Notion Of Compatibility Research Articles

Matrix weighted $$\alpha $$-modulation spaces

AbstractGiven a matrix-weight W in the Muckenhoupt class $$\textbf{A}_p({{\mathbb {R}}}^n)$$ A p ( R n ) , $$1\le p<\infty $$ 1 ≤ p < ∞ , we introduce corresponding vector-valued continuous and discrete $$\alpha $$ α -modulation spaces $$M^{s,\alpha }_{p,q}(W)$$ M p , q s , α ( W ) and $$m^{s,\alpha }_{p,q}(W)$$ m p , q s , α ( W ) and prove their equivalence through the use of adapted tight frames. Compatible notions of molecules and almost diagonal matrices are also introduced, and an application to the study of Fourier multipliers on vector valued spaces is given.

Equivalent Notions in the context of compatible Endo-Lie Algebras

In this article, we introduce a notion of compatibility between two Endo-Lie algebras defined on the same linear space. Compatibility means that any linear combination of the two structures always induces a new Endo-Lie algebras structure. In this case of compatibility, we show that the notions of bialgebras, standard Manin triples and matched pairs are equivalent. We find this equivalence for the case of compatible Lie algebras since this is a particular case of compatible Endo-Lie algebras.

COMMON FIXED POINT THEOREMS FOR WEAKLY COMPATIBLE MAPPINGS IN COMPLETE METRIC SPACES

IJungck and Rhoades [13] introduced the notion of coincidentally commuting (weakly compatible) mappings, which is weaker than compatibility. Many interesting, fixed point theorems for weakly compatible maps satisfying contractive type conditions have been obtained by various authors. Goyal [5,6] prove some common fixed point theorems for six mappings involving rational contractive conditions by using notions of compatibility, weak compatibility and commutativity, in complete metric spaces. In this paper, we prove a common fixed point theorem for three pairs of weakly compatible mappings in complete metric spaces satisfying a rational inequality without any continuity requirement which generalize several previously known results due to Imdad and Ali [7], Goyal [5], Imdad-Khan [8], JeongRhoades [9] and others.

On Intuitionistic Fuzzy Neutrosophic Soft Ideal Topological Spaces

The purpose of this paper is to introduce the notion of intuitionistic fuzzy neutronsophic soft ideal in Intuitionistic fuzzy neutronsophic soft set theory. The concept of intuitionistic fuzzy neutrosophic soft local function is also introduced. These concepts are discussed with a view to find new intuitionistic fuzzy neutronsophic soft topologies from the original one. The basic structure, respecially a basic for such generated Intuitionistic fuzzy neutronsophic soft topologies also studied here. Finally, the notion of compatibility of intuitionistic fuzzy neutronsophic soft ideals with Intuitionistic fuzzy neutrosophic soft topologies is introduced and some equivalent conditions concerning, this topic are established here.

Polytope compatibility—From quantum measurements to magic squares

Several central problems in quantum information theory (such as measurement compatibility and quantum steering) can be rephrased as membership in the minimal matrix convex set corresponding to special polytopes (such as the hypercube or its dual). In this article, we generalize this idea and introduce the notion of polytope compatibility, by considering arbitrary polytopes. We find that semiclassical magic squares correspond to Birkhoff polytope compatibility. In general, we prove that polytope compatibility is in one-to-one correspondence with measurement compatibility, when the measurements have some elements in common and the post-processing of the joint measurement is restricted. Finally, we consider how much tuples of operators with appropriate joint numerical range have to be scaled in the worst case in order to become polytope compatible and give both analytical sufficient conditions and numerical ones based on linear programming.

Integral Type Contraction in Dislocated Metric Spaces

In this paper, by using the notion of compatibility, weak compatibility, occasionally weak compatibility and commutativity, we establish some common fixed point theorems for six mappings satisfying integral type contractive conditions in complete dislocated metric spaces. Our work improves and extends some earlier results in the literature.

R-Compatible Ideals of topological spaces

Abstract. This paper's goal is to present the idea of regular-compatibility of ideals by replaced the open set is Regular-open set and with respect to topology, which is abbreviated as (τ ∼ R I ), Using a brand-new local function termed the regular-local function A(*R) (I, T), it is also possible to examine the connection between this idea and the idea of the R-compatibility of an ideal with I. A few comparable circumstances are established. By employing the new operator is Regular -psi set short (ΨR(A)), we further analyze the characterizations of Regular -compatibility with the aid of this local function. And the relationship between them. Several notions of compatibility between a partially ordered set and a topology on its underlying set are comparable to separation axioms and other well-known ideas from general topology.

