Topological Indices of Novel Drugs Used in Cardiovascular Disease Treatment and Its QSPR Modeling by Fozia Bashir Farooq, Nadeem Ul Hassan Awan, Saima Parveen, Nazeran Idrees, Salma Kanwal, Tarig A. Abdelhaleem

“…A topological index is a score function that changes each molecular structure to a unique real number. It aids in determining the physicochemical and biological properties of a wide range of drugs, and it more accurately reflects the theoretical properties of drugs. …”
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First General Zagreb Index of Generalized F-sum Graphs by H. M. Awais, Muhammad Javaid, Akbar Ali

“…The first general Zagreb (FGZ) index (also known as the general zeroth-order Randić index) of a graph G can be defined as MγG=∑uv∈EGdGγ−1u+dGγ−1v, where γ is a real number. As MγG is equal to the order and size of G when γ=0 and γ=1, respectively, γ is usually assumed to be different from 0 to 1. …”
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Scrambler blind recognition method based on soft information by Ze-liang CHEN, Hua PENG, Ke-xian GONG, Pei-dong YU

“…Two scrambler blind recognition methods based on soft information were proposed for received signal in non-cooperative ways.The first method established a cost function of the scrambler coefficients by using the soft information,and adopted the optimization theory of real number field for positive solution.So it didn’t need to traverse the closed set of test polynomial any more.The second method built conformity degree concept with the soft information,and used the size of conformity of each test scrambler polynomial as the discriminant criteria.So it made more full use of the received information compared to the hard sentence recognition algorithm.Simulation results show that the first method can shorten the recognition time of a synchronous scrambler polynomial from 5 min 18 s to 8 s compared with the traversal method put forward by Cluzeau,and the second method has 2 dB SNR gain when to achieve the relatively high accuracy compared with the hard sentence recognition algorithm.…”
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Trajectory Synthesis of Aircraft Cabin Door Lifting Mechanism Based on the Homotopy Continuation Method by Peng Jiyou, Hang Lubin, Liu Anxin, Wu Borui, Huang Xiaobo, Wu Yang

“…Based on the ordered single open chain method, the trajectory synthesis kinematic equations of two single open chain units of the lifting mechanism are established; the variables of the equations are grouped into homogeneous groups and the Bezout number is only 320, which reduce the homotopy tracking path; by constructing the initial equations and solving the homotopy equations, six sets of non-negative real number configuration solutions of rod length are obtained, and the corresponding configuration of single open chain element combination is drawn. …”
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Multiobjective Synthesis of Linear Arrays by Using an Improved Genetic Algorithm by Bo Yang

“…The proposed method is compared with real number particle swarm optimization (RNPSO) and quantized particle swarm optimization (QPSO) as applied in the pattern synthesis of a linear thinned array and a digital phased array. …”
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Positive Solutions to Boundary Value Problems of Nonlinear Fractional Differential Equations by Yige Zhao, Shurong Sun, Zhenlai Han, Qiuping Li

“…We study the existence of positive solutions for the boundary value problem of nonlinear fractional differential equations D0+αu(t)+λf(u(t))=0, 0<t<1, u(0)=u(1)=u'(0)=0, where 2<α≤3 is a real number, D0+α is the Riemann-Liouville fractional derivative, λ is a positive parameter, and f:(0,+∞)→(0,+∞) is continuous. …”
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The product of r−k and ∇δ on ℝm by C. K. Li

“…Cheng and Li (1991) utilized a net δϵ(x) (similar to the δn(x)) and the normalization procedure of μ(x)x+λ to deduce a commutative neutrix product of r−k and δ for any positive real number k. The object of this paper is to apply Pizetti's formula and the normalization procedure to derive the product of r−k and ∇δ (∇ is the gradient operator) on ℝm. …”
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On the foundations of weak fuzzy complex-real functions by Lama Razouk, Suliman Mahmoud, Mohamad Ali

“…So, we build a special transformation function that has an important role in working with variables from a Real number set instead of a WFC set. We study its algebraic properties and models. …”
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Privacy preserving based on differential privacy for weighted social networks by Li-hui LAN, Shi-guang JU

