Maximal Set Research Articles

A new self-adaptive inertial CQ-algorithm for solving convex feasibility and monotone inclusion problems

Abstract Using a dynamical step size technique, a new self-adaptive CQ-algorithm is proposed in the presence of an inertial term to find the solution of convex feasibility problem and monotone inclusion problem involving a finite number of maximal monotone set valued operators. To do this, in certain Banach spaces, we construct an algorithm which converges to the fixed point of right Bregman strongly nonexpansive mappings and coincidentally solves the convex feasibility and monotone inclusion problems. Strong convergence of the algorithm is achieved without computation of the associated operator norms. Interesting numerical examples which illustrate the implementation and efficiency of our scheme are also given. Results obtained via this work improve and extend on previous results of its kind, in the literature.

BENIGN PLEURAL SCHWANNOMA WITH PLEURAL EFFUSIONS AND NECROTIZING PNEUMONIA

BENIGN PLEURAL SCHWANNOMA WITH PLEURAL EFFUSIONS AND NECROTIZING PNEUMONIA

SO(4) multicriticality of two-dimensional Dirac fermions

We study quantum multicritical behavior in a (2+1)-dimensional Gross-Neveu-Yukawa field theory with eight-component Dirac fermions coupled to two triplets of order parameters that act as Dirac masses, and transform as $(1,0) + (0,1)$ representation under the SO(4)$\simeq$SO(3)$\times$SO(3) symmetry group. This field theory is relevant to spin-1/2 fermions on honeycomb or $\pi$-flux lattices, for example, near the transition points between an $s$-wave superconductor and a charge-density wave, on one side, and N\'eel order, on the other. Two triplets of such order parameters always allow for a common pair of two other order parameters that would complete them to the maximal set of compatible (anticommuting) orders of five. We first derive a unitary transformation in the Nambu (particle-hole) space which maps any two such triplets, possibly containing some superconducting orders, onto purely insulating order parameters. This allows one to consider a universal SO(4) Gross-Neveu-Yukawa description of the multicriticality without any Nambu doubling. We then proceed to derive the renormalization-group flow of the coupling constants at one-loop order in $4-\epsilon$ space-time dimensions, allowing also a more general set of order parameters transforming under SO($n_a$)$\times$SO($n_b$). While for $n_a=n_b > 2 $ in the bosonic sector and with fermions decoupled there is a stable fixed point of the flow, the Yukawa coupling to fermions quickly leads to its elimination by a generic fixed-point collision in the relevant range of fermion flavor numbers $N_f$. This suggests the replacement of the critical behavior by a runaway flow in the physical case $n_a=n_b=3$. The structure of the RG flow at $n_a\neq n_b$ is also discussed, and some non-perturbative arguments in favor of the stability of the decoupled critical point when $n_a=3$ and $n_b=1$ in $D=2+1$ are provided.

Characterization and computation of control invariant sets for linear impulsive control systems

Impulsive control systems are suitable to describe and control a venue of real-life problems, going from disease treatment to aerospace guidance. The main characteristic of such systems is that they evolve freely in-between impulsive actions, which makes it difficult to guarantee its permanence in a given state-space region. In this work, we develop a method for characterizing and computing approximations to the maximal control invariant sets for linear impulsive control systems, which can be explicitly used to formulate a set-based model predictive controller. We approach this task using a tractable and non-conservative characterization of the admissible state sets, namely the states whose free response remains within given constraints, emerging from a spectrahedron representation of such sets for systems with rational eigenvalues. The so-obtained impulsive control invariant set is then explicitly used as a terminal set of a predictive controller, which guarantees the feasibly asymptotic convergence to a target set containing the invariant set. Necessary conditions under which an arbitrary target set contains an impulsive control invariant set (and moreover, an impulsive control equilibrium set) are also provided, while the controller performance are tested by means of two simulation examples.

