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This paper deals with the hidden structure of prime numbers. Previous numerical studies have already indicated a fractal-like behavior of prime-indexed primes. The construction of binary images enables us to generalize this result. In fact, two-integer sequences can easily be converted into a two-color image. In particular, the resulting method shows that both the coprimality condition and Ramanujan primes resemble the Minkowski island and Cantor set, respectively. Furthermore, the comparison between prime-indexed primes and Ramanujan primes is introduced and discussed. Thus the Cantor set covers a relevant role in the fractal-like description of prime numbers. The results confirm the feasibility of the method based on binary images. The link between fractal sets and chaotic dynamical systems may allow the characterization of the Hénon map only in terms of prime numbers.

South Korean Prime Minister Han Duck-soo addressed the nation March 24 after he was reinstated as acting president by the Constitutional Court.

During his political career, Helmut Kohl used his own life story to promote a normalization of German nationalism and to overcome the stigma of the Nazi period. In the context of the cold war and the memory of the fascist past, he was able to exploit the combination of his religious, generational, regional, and educational (he has a PhD in History) experiences by connecting nationalist ideas to particular biographical narratives. Kohl presented himself as the embodiment of \"normality\": a de-radicalized German nationalism which was intended to eclipse any anti-Western and post-national peculiarities. This book takes a biographical approach to the study of nationalism by examining its manifestation in Helmut Kohl and the way he historicized Germany's past.

Canada’s Prime Minister Justin Trudeau announced on Jan. 6 that he will resign against the backdrop of President-elect Donald Trump’s tariff threats.

Israel struck dozens of locations in Beirut on Nov. 26, even as Prime Minister Benjamin Netanyahu said he would recommend a cease-fire proposal.

In this paper, we consider certain special sine, tangent, and cotangent symmetric matrices, along with their associated integer matrices. We present interesting relationships that connect these matrices. Relevant examples of the corresponding matrices are also provided, along with several intriguing problems. A separate section includes proofs of the main theorems, which we believe are noteworthy in their own right.

Since its development, prime editing has been applied to human pluripotent stem cells (hPSCs) – a cell type typically challenging to edit – for various applications, including disease modeling and therapeutic correction.Various optimization strategies targeting the design of prime-editing components and their delivery methods have been implemented in hPSCs to enhance editing efficiency.The precision of prime editing, coupled with the versatility of hPSCs, holds immense promise for future clinical applications. Prime editing, first introduced in 2019, is a precise and efficient genome-editing technique with applications across various organisms and cell lines, including human pluripotent stem cells (hPSCs). Despite its revolutionary potential, prime editing of hPSCs often shows low efficiency, hindered by current delivery methods and DNA repair mechanisms. In this review, we explore prime editing of hPSCs, emphasizing the optimization necessary for creating ex vivo and in vitro disease models, which are critical for developing personalized therapeutics. We discuss key prime-editing methods for hPSCs, optimization strategies, tools available for prime editing, and the rigorous quality control required before and after genome engineering for downstream applications. Prime editing, first introduced in 2019, is a precise and efficient genome-editing technique with applications across various organisms and cell lines, including human pluripotent stem cells (hPSCs). Despite its revolutionary potential, prime editing of hPSCs often shows low efficiency, hindered by current delivery methods and DNA repair mechanisms. In this review, we explore prime editing of hPSCs, emphasizing the optimization necessary for creating ex vivo and in vitro disease models, which are critical for developing personalized therapeutics. We discuss key prime-editing methods for hPSCs, optimization strategies, tools available for prime editing, and the rigorous quality control required before and after genome engineering for downstream applications.