“…Focusing on the weak protection problems in privacy preservation of weighted social networks publication,a privacy preserving method based on differential privacy was put forward for strong protection of edges and edge weights.The WSQuery query model was proposed meeting with differential privacy on weighted social networks,could capture the structure of weighted social networks and returned the triple sequences as the query result set.The WSPA algorithm was designed according to the WSQuery model,could map the query result set into a real number vector and injected Laplace noise into the vector to realize privacy protection.The LWSPA algorithm was put forward because of the high error of the WSPA algorithm,partitioned the triples sequence of the query results into multiple subsequences,constructed the algorithms for each subsequence according with differential privacy and reduced the error and improved the data util-ity.The experimental results demonstrate that the proposed method can provide strong protection for privacy information,simultaneously the utility of the released weighted social networks is still acceptable.…”
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Verhulst Model of Interval Grey Number Based on Information Decomposing and Model Combination by Bo Zeng, Chuan Li, Guo Chen, Wang Zhang

“…In this paper, the interval grey number is divided into two real number parts, that is, “white” and “grey” parts. …”
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Rolling Bearing Fault Diagnosis Based on SVM Optimized with Adaptive Quantum DE Algorithm by Yuanyuan Li, Qichun Sun, Hua Xu, Xiaogang Li, Zhijun Fang, Wei Yao

“…First, the traditional differential evolution is rewritten based on real number encoded into a qubit encoding. Second, this study proposes an adaptive quantum rotation gate and uses this gate to update the probability amplitude of the qubits. …”
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The General (α,3)-Path Connectivity Indices of Polycyclic Aromatic Hydrocarbons by Haiying Wang, Chuantao Li

“…Furthermore, we exactly derive the monotonicity and the extremal values of R3α(PAHn) for any real number α. These valuable results could produce strong guiding significance to these applied sciences.…”
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The politics of subterranean atmospheres in China: a study of contemporary chinese mining art by Marijn Nieuwenhuis

“…Official reports suggest that over half a million people, almost exclusively rural migrants, live with the incurable disease. The real number could be 10 times as high (SCMP, 2021). …”
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On direct and inverse problems related to some dilated sumsets by Kaur, Ramandeep, Singh, Sandeep

“…Let $A$ be a nonempty finite set of integers. For a real number $m$, the set $m\cdot A=\lbrace ma: a\in A\rbrace $ denotes the set of $m$-dilates of $A$. …”
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Brock's approaching zero method improved as approaching fixed point frequency to solve optimum damping ratio of dynamic vibration absorber in machine tools and experimental confirm... by Hongliang Tian, Xixiao Liang, Xuan Du

“…Some exact closed-form solutions, for example displacement amplitude gain, fixed point coordinate, and optimum damping ratio, were deduced with the real number form of differential equation of load motion and employing L'Hospital first rule. …”
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Some Inequalities between General Randić-Type Graph Invariants by Imran Nadeem, Saba Siddique, Yilun Shang

“…The general Randić and zeroth-order general Randić indices are Randić-type graph invariants and are defined for a graph G with vertex set V as RαG=∑υi∼υjdidjα and QαG=∑vi∈Vdiα, respectively, where α is an arbitrary real number, di denotes the degree of a vertex υi, and υi∼υj represents the adjacency of vertices υi and υj in G. …”
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Fuzzy Case-Based Reasoning in Product Style Acquisition Incorporating Valence-Arousal-Based Emotional Cellular Model by Fuqian Shi, Jiang Xu, Shouqian Sun

“…Emotional cellular (EC), proposed in our previous works, is a kind of semantic cell that contains kernel and shell and the kernel is formalized by a triple- L = <P, d, δ>, where P denotes a typical set of positive examples relative to word-L, d is a pseudodistance measure on emotional two-dimensional space: valence-arousal, and δ is a probability density function on positive real number field. The basic idea of EC model is to assume that the neighborhood radius of each semantic concept is uncertain, and this uncertainty will be measured by one-dimensional density function δ. …”
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Minimum Variable Connectivity Index of Trees of a Fixed Order by Shamaila Yousaf, Akhlaq Ahmad Bhatti, Akbar Ali

“…The variable connectivity index for graph G is defined as ∑vw∈EGdv+γdw+γ−1/2, where γ is a nonnegative real number, EG is the edge set of G, and dt denotes the degree of an arbitrary vertex t in G. …”
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QSPR Modeling of Fungicides Using Topological Descriptors by Saima Parveen, Fatima Saeed, Fozia Bashir Farooq, Nusrat Parveen, Nazeran Idrees, Sumiya Nasir, Rakotondrajao Fanja

“…A topological index is a real number that is obtained from a chemical graph’s structure. …”
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A New Double Color Image Watermarking Algorithm Based on the SVD and Arnold Scrambling by Ying Li, Musheng Wei, Fengxia Zhang, Jianli Zhao

“…In the process of the algorithm, we only need to perform real number algebra operations, which have very low computational complexity and are more effective than the one using the quaternion SVD of color image.…”
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