An Inverse Problem for the Relativistic Boltzmann Equation

We consider an inverse problem for the Boltzmann equation on a globally hyperbolic Lorentzian spacetime $(M,g)$ with an unknown metric $g$. We consider measurements done in a neighbourhood $V\subset M$ of a timelike path $\mu$ that connects a point $x^-$ to a point $x^+$. The measurements are modelled by a source-to-solution map, which maps a source supported in $V$ to the restriction of the solution to the Boltzmann equation to the set $V$. We show that the source-to-solution map uniquely determines the Lorentzian spacetime, up to an isometry, in the set $I^+(x^-)\cap I^-(x^+)\subset M$. The set $I^+(x^-)\cap I^-(x^+)$ is the intersection of the future of the point $x^-$ and the past of the point $x^+$, and hence is the maximal set to where causal signals sent from $x^-$ can propagate and return to the point $x^+$. The proof of the result is based on using the nonlinearity of the Boltzmann equation as a beneficial feature for solving the inverse problem.

A physics‐based model reduction approach for node‐to‐segment contact problems in linear elasticity

AbstractThe article presents a novel model order reduction method for mechanical problems in linear elasticity with nonlinear contact conditions. Recently, we have proposed an efficient reduction scheme for the node‐to‐node formulation [Manvelyan et al., Comput Mech 68, 1283–1295 (2021)] that leads to linear complementarity problems (LCPs). Here, we enhance the underlying contact problem to a node‐to‐segment formulation, which leads to quadratic inequalities as constraints. The adjoint system corresponds to a nonlinear complementarity problem that describes the Lagrange multiplier. The latter is solved by a Newton‐type iteration based on a LCP solver in each time step. Since the maximal set of potential contact nodes is predefined, an additional substructuring by Craig–Bampton can be performed. This contact treatment turns out to be necessary and allows exclusion of the Lagrange multipliers and the nodal displacements at contact from reduction. The numerical solutions of the reduced contact problem achieve high accuracy and the dynamic contact carries over the behavior of the full order model. Moreover, if the contact area is small compared to the overall structure, the reduction scheme performs very efficiently. The performance of the resulting reduction method is assessed on two 2D computational examples from linear elasticity.

Wellfoundedness proof with the maximal distinguished set

In Arai (An ordinal analysis of a single stable ordinal, submitted) it is shown that an ordinal $$\sup _{N<\omega }\psi _{\varOmega _{1}}(\varepsilon _{\varOmega _{{\mathbb {S}}+N}+1})$$ is an upper bound for the proof-theoretic ordinal of a set theory $$\mathsf {KP}\ell ^{r}+(M\prec _{\Sigma _{1}}V)$$ . In this paper we show that a second order arithmetic $$\Sigma ^{1-}_{2}{\mathrm {-CA}}+\Pi ^{1}_{1}{\mathrm {-CA}}_{0}$$ proves the wellfoundedness up to $$\psi _{\varOmega _{1}}(\varepsilon _{\varOmega _{{\mathbb {S}}+N+1}})$$ for each N. It is easy to interpret $$\Sigma ^{1-}_{2}{\mathrm {-CA}}+\Pi ^{1}_{1}{\mathrm {-CA}}_{0}$$ in $$\mathsf {KP}\ell ^{r}+(M\prec _{\Sigma _{1}}V)$$ .

An asymptotically optimal construction of almost affinely disjoint subspaces

A family of k-dimensional subspaces of Fqn, which forms a partial spread, is called L-almost affinely disjoint (or briefly [n,k,L]q-AAD) if each affine coset of a member of this family intersects with only at most L subspaces from the family. The notion of AADs was introduced and its connections with some problems in coding theory were presented by Liu et al. (2021) in [27]. In particular, Liu et al. investigated the size of maximal such sets and presented a conjecture. They also proved that their conjecture is true for k=1 and k=2 when L is sufficiently large. In this work, we give some constructions of large AADs for n≥3k, hence•improve the lower bound of Liu et al. and•prove that their conjecture is still true for k≥3 when n=3k. Our constructions are based on the usage of some certain maximum rank distance codes together with a modified version of the lifting idea and linkage construction.

A Small Maximal Sidon Set in ${\mathbb{Z}}_2^n$

A Sidon set is a subset of an Abelian group with the property that each sum of two distinct elements is distinct. We construct a small maximal Sidon set of size $O((n \cdot 2^n)^{1/3})$ in the group ${\mathbb{Z}}_2^n$, generalizing a result of Ruzsa concerning maximal Sidon sets in the integers.

