Explicit Description Research Articles

Optimal Ratcheting of Dividends in a Brownian Risk Model

We study the problem of optimal dividend payout from a surplus process governed by Brownian motion with drift under the additional constraint of ratcheting, i.e., the dividend rate can never decrease. We solve the resulting two-dimensional optimal control problem, identifying the value function to be the unique viscosity solution of the corresponding Hamilton--Jacobi--Bellman equation. For finitely many admissible dividend rates we prove that threshold strategies are optimal, and for any closed interval of admissible dividend rates we establish the $\varepsilon$-optimality of curve strategies. This work is a counterpart of [H. Albrecher, P. Azcue, and N. Muler, SIAM J. Control Optim., 58 (2020) pp. 1822--1845], where the ratcheting problem was studied for a compound Poisson surplus process with drift. In the present Brownian setup, calculus of variation techniques allow us to obtain a much more explicit analysis and description of the optimal dividend strategies. We also give some numerical illustrations of the optimality results.

The representations of racism in immigrant students’ essays in Greece

Abstract Racism as a means for accomplishing homogeneity is at the center of this study which draws on Critical Discourse Analysis and focuses on descriptions of racist behaviors included in immigrant students’ school essays. We investigate how the dominant assimilative and homogenizing discourse operates in Greece and how immigrant students position themselves towards this dominant discourse. Our analysis focuses on the ways the immigrant students of our sample construct legitimizing and hybrid resistance identities. We demonstrate that legitimizing identities are found in the vast majority of the essays of our data due to the racist behaviors experienced by immigrant people. On the other hand, the explicit description of such behaviors appears only in few essays. We argue that in these few essays, via referring to racist behaviors of majority people against them, immigrant students manage to build hybrid resistance identities.

The Anticanonical Complex for Non-degenerate Toric Complete Intersections

The anticanonical complex generalizes the Fano polytope from toric geometry and has been used to study Fano varieties with torus action so far. We provide an explicit description of the anticanonical complex for complete intersections in toric varieties defined by non-degenerate systems of Laurent polynomials. As an application, we classify the terminal Fano threefolds that are embedded into a fake weighted projective space via a general system of Laurent polynomials.

Structure of the associated groups of quandles

The associated groups of quandles play an important rôle in understanding quandles themselves. In this paper, we give several explicit descriptions of structure of associated groups by introducing certain quotient groups of them.

Kuhn's equivalence theorem for games in product form

We propose an alternative to the tree representation of extensive form games. Games in product form represent information with σ-fields over a product set, and do not require an explicit description of the play temporal ordering, as opposed to extensive form games on trees. This representation encompasses games with continuum of actions and imperfect information. We adapt and prove Kuhn's theorem — regarding equivalence between mixed and behavioral strategies under perfect recall — for games in product form with continuous action sets.

Acoustical impacts on hard disk drive dynamics

Acoustical output from air movers in computing systems can reach sufficiently high sound pressure levels and in frequency bands such that performance of Hard Disk Drives (HDD) is degraded. In this paper air mover acoustical characteristics and comparisons to standalone measurements and models relevant to the performance issues are explored. Sound pressure levels, frequency bands, directivity, and explicit source descriptions are considered for air mover sources, and duct transmission, statistical energy, acoustic diffusion, and measured transfer factors are considered for noise transmission along acoustic path(s) from air mover to HDD within computing systems.

On the computation of Hopf 2-cocycles with an example of diagonal type

AbstractWe present a framework for the computation of the Hopf 2-cocycles involved in the deformations of Nichols algebras over semisimple Hopf algebras. We write down a recurrence formula and investigate the extent of the connection with invariant Hochschild cohomology in terms of exponentials. As an example, we present detailed computations leading to the explicit description of the Hopf 2-cocycles involved in the deformations of a Nichols algebra of Cartan type $A_2$ with $q=-1$ , a.k.a. the positive part of the small quantum group $\mathfrak{u}^+_{\sqrt{-\text{1}}}(\mathfrak{sl}_3)$ . We show that these cocycles are generically pure, that is they are not cohomologous to exponentials of Hochschild 2-cocycles.

Crystal structure on K-hives of type A

We show that a set of K-hives is isomorphic as a crystal to the crystal basis of the irreducible highest weight module on a quantized enveloping algebra of type A. Also, we explicitly describe the crystal structure on K-hives. To introduce this structure, we construct an embedding similar to the Far-Eastern reading for K-hives. Moreover, we provide an explicit description of the crystal structure by constructing the Middle-Eastern reading for K-hives.

On binomials and algebraic closure of some pseudofinite fields

We give a criterion when a polynomial is irreducible over a pseudofinite field. As an application we give an explicit description of algebraic closure of some pseudofinite fields of zero characteristic.