Tail-dependence, exceedance sets, and metric embeddings

There are many ways of measuring and modeling tail-dependence in random vectors: from the general framework of multivariate regular variation and the flexible class of max-stable vectors down to simple and concise summary measures like the matrix of bivariate tail-dependence coefficients. This paper starts by providing a review of existing results from a unifying perspective, which highlights connections between extreme value theory and the theory of cuts and metrics. Our approach leads to some new findings in both areas with some applications to current topics in risk management.We begin by using the framework of multivariate regular variation to show that extremal coefficients, or equivalently, the higher-order tail-dependence coefficients of a random vector can simply be understood in terms of random exceedance sets, which allows us to extend the notion of Bernoulli compatibility. In the special but important case of bivariate tail-dependence, we establish a correspondence between tail-dependence matrices and L^1- and ell _1-embeddable finite metric spaces via the spectral distance, which is a metric on the space of jointly 1-Fréchet random variables. Namely, the coefficients of the cut-decomposition of the spectral distance and of the Tawn-Molchanov max-stable model realizing the corresponding bivariate extremal dependence coincide. We show that line metrics are rigid and if the spectral distance corresponds to a line metric, the higher order tail-dependence is determined by the bivariate tail-dependence matrix.Finally, the correspondence between ell _1-embeddable metric spaces and tail-dependence matrices allows us to revisit the realizability problem, i.e. checking whether a given matrix is a valid tail-dependence matrix. We confirm a conjecture of Shyamalkumar and Tao (2020) that this problem is NP-complete.

Characterizing and quantifying the incompatibility of quantum instruments

Incompatibility of quantum devices is one of the cornerstones of quantum theory, and the incompatibility of quantum measurements and channels has been linked to quantum advantage in certain information-theoretic tasks. In this work, we focus on the less well explored question of the incompatibility of quantum instruments, that is, devices that describe the measurement process in its entirety, accounting for both the classical measurement outcome and the quantum postmeasurement state. In particular, we focus on the recently introduced notion of parallel compatibility of instruments, which has been argued to be a natural notion of instrument compatibility. We introduce, in a manner similar to the case of measurements and channels, the incompatibility robustness of quantum instruments and derive universal bounds on it. We then prove that postprocessing of quantum instruments is a free operation for parallel compatibility. Last, we provide families of instruments for which our bounds are tight and families of compatible indecomposable instruments.

Approximate Bayesian implementation and exact maxmin implementation: An equivalence

This paper provides a micro-foundation for approximate incentive compatibility using ambiguity aversion. In particular, we propose a novel notion of approximate interim incentive compatibility, approximate local incentive compatibility, and establish an equivalence between approximate local incentive compatibility in a Bayesian environment and exact interim incentive compatibility in the presence of a small degree of ambiguity. We then apply our result to the implementation of efficient allocations. In particular, we identify two economic settings—including ones in which approximately efficient allocations are implementable and ones in which agents are informationally small—in which efficient allocations are approximately locally implementable when agents are Bayesian. Applying our result to those settings, we conclude that efficient allocations are exactly implementable when agents perceive a small degree of ambiguity.

Reconstructing quantum theory from its possibilistic operational formalism

We develop a possibilistic semantic formalism for quantum phenomena from an operational perspective. This semantic system is based on a Chu duality between preparation processes and yes/no tests, the target space being a three-valued set equipped with an informational interpretation. A basic set of axioms is introduced for the space of states. This basic set of axioms suffices to constrain the space of states to be a projective domain. The subset of pure states is then characterized within this domain structure. After having specified the notions of properties and measurements, we explore the notion of compatibility between measurements and of minimally disturbing measurements. We achieve the characterization of the domain structure on the space of states by requiring the existence of a scheme of discriminating yes/no tests, necessary condition for the construction of an orthogonality relation on the space of states. This last requirement about the space of states constrain the corresponding projective domain to be ortho-complemented. An orthogonality relation is then defined on the space of states and its properties are studied. Equipped with this relation, the ortho-poset of ortho-closed subsets of pure states inherits naturally a structure of Hilbert lattice. Finally, the symmetries of the system are characterized as a general subclass of Chu morphisms. We prove that these Chu symmetries preserve the class of minimally disturbing measurements and the orthogonality relation between states. These symmetries lead naturally to the ortho-morphisms of Hilbert lattice, defined on the set of ortho-closed subsets of pure states.