Maximal antipodal sets of E6 and some compact symmetric spaces

We explicitly classify congruent classes of maximal antipodal sets of E6 and some compact symmetric spaces related to E6. Moreover, we give realizations of these compact symmetric spaces by using some subalgebras of the complex exceptional Jordan algebra JC. In this realization, we explicitly describe congruent classes of maximal antipodal sets of these compact symmetric spaces.

LINGUISTIC ASPECT OF THE CATEGORY OF POLITENESS IN ADVERTISING DISCOURSE

The paper highlights the correlation between the concepts of etiquette and politeness in terms of advertising discourse. It is stated modern research on language and speech is becoming more and more interdisciplinary, focusing on functioning the language in various social and cultural contexts. Differentiation of the concepts of etiquette, politeness and etiquetization is considered. Etiquette is the broadest concept that can be defined as the objectification of existing norms of social relations in society. Politeness as a complex sociocultural phenomenon, contributing to the success of communication, is one of the means of expression of etiquette. Etiquetization is a principle of speech politeness, which is designed to facilitate the flow of communication and achieve the goals of the addressee. The category of etiquette in advertising discourse is realized through the category of etiquetization on the basis of the main features of speech politeness: care for the recipient (facilitating the perception of information by the recipient) and modulation of categorical and non-categorical nomination with predominance of non-categorical (based on objectivity, impartiality and persuasiveness). The main means of politeness include caring for the addressee (facilitating the recipient’s perception of information) and modulating the categorical and non-categorical nomination with a predominance of non-categorical (based on objectivity, impartiality and motivation) to convince the addressee of that or another statement. Politeness as a manifestation of the purposefulness of language behavior is mostly considered on the basis of rhetorical pragmatics, determining the speaker’s illocutionary goals (which speech acts are conveyed through utterances) and their social goals (speaker status depending on his courtesy, truthfulness, and irony) as well as distinguishing between interpersonal rhetoric and textual rhetoric, each consisting of a set of maxims. Keywords: advertising discourse; etiquette; etiquetization; politeness; rhetorical pragmatics.

Fine properties of solutions to the Cauchy problem for a fast diffusion equation with Caffarelli–Kohn–Nirenberg weights

We investigate fine global properties of nonnegative, integrable solutions to the Cauchy problem for the Fast Diffusion Equation with weights (WFDE) $u_t=|x|^\gamma\mathrm{div}\left(|x|^{-\beta}\nabla u^m\right)$ posed on $(0,+\infty)\times\mathbb{R}^d$, with $d\ge 3$, in the so-called good fast diffusion range $m_c<m<1$, within the range of parameters $\gamma, \beta$, optimal for the validity of the so-called Caffarelli-Kohn-Nirenberg inequalities. It is a natural question to ask in which sense such solutions behave like the Barenblatt $\mathfrak{B}$ (fundamental solution): for instance, asymptotic convergence, i.e. $\|u(t)-\mathfrak{B}(t)\|_{{\rm L}^p(\mathbb{R}^d)}\xrightarrow[]{t\to\infty}0$, is well known for all $1\le p\le \infty$, while only few partial results tackle a finer analysis of the tail behaviour. We characterize the maximal set of data $\mathcal{X}\subset{\rm L}^1_+(\mathbb{R}^d)$ that produces solutions which are pointwise trapped between two Barenblatt (Global Harnack Principle), and uniformly converge in relative error (UREC), i.e. ${\rm d}_\infty(u(t))=\|u(t)/\mathcal{B}(t)-1\|_{{\rm L}^\infty(\mathbb{R}^d)}\xrightarrow[]{t\to\infty}0$. Such characterization is in terms of an integral condition on $u(t=0)$. To the best of our knowledge, analogous issues for the linear heat equation $m=1$, do not possess such clear answers. Our characterization is also new for the classical, non-weighted, FDE. We are able to provide minimal rates of convergence to $\mathcal{B}$ in different norms. Such rates are almost optimal in the non weighted case, and become optimal for radial solutions. To complete the panorama, we show that solutions with data in ${\rm L}^1_+(\mathbb{R}^d)\setminus\mathcal{X}$, preserve the same "fat" spatial tail for all times, hence UREC fails.

