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In this study, we analysed a moving crack at the interface of an infinitely long piezoelectric bilayer using the Dugdale–Barenblatt yield (DBY) model and the polarisation saturation (PS) model. To model the moving crack problem, a Yoffe‐type crack moves at a constant subsonic speed on the interface of an infinitely long piezoelectric bilayer. The crack faces are assumed to be semi‐permeable, and at the boundary of the bilayer, in‐plane electrical and out‐of‐plane mechanical stresses are applied. Due to the application of electro‐mechanical loads, cracks propagate, mechanical yielding zones and electric saturation zones are developed. To arrest the crack from further propagation, mechanical yield stress and saturation electric displacement are applied at the developed zones. To address this problem analytically and numerically, the mixed boundary value problem is transformed into a set of coupled Fredholm integral equations (FIEs) of the second kind using the Fourier transform and the Copson method. The closed‐form analytical expressions for the length of the electrical saturation zone (ESZ), whether longer, shorter or equal to the mechanical yielding zone (MYZ), show dependence on external electro‐mechanical loads under semi‐permeable crack conditions. The algorithm to solve the electric crack condition parameter (ECCP) has been defined using numerical discretization and the bisection method. Illustrative examples demonstrate the proposed technique's effectiveness and suitability for Yoffe‐type moving cracks. The numerical results show the convergence of the ECCP. Furthermore, the numerical results show how mechanical and electrical zone lengths and energy release rate (ERR) are affected by electrical and mechanical loads, strip thickness and crack velocity. In addition, the size of the mechanical yielding zone is consistently promoted by electrical load, while the promotion or prevention of the electrical saturation zone by mechanical load depends on the relative sizes of the nonlinear zones. [ABSTRACT FROM AUTHOR]

Prokaryotes are ubiquitous in the biosphere, important for human health and drive diverse biological and environmental processes. Systematics of prokaryotes, whose origins can be traced to the discovery of microorganisms in the 17th century, has transitioned from a phenotype-based classification to a more comprehensive polyphasic taxonomy and eventually to the current genome-based taxonomic approach. This transition aligns with a foundational shift from studies focused on phenotypic traits that have limited comparative value to those using genome sequences. In this context, Bergey's Manual of Systematics of Archaea and Bacteria (BMSAB) and Bergey's International Society for Microbial Systematics (BISMiS) play a pivotal role in guiding prokaryotic systematics. This review focuses on the historical development of prokaryotic systematics with a focus on the roles of BMSAB and BISMiS. We also explore significant contributions and achievements by microbiologists, highlight the latest progress in the field and anticipate challenges and opportunities within prokaryotic systematics. Additionally, we outline five focal points of BISMiS that are aimed at addressing these challenges. In conclusion, our collaborative effort seeks to enhance ongoing advancements in prokaryotic systematics, ensuring its continued relevance and innovative characters in the contemporary landscape of genomics and bioinformatics. [ABSTRACT FROM AUTHOR]

In this article, we have derived some integral transforms of the polynomial weighted incomplete H-functions and incomplete ̄H-functions. The obtained image formulas are of general nature and may, as special cases, give rise to integral transforms involved with the H-functions and ̄H-functions.

In this paper, the problem of two equal collinear cracks is analytically studied for two-dimensional (2D) arbitrarily polarized magneto-electro-elastic materials. The electric and magnetic poling directions make arbitrary angles with the crack line. The Stroh's formalism and complex variable methodology is utilized to reduce the problem into non-homogeneous Riemann Hilbert problem. This numerical problem is then comprehended with the Riemann Hilbert way to obtain the intensity factors for stress, electric displacement and magnetic induction. A numerical contextual analysis is displayed for the BaTiO3 – CoFe2O4 composite. The numerical examination demonstrates that the change in electric/magnetic poling directions influences the intensity factors.

The present article introduces and studies the Fredholm-type integral equation with an incomplete I-function (IIF) and an incomplete Ī -function (IĪF) in its kernel. First, using fractional calculus and the Mellin transform principle, we solve an integral problem involving IIF. The idea of the Mellin transform and fractional calculus is then used to analyse an integral equation using the incompleteĪ-function. This is followed by the discovery and investigation of several important exceptional cases. This article's general discoveries may yield new integral equations and solutions. The desired outcomes seem to be very helpful in resolving many real-world problems whose solutions represent different physical phenomena. And also, findings help solve introdifferential, fractional differential, and extended integral equation problems. [ABSTRACT FROM AUTHOR]

In this study, we present and examine a fractional integral operator with an I$$ I $$‐function in its kernel. This operator is used to solve several fractional differential equations (FDEs). FDE has a set of particular cases whose solutions represent different physical phenomena. Much mathematical physics, biology, engineering, and chemistry problems are identified and solved using FDE. We first solve the FDE and the integral operator for the incomplete I$$ I $$‐function (I I$$ I $$F) for the generalized composite fractional derivative (GCFD). This is followed by the discovery and investigation of several important exceptional cases. The significant finding of this study is a first‐order integer‐differential equation of the Volterra type that clearly describes the unsaturated nature of free‐electron lasers. [ABSTRACT FROM AUTHOR]

In the present work, a novel and even more generalized fractional kinetic equation has been formulated in terms of polynomial weighted incomplete H-function, incomplete Fox-Wright function and incomplete generalized hypergeometric function, considering the importance of the fractional kinetic equations arising in the various science and engineering problems. All the derived findings are of natural type and can produce a variety of fractional kinetic equations and their solutions. [ABSTRACT FROM AUTHOR]

In this article, we have studied solutions of a generalised multiorder fractional partial differential equations involving the Caputo time‐fractional derivative and the Riemann–Liouville space fractional derivatives using Laplace–Fourier transform technique. Proposed generalised multiorder fractional partial differential equation is reducible to Schrödinger equation, wave equation and diffusion equation in a more general sense, and hence, solutions of these equations are specifically noted. Not only this, solutions of equation proposed in the stochastic resetting theory in the context of Brownian motion can also be found in a general regime. [ABSTRACT FROM AUTHOR]