OntoStrength: An Ontology for Psychomotor Strength Development

An ontology is a formal, explicit description of concepts and relations from a domain while considering underlying properties, restrictions, and instances.With the advancement of the Semantic Web, the rise of the Educational Semantic Web, and the lack of uniformity between approaches for knowledge representation, ontologies are becoming more and more popular, including adaptive learning environments such as the Intelligent Tutoring Systems (ITSs). OntoStrength is an ontology developed to support the Selfit ITS, a platform that aims to improve the fundamental human psychomotor skills and, more specifically, bio-motor strength abilities. The goal of Selfit is to prevent the negative consequences of a sedentary lifestyle and accidents involving inadequate strength skills. Most ontologies in the sports domain support the development of digital solutions for sports performance and data collected during competitions. In contrast, OntoStrength’s goal is to contribute to the development of digital solutions dedicated to bio-motor strength ability analysis. OntoStrength considers other bio-motor skills like speed, endurance, or flexibility, as well as other activities like muscle analysis, movement patterns, or training load management, to support sport, professional and daily-life activities. OntoStrength enables the personalization of strength development programs in the Selfit ITS by providing a comprehensive data layer for its student, domain, and tutoring models.

Explicit description of all deflators for market models under random horizon with applications to NFLVR

This paper considers an initial market model, specified by its underlying assets S and its flow of information F, and an arbitrary random time τ which might not be an F-stopping time. As the death time and the default time (that τ might represent) can be seen when they occur only, the progressive enlargement of F with τ sounds tailor-fit for modeling the new flow of information G that incorporates both F and τ. In this setting of informational market, the first principal goal resides in describing as explicitly as possible the set of all deflators for (Sτ,G), while the second principal goal lies in addressing the No-Free-Lunch-with-Vanishing-Risk concept (NFLVR hereafter) for (Sτ,G). Besides this direct application to NFLVR, the set of all deflators constitutes the dual set of all “admissible” wealth processes for the stopped model (Sτ,G), and hence it is vital in many hedging and pricing related optimization problems. Thanks to the results of Choulli et al. (2020), on martingales classification and representation for progressive enlarged filtration, our two main goals are fully achieved in different versions, when the survival probability never vanishes. The results are illustrated on the two particular cases when (S,F) follows the jump-diffusion model and the discrete-time model.

Partially ordered fuzzy power set monads on the category of L-sets and their associated categories of topological space objects

For a GL-monoid L with a complete lattice L underneath, this paper considers the L-unbalanced power object monad on the category Set(L) of L-sets, and introduces a new monad on Set(Lop) called the L-power L-set monad. The Kleisli and Eilenberg-Moore categories of these monads are studied. Both monads are enhanced to partially ordered monads that allow us to apply the theory of topological space objects developed by Ulrich Höhle. We give the explicit descriptions of the category of topological space objects in Set(L) with respect to the partially ordered L-unbalanced power object monad and the category of topological space objects in Set(Lop) with respect to the partially ordered L-power L-set monad. Furthermore, it is shown that the L-power L-set monad on Set(Lop) determines a monad on Set(L) in a one-to-one manner, and all existing results can be directly converted into this monad.

A systematic analysis of the memory term in coarse-grained models: The case of the Markovian approximation

The systematic development of coarse-grained (CG) models via the Mori–Zwanzig projector operator formalism requires the explicit description of a deterministic drift term, a dissipative memory term and a random fluctuation term. The memory and fluctuating terms are related by the fluctuation–dissipation relation and are more challenging to sample and describe than the drift term due to complex dependence on space and time. This work proposes a rational basis for a Markovian data-driven approach to approximating the memory and fluctuating terms. We assumed a functional form for the memory kernel and under broad regularity hypothesis, we derived bounds for the error committed in replacing the original term with an approximation obtained by its asymptotic expansions. These error bounds depend on the characteristic time scale of the atomistic model, representing the decay of the autocorrelation function of the fluctuating force; and the characteristic time scale of the CG model, representing the decay of the autocorrelation function of the momenta of the beads. Using appropriate parameters to describe these time scales, we provide a quantitative meaning to the observation that the Markovian approximation improves as they separate. We then proceed to show how the leading-order term of such expansion can be identified with the Markovian approximation usually considered in the CG theory. We also show that, while the error of the approximation involving time can be controlled, the Markovian term usually considered in CG simulations may exhibit significant spatial variation. It follows that assuming a spatially constant memory term is an uncontrolled approximation which should be carefully checked. We complement our analysis with an application to the estimation of the memory in the CG model of a one-dimensional Lennard–Jones chain with different masses and interactions, showing that even for such a simple case, a non-negligible spatial dependence for the memory term exists.

Edge partitions of the complete graph and a determinant-like function

In this paper we prove the case \(dim(V_3)=3\) of a conjecture of the second author about the exterior operad \({\Lambda }^{S^2}_{V_d}\). For this we introduce a collection of natural involutions on the set of homogeneous cycle-free d-partitions of the complete graph \(K_{2d}\), and show that these involutions correspond to the relations in \({\Lambda }^{S^2}_{V_d}(2d+1)\). When \(d=3\) this correspondence allows us to give an explicit description of a determinant-like map and to settle the above mentioned conjecture.

