Characterization Theorem Research Articles

The dynamics and behavior of logarithmic type fuzzy difference equation of order two.

Fuzzy difference equations are becoming increasingly popular in fields like engineering, ecology, and social science. Difference equations find numerous applications in real-life problems. Our study demonstrates that the logarithmic-type fuzzy difference equation of order two possesses a nonnegative solution, and an equilibrium point, and exhibits asymptotic behavior. [Formula: see text] Where, xi represents the sequence of fuzzy numbers, and the parameters α, β, A, along with the initial conditions x-1 and x0, are positive fuzzy numbers. The characterization theorem is employed to convert each single logarithmic fuzzy difference equation into a set of two crisp logarithmic difference equations within a fuzzy environment. We evaluated the stability of the equilibrium point of the fuzzy system. Utilizing variational iteration techniques, the method of g-division, inequality skills, and a theory of comparison for logarithmic fuzzy difference equations, we investigated the governing equation dynamics, including its boundedness, existence, and both local and global stability analysis. Additionally, we provided some numerical solutions for the equation describing the system to verify our results.

Multidimensional Fractional Calculus: Theory and Applications

In this paper, we introduce several new types of partial fractional derivatives in the continuous setting and the discrete setting. We analyze some classes of the abstract fractional differential equations and the abstract fractional difference equations depending on several variables, providing a great number of structural results, useful remarks and illustrative examples. Concerning some specific applications, we would like to mention here our investigation of the fractional partial differential inclusions with Riemann–Liouville and Caputo derivatives. We also establish the complex characterization theorem for the multidimensional vector-valued Laplace transform and provide certain applications.

Characterization and analysis of generalized grey incomplete gamma noise

The grey incomplete gamma distributions was established by one of the authors in a previous publication. In this article we use the Kondratiev characterization theorem to identify those via a suitable Laplace transform with holomorphic functions with suitable properties. We establish theorems for the integration and convergence of sequences of these distributions. As direct applications of these analytic tools we give the examples of Donsker's delta function, identify the time-derivative of the process as a suitable distribution and define the Gamma grey Ornstein–Uhlenbeck process.

SCREEN PSEUDO-SLANT LIGHTLIKE SUBMERSIONS FROM INDEFINITE SASAKIAN MANIFOLDS ONTO LIGHTLIKE MANIFOLDS

As a generalization of screen slant lightlike submersions, we introduce the notion of screen pseudo-slant lightlike submersions from indefinite Sasakian manifolds onto lightlike manifolds. We give examples and prove a characterization theorem for the existence of such lightlike submersions. We also obtain integrability conditions of distributions involved in the definition of this class of lightlike submersions. Further, we find necessary and sufficient conditions for foliations determined by these distributions to be totally geodesic.

On a Weighting Technique for Multiple Cost Optimization Problems with Interval Values

This paper deals with a weighting technique for a class of multiple cost optimization problems with interval values. More specifically, we introduce a multiobjective interval-valued controlled model and investigate it by applying the weighting method. In this regard, several characterization theorems are derived. Moreover, a numerical example is formulated. Based on the provided illustrative example and performing a comparative analysis of the results obtained using the weighting technique versus traditional optimization methods, we can easily conclude the effectiveness of the weighting technique in solving multiple cost optimization problems, that is, the conversion of a vector problem to a scalar one.

Lattice Algebraic Structures on LDMFS Domains

The premise of the soft set was designed to model vague ideas. In this kind of model, where the set of parameters exhibits some degree of order, lattice order theory is quite beneficial. For researchers studying uncertainty, the notion of soft sets, lattices, and fuzzy sets has proven essential. In this study, the postulation of the Lattice ordered Linear Diophantine Multi-Fuzzy Soft Set (LLDMFSS) is laid out. The fundamental objective of this study is the formation of hybrid algebraic structures for LLDMFSS. Particularly, the characteristics of complete lattice, modular lattice, and distributive lattice were inhibited in LLDMFSS, and some pertinent findings were obtained. Subsequently, the modular and distributive LLDMFSS characterization theorem was implemented. The notion of the direct product for two LLDMFSSs was then addressed.

Characterization of rankings generated by pseudo-Boolean functions

In this paper we pursue the study of pseudo-Boolean functions as ranking generators. The objective of the work is to find new insights between the relation of the degree m of a pseudo-Boolean function and the rankings that can be generated by these insights. Based on a characterization theorem for pseudo-Boolean functions of degree m, several observations are made. First, we verify that pseudo-Boolean functions of degree m<n, where n is the search space dimension, cannot generate all the possible rankings of the solutions. Secondly, the sufficient condition for a ranking to be generated by a pseudo-Boolean function of dimension (n−1) is presented, and also the necessary condition is conjectured. Finally, we observe that the same argument is not sufficient to prove which ranking can be generated by pseudo-Boolean functions of degree m<n−1.

