Difference double sequence of complex uncertain variables defined by Orlicz function

In this paper, we introduce the difference double sequence of complex uncertain variables defined by Orlicz function. We study some of their properties like solidness, symmetricity, and completeness and prove some inclusion results.

A short note on sign changes and non-vanishing of Fourier coefficients of half-integral weight cusp forms

We study sign changes and non-vanishing of a certain double sequence of Fourier coefficients of cusp forms of half-integral weight.

Double Synchronous Unified Virtual Oscillator Control for Asymmetrical Fault Ride-Through in Grid-Forming Voltage Source Converters

A double synchronous unified virtual oscillator controller (dsUVOC) is proposed for grid-forming voltage source converters to achieve synchronization to the fundamental frequency positive- and negative-sequence components of unbalanced or distorted grids. The proposed controller leverages a positive- and a negative-sequence virtual oscillator, a double-sequence current reference generator, and a double-sequence vector limiter. Under fault conditions, the controller enables to clamp the converter output current below the maximum value limited by the converter hardware while retaining synchronization without a phase-locked-loop (PLL) regardless of the balanced or unbalanced nature of grid faults. Consequently, balanced and unbalanced fault ride-through can be achieved without the need for switching to a back-up controller. The paper presents the systematic development of the double-synchronous structure along with detail design and implementation guidelines. Validation of the proposed controller is provided through extensive control-hardware-in-the-loop (CHIL) and laboratory hardware experiments.

New Results on I 2 -Statistically Limit Points and I 2 -Statistically Cluster Points of Sequences of Fuzzy Numbers

In this paper, some existing theories on convergence of fuzzy number sequences are extended to I 2 -statistical convergence of fuzzy number sequence. Also, we broaden the notions of I -statistical limit points and I -statistical cluster points of a sequence of fuzzy numbers to I 2 -statistical limit points and I 2 -statistical cluster points of a double sequence of fuzzy numbers. Also, the researchers focus on important fundamental features of the set of all I 2 -statistical cluster points and the set of all I 2 -statistical limit points of a double sequence of fuzzy numbers and examine the relationship between them.

A Generalized of Nörlund Ideal Convergent Double Sequence Spaces

In this paper, by using the Nörlund mean Nt and the notion of ideal double convergence, we introduce new sequence spaces c0Ι2 (Nt), and ℓ∞I2 (Nt). Besides, we study some topological and algebraic properties on these spaces. Furthermore, some inclusion concerning these spaces are proved.

Some New Observations on Wijsman ℐ 2 -Lacunary Statistical Convergence of Double Set Sequences in Intuitionistic Fuzzy Metric Spaces

In this study, we investigate the notions of the Wijsman ℐ 2 -statistical convergence, Wijsman ℐ 2 -lacunary statistical convergence, Wijsman strongly ℐ 2 -lacunary convergence, and Wijsman strongly ℐ 2 -Cesàro convergence of double sequence of sets in the intuitionistic fuzzy metric spaces (briefly, IFMS). Also, we give the notions of Wijsman strongly ℐ 2 ∗ -lacunary convergence, Wijsman strongly ℐ 2 -lacunary Cauchy, and Wijsman strongly ℐ 2 ∗ -lacunary Cauchy set sequence in IFMS and establish noteworthy results.

On the domain of difference double sequence spaces of arbitrary orders

The prime objective of this paper is to define a new double difference operator with arbitrary order via which new classes of difference double sequences are introduced. Results on topological structures, dual spaces and four-dimensional matrix mappings related to the proposed difference double sequence spaces are discussed. As an application of this work, the proposed operator is being used to approximate partial derivatives of fractional orders. Some numerical examples are also given in support of the validity or the clear visualization of the results obtained.

IDEAL CONVERGENCE OF DOUBLE SEQUENCES OF CLOSED SETS

In the present paper, we introduce the concepts of ideal inner and ideal outer limits which always exist even if empty sets for double sequences of closed sets in Pringsheim's sense. Next, we give some formulas for finding ideal inner and outer limits in a metric space. After then, we define Kuratowski ideal convergence of double sequences of closed sets by means of the ideal inner and ideal outer limits of a double sequence of closed sets. Additionally, we give some examples that our result is more general than the results obtained before.