Localizable sets and the localization of a ring at a localizable set

The aim of the paper is to develop the most general theory of one-sided fractions. The concepts of localizable set, localization of a ring and a module at a localizable set are introduced and studied. Localizable sets are generalization of Ore sets and denominator sets, and the localization of a ring/module at a localizable set is a generalization of localization of a ring/module at a denominator set. For a semiprime left Goldie ring, it is proven that the set of maximal left localizable sets that contain all regular elements is equal to the set of maximal left denominator sets (and they are explicitly described). For a semiprime Goldie ring, it is proven that the following five sets coincide: the maximal Ore sets, the maximal denominator sets, the maximal left or right or two-sided localizable sets that contain all regular elements (and they are explicitly described).

Infinite families of optimal systems of biangular lines related to representations of [formula omitted

A line packing is optimal if its coherence is as small as possible. Most interesting examples of optimal line packings are achieving equality in some of the known lower bounds for coherence. In this paper two infinite families of real and complex biangular line packings are presented. New packings achieve equality in the real or complex second Levenshtein bound respectively. Both infinite families are constructed by analyzing well known representations of the finite groups SL(2,Fq). Until now the only known infinite families meeting the second Levenshtein bounds were related to the maximal sets of mutually unbiased bases (MUB). Similarly to the line packings related to the maximal sets of MUBs, the line packings presented here are related to the maximal sets of mutually unbiased weighing matrices. Another similarity is that the new packings are projective 2-designs. The latter property together with sufficiently large cardinalities of the new packings implies some improvement on largest known cardinalities of real and complex biangular tight frames.

Near infrared spectroscopy calibration strategies to predict multiple nutritional parameters of pasture species from different functional groups

Near infrared reflectance (NIR) spectroscopy has been used by the agricultural industry as a rapid and inexpensive technique to quantify nutritional chemistry in plants. The aim of this study was to evaluate the performance of NIR calibrations in predicting the nutritional composition of ten pasture species that underpin livestock industries in many countries. The species comprised a range of functional diversity (C3 legumes; C3/C4 grasses; annuals/perennials) and origins (tropical/temperate; introduced/native) that grew under varied environmental conditions (control and experimentally induced warming and drought) over a period of more than two years ( n = 2622). A maximal calibration set including 391 samples was used to develop and evaluate calibrations for all ten pasture species (global calibrations), as well as for subsets comprised of the plant functional groups. This study found that the global calibrations were appropriate to predict the six key nutritional quality parameters for the studied pasture species, with the highest estimation quality found for ash (ASH), crude protein (CP), amylase-treated neutral detergent fibre (aNDF) and acid detergent fibre (ADF), and the lowest for ether extract (EE) and acid detergent lignin (ADL) parameters. The plant functional group calibrations for C3 grasses performed better than the global calibrations for ASH, CP, ADF and EE parameters, whereas for C3 legumes and C4 grasses the functional group calibrations performed less well than the global calibrations for all nutritional parameters of these groups. Additionally, the calibrations were able to capture the range of variation in forage nutritional quality caused by future climate scenarios of warming and severe drought.

Stability of finite horizon optimisation based control without terminal weight

This paper presents a stability analysis tool for model predictive control (MPC) where control action is generated by optimising a cost function over a finite horizon. Stability analysis of MPC with a limited horizon but without terminal weight is a well-known challenging problem. We define a new value function based on an auxiliary one-step optimisation related to stage cost, namely optimal one-step value function (OSVF). It is shown that a finite horizon MPC can be made to be asymptotically stable if OSVF is a (local) control Lyapunov function (CLF). More specifically, by exploiting the CLF property of OSFV to construct a contractive terminal set, a new stabilising MPC algorithm (CMPC) is proposed. We show that CMPC is recursively feasible and guarantees stability under the condition that OSVF is a CLF. Checking this condition and estimation of the maximal terminal set are discussed. Numerical examples are presented to demonstrate the effectiveness of the proposed stability condition and corresponding CMPC algorithm.

