Characterization Theorem Research Articles

Vague Weak Interior Ideals of Γ-Semirings

The notion of a ((complete-) normal) vague weak interior ideal on a (regular) Γ-semiring is defined. It is proved that the set of all vague weak interior ideals forms a complete lattice. Also, a characterization theorem for a regular Γ-semiring in terms of vague weak interior ideals is derived. Another interesting consequence of the main result is that the cardinal of a non-constant maximal element in the set of all (complete-) normal vague weak interior ideals is 2.

Constructing models for spherical and elliptical densities

Abstract The article provides construction algorithms for consistent model classes of continuous spherical and elliptical distributions. The algorithms are based on characterization theorems for consistent families of generator functions. This characterization uses the term of complete monotonicity. The algorithms are applied to several examples of generators leading to consistent families of generators with explicit formulas for marginal densities of arbitrary dimension.

ON 2-ABSORBING IDEALS IN COMMUTATIVE Γ− SEMIRINGS

In this paper, our aim is to study the results of 2-absorbing ideals and weakly 2-absorbing ideals in a commutative Γ− semirings which is a generalization of prime ideals of a commutative Γ− semirings. Finally, we prove a characterization theorem for 2-absorbing and weakly 2-absorbing ideals in terms of k- extension of an ideal in a commutative Γ− semiring.

Geometry of Warped Product Hemi-Slant Submanifolds of an S-Manifold

The purpose of this paper is to investigate a warped product of hemi-slant submanifolds on an S-manifold. We prove many interesting results for the existence of warped product hemi-slant submanifold of the type Mθ×fM⊥ with ξα∈Mθ of an S-manifold. For such submanifolds, a characterization theorem is proven. In addition, we form an inequality for the squared norm of the second fundamental form in terms of the warping function and the slant angle. We also provide some examples, and the equality case is also considered.

The strong fuzzy variational Henstock multiple integral on n-dimensional fuzzy number space

In this paper, we define strongly fuzzy variational Henstock multiple integral and fuzzy Henstock integral by support functions on n-dimensional fuzzy number space. And we prove these two types of integrals are equivalent. After that, we propose the support-based derivative for strongly fuzzy variational Henstock integral functions and obtain the necessary and sufficient conditions for this differential. By the properties of ACGδ⁎⁎, we use the concepts of inner small variation and singular point covering to derive some characterization theorems of the primitives for strongly fuzzy variational Henstock integral. Finally, the Dominated Convergence Theorem for SFVH integral is obtained in the sense of UACGδ⁎⁎.

The Fisher metric as a metric on the cotangent bundle

The Fisher metric on a manifold of probability distributions is usually treated as a metric on the tangent bundle. In this paper, we focus on the metric on the cotangent bundle induced from the Fisher metric with calling it the Fisher co-metric. We show that the Fisher co-metric can be defined directly without going through the Fisher metric by establishing a natural correspondence between cotangent vectors and random variables. This definition clarifies a close relation between the Fisher co-metric and the variance/covariance of random variables, whereby the Cramér-Rao inequality is trivialized. We also discuss the monotonicity and the invariance of the Fisher co-metric with respect to Markov maps, and present a theorem characterizing the co-metric by the invariance, which can be regarded as a cotangent version of Čencov’s characterization theorem for the Fisher metric. The obtained theorem can also be viewed as giving a characterization of the variance/covariance.

Minimal Prime and Semiprime Submodules

Prime and semiprime submodules are important generalizations of prime and semiprime ideals to module theory over commutative rings. However, minimal or smallest prime/semiprime submodules have received comparatively less attention. This paper furthers the theory of minimal prime and minimal semiprime submodules through several new directions. After formally introducing these concepts, we establish characterization theorems for minimal prime submodules based on intersections of primes and associated primes. A complete structure theory is also developed for minimal semiprime submodules, allowing their description up to isomorphism. We introduce prime and semiprime operators which stably preserve primeness properties between modules. Results on the persistence of minimal primeness of submodules under such operators are proved. Connections of our minimal semiprime characterization back to classic ring theory are highlighted, recovering past results on minimal prime ideals. Overall, this paper significantly expands the foundations of minimal prime and semiprime submodules, while opening up many new questions at this nexus of module and ring theory.

