A thin film of 7-oxo-thiazolopyrimidine-3,8-dicarbonitrile derivative [7-ThPyDi]TF was prepared using a spin coating technique. The surface morphology and molecular structure are studied using various techniques such as XRD, FTIR, and scanning electron microscope (SEM). Moreover, the quantum chemical calculations were carried out through time-dependent density functional theory (TD-DFT) to investigate some reactivity descriptors such as softness and electronegativity. Also, Au/[7-ThPyDi]TF/p-Si/Al heterojunction diodes were fabricated. It was revealed that the energy bandgap value of [7-ThPyDi] as an organic thin film is 3.58 eV for direct transitions and 3.94 eV for indirect transitions, respectively, and this value falls within the semiconductor material range. The atomic force microscope demonstrated that the surface roughness of the thin film is approximately 32.2 nm. Because of its high refractive index, this material has the potential application as an antireflection coating for solar cells and as lenses with a wide focal range. We investigated a blue luminescent thiazolopyrimidine compound; the maximum emission in the more aggregated state (higher solution concentration) exhibits a notable blue shift compared to the more diluted solution. This uncommon phenomenon has been understood by structural analyses using density functional theory. The chemical structure of the molecule [planar conjugated cores and strong polar groups (–CO and –CN)] enables it to interact with both itself and the polar solvent. The intermolecular interactions result in the bending of the conjugated plane. As a result, the blue shift happens upon aggregation when the conjugated effect becomes weaker. The studied molecule gave different emission colors (blue, yellow, and reddish green) depending on the molecular packing.

In the present paper, we introduce new types of generalized closed sets called ij -pre-generalized closed sets and study some of their properties in bitopological spaces. Also, we use them to construct new types of separation axioms. Further, we introduce and study the concepts of pairwise operation pc-open sets and pairwise operation pc-separation axioms in bitopological spaces. Several interesting characterizations of different spaces are discussed. The relationships between these spaces are given.

DOI: 10.2478/tmmp-2023-0027

In this article, we introduce two new rough set models based on the concept of double fuzzy relations. These models are called optimistic and pessimistic multi-granulation double fuzzy rough sets. We discuss their properties and explore the relationship between these new models and double fuzzy rough sets. Our study focuses on the lower and upper approximations of these models, which generalize the conventional rough set model. In addition, we suggest that the development of the multi-granulation double fuzzy rough set model is significant for the generalization of the rough set model.
 

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The aim of this work is to demonstrate various an interesting recursion formulas, dierential
and integral operators, integration formulas, and innite summation for each of Horn's hypergeometric
functions H1, H2, H3, H4, H5, H6 and H7 by the contiguous relations of Horn's hypergeometric series.
Some interesting dierent cases of our main consequences are additionally constructed.

Inspired by the recent work Sahin and Agha gave recursion formulas for G1 and G2 Horn
hypergeometric functions (Sahin and Agha in Miskolc Math Notes 16(2):1153–1162, 2015).
The object of work is to establish several new recursion relations, relevant differential recursion
formulas, new integral operators, infinite summations and interesting results for Horn’s
hypergeometric functions G1, G2 and G3.

Agarwal et al. (2021) established the extension of several fundamental contiguous relations for GB. Our aim in this work is to investigate several properties of differentiation formulas, differential equations, recursion relations, differential recursion relations, confluence formulas, series representations, integration formulas, and infinite summations for Horn’s hypergeometric function GB of three variables. Some well-known particular cases have additionally been given.

The main aim of this work is to derive the q-recurrence relations, q-partial derivative relations
and summation formula of bibasic Humbert hypergeometric function 1 on two independent
bases q and q1 of two variables and some developments formulae, believed to be new, by using
the conception of q-calculus.

In this paper, we derive some classical and fractional properties of the ??? matrix function by using the Hilfer fractional operator. The theory of special matrix functions is the theory of those matrices that correspond to special matrix functions such as the gamma, beta, and Gauss hypergeometric matrix functions. We will also show the relationship with other generalized special matrix functions in the context of the Konhauser and Laguerre matrix polynomials.

The main aim of present work is to investigate the dynamics of the chaotic nonlinear distributed order Lü model (DOLM). The distributed order (DO) derivative is used for describing the viscoelasticity of various technical models and materials. The modified spectral numerical method is used to evaluate the numerical solutions for DOLM. Using nonlinear feedback control and the Lyapunov direct approach, the adaptive synchronization of two chaotic distributed order models (DOMs) is presented. We state a theorem to drive analytical controllers which are used to achieve our synchronization. The DOLM is introduced as an example of DOMs to verify the validity of our analytical results. Numerical computations are displayed to show the agreement between both analytical and numerical results. The DOMs appear in many applications in engineering and physics, e.g., image encryption and electronic circuits (ECs). Based on our proposed synchronization, the encryption and decryption of color images are studied. Information entropy, visual analysis and histograms are calculated, together with the experimental results of image encryption and decryption. We design the EC of the DOLM using the Multisim circuit simulator for the first time to our knowledge. Using electronic circuit simulation, we achieved the same results for the numerical treatment of our synchronization. Other ECs can be similarly designed for other DOMs.