New results on spectral synthesis

In our former paper we introduced the concept of localization of ideals in the Fourier algebra of a locally compact Abelian group. It turns out that localizability of a closed ideal in the Fourier algebra is equivalent to the synthesizability of the annihilator of that closed ideal which corresponds to this ideal in the measure algebra. This equivalence provides an effective tool to prove synthesizability of varieties on locally compact Abelian groups. In this paper we utilize this tool to show that when investigating synthesizability of a variety, roughly speaking compact elements of the group can be neglected. Our main result is that spectral synthesis holds on a locally compact Abelian group G if and only if it holds on G/B, where B is the closed subgroup of all compact elements. In particular, spectral synthesis holds on compact Abelian groups. Also we obtain a simple proof for the characterization theorem of spectral synthesis on discrete Abelian groups.

Hyperbolic width functions and characterizations of bodies of constant width in the hyperbolic space

We discuss basic properties of several different width functions in the n-dimensional hyperbolic space such as continuity, and we also define a new hyperbolic width as the extension of Leichtweiss’ width function. Then we prove a characterization theorem of bodies of constant width regarding the aforementioned notions of hyperbolic width.

A Characterization of the Operator Entropy in terms of an Isometry Property Related to Trace Norms

In this paper, we introduce two new mean operators acting on trace class operators, and using the mean operators, we provide a new characterization theorem of operator entropy in terms of an isometry property between two trace norms. It is a very important point that we can characterize the operator entropy only using the isometry property for a continuous operator on some class of density operators.

Characterizations of Pointwise Hemi-Slant Warped Product Submanifolds in LCK Manifolds

In this paper, we investigate the pointwise hemi-slant submanifolds of a locally conformal Kähler manifold and their warped products. Moreover, we derive the necessary and sufficient conditions for integrability and totally geodesic foliation. We establish characterization theorems for pointwise hemi-slant submanifolds. Several fundamental results that extend the CR submanifold warped product in Kähler manifolds are proven in this study. We also provide some non-trivial examples and applications.

N-absorbing ideal factorization in commutative rings

In this article, we show that Mori domains, pseudo-valuation domains, and n-absorbing ideals, the three seemingly unrelated notions in commutative ring theory, are interconnected. In particular, we prove that an integral domain R is a Mori locally pseudo-valuation domain if and only if each proper ideal of R is a finite product of 2-absorbing ideals of R. Moreover, every ideal of a Mori locally almost pseudo-valuation domain can be written as a finite product of 3-absorbing ideals. To provide concrete examples of such rings, we study rings of the form A + XB [ X ] where A is a subring of a commutative ring B and X is indeterminate, which is of independent interest, and along with several characterization theorems, we prove that in such a ring, each proper ideal is a finite product of n-absorbing ideals for some n ≥ 2 if and only if A ⊆ B is essentially a finite product of field extensions. A complete description of when an order of a quadratic number field is a locally pseudo valuation domain, a locally almost pseudo valuation domain or a locally conducive domain is given.

The omega-reducibility of pseudovarieties of ordered monoids representing low levels of concatenation hierarchies

We deal with the question of the [Formula: see text]-reducibility of pseudovarieties of ordered monoids corresponding to levels of concatenation hierarchies of regular languages. A pseudovariety of ordered monoids [Formula: see text] is called [Formula: see text]-reducible if, given a finite ordered monoid M, for every inequality of pseudowords that is valid in [Formula: see text], there exists an inequality of [Formula: see text]-words that is also valid in [Formula: see text] and has the same “imprint” in M. Place and Zeitoun have recently proven the decidability of the membership problem for levels [Formula: see text], 1, [Formula: see text] and [Formula: see text] of concatenation hierarchies with level 0 being a finite Boolean algebra of regular languages closed under quotients. The solutions of these membership problems have been found by considering a more general problem of separation of regular languages and its further generalization — a problem of covering. Following the results of Place and Zeitoun, we prove that, for every concatenation hierarchy with level 0 being represented by a locally finite pseudovariety of monoids, the pseudovarieties corresponding to levels [Formula: see text] and [Formula: see text] are [Formula: see text]-reducible. As a corollary of these results, we obtain that, for every concatenation hierarchy with level 0 being represented by a locally finite pseudovariety of monoids, the pseudovarieties corresponding to levels [Formula: see text] and [Formula: see text] are definable by [Formula: see text]-inequalities. Furthermore, in the special case of the Straubing–Thérien hierarchy, using a characterization theorem for level 2 by Place and Zeitoun, we obtain that the level 2 is definable by [Formula: see text]-identities.