Fuzzy Sᵦ-compactness and fuzzy Sᵦ-closed spaces

The aim of this paper is to introduce the notion of fuzzy Sβ -compactness. Some of the basic properties and characterization theorems would be investigated of this newly defined compactness in fuzzy setting. We would also introduce and study fuzzy Sβ - closed spaces.

Moment functions of higher rank on some types of hypergroups

We consider moment functions of higher order. In our earlier paper, we have already investigated the moment functions of higher order on groups. The main purpose of this work is to prove characterization theorems for moment functions on the multivariate polynomial hypergroups and on the Sturm–Liouville hypergroups. In the first case, the moment generating functions of higher rank are partial derivatives (taken at zero) of the composition of generating polynomials of the hypergroup and functions whose coordinates are given by the formal power series. On Sturm–Liouville hypergroups the moment functions of higher rank are restrictions of even smooth functions that also satisfy certain boundary value problems. The second characterization of moment functions of higher rank on Sturm–Liouville hypergroups is given by means of an exponential family. In this case, the moment functions of higher rank are partial derivatives of an appropriately modified exponential family again taken at zero.

Analysis on the behavior of the logistic fixed effort harvesting model through the difference equation under uncertainty

ABSTRACT In this article, a logistic fixed effort harvesting model is architected in an imprecise, discrete dynamical frame of mathematical logic. The fuzzy difference equation explores the philosophy behind the computational structure that represents the underflowing discrete behaviour and uncertainty associated with the modelling through discrete calculus and fuzzy decision-making mechanisms. The nonlinear fuzzy difference equations with different initial conditions and coefficients as fuzzy numbers are manifested to recognize the model. Interestingly, the fuzzy difference equations identified in this article can be imparted into a system of crisp difference equations by the characterization theorem. The equilibrium points are traced, and their corresponding stability criteria are analyzed considering different fuzzy cases. The merits and applicability of the proposed theory have been validated through numerical simulation and graphical visualization.

Moment Properties of Record Values from Rayleigh Lomax Distribution and Characterization

In this paper we have obtained explicit expressions for single and product moments of upper record values from Rayleigh Lomax distribution. Also, recursive relationships between moments of upper records are developed. The characterization theorems based on recurrence relations and conditional expectation are also presented.

On characterizing proper max-point-tolerance graphs

Max-point-tolerance graphs (MPTG) were introduced by Catanzaro et al. in 2017 as a generalization of interval graphs. This graph class has many practical applications in the study of the human genome as well as in signal processing for networks. The same class of graphs was also studied by Soto and Caro in 2015 with a different name, p -BOX(1) graphs. In our article, we consider a natural subclass of max-point-tolerance graphs, namely, proper max-point-tolerance graphs (proper MPTG), where intervals associated with the vertices are not contained in each other properly. We present the first characterization theorem of this graph class by defining certain linear ordering on the vertex set. In the course of this study, we prove proper max-point-tolerance graphs are asteroidal triple-free, and perfect. We also find that proper max-point-tolerance graphs are equivalent to unit max-point-tolerance graphs. Further, we show that MPTG (proper MPTG) and max-tolerance graphs (proper max-tolerance graphs) are incomparable. In conclusion, we demonstrate relations between proper MPTG with other variants of MPTG and max-tolerance graphs.

Stochastic quantization of laser propagation models

This paper identifies certain interesting mathematical problems of stochastic quantization type in the modeling of Laser propagation through turbulent media. In some of the typical physical contexts, the problem reduces to stochastic Schrödinger equation with space–time white noise of Gaussian or Poisson or Lévy type. We identify their mathematical resolution via stochastic quantization. Nonlinear phenomena such as Kerr effect can be modeled by a stochastic nonlinear Schrödinger equation in the focusing case with space–time white noise. A treatment of stochastic transport equation, the Korteweg–De Vries equation as well as a number of other nonlinear wave equations with space–time white noise is also given. The main technique is the S-transform (we will actually use the closely related Hermite transform) which converts the stochastic partial differential equation (PDE) with space–time white noise to a deterministic PDE defined on the Hida–Kondratiev white noise distribution space. We then utilize the inverse S-transform/Hermite transform known as the characterization theorem combined with the infinite-dimensional implicit function theorem for analytic maps to establish local existence and uniqueness theorems for path-wise solutions of this class of problems. The particular focus of this paper on singular white noise distributions is motivated by practical situations where the refractive index fluctuations in the propagation medium in space and time are intense due to turbulence, ionospheric plasma turbulence, marine-layer fluctuations, etc. Since a large class of PDEs, that arise in nonlinear wave propagation, have polynomial-type nonlinearities, white noise distribution theory is an effective tool in studying these problems subject to different types of white noises.

