The Scientific Elements is an international book series, maybe with different subtitles. This series is devoted to the applications of Smarandache?s notions and to mathematical combinatorics. These are two heartening mathematical theories for sciences and can be applied to many fields. This book selects 12 papers for showing applications of Smarandache's notions, such as those of Smarandache multi-spaces, Smarandache geometries, Neutrosophy, etc. to classical mathematics, theoretical and experimental physics, logic, cosmology. Looking at these elementary applications, we can experience their great potential for developing sciences. 12 authors contributed to this volume: Linfan Mao, Yuhua Fu, Shenglin Cao, Jingsong Feng, Changwei Hu, Zhengda Luo, Hao Ji, Xinwei Huang, Yiying Guan, Tianyu Guan, Shuan Chen, and Yan Zhang.

Paper 1: Differential curves, Bertrand curves pair, ruled surfaces. Paper 2: (my paper) Banach space, Smarandache multispace, complex system, non-solvable equation, mathematical combinatorics. Paper 3: Zagreb index, molecular topological index, bipartite graph. Paper 4: D-conformal curvature tensor, η-Einstein manifold. Paper 5: Hypergraph, Smarandachely linear. Paper 6: Ruled surface, parallel surface. Paper 7: Smarandachely H-rainbow connected, rainbow connected, rainbow connection number. Paper 8: Darboux vector, Smarandache curves. Paper 9: Smarandache power root mean labeling, F-root square mean labeling. Paper 10: Smarandachely k-prime labelling, k-prime labelling. Paper 11: graceful labeling, α-labeling. Paper 12: supereulerian digraph, semicomplete digraph, locally semicomplete multipartite digraph. Paper 13: Smarandachely edge m-labeling, skolem mean labeling. Keywords: Smarandache multispace, Smarandachely linear, Smarandachely H-rainbow connected, Smarandache power root mean labeling, Smarandachely k-prime labelling, Smarandachely edge m-labeling

“Neutrosophic Sets and Systems” has been created for publications on advanced studies in neutrosophy, neutrosophic set, neutrosophic logic, neutrosophic probability, neutrosophic statistics that started in 1995 and their applications in any field, such as the neutrosophic structures developed in algebra, geometry, topology, etc.

Contributors to current issue (listed in papers’ order): Ibrahim Yasser, Abeer Twakol, A. A. Abd El-Khalek, A. A. Salama, Ahmed Sharaf Al-Din, Issam Abu Al-Qasim, Rafif Alhabib, Magdy Badran, Remya P. B, Francina Shalini, Masoud Ghods, Zahra Rostami, A. Sahaya Sudha, Luiz Flavio Autran Monteiro Gomes, K.R. Vijayalakshmi, Prakasam Muralikrishna, Surya Manokaran, Nidhi Singh, Avishek Chakraborty, Soma Bose Biswas, Malini Majumdar, Rakhal Das, Binod Chandra Tripathy, Nidhi Singh, Avishek Chakraborty, Nilabhra Paul, Deepshikha Sarma, Akash Singh, Uttam Kumar Bera, Fatimah M. Mohammed, Sarah W. Raheem, Muhammad Riaz, Florentin Smarandache, Faruk Karaaslan, Masooma Raza Hashmi, Iqra Nawaz, Kousik Das, Sovan Samanta, Kajal De, Xavier Encarnacion, Nivetha Martin, I. Pradeepa, N. Ramila Gandhi, P. Pandiammal, Aiman Muzaffar, Md Tabrez Nafis, Shahab Saquib Sohail, Abhijit Saha, Jhulaneswar Baidya, Debjit Dutta, Irfan Deli, Said Broumi, Mohsin Khalid, Neha Andaleeb Khalid, Md. Hanif Page, Qays Hatem Imran, Shilpi Pal, S. Satham Hussain, Saeid Jafari, N. Durga, Hanieh Shambayati, Mohsen Shafiei Nikabadi, Seyed Mohammad, Ali Khatami Firouzabadi, Mohammad Rahmanimanesh, Mujahid Abbas, Ghulam Murtaza, K. Porselvi, B. Elavarasan, Y. B. Jun, Chinnadurai V, Sindhu M P, K.Radhika, K. Arun Prakash, Malayalan Lathamaheswari, Ruipu Tan, Deivanayagampillai Nagarajan, Talea Mohamed, Assia Bakali, Nivetha Martin, R. Dhavaseelan, Ali Hussein Mahmood Al-Obaidi, Suman Das, Surapati Pramanik, Madad Khan, Muhammad Zeeshan, Saima Anis, Abdul Sami Awan, M. Sarwar Sindhu, Tabasam Rashid, Agha Kashif, Rajesh Kumar Saini, Atul Sangal, Manisha.

“Neutrosophic Sets and Systems” has been created for publications on advanced studies in neutrosophy, neutrosophic set, neutrosophic logic, neutrosophic probability, neutrosophic statistics that started in 1995 and their applications in any field, such as the neutrosophic structures developed in algebra, geometry, topology, etc.

“Neutrosophic Sets and Systems” has been created for publications on advanced studies in neutrosophy, neutrosophic set, neutrosophic logic, neutrosophic probability, neutrosophic statistics that started in 1995 and their applications in any field, such as the neutrosophic structures developed in algebra, geometry, topology, etc.

Papers on flexibility of Embeddings of a Halin Graph on the Projective Plane, curvature Equations on Combinatorial Manifolds with Applications to Theoretical Physics, a Pair of Smarandachely Isotopic Quasigroups and Loops of the Same Variety, and similar topics. Contributors: Arun S. Muktibodh, Han Ren, Yun Bai, Yuhua Fu, Anjie Fushenglin Cao, Guangxuan Wang, and others.