The Modified Trapezoidal Rule for Computing Hypersingular Integral on Interval by Jin Li, Xiuzhen Li

“…The modified trapezoidal rule for the computation of hypersingular integrals in boundary element methods is discussed. When the special function of the error functional equals zero, the convergence rate is one order higher than the general case. …”
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On Modifications of the Gamma Function by Using Mittag-Leffler Function by Asifa Tassaddiq, Abdulrahman Alruban

“…Present motivation is to define a new special function by modification in the original gamma function with Mittag-Leffler function. …”
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SCATTERING OF CIRCULAR CAVITY IN CIRCULAR DOMAIN TO SH WAVES by WANG Ping, JIANG ShanTao

“…The scattering problem of the circular cavity in the circular domain to the elastic waves is one of the main research objects in NDT（ Non-destructive testing） applications which has not been solved theoretically till now,the complex method,special function addition formulae and the wave function expansion method are employed to study the dynamic response problem of the circular cavity defect in the circular domain to the out-of-plane distributing loading acting on the outside of the circular domain,theoretical computation method of the stress concentration factors（ DSCF） on the boundary of the circular cavity defect is given,and the variations of the DSCF of the defect boundary along with the disturbing frequency and the loading location are investigated,numerical examples are given to verify the theoretical conclusions and show the influence of the boundaries and the loads to DSCF.…”
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Design of Key Joint Reducer for Heavy-duty Teleoperation Manipulator by Zhou Zhenguo, Bai Xiaowei, Zhou Zibo

“…Because of the key joint of the manipulator will bear excessive load during maintenance,and the main reducer of the manipulator must have a self-locking function,and special functional requirements such as space for cable channels are reserved in the middle of the main reducer. …”
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Investigation and analysis of the weakness and efficiency of generalized cycling attacks on RSA modulus by JIANG Zheng-tao1, HUAI Jin-peng2, WANG Yu-min4

“…The efficiency of attacking methods on secure RSA modulus was investigated.It was pointed out by analysis that since the success probability of some attack methods was neglectable,these methods could not be regarded as the reason for choosing strongly secure RSA modulus.In consideration of the analysis of attack methods,the signification of secure RSA modulus was summarized,which enhanced the efficiency of selecting secure parameters in practice.The result that the difference between two RSA primes d=|p-q| must not be too small was further investigated,and the d might be seen as a special case when dl,m=ql-pm（l,m∈Z+） was small.From the analysis,it could be figured out that the randomness of the relation between the two primes should not be neglected during selecting RSA modulus.To improve the security,it should be avoided to have some specially functional relations between the two primes when choosing a…”
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Preparation and Study of Multi-Heteroatom Carbon Nanotube as Excellent Electrocatalyst for Oxygen Reduction Reaction Using Polydopamine Derivative by Jian Yang, Lihong Niu, Zhijun Zhang, Liang Yan, Lingjun Chou

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Develop Approach to Predicate Software Reliability Growth Model Parameters Based on Machine learning by anfal A. Fadhil, Asmaa’ H. AL_Bayati, Ibrahim Ahmed Saleh

“…Thus, this paper inspects the reliability of software applications as a substantial feature of this application and helps determine the extent of software reliability in performing specialized functions. This goal is accomplished by calculating the parameters of software reliability growth models (SRGMs). …”
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Shaking Table Tests on Earthquake Response Characterization of a Complex Museum Isolated Structure in High Intensity Area by Wenguang Liu, Chuan Qin, Yang Liu, Wenfu He, Qiaorong Yang

“…Owing to special functional requirements of museum, such as great space and story height for exhibitions, large floor slab openings in plan and long span truss in elevation are becoming increasingly considered in museum design, which leads to challenges to structural safety. …”
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On Analytical Continuation of the Horn’s Hypergeometric Functions <i>H</i>₃ and Their Ratios by Roman Dmytryshyn, Tamara Antonova, Sofiia Hladun

“…This paper also contains an example of the presentation and continuation of some special function and an analysis of numerical results.…”
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Stability of Real Parametric Polynomial Discrete Dynamical Systems by Fermin Franco-Medrano, Francisco J. Solis