Local and global deference

A norm of local expert deference says that your credence in an arbitrary proposition A, given that the expert’s probability for A is n, should be n. A norm of global expert deference says that your credence in A, given that the expert’s entire probability function is E, should be E(A). Gaifman taught us that these two norms are not equivalent. Stalnaker conjectures that Gaifman’s example is “a loophole”. Here, I substantiate Stalnaker’s suspicions by providing characterisation theorems which tell us precisely when the two norms come apart. They tell us that, in a good sense, Gaifman’s example is the only case where the two norms differ. I suggest that the lesson of the theorems is that Bayesian epistemologists need not concern themselves with the differences between these two kinds of norms. While they are not strictly speaking equivalent, they are equivalent for all philosophical purposes.

On a characterization theorem in the space [formula omitted

By Heyde's theorem, the class of Gaussian distributions on the real line is characterized by the symmetry of the conditional distribution of one linear form of independent random variables given another. We prove an analogue of this theorem for two independent random vectors taking values in the space Rn. The obtained class of distributions consists of convolutions of Gaussian distributions and a distribution supported in a subspace, which is determined by coefficients of the linear forms.

On the Jensen convexity of quasideviation and Bajraktarević means

AbstractMotivated by the characterization theorem about the Jensen convexity of quasiarithmetic means obtained by the authors in 2021, our main goal is to establish a characterization of the Jensen convexity of quasideviation as well as of Bajraktarević means without any additional and unnatural regularity assumptions.

On Quasi Hemi-Slant Submersions

The paper deals with the notion of quasi hemi-slant submersions from Lorentzian para Sasakian manifolds onto Riemannian manifolds. These submersions are generalization of hemi-slant submersions and semi-slant submersions. In this paper, we also study the geometry of leaves of distributions which are involved in the definition of the submersion. Further, we obtain the conditions for such distributions to be integrable and totally geodesic. Moreover, we also give the characterization theorems for proper quasi hemi-slant submersions and provide some examples of it.

Pointwise bi-slant lightlike submanifolds and their warped products

We introduce the general notion of pointwise bi-slant lightlike submanifolds of indefinite almost Hermitian manifolds. At first, we give a characterization theorem for the existence of pointwise bi-slant lightlike submanifolds and present one non-trivial example for this class of submanifolds. Further, the conditions of the integrability are derived for the distributions associated with such submanifolds. Finally, we investigate the existence of warped product pointwise bi-slant lightlike submanifolds of indefinite Kaehler manifolds.

Characterization theorem for strict third-degree semiclassical forms of class one obtained via cubic decomposition

Based on their third-degree character, we give a complete description of a large family of semiclassical forms of class one. A characterization theorem for all strict third-degree semiclassical forms of class one arising via the cubic decomposition W_{3n}(x)=P_n(x^3+qx+r) , q, r\in\mathbb{C} , n\geq 0 , is stated and proved. In fact, by using the Stieltjes function and the moments of those forms, this theorem gives necessary and sufficient conditions that characterize and identify all these forms, and we present their link with the Jacobi forms \mathcal{V}_q^{k, l}=\mathcal{J}(k+q/3,l-q/3) , k+l\geq-1 , k, l \in \mathbb{Z} , q\in\{1,2\} .

Construction and approximation for a class of feedforward neural networks with sigmoidal function

As we know, feedforward neural networks (FNNs) with sigmoidal activation function are universal approximators. Theoretically, for any continuous function defined on a compact set, there exists an FNN such that the FNN can approximate the function with arbitrary accuracy, which constitutes a theoretical guarantee that FNN can be used as an efficient learning machine. This paper addresses the construction and approximation for FNNs. We construct an FNN with sigmoidal activation function and estimate its approximation error. In particular, an inverse theorem of the approximation is established, which implies the equivalence characterization theorem of the approximation and reveals the relationship between the topological structure of the FNN and its approximation ability. As keys in this study, the concepts of modulus of continuity of function, K-functional, and their relationship are utilized, and two Bernstein-type inequalities are established.