The second variation of the Hodge norm and higher Prym representations

AbstractLet denote a rational cohomology class, and let denote its Hodge norm. We recover the result that is a plurisubharmonic function on the Teichmüller space , and characterize complex directions along which the complex Hessian of vanishes. Moreover, we find examples of such that is not strictly plurisubharmonic. As part of this construction, we find an unbranched covering such that the subgroup of generated by lifts of simple curves from is strictly contained in . Finally, combining the characterization theorem with the Riemann–Roch, and the Li–Yau [Invent. Math. 69 (1982), no. 2, 269–291] gonality estimate, we show that geometrically uniform covers of satisfy the Putman–Wieland Conjecture about the induced Higher Prym representations.

A New Notion of Fuzzy Function Ideal Convergence

P.M. Pu and Y.M. Liu extended Moore-Smith’s convergence of nets to fuzzy topology and Y.M. Liu provided analogous results to J. Kelley’s classical characterization theorem of net convergence by introducing the notion of fuzzy convergence classes. In a previous paper, the authors of this study provided modified versions of this characterization by using an alternative notion of convergence of fuzzy nets, introduced by B.M.U. Afsan, named fuzzy net ideal convergence. Our main scope here is to generalize and simplify the preceding results. Specifically, we insert the concept of a fuzzy function ideal convergence class, L, on a non-empty set, X, consisting of triads (f,e,I), where f is a function from a non-empty set, D, to the set FP(X) of fuzzy points in X, which we call fuzzy function, e∈FP(X), and I is a proper ideal on D, and we provide necessary and sufficient conditions to establish the existence of a unique fuzzy topology, δ, on X, such that (f,e,I)∈L iff fI-converges to e, relative to the fuzzy topology δ.

Polynomial Equations for Additive Functions I: The Inner Parameter Case

The aim of this sequence of work is to investigate polynomial equations satisfied by additive functions. As a result of this, new characterization theorems for homomorphisms and derivations can be given. More exactly, in this paper the following type of equation is considered ∑i=1nfi(xpi)gi(xqi)=0x∈F,\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\begin{aligned} \\sum _{i=1}^{n}f_{i}(x^{p_{i}})g_{i}(x^{q_{i}})= 0 \\qquad \\left( x\\in \\mathbb {F}\\right) , \\end{aligned}$$\\end{document}where n is a positive integer, F⊂C\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathbb {F}\\subset \\mathbb {C}$$\\end{document} is a field, fi,gi:F→C\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f_{i}, g_{i}:\\mathbb {F}\\rightarrow \\mathbb {C}$$\\end{document} are additive functions and pi,qi\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$p_i, q_i$$\\end{document} are positive integers for all i=1,…,n\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$i=1, \\ldots , n$$\\end{document}.

Old and new joint characterizations of leximin and variants of rank-weighted utilitarianism.

This paper proposes a new class of efficient and equitable social welfare orderings, a generalized leximin rule that includes rank-weighted utilitarianism, leximin, and their lexicographic compositions. While the famous Deschamps and Gevers' joint characterization theorem shows that a Paretian, anonymous, separable social welfare ordering must be either weak utilitarianism, leximin, or leximax under the assumption of cardinal full comparability, this study provides a new joint characterization theorem in which imposing rank-separability, instead of separability, enables acceptable social welfare ordering to be the generalized leximin rule. This result is proven by an intuitive and easy-to-understand method, which also helps show the mechanism by which a class of Paretian, anonymous, and separable social welfare orderings is limited to weak utilitarianism and leximin.

Semi-Slant Lightlike Submanifolds of Golden Semi-Riemannian Manifolds

The aim of our paper is to introduce the notion of semi-slant lightlike submanifolds of golden semi-Riemannian manifolds. We give non-trivial examples of semi-slant lightlike submanifolds and provide a characterization theorem of such submanifolds. Further, we obtain necessary and sufficient conditions for integrability of the distributions and investigate the geometry of the leaves of the foliation determined by the distributions. We also obtain a necessary and sufficient condition for the induced connection to be a metric connection. Finally, we obtain necessary and sufficient condition for mixed-geodesic semi-slant lightlike submanifold of golden semi-Riemannian manifold.

Permuting Tri-Derivations on Posets

Let P be a partially ordered set (poset). The main objective of the present paper is to introduce and study the idea of permuting tri-derivations of posets. Several characterization theorems involving permuting tri-derivations are given. In particular, we prove that if d1 and d2 are two permuting tri-derivations of P with traces ϕ1 and ϕ2, then ϕ1 ≤ ϕ2 if and only if ϕ2(ϕ1(x)) = ϕ1(x) for all x ∈ P.

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.