“…The stability of the fixed points of canonical polynomial maps has been found to depend solely on a special function termed Product Position Function for a given fixed point. …”
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Crystal structure of dipyridine-k1N-tris(2,2,6,6-tetramethyl-5-oxohept-3-en-3-olato-k2O,O′)dysprosium(III), DyC43H67O6N2 by Ling Bo-Kai, Huang Ling-Yu

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Crystal structure of tetraaqua-bis(ethanol-κO)-tetrakis(μ2-trifluoroacetate-κ2O:O′)-bis(trifluoroacetate-κ2O)digadolinium(III) Gd2C16H20O18F18 by Ling Bo-Kai, Huang Ling-Yu

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Lipschitz Analysis of g-Phase Retrievable Frames by Mohammad Ali Hasankhani Fard

“…A g-phase retrievable frame is a $\lambda$-phase retrievable frame in finite dimensional Hilbert space $\mathcal{H}_n$, where $\lambda$ is an special function, which is called phase coefficient function. …”
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Singular Solutions to a (3 + 1)-D Protter-Morawetz Problem for Keldysh-Type Equations by Nedyu Popivanov, Tsvetan Hristov, Aleksey Nikolov, Manfred Schneider

“…We consider a properly defined, in a special function space, generalized solution to problem PK for which existence and uniqueness theorems hold. …”
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Engineering chiral mesoporous silica nanoparticles: Template design and structural control for advanced applications by Yu Yin, Wu Wei, Kai Zhang

“…These helical structures endow CMSNs with specialized functionalities, enabling their applications in chiral catalysis, enantioselective recognition, chiral separation, drug delivery, and optical devices, making them a focal point in materials and biomedical research. …”
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Paley and Hardy's inequalities for the Fourier-Dunkl expansions by Anis Elgarna

“…Originality/value – Dunkl theory is a generalization of Fourier analysis and special function theory related to root systems. Establishing Paley and Hardy's inequalities in these settings is a participation in extending the Dunkl harmonic analysis as it has many applications in mathematical physics and in the framework of vector valued extensions of multipliers.…”
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Mechanisms and environmental factors shaping the ecosystem of brain macrophages by Silvia Penati, Simone Brioschi, Zhangying Cai, Claudia Z. Han, Claudia Z. Han, Marco Colonna, Marco Colonna

“…Microglia and BAMs are phenotypically and epigenetically distinct and exhibit highly specialized functions tailored to their environmental niches. …”
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A state-of-the-art review of research on the use of calcined bauxite aggregate in civil engineering by Yalin Liu, Chengze Li, Ya Wei, Linbing Wang

“…It has promising application value in the field of civil engineering with special functional needs. This study describes in detail the macroscopic and microscopic properties of CB aggregates, analyzes and summarizes the current research status of CB aggregates in many aspects: 1) review the technique related to the manufacture of ultra-high performance concrete (UHPC) with CB aggregate, and systematically explain its mechanism in affecting the mechanical properties of UHPC; 2) clarify the potential and advantage of CB aggregates as internal curing agents, and elaborate the shrinkage reduction mechanism and the influence law when used in UHPC; 3) summarize the evaluation index system of CB aggregate in abrasion and skid resistance of pavement materials, as well as introduce related research and engineering applications of high friction surface treatment; 4) discuss the advantages of CB aggregate in preparation of high-impact resistant cementitious materials and its influence mechanism. …”
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A Comprehensive Analysis of Robustness in Interdependent Mechatronic Systems under Attack Strategies by Gang Xu, Yanhui Wang, Yucheng Hao, Limin Jia, Zeyun Yang, Zhichao He

“…With the development of mechatronic systems, different kinds of subsystems within them are highly correlated to each other due to the demand for the special function. To assess the robustness in the mechatronic system under various disturbances, we build an interdependent mechatronic system as an interdependent machine-electricity-communication network (IMECN) and adopt the improved cascading failure model where the occurrence of the failure propagation is decided by a proportion threshold δ. …”
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Minimal presynaptic protein machinery governing diverse kinetics of calcium-evoked neurotransmitter release by Dipayan Bose, Manindra Bera, Christopher A. Norman, Yulia Timofeeva, Kirill E. Volynski, Shyam S. Krishnakumar

“…These findings provide a direct demonstration that a small set of proteins is sufficient to account for how nerve terminals adapt and regulate the calcium-evoked neurotransmitter exocytosis process to support their specialized functions in the nervous system.…”
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