Combinatorial interpretation of Kazhdan–Lusztig basis elements indexed by 45312-avoiding permutations in 𝔖6

Abstract Deodhar [Geom. Dedicata 36, no. 1 (1990)] introduced the defect statistic on subexpressions of reduced expressions in the symmetric group 𝔖 n to construct an algorithmic description of the Kazhdan–Lusztig basis of the Hecke algebra H n (q). This led Billey–Warrington [J. Algebraic Combin. 13, no. 2 (2001)] and the second author [J. Pure Appl. Algebra 212 (2008)] to state very explicit combinatorial descriptions of the basis elements indexed by permutations avoiding certain patterns. We extend the above work by producing an exhaustive list of graphical representations of Kazhdan–Lusztig basis elements indexed by 45312-avoiding permutations w ∈𝔖5, 𝔖6.

Geometric consistency of Manin's conjecture

We conjecture that the exceptional set in Manin's conjecture has an explicit geometric description. Our proposal includes the rational point contributions from any generically finite map with larger geometric invariants. We prove that this set is contained in a thin subset of rational points, verifying that there is no counterexample to Manin's conjecture which arises from an incompatibility of geometric invariants.

On the growth of even K-groups of rings of integers in p-adic Lie extensions

Let $p$ be an odd prime number. In this paper, we study the growth of the Sylow $p$-subgroups of the even $K$-groups of rings of integers in a $p$-adic Lie extension. Our results generalize previous results of Coates and Ji-Qin, where they considered the situation of a cyclotomic $\mathbb{Z}_p$-extension. Our method of proof differs from these previous work. Their proof relies on an explicit description of certain Galois group via Kummer theory afforded by the context of a cyclotomic $\mathbb{Z}_p$-extension, whereas our approach is via considering the Iwasawa cohomology groups with coefficients in $\mathbb{Z}_p(i)$ for $i\geq 2$. We should mention that this latter approach is possible thanks to the Quillen-Lichtenbaum Conjecture which is now known to be valid by the works of Rost-Voevodsky. We also note that the approach allows us to work with more general $p$-adic Lie extensions that do not necessarily contain the cyclotomic $\mathbb{Z}_p$-extension, where the Kummer theoretical approach does not apply. Along the way, we study the torsionness of the second Iwasawa cohomology groups with coefficients in $\mathbb{Z}_p(i)$ for $i\geq 2$. Finally, we give examples of $p$-adic Lie extensions, where the second Iwasawa cohomology groups can have nontrivial $\mu$-invariants.

Clairaut surfaces in Euclidean three-space

In this note, we investigate local isometric immersion of Clairaut metrics in Euclidean three-space. A Clairaut metric is determined up to isometry by a single function of one variable. We show that an isometric immersion is formally determined by two functions of one variable, uniquely up to coordinate reflection and ambient Euclidean motions. Further, if the Clairaut metric and these two functions are real-analytic, there exists a local isometric immersion realizing these data. We give a more explicit description for a finite-dimensional family of examples.

Resolution of Singularities of the Orbit Spaces $$G_{n,2}/T^n$$

The problem of the description of the orbit space $X_{n} = G_{n,2}/T^n$ for the standard action of the torus $T^n$ on a complex Grassmann manifold $G_{n,2}$ is widely known and it appears in diversity of mathematical questions. A point $x\in X_{n}$ is said to be a critical point if the stabilizer of its corresponding orbit is nontrivial. In this paper, the notion of singular points of $X_n$ is introduced which opened the new approach to this problem. It is showed that for $n>4$ the set of critical points $\text{Crit}X_n$ belongs to our set of singular points $\text{Sing}X_{n}$, while the case $n=4$ is somewhat special for which $\text{Sing}X_4\subset \text{Crit}X_4$, but there are critical points which are not singular. The central result of this paper is the construction of the smooth manifold $U_n$ with corners, $\dim U_n = \dim X_n$ and an explicit description of the projection $p_{n} : U_{n}\to X_{n}$ which in the defined sense resolve all singular points of the space $X_n$. Thus, we obtain the description of the orbit space $G_{n,2}/T^n$ combinatorial structure. Moreover, the $T^n$-action on $G_{n,2}$ is a seminal example of complexity $(n-3)$ - action. Our results demonstrate the method for general description of orbit spaces for torus actions of positive complexity.

From text to screen: Gentleman Jack then and now

As part of the growing genre of post-heritage quality drama for television, Sally Wainwright’s BBC-HBO production of Gentleman Jack stands out in terms of its close adherence to the original Lister diaries. While in many ways season one of Gentleman Jack follows the conventional narrative of courtship and marriage that defines much historical costume drama—as in, for example, the adaptations of Jane Austen novels—it also continually subverts the form through its unique queer content, closely based on the Lister diaries. While Gentleman Jack is not the BBC’s first queer lesbian historical series, the uniqueness of the source text, which includes explicit descriptions of Lister’s sexual practices in code, positions the series as ground-breaking in terms of prime-time television. This essay considers the ways in which the series adapts, mediates and reconfigures the original diaries for a contemporary audience. It will analyze how these transcriptions are supplemented through the performative and the visual and how to read the ideological coding of episodes that move away from the diaries into the realm of the fictional, such as the Lister-Walker marriage proposal at the end of the series. It also asks what the responsibility of the series is to the historical archive on the one hand, and to its contemporary audience on the other.