Let  be a non-trivial simple graph. A dominating set in a graph is a set of vertices such that every vertex not in the set is adjacent to at least one vertex in the set. A subset  is a minimum neighborhood dominating set if  is a dominating set and if for every  holds. The minimum cardinality of the minimum neighborhood dominating set of a graph  is called as minimum neighborhood dominating number and it is denoted by  . A minimum neighborhood dominating set is a dominating set where the intersection of the neighborhoods of all vertices in the set is as small as possible, (i.e., ). The minimum neighborhood dominating number, denoted by , is the minimum cardinality of a minimum neighborhood dominating set. In other words, it is the

In this work, the performance of the receiver in a quantum cryptography system based on BB84 protocol is scaled by calculating the Quantum Bit Error Rate (QBER) of the receiver. To apply this performance test, an optical setup was arranged and a circuit was designed and implemented to calculate the QBER. This electronic circuit is used to calculate the number of counts per second generated by the avalanche photodiodes set in the receiver. The calculated counts per second are used to calculate the QBER for the receiver that gives an indication for the performance of the receiver. Minimum QBER, 6%, was obtained with avalanche photodiode excess voltage equals to 2V and laser diode power of 3.16 nW at avalanche photodiode temperature of -10

Objectives: The research aims to demonstrate the integration between Quantum Computing (QC) and Predictive Analysis (PA) and their role in reducing costs while achieving Sustainable Development Goals (SDGs). The study addresses the inefficiencies in calculating and measuring product costs under traditional systems and examines how QC and PA can enhance cost reduction and product quality to better meet customer needs. Additionally, the research seeks to strengthen the theoretical framework with practical applications, illustrating how this integration improves a company’s competitive position while promoting social, environmental, and economic sustainability.   Methods: The study employs a descriptive analytical approach, focusi

In this article, a short review on the feature of reality and locality in quantum optics is given.
The Bell inequality and the Bell states are introduced to show their direct use in quantum computer and
quantum teleportation. Moreover, quantum cryptography is discussed in some details regarding basic
ideas and practical considerations. In addition, a case study involving distillation of a quantum key based
on the given fundamentals is presented and discussed.

In this communication, introduce the split Mersenne and Mersenne-Lucas hybrid quaternions, also obtaining generating functions and Binet formulas for these hybrid quaternions and investigating some properties among them.

This work is a trial to ensure the absolute security in any quantum cryptography (QC) protocol via building an effective hardware for satisfying the single-photon must requirement by controlling the value of mean photon number. This was approximately achieved by building a driving circuit that provide very short pulses (≈ 10 ns) for laser diode -LD- with output power of (0.7-0.99mW) using the available electronic components in local markets. These short pulses enable getting faint laser pulses that were further attenuated to reach mean photon number equal to 0.08 or less.

         Continuous functions are novel concepts in topology. Many topologists contributed to the theory of continuous functions in topology. The present authors continued the study on continuous functions by utilizing the concept of gpα-closed sets in topology and introduced the concepts of weakly, subweakly and almost continuous functions. Further, the properties of these functions are established.

This paper deals with a dilapidated urban part with a proposal to renew it and return it to the life cycle of the city, as in the neighborhood of Al-Mdawar, adjacent to the port of Beirut. It discusses the challenges and the need for renewal, the causes of urban deterioration, the urban development approach and the history of the regulations applied to Beirut, In the studied area. It also proposes solutions to improve its lifestyle based on urban planning tools and design to achieve people's aspirations, preserve identity and rearrange its integration with the Beirut central district area.