On Minimax Detection of Gaussian Stochastic Sequences with Imprecisely Known Means and Covariance Matrices

We consider the problem of detecting (testing) Gaussian stochastic sequences (signals) with imprecisely known means and covariance matrices. An alternative is independent identically distributed zero-mean Gaussian random variables with unit variances. For a given false alarm (1st-kind error) probability, the quality of minimax detection is given by the best miss probability (2nd-kind error probability) exponent over a growing observation horizon. We study the maximal set of means and covariance matrices (composite hypothesis) such that its minimax testing can be replaced with testing a single particular pair consisting of a mean and a covariance matrix (simple hypothesis) without degrading the detection exponent. We completely describe this maximal set.

Hesitant Fuzzy Maximal and Minimal Clopen Sets

This article is to study the notions of hesitant fuzzy minimal clopen and hesitant fuzzy maximal clopen sets. In this article, we have proved hesitant fuzzy maximal and minimal clopen sets are independent to hesitant fuzzy minimal and maximal open sets(resp. closed sets). Using hesitant fuzzy disconnectedness certain properties of both hesitant fuzzy minimal and maximal clopen sets are discussed.

The Use of Nitric Oxide as a Rescue Modality for Severe Adult Acute Respiratory Distress Syndrome Patients, Including COVID-19, in Critical Care Rotor Transport: A Retrospective Community Outcome Study

ObjectiveSevere acute respiratory distress syndrome (ARDS) mortality increases in smaller outlying facilities, and patients (especially those diagnosed with coronavirus disease 2019 [COVID-19]) are often “stuck” at these facilities. These patients are on maximal ventilator settings and are often in the prone position. Our purpose was to show that with the use of inhaled nitric oxide (iNO), a “community-based” rotor wing critical care transport (CCT) team can safely, consistently, and effectively transport these extremely precarious patients to the tertiary care that is needed. MethodsThis was a retrospective database review of 50 patients (39 patients with COVID-19) transported between 2017 and 2021 in whom iNO was brought to the bedside and initiated by the rotor wing critical care transport team. The review included patient demographics, vital signs, and ventilator settings from the sending hospital, in-flight, and the receiving hospital. We reviewed the transition from transport to venovenous extracorporeal membrane oxygenation (if applicable), hospital disposition, and length of stay from the receiving hospital side. Concerning the actual transport, we reviewed the mode of transport, the sending facility size, and the distances covered. ResultsUpon arrival at the sending facilities, we found severely ill patients with almost half (46%) in the prone position or recently transitioned from a prone position within the last 2 hours. Eighty-six percent were pharmaceutically paralyzed, and 44% were in shock. There was a younger and heavier predominance with an average age of 44 years and an average weight of 103 kg. Thirty-nine patients were diagnosed with COVID-19. The other 11 had a mix of non–COVID-19 ARDS, pulmonary embolism, and pulmonary edema. The patients presented from 27 different community hospitals. Forty-four percent were from small referring hospitals that had less than 200 beds. Twenty-eight patients were transported by a Bell 407 helicopter, 18 with an Airbus H135 helicopter, and 4 by ground ambulance. Forty-one percent of patients were transported within 25 miles, and 4 patients were transferred from > 100 miles away. All 50 patients were safely transported without significant deterioration or significant pulmonary pressure increases. Thirty-seven patients were placed on venovenous extracorporeal membrane oxygenation (34 of those patients cannulated within 2 hours of arrival). The overall mortality rate was 27%, and the COVID-19 mortality rate was 24%. ConclusioniNO retrieval for severe ARDS can be safely and effectively completed within the COVID-19 population and the nonacademic community setting using helicopters prevalent in the global air medical industry (Bell 407 and Airbus H135).

Farsighted objections and maximality in one-to-one matching problems

We characterize the set of stable matchings when individuals are farsighted and when they choose their objections optimally along a farsighted objection path. We use a solution concept called maximal farsighted set (MFS), which is an adaptation of the concepts developed in Dutta and Vohra (2017) and Dutta and Vartiainen (2020) to one-to-one matching problems. MFS always exists, but it need not be unique. There is a unique largest MFS that contains all other, which is equal to the largest consistent set of Chwe (1994). This implies that the largest consistent set embodies the idea of maximality in one-to-one matching problems.