Unusually Combined Lexemes as Means of Creating Uncertainty in English Postmodern Short-Short Stories

The issue of words combinations draws attention of linguists starting from the second half of the XX c. until the present day. This study is focused on the research of semantic mechanisms of unusually combined lexemes and unexpected collocations in English postmodern short-short stories. Reconsideration of the literary past and ironic view on traditional poetic canons are reflected in postmodern literary texts due to the principles of postmodern poetics. Being distinctive feature of postmodern literature in general, uncertainty creates multiplicity of meanings of entire literary text, as well as separate unexpected collocations, by means of unusually combined lexemes. The aim of the study is to elaborate the phenomenon of valence violation, created by unusually combined lexemes and unexpected collocations in English postmodern short-short stories. To achieve this goal, it is necessary to define the notion of valence and lexeme compatibility, to identify types of valence violation in lexemes combinations, and to provide their possible interpretation. Functioning in English postmodern short-short stories such language units widen boundaries of their usage and their combinatorial profile. Unusually combined lexemes focus the reader’s attention and provoke a cognitive mechanism of continuous searching for a hidden meaning of unexpected collocations and the general message of a literary text. In this research unusually combined lexemes are regarded as special markers of postmodern short-short story genre for which violation of text structure, violation of usual relations between lexemes in logic, semantic and syntactic aspects are quite common.

Incompatibility of observables, channels and instruments in information theories

Every theory of information, including classical and quantum, can be studied in the framework of operational probabilistic theories—where the notion of test generalizes that of quantum instrument, namely a collection of quantum operations summing to a channel, and simple rules are given for the composition of tests in parallel and in sequence. Here we study the notion of compatibility for tests of a causal operational probabilistic theory. Following the quantum literature, we first introduce the notion of strong compatibility, and then we illustrate its ultimate relaxation, that we deem weak compatibility. It is shown that the two notions coincide in the case of observation tests—which are the counterpart of quantum POVMs—while there exist weakly compatible channels that are not strongly compatible. We prove necessary and sufficient conditions for a theory to exhibit incompatible tests. We show that a theory admits of incompatible tests if and only if some information cannot be extracted without disturbance.

Lexico-semantic compatibility of words in Kazakh

The article examines the difference between the notions of compatibility and valency and distinguishes the types of combinations in the linguistic system. The aim of the article is to investigate the functions and types of combinations as a linguistic category. The article uses deductive, inductive methods and content analysis methods. The criterion of lexical combination in the linguistic system is analyzed. The potential of the combination of Kazakh words has also been considered. The analysis of the linguistic material has led us to the conclusion that lexical word combinations with an indicative component have an appositive potential. The study of the types of word combinations led to the hypothesis that the valency can be not only structural, stylistic, functional, but also semantic. The valency of words, although extremely important, is not dominant in determining their combinatorics. More important here seems to be their position of compatibility in meaning. The valence properties of the Kazakh language are described; the distinctive features of the manifestation of valence properties are revealed. The results of the analysis of valence properties of Kazakh vocabulary can also be used in the study of the valence theory of general linguistics. When studying the valence properties of a language, the analysis of its lexical semantics and the determination of its belonging to semantic groups characterized by a field structure is at the core.

Lexico-semantic compatibility of words in Kazakh

The article examines the difference between the notions of compatibility and valency and distinguishes the types of combinations in the linguistic system. The aim of the article is to investigate the functions and types of combinations as a linguistic category. The article uses deductive, inductive methods and content analysis methods. The criterion of lexical combination in the linguistic system is analyzed. The potential of the combination of Kazakh words has also been considered. The analysis of the linguistic material has led us to the conclusion that lexical word combinations with an indicative component have an appositive potential. The study of the types of word combinations led to the hypothesis that the valency can be not only structural, stylistic, functional, but also semantic. The valency of words, although extremely important, is not dominant in determining their combinatorics. More important here seems to be their position of compatibility in meaning. The valence properties of the Kazakh language are described; the distinctive features of the manifestation of valence properties are revealed. The results of the analysis of valence properties of Kazakh vocabulary can also be used in the study of the valence theory of general linguistics. When studying the valence properties of a language, the analysis of its lexical semantics and the determination of its belonging to semantic groups characterized by a field structure is at the core.

