators acting from a Banach lattice into an AM-space, AM-compactness is stable under lattice operations. Moreover, the space of absolutely norm bounded AM-compactorthogonally additive operators from a Banach lattice into an AM-space is a Banach lattice, and on such AM-spaces with the weak Fatou property, norm boundedness coincides with absolute norm boundedness.

Hyers-Ulam And Hyers-Ulam Rassias Stability Of Caputo Fractional Hahn Difference Equations, Karima Mohamed Oraby, Alaa E. Hamza, Afrah Al-Bossly

Turkish Journal of Mathematics

​In this paper, we investigate Hyers–Ulam and Hyers–Ulam–Rassias stability for fractional linear Hahn difference equations of Caputo Type. To the best of our knowledge, this is the first work concerning Hyers–Ulam type stability in the framework of Caputo fractional Hahn difference equations, thereby filling a significant gap in the literature on fractional stability theory. Our approach is based on establishing an equivalence between the fractional Hahn difference initial value problem and a corresponding fractional integral equation, via the Caputo–Hahn inversion formula. These results lay a strong groundwork for analyzing the stability of Hahn fractional systems, which could be useful in …

Digital Commons Statistics For September 2026, Liberty University

Digital Commons Statistics

No abstract provided.

Eco Contemporáneo Magazine: Translation And Counterculture From 1960´S Buenos Aires, Damían Deamici

INTI: Revista de literatura hispánica

No abstract provided.

Paisajes Peruanos Transcontinentales: Mario Vargas Llosa. Paisajes Peruanos Translinguales: Daniel Alarcón, Ottmar Ette

INTI: Revista de literatura hispánica

No abstract provided.

Luigi Giuseppe (Giorgio)1 Racca Y Oreste Sola: Dos Piamonteses En Argentina En La Época De La Inmigración Masiva, María Teresa Sanhueza

INTI: Revista de literatura hispánica

No abstract provided.

Vargas Llosa Y El Fuego De La Tribu, Julio Ortega

INTI: Revista de literatura hispánica

No abstract provided.

Cuatro Microrrelatos, Javier De Nevascués

INTI: Revista de literatura hispánica

No abstract provided.