Orderings and valuations in hyperfields

We introduce and study in detail the notion of compatibility between valuations and orderings in real hyperfields. We investigate their relation with valuations and orderings induced on factor and residue hyperfields. Much of the theory from real fields can be generalized to real hyperfields; we point out facts that cannot. We generalize the Baer-Krull theorem to real hyperfields.

Orthogonal symmetric matrices and joins of graphs

We introduce a notion of compatibility for multiplicity matrices. This gives rise to a necessary condition for the join of two (possibly disconnected) graphs G and H to be the pattern of an orthogonal symmetric matrix, or equivalently, for the minimum number of distinct eigenvalues q of G∨H to be equal to two. Under additional hypotheses, we show that this necessary condition is also sufficient. As an application, we prove that q(G∨H) is either two or three when G and H are unions of complete graphs, and we characterise when each case occurs.

Dirac structures and Nijenhuis operators

We introduce a notion of compatibility between (almost) Dirac structures and (1,1)-tensor fields extending that of Poisson–Nijenhuis structures. We study several properties of the “Dirac–Nijenhuis” structures thus obtained, including their connection with holomorphic Dirac structures, the geometry of their leaves and quotients, as well as the presence of hierarchies. We also consider their integration to Lie groupoids, which includes the integration of holomorphic Dirac structures as a special case.

Ground-Motion Evaluation of Hybrid Seismic Velocity Models

Abstract Cost-effective strategies for enhancing seismic velocity models are an active research topic. The recently developed hybridization technique shows promise in improving models used for deterministic earthquake hazard evaluation. We augment the results of Ajala and Persaud (2021) by exploring other hybrid models generated using 13 sets of embedding parameters—taper widths and subvolumes—and summarize their effect on waveform predictions up to a minimum period of 2 s. Our results introduce the notion of compatibility as a consideration by showing that the same basin models embedded into two different regional models can produce notably different outcomes. In contrast to most of our hybrid Harvard models that produce better matching ground motions, only one of the hybrid models generated using the Southern California Earthquake Center model as a regional model gives a closer match to the waveforms. Similar results are obtained at higher frequencies; however, improvements due to hybridization are reduced. A potential explanation for these results may be the limited high spatial frequencies in the travel time tomography basin models and the >5–6 s wavefield-dominated adjoint regional models. Although the strongly tapered compatible hybrid models tend to produce better results, we find instances of improvements even with merging artifacts.

Incentive-Compatible Forecasting Competitions

We initiate the study of incentive-compatible forecasting competitions in which multiple forecasters make predictions about one or more events and compete for a single prize. We have two objectives: (1) to incentivize forecasters to report truthfully and (2) to award the prize to the most accurate forecaster. Proper scoring rules incentivize truthful reporting if all forecasters are paid according to their scores. However, incentives become distorted if only the best-scoring forecaster wins a prize, since forecasters can often increase their probability of having the highest score by reporting more extreme beliefs. In this paper, we introduce two novel forecasting competition mechanisms. Our first mechanism is incentive compatible and guaranteed to select the most accurate forecaster with probability higher than any other forecaster. Moreover, we show that in the standard single-event, two-forecaster setting and under mild technical conditions, no other incentive-compatible mechanism selects the most accurate forecaster with higher probability. Our second mechanism is incentive compatible when forecasters’ beliefs are such that information about one event does not lead to belief updates on other events, and it selects the best forecaster with probability approaching one as the number of events grows. Our notion of incentive compatibility is more general than previous definitions of dominant strategy incentive compatibility in that it allows for reports to be correlated with the event outcomes. Moreover, our mechanisms are easy to implement and can be generalized to the related problems of outputting a ranking over forecasters and hiring a forecaster with high accuracy on future events.This paper was accepted by Yan Chen, behavioral economics and decision analysis.Funding: This work was supported by the European Research Council [Grant ERC StG 307036] and the National Science Foundation [